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dissertation entitled

ADVANCING THERMOELECTRIC RESEARCH WITH NEW
MEASUREMENT SYSTEMS AND THERMOELECTRIC MODELING
FOR AC ELECTRICAL MEASUREMENTS

presented by

Adam Damin Downey

has been accepted towards fulfillment
of the requirements for the

 

 

Ph. D. degree in Electrical & Computer
Mneering

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MAY BE RECALLED with earlier due date if requested.

 

 

 

DATE DUE DATE DUE DATE DUE
m 2 i: 2008
JUN2§20091-09.08
0627D9‘

 

 

 

 

 

 

 

 

 

 

 

 

 

2/05 p:/ClRC/DateDue.indd-p.1

 

ADVANCING THERMOELECTRIC RESEARCH WITH NEW MEASUREMENT
SYSTEMS AND THERMOELECTRIC MODELING FOR AC ELECTRICAL
MEASUREMENTS
By

Adam Darwin Downey

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Electrical and Computer Engineering

2006

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ADVANCING THERMOELECTRIC RESEARCH WITH NEW MEASUREMENT
SYSTEMS AND THERMOELECTRIC MODELING FOR AC ELECTRICAL
MEASUREMENTS
By

Adam Darwin Downey

Bulk thermoelectric materials are created and studied at Michigan State University
(MSU) for use in high temperature power generation devices. These new materials
exhibit figures of merit, ZT, which approach values of 2 near 800K, and are being used to
develop power generators that convert heat flow to electricity. To help with the
development of the thermoelectric materials, new measurement systems are needed to
evaluate the components of the figure of merit (electrical conductivity, thermal
conductivity, and thermopower).

In this research work, two measurement systems are developed for the
simultaneous measurements of electrical conductivity, thermal conductivity, and
thermopower. Both systems use a new "drifting in temperature" technique where
measurements are made as the overall sample temperature Slowly drifts in time. The first
system called the “Drifi System”, is for low temperature measurements (100K to 300K)
and the second system, “Ultra High Temp System”, is for high temperature
measurements (300K to 900K). The accuracy of these systems was verified using
reference materials. The Ultra High Temp System has become a very usefirl tool in the
investigation of new thermoelectric materials as doping concentrations and material

synthesis parameters are changed.

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In addition to this research, the AC impedance characteristics of thermoelectric
modules and single pellets were investigated. This research led to the development of a
new AC model for thermoelectric modules using AC electrical measurements by
comparing the impedance behavior of thermoelectric modules to a simple RC circuit. The
modeling of thermoelectric materials was then expanded upon by the application of
transmission line theory to describe the thermal dynamic behavior in a module. This new
model could be applied to commercially available modules as well as unicouples, and
single thermoelectric pellets. Infrared imaging was used to verify the existence of a
thermal wave developing along the module legs due to an AC electrical signal at the
module's inputs. This thermal wave can be modeled with the transmission line theory,
but not with the simple RC one-port model.

Finally, this research discusses a new ZT measurement system for rapid figure of
merit measurements of new materials. This system is capable of measuring the figure of
merit on more than 30 samples per week at room temperature. For the first time, large
amounts of data can be collected for statistical analysis on doping concentrations and

thermal processing to determine the optimal sample preparation conditions.

Copyright by
ADAM DARWIN DOWNEY
2006

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ACKNOWLEDGMENTS

I would like to thank my advisor Dr. Timothy P. Hogan. He has been a major
factor in my enthusiasm for research and my desire to pursue a PhD. It has been a great
experience to be a part of his research team and be surrounded by people with such great
attitudes, ethics, and working manner. Dr. Hogan’s guidance in this thesis is very much
appreciated. I would also like to thank all of the Hogan’s Heroes and all the people with

whom I have worked with in the thermoelectric project.

I would like to thank Dr. Mercouri Kanatzidis, Dr. Tim Grotjohn, Dr. Donnie
Reinhard, and Dr. Gregory Wierzba for taking the time to review my thesis, attending my

presentation and contributing to some helpful discussions.

I would like to especially thank my wife, Cori, my parents, my parents-in-Iaw,

family, and friends for all of their support throughout the years.

F inancia] support from the Office of Naval Research (Contract No. N00014-02-1-

0867 MURI program) is gratefully acknowledged.

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TABLE OF CONTENTS

List of Tables ..................................................................................................................... iv
List of Figures ...................................................................................................................... v
Chapter 1: Introduction to Therrnoelectrics Research ........................................................ l
1.1 Introduction ............................................................................................................... 1
1.2 Thesis Outline ........................................................................................................... 3
Chapter 2: Thermoelectric Fundamentals ........................................................................... 4
2.1 Introduction ............................................................................................................... 4
2.2 Peltier Effect ............................................................................................................. 6
2.3 Thomson Effect ......................................................................................................... 7
2.4 Wiedemann-Franz Law ............................................................................................. 8
2.5 Thermocouples ........................................................................................................ 10
2.6 Seebeck Effect ........................................................................................................ 14
2.7 Thermoelectric Modules ......................................................................................... 17
Chapter 3: History and Current Developments ................................................................. 23
3.1 Introduction ............................................................................................................. 23
3.2 Renewed Interest in TE Research ........................................................................... 23
3.3 List of TE Materials ................................................................................................ 24
3.4 Techniques of Characterization .............................................................................. 29
3.4.1 Steady-State Technique (Thermal Conductivity) ................................................ 29
3.4.2 Harman Technique (Thermal Conductivity and ZT) ........................................... 31
3.4.3 Pulse Technique (Therrnopower and Thermal Conductivity) ............................. 31
3.4.4 Modified Harman Technique (ZT) ....................................................................... 33
3.5 Measurement Systems at MSU ............................................................................... 34

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3.5.1 Room Temperature Electrical Conductivity Scanning Probe .............................. 34

3.5.2 4-Sample System ................................................................................................. 37
3.5.3 High Temperature System (HTS) ........................................................................ 38
3.5.4 Device Testing System (DTS) ............................................................................. 40
3.6 Properties of TE materials at MSU ......................................................................... 41
Chapter 4: Drift System .................................................................................................... 45
4.1 Introduction ............................................................................................................. 45
4.2 Drift System Setup and Mounting .......................................................................... 45
4.3 Drifi System Automation ........................................................................................ 51
4.3.1 Thermal Conductivity Measurements .................................................................. 52
4.3.2 Thermopower and Electrical Conductivity Measurements ................................. 54
4.3.3 Program Description ............................................................................................ 54
4.4 Verification of the System ...................................................................................... 55
4.5 Limitations of the System ....................................................................................... 57
4.6 Conclusion .............................................................................................................. 58
Chapter 5: Ultra High Temperature Measurement System ............................................... 59
5.1 Introduction ............................................................................................................. 59
5.2 UHT System ..................................................................... 59
5.2.1 Furnace ................................................................................................................. 60
5.2.2 ProboStat .............................................................................................................. 62
5.2.3 Measurement Equipment ..................................................................................... 65
5.2.4 Vacuum Pump ...................................................................................................... 66
5.2.5 Sample Mounting ................................................................................................. 68
5.3 Electrical Conductivity Measurement .................................................................... 69
5.4 Measuring Thermopower Using a Pulsing Technique ........................................... 7O

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5.6 The Built System .................................................................................................... 76
5.7 Verification of the UHT System ............................................................................. 78
5.8 Further Developments and Future Improvements .................................................. 82
5.9 Conclusion .............................................................................................................. 84
Chapter 6: Impedance Spectroscopy of Thermoelectric Materials and Devices .............. 86
6.1 Introduction ............................................................................................................. 86
6.2 Existing Research in Scientific Community ........................................................... 87
6.3 Frequency Dependent Experimental Measurement ................................................ 88
6.4 Experimental Setup ................................................................................................. 89
6.5 Lock In Amplifier ................................................................................................... 91
6.5.1 Magnitude and Phase ........................................................................................... 94
6.6 Example Data using Tellurex Module .................................................................... 95
6.7 Analysis of the Data ................................................................................................ 97
6.8 More Sample Measurement Setups ........................................................................ 98
6.8.1 Single Sample ZT Measurements ........................................................................ 98
6.8.2 Inline PN Module ............................................................................................... 105
6.8.3 Unicouples and Multicouple Modules ............................................................... 108
6.9 System Program .................................................................................................... 110
Chapter 7: RC-One Port Method .................................................................................... 111
7.1 Introduction ........................................................................................................... 111
7.2 Development of RC One-Port Model ................................................................... 11 1
7.2.1 Comparing Data to Simple RC Circuit .............................................................. 112
7.2.2 Thermal Impedance ........................................................................................... 119
7.2.3 Final Model ........................................................................................................ 121

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7.3 Circle Plot ............................................................................................................. 124
Chapter 8: Thermal Transmission Line Model ............................................................... 128
8.1 Introduction ........................................................................................................... 128
8.2 Thermal Dynamics ................................................................................................ 128
8.3 Comparing Thermal Dynamics with Transmission Line Theory ......................... 132
8.4 Applying Thermal Transmission Line Model ...................................................... 134
8.4.1 Thermal TLINE Model for Commercial Module .............................................. 134
8.4.2 Thermally Grounding One Side of Module ....................................................... 138
8.4.3 TTLM for Inline PN Module ............................................................................. 141
8.4.4 Thermal TLINE model for single pellet measurements .................................... 146
8.5 Development and Curve Fitting to the Thermal Transmission Line Model ......... 150
8.5.1 Development of AC model for Electrical Transmission Lines .......................... 151
8.5.2 Incorporation of RC One-Port Program ............................................................. 155
8.5.3 Curve Fitting the Probe Positioning ................................................................... 155
8.5.4 Curve Fitting for Heat Capacitance ................................................................... 157
8.5.5 Final Program .................................................................................................... 161
8.6 Thermal Imaging ................................................................................................... 162
8.7 Comparing ZT Direct Measurements to Using Individual Measurements ........... 167
Chapter 9: ZT Measurements at High Temperatures ...................................................... 171
9.1 Introduction ........................................................................................................... 171
9.2 Evaluation of Radiation Losses ............................................................................ 171
9.2.1 The Effect of Radiation on ZT Measurements .................................................. 177
9.2.2 Example Calculation (MSU TE Materials) ....................................................... 178
9.2.3 Example Calculation (Small Constantan Sample) ............................................. 182

ix

9.2.4 Can a Correction for Radiation be made to the calculation? ............................. 183

9.3 Thermal Conductivity of the Measurement Wires ............................................... 184
9.4 Example Measurements of ZT up to Higher Temperatures .................................. 187
9.4.1 Comparing ZT measurements Using AngSbTe Sample .................................. 188
9.4.2 Comparing Radiation Losses using PbTe with Nanoparticals of PbS ............... 194
9.4.3 Testing ZT of p—type SiGe and Correcting for Emissivity ................................ 196
Chapter 10: ZT of Constantan ......................................................................................... 201
10.1 Introduction ......................................................................................................... 201
10.2 Establishing Constantan as a reference material ................................................. 201
10.3 Measurement of Constantan ............................................................................... 206
10.4 Experimental Results .......................................................................................... 212
Chapter 11: Rapid ZT Measurements ............................................................................. 216
11.1 Introduction ......................................................................................................... 216
11.2 Frequency Shifting by Sample Dimensions ........................................................ 216
11.3 Phase Angle with Simple RC Circuit ................................................................. 220
11.4 Phase Analysis for Thermal TLINE model ........................................................ 224
11.4.1 Area Under the Phase Plot ............................................................................... 226
11.4.2 Applying a Correction to the Absolute Maximum Phase for ZT
Calculations ................................................................................................................ 229
Chapter 12: Measuring Resistance of a TB Module using Alternating Digital
Pulses at Various Frequencies ........................................................................................ 230
12.1 Introduction ......................................................................................................... 230
12.2 Automated Program ............................................................................................ 231
12.3 Room Temperature Measurements in Atmosphere ............................................ 232
12.4 Room Temperature Measurements in High Vacuum ......................................... 235
12.5 Monitoring the Voltages ..................................................................................... 237

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Chapter 13: ZT Machine ................................................................................................. 241
13.1 Introduction ......................................................................................................... 241
13.2 Method of Measurement ..................................................................................... 243
13.2.1 Mounting Current Leads .................................................................................. 245
13.2.2 Mounting Voltage Probes ................................................................................ 245
13.2.3 Measurement Process ...................................................................................... 248
13.3 The Assembled System ....................................................................................... 250
13.4 Example Data ...................................................................................................... 253
13.5 Conclusion .......................................................................................................... 256

Chapter 14: Conclusion/Future Work ............................................................................. 258
14.1 Conclusion .......................................................................................................... 258
14.2 Future Work ........................................................................................................ 260

Appendix A: Properties of Materials ............................................................................... 262

Appendix B: Constantan Wire ......................................................................................... 263
3.1 Introduction ........................................................................................................... 263
8.2 Setup ...................................................................................................................... 263
8.3 Results ................................................................................................................... 264

Appendix C: Radiation Losses of Sim’s HT System and High

Temperature ZT Measurements ....................................................................................... 266
CI Introduction ........................................................................................................... 266
C2 Evaluation of Radiation Losses ............................................................................. 266
C3 Comparing Radiation from ZT measurements and Sim’s HT
System .......................................................................................................................... 272

Appendix D: Useful Programs ......................................................................................... 274
D.1 Frequency Sweep Generator (Program) ................................................................ 274

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D3 Triangular Minimizing Method (Program) ........................................................... 276

DA Converting Impedance Properties of a TE module to Actual

Properties ..................................................................................................................... 278
References ....................................................................................................................... 279

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LIST OF TABLES

Thermocouple types and their corresponding Seebeck voltage ...................... ll
Thermopower of various metals ...................................................................... 17
AC TEM model results .................................................................................. 122
Commercially available TE module component properties .......................... 136
Truth table for curve fitting routine ............................................................... 160
Sample specifications .................................................................................... 178
Thermal conductivities of various materials ................................................ 262
Emissivity values of various materials ......................................................... 262

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Figure 2-1: Peltier effect diagram ....................................................................................... 6
Figure 2-2: Thomson effect diagram .................................................................................. 7
Figure 2-3: Type-E thermocouple spark—welded together using 25 .4pm in

diameter wire. .................................................................................................................... 10
Figure 2-4: Single ended thermocouple ............................................................................ 1 1
Figure 2-5: Typical thermocouple setup for temperature measurements ......................... 12
Figure 2-6: Seebeck effect on an aluminum rod ............................................................... 14
Figure 2-7: PN Thermoelectric Modules. (a) Cooling applications. (b) Power
generation. .......................................................................................................................... 18
Figure 2-8: Thermoelectric module consisting of many unicouples. ............................... 19

Figure 2-9: Examples of thermoelectric modules. (a) is stacked module, (b) and
(c) are modules of difference sizes 19

Figure 2-10: (a) Current from an n-type semiconductor to the metal results in heat
absorption at the junction. (b) Current from the metal to an n-type semiconductor

results in heat release at the junction. [1] ........................................................................... 20
Figure 3-1: Best ZT values obtained for a variety of materials ........................................ 28
Figure 3-2: Diagram of measuring thermal conductivity using the steady—state

technique ............................................................................................................................ 30
Figure 3-3: Pulse technique example. (a) Plot of heater voltage vs time. (b) Plot

of AV vs time. (c) Plot of AT vs time. (d) Plot of AV vs AT. .......................................... 32
Figure 3-4: Room Temperature Scanning Probe .............................................................. 36
Figure 3-5: Room Temperature Scanning Probe diagram ................................................ 36

Figure 3-6: (Left) Each probe typically measures 20 data points. Here is an

example showing 9 probes each taking 20 measurements. (Distance between

probes is not indicated on this graph). (Right) Each probe takes the average

measured voltage and is plotted versus position. This slope is then used in the
calculation of the average electrical conductivity between the measured distances. ........ 37

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System ................................................................................................................................ 38
Figure 3-8: Typical sample mounted in HTS ................................................................... 39
Figure 3-9: HTS Cryostat .................................................................................................. 39
Figure 3-10: Picture of DTS ............................................................................................. 41
Figure 3-11: Plot of therrnopower versus temperature for n-type LAST materials .......... 42
Figure 3-12: Plot of electrical conductivity versus temperature for n-type LAST

materials ............................................................................................................................. 43
Figure 3-13: Plot of thermopower versus temperature of p-type LASTT materials ......... 44
Figure 3-14: Plot of electrical conductivity versus temperature of p-type LASTT

materials ............................................................................................................................. 44
Figure 4-1: Drift System chamber with LN2 dewar and vacuum system ......................... 46
Figure 4-2: Drift System measurement equipment ........................................................... 47

Figure 4-3: (Left) Individual sample stage with a sample mounted. (Right) Main
stage without radiation cap shown a four sample stages with their radiation caps

on ........................................................................................................................................ 48
Figure 4-4: (Lefi) Sample stage on main stage without radiation cap. (Right)

Sample stage on main stage with radiation cap. ................................................................ 49
Figure 4—5: Main stage with radiation cap on. .................................................................. 49
Figure 4-6: Drift System main chamber (Left) and inside shafi with sample stages

(right) ................................................................................................................................. 50
Figure 4-7: Wiring diagram for mounting each sample .................................................... 51
Figure 4-8: Plot of AT for sample rising in temperature (Left) and falling in

temperature (Right) with the curve fits projected out further in time. ............................... 53
Figure 4-9: Diagram of sample mounted for Drifi System ............................................... 54
Figure 4-10: Plot of temperature versus time for the Drift System. Automated

data collection is started when the temperature reaches a minimum value. ...................... 55
Figure 4-11: Plot of AT versus time for heating and cooling of the sample. .................... 56

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sample. (Lefi) Plot of electrical conductivity versus temperature. (Right) Plot of

thermal conductivity versus temperature. .......................................................................... 56
Figure 4-13: Plot of thermopower of stainless steel versus temperature. ......................... 57
Figure 4-14: Adding aluminum foil to make thermal contact to walls of chamber .......... 58
Figure 4—15: Plot of temperature versus time of the Drifi System afier adding

aluminum to the main sample stage. .................................................................................. 58
Figure 5-1: ThermCrafi split tube fumace ........................................................................ 61
Figure 5-2: ThermCrafi temperature controller ................................................................ 62
Figure 5-3: NorECs ProboStat .......................................................................................... 63
Figure 5—4: Base of Probostat ........................................................................................... 64
Figure 5-5: Diagram for the base of the Probostat unit .................................................... 65
Figure 5-6: Measurement equipment ................................................................................ 66
Figure 5-7: Varian vacuum pump ..................................................................................... 67
Figure 5-8: Electrical noise in measurements due to vacuum pump connection .............. 67
Figure 5-9: Mounting a sample for measurement (TC = thermocouple) .......................... 69
Figure 5-10: Measurement setup ...................................................................................... 70
Figure 5-11: Front panel view of the LabVIEW program for the UHT System ............... 76
Figure 5-12: UHT System ................................................................................................. 77
Figure 5-13: Typical data collected for UHT System ....................................................... 78
Figure 5-14: Platinum wire reference ............................................................................... 79
Figure 5-15: Platinum wire electrical conductivity measurements ................................... 79
Figure 5-16: Platinum wire thermopower measurements ................................................. 80
Figure 5-17: Plot of thermopower versus temperature of a LAST sample showing

good agreement between the UHT and HT System ........................................................... 81
Figure 5-18: Plot of electrical conductivity of 3 LAST sample showing good

agreement between the UHT and HT System .................................................................... 81

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Figure 5-19: Plot of a thermopower and electrical conductivity of a new TE

material using potassium using UHT System .................................................................... 82
Figure 5-20: Stainless steel foil that is grounded was used as an electrical shield

to eliminate noise being emitted from the furnace ............................................................. 83
Figure 5-21: Picture of UHT System adapted for ZT direct measurements by

dangling a sample in a high temperature environment ...................................................... 84
Figure 6-1: Electrical circuit describing the electrical properties of a TE module ........... 88
Figure 6-2: Experimental setup for AC measurements ..................................................... 89
Figure 6-3: Lock-in signal example .................................................................................. 93
Figure 6—4: Magnitude and phase of the impedance of a Tellurex TE module ................ 96
Figure 6-5: Plot of magnitude versus frequency for high vacuum and atmospheric
conditions ........................................................................................................................... 96
Figure 6—6: Single TE pellet for ZT measurements including contacts ............................ 99
Figure 6-7: Single TE pellet for ZT measurements in four-point configuration ............ 100
Figure 6-8: Detailed view of a single TE pellet connection ........................................... 100
Figure 6-9: Electrical and thermal model of setup .......................................................... 101
Figure 6-10: Equations for Figure 6-9 ............................................................................ 102
Figure 6-11: Inline TE module including contacts ......................................................... 107
Figure 6—12: Inline TE module in four point probe configuration .................................. 107
Figure 6-13: Inline module with thermal circuit overlay (DC steady state) ................... 107
Figure 6-14: Unicouple TE module for ZT measurement .............................................. 109
Figure 6-15: Typically unicouple module with thermal circuit overlayed (DC

steady state) ...................................................................................................................... 109
Figure 7-1: RC circuit ..................................................................................................... 112
Figure 7-2: Curve fitting experimental data to an impedance equation of the

circuit shown in Figure 7-1 .............................................................................................. 114
Figure 7-3: First Foster Technique circuit ...................................................................... 1 15
Figure 7-4: Using First Foster Technique for TE Module .............................................. 116

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Figure 7-6: Comparison of impedance between circuits ................................................ 119
Figure 7-7: Thermal impedance related to electrical impedance .................................... 121
Figure 7-8: AC thermal-electrical model for a TB module ............................................. 122
Figure 7-9: Front panel view of the RC One-Port Method LabVIEW program ............. 123
Figure 7-10: Imaginary versus real impedance plot ....................................................... 127
Figure 8-1: Components of a TB module ....................................................................... 129
Figure 8-2: Thermal dynamics of a 2-D material ........................................................... 129
Figure 8-3: Transmission Line Model ............................................................................ 132
Figure 8-4: Applying Thermal TLINE model ................................................................ 134
Figure 8-5: Commercially available TE module ............................................................ 135
Figure 8-6: Setup LabVIEW vi for commercially available TE module ........................ 136
Figure 8-7: Experimental data, RC One-Port fit, and Thermal TLINE fit to data

for commercially available TE module ............................................................................ 138
Figure 8-8: Curve fitting thermal transmission line model ............................................. 138
Figure 8-9: Ideal thermal ground one side of TE module ............................................... 140
Figure 8-10: Compare ideal thermal ground with experimental data ............................. 140
Figure 8-11: Theoretical poor thermal ground compared to experimental data ............. 141
Figure 8-12: Inline TE module using LAST material ..................................................... 142

Figure 8-13: Comparison between Transmission Line Model and RC-One Port
Model ............................................................................................................................... 142

Figure 8-14: Possible temperature profile at one instance in time along the length
of an inline pn TE module using a low frequency electrical current that is close to

the pole of the impedance function .................................................................................. 143
Figure 8-15: Thermal circuit showing the thermally grounded ends of an inline

pn TE module ................................................................................................................... 144
Figure 8-16: Thermal circuit showing the simplified schematic of Figure 8-15 ............ 144

xviii

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Figure 8-17: PN inline module consisting of BizTe3 from commercially available
module and bonded together using woods metal ............................................................. 145

Figure 8-18: Plot of a pn inline module consisting of BizTe3 from commercially
available module showing magnitude and phase of the impedance versus

frequency .......................................................................................................................... 145

Figure 8-19: Percent error ............................................................................................... 146

Figure 8-20: Single TE pellet of p-type material (Nao_ngzoSbo_6Te22) ........................... 146

Figure 8-21: Plot of single TE pellet showing magnitude and phase of the

impedance measurements of a p-type sample (Na0.8PbZOSb0.6Te22) ........................... 147
1 Figure 8-22: Percent error ............................................................................................... 147

Figure 8-23: Possible temperature profile at once instance in time along n-type
sample using a low frequency (close to the pole) voltage source across sample ............ 148

Figure 8-24: Possible temperature profile at one instance in time along n-type
sample using a fi'equency where the dip in the data is created ........................................ 148

Figure 8-25: LabVIEW program using Thermal TLINE model to indicate

temperature profile along the length of the sample at an instance in time where the

ends of the sample are at the maximum difference. The frequency of oscillation is

at a value where there is a dip in the magnitude versus frequency data .......................... 149

Figure 8-26: LabVIEW program using Thermal TLINE model to indicate

temperature profile along the length of the sample at an instance in time when

there is a thermal wave. The frequency is at the value where there is a dip in the
magnitude versus frequency data. .................................................................................... 149

Figure 8-27: Electrical circuit schematic using a transmission line ............................... 151

Figure 8-28: Font panel view of the LabVIEW program modeling transmission
lines .................................................................................................................................. 153

Figure 8-29: Front panel view of the LabVIEW program to test the frequency
dependence for the transmission line program. This figure displays an example of

testing an RG-58 cable. .................................................................................................... 154
Figure 8-30: Diagram of probe positioning .................................................................... 156
Figure 8-31: Front panel view of the LabVIEW program "TLineTE Materialvi"

showing the results of probe positioning ......................................................................... 157
Figure 8-32: Example MSE function versus capacitance values .................................... 159
Figure 8-33: Front panel view for the TLINE curve fitting LabVIEW program ............ 162

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Figure 8-34: TE module setup for thermal imaging ....................................................... 163

Figure 8-35: (A) Picture of TE module. (B) Same device painted black .................... 164
Figure 8-36: TE module place in box painted black ....................................................... 164
Figure 8-37: Infrared camera .......................................................................................... 164
Figure 8-38: Thermal images .......................................................................................... 166
Figure 8-39: Plot of electrical conductivity versus temperature for

Ago_43Pb13Sb1_2Tezo ........................................................................................................... 167
Figure 8-40: Plot of thermopower versus temperature for Ago.43Pblng1.2Tezo .............. 168
Figure 8-41: Plot of magnitude and phase of the impedance versus frequency for
Ago,43ijssb1_2Tezo ........................................................................................................... l 69
Figure 8-42: Plot of electrical conductivity and thermopower for LAST sample
Ago_29Pb13_61 Sbongejg ...................................................................................................... 169
Figure 8-43: Plot of magnitude and phase of the impedance versus frequency for
Ago.29Pb13,6]Sbo_23T619 ...................................................................................................... l 70
Figure 9-1: Diagram for the steady state analysis of radiation losses for applied

DC current ........................................................................................................................ 172
Figure 9-2: Sample divided into four regions. Linear temperature gradient along

the length of the sample. .................................................................................................. 174
Figure 9—3: Temperature profile at 300K where AT = 1 ................................................. 179
Figure 9-4: Effective radiated power versus AT for a specific example ......................... 180
Figure 9-5: Thermal resistance due to radiation for specific example ............................ 180
Figure 9-6: Radiation resistance versus temperature for specific example (AT is

small) ................................................................................................................................ 181
Figure 9-7: Effective radiation resistance versus temperature where AT = 1 ................. 183

Figure 9-8: (A) Sample mounted in UHT System for ZT meter measurements.
(B) Diagram of the sample dangling from the measurement wires attached to the
ends of the sample ............................................................................................................ 185

Figure 9-9: Plot of electrical conductivity and thermopower versus temperature
for EQE74R2P253TopC .................................................................................................. 189

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Figure 9-10: Plot of measured thermal conductivity versus temperature of
KF2242R3C [3] ............................................................................................................... 190

Figure 9-11: Plot of electrical conductivity versus temperature for KF2242R3C .......... 190

Figure 9-12: Plot of calculated lattice contribution to thermal conductivity versus
temperature ...................................................................................................................... 191

Figure 9-13: Plot of calculated thermal conductivity versus temperature for
EQE74R2P253TopC ........................................................................................................ 1 92

Figure 9-14: Plot of direct ZT measurements using magnitude impedance versus
frequency at multiple temperatures for EQE74R2P253TopC ......................................... 193

Figure 9-15: Plot of ZT versus temperature. (Line) Estimated ZT using standard
measurements of electrical conductivity, thermopower, and thermal conductivity.
(Dots) Direct ZT measurements using impedance of the sample ................................... 193

Figure 9-16: Plot of high temperature direct ZT measurements using magnitude
impedance versus frequency. ........................................................................................... 194

Figure 9-17: Plot of electrical conductivity and thermopower versus temperature
for JAE143P226-B ........................................................................................................... 195

Figure 9-18: Plot of measurement thermal conductivity (including radiation
losses) versus temperature for JAE143P226-B ................................................................ 195

Figure 9-19: Plot of ZT versus temperature. (Squares) ZT calculated using the
standard method. (Circles) ZT direct measurements from impedance of the

sample. ............................................................................................................................. 196
Figure 9-20: (a) Si7sGe22 Sample with platinum wires (dia = 0.003 inch) resistive

welded to sample. (b) SiGe sample suspended in UHT System. .................................... 197
Figure 9—21: Resistance versus fi'equency at various temperatures of Singezz ............. 198

Figure 9-22: Measured resistivity of Si7gGe22 sample compared to Ames Lab
measurements ................................................................................................................... 198

Figure 9-23: ZT values measured versus temperature compared to p-type
SigoGezo. This plot shows the raw ZT value collected and the ZT correct for the
measurement wires ........................................................................................................... 200

Figure 9-24: Measured ZT of Si73Ge22 that has been corrected for radiation losses

using an emissivity value of 0.7 ....................................................................................... 200
Figure 10-1: Output voltage for Type-T thermocouple from NIST ............................... 203
Figure 10-2: Thermopower of Type-T thermocouple from derivative ........................... 203

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Figure 10-3: Thermopower of copper from Roberts (squares) with curve fit on

top (line) ........................................................................................................................... 204
Figure 10-4: Thermopower of constantan based on published thermopower of

copper and NIST data for Type-T thermocouple ............................................................. 204
Figure 10-5: Thermal conductivity of constantan from two published sources ............. 205
Figure 10-6: Calculated ZT of constantan ...................................................................... 205
Figure 10-7: Setup for single TE pellet ........................................................................... 206
Figure 10-8: Detailed view of a single TE pellet connection ......................................... 206
Figure 10-9: Thermopower of platinum from published data (Roberts) ........................ 207
Figure 10-10: Electrical and thermal model of setup ...................................................... 208
Figure 10-11: Equations for Figure 10-10 ...................................................................... 209
Figure 10-12: Mounting constantan wire for ZT measurement ...................................... 212
Figure 10-13: Constantan wire (dia = 0.02” = 0.508mm) probe spacings ...................... 212
Figure 10-14: Magnitude of impedance versus frequency at multiple temperatures ...... 213
Figure 10-15: Phase of impedance versus frequency at multiple temperatures .............. 214
Figure 10-16: Correction factor for measuring constantan using platinum wires .......... 214
Figure 10-17: Experimental results for measuring ZT of constantan ............................. 215
Figure 11-1: Adjusting sample dimensions to change the frequency range of the
impedance. ....................................................................................................................... 219
Figure 11-2: Example of long versus a short sample showing that the minimum

phase occurs at a higher frequency of a short sample versus along sample. .................. 220
Figure 11-3: RC circuit ................................................................................................... 220
Figure 11-4: ZT versus max absolute phase angle for RC circuit equivalent ................. 224

Figure 11-5: Phase versus Frequency. Absolute maximum phase angle is
different for the three measurements even though the ZT value is the same. ................. 225

Figure 11-6: Phase versus Log Frequency. Area under the curve for all three
cases is approximately equal for a given ZT value. ......................................................... 226

Figure 11-7: Phase and Magnitude plots versus log frequency ...................................... 228

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Figure 12-1: Front panel view of LabVIEW program for automated data
collection of the resistance of the TE module for various frequencies. ........................... 232

Figure 12-2: Plot showing resistance measurements of a module in atmosphere
using multiple current values (lmA - 80mA). ................................................................. 233

Figure 12-3: Plot showing resistance measurements of a module in atmosphere
using multiple current values (100mA - 260mA). ........................................................... 234

Figure 12—4: Plot showing resistance measurements of a module in atmosphere at
each fiequency versus multiple current values (1 mA - 260mA). .................................... 234

Figure 12-5: Plot showing resistance measurements of a module in high vacuum
using multiple current values (lmA - 50mA). ................................................................. 235

Figure 12-6: Plot showing resistance measurements of a module in high vacuum
using multiple current values (60mA - 300mA). ............................................................. 236

Figure 12-7: Plot showing resistance measurements of a module in high vacuum
at each frequency versus multiple current values (lmA - 50mA). .................................. 236

Figure 12-8: Plot showing resistance measurements of a module in atmosphere at
each frequency versus multiple current values (lmA - 500mA). .................................... 237

Figure 12-9: Plot of voltage versus time across TE module using a 1 second delay
and 10mA. ........................................................................................................................ 238

Figure 12-10: Plot of voltage versus time across TE module using a 2 second
delay and 10mA. .............................................................................................................. 238

Figure 12-11: Plot of voltage versus time across TE module using a 15 second
delay and 10mA. .............................................................................................................. 239

Figure 12-12: Plot of voltage versus time across TE module using a 15 second
delay and 140mA. ............................................................................................................ 239

Figure 12-13: Plot of voltage versus time across TE module using a 20 second
delay and 500mA. ............................................................................................................ 240

Figure 13-1: Picture of 100g ingot of LAST material sliced up into 5mm thick
coins. This picture shows the cracking in the sample throughout the ingot and is

affected by the cooling profile. ........................................................................................ 241
Figure 13-2: Diagram of TE sample mounted for ZT measurements ............................. 245
Figure 13-3: Copper wire (0.003" in diameter) welded to a LAST TE material

(5mm x 5mm x 7mm) ...................................................................................................... 246
Figure 13-4: Close-up of Figure 13-3 ............................................................................. 247

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Figure 13-5: Microscopic image of copper wire welded to LAST sample showing

the small size of the contact area ..................................................................................... 247
Figure 13-6: HotSpot thermocouple welder ................................................................... 248
Figure 13-7: Plot of current through sample and measurement locations ...................... 250
Figure 13-8: Assemble ZT Machine (Inside view with 16 samples mounted) ............... 251
Figure 13-9: Top 8 samples mounted in ZT Machine .................................................... 252
Figure 13-10: Bottom 8 samples mounted in ZT Machine ............................................. 252
Figure 13-11: Small TE module from Marlow Industries .............................................. 253
Figure 13-12: Resistance versus frequency plot for BizTe3 Marlow Industries TE

module .............................................................................................................................. 254
Figure 13-13: Resistance versus frequency for single LAST pellet ............................... 255

Figure 13-14: Resistance versus frequency for single pellet PbTe+Sb(16%).
Here, ZT value is 0.07. HT System gets the same ZT value using measured
thermal conductivity at room temperature. ...................................................................... 255

Figure 13-15: Plot of room temperature ZT values for many TE samples of LAST
composition where different compositions and heating/cooling profiles where
used in the manufacturing process. .................................................................................. 256

Figure 13-16: Plot of temperature dependant ZT values for LAST materials and
PbTe. This shows how the ZT results compare at room temperature. ............................ 257

Figure B-1: Constantan wire (a) mounted in HT system (b) for thermopower and
electrical conductivity measurements .............................................................................. 263

Figure B-2: Thermopower of constantan found experimentally using MSU’s HT

System and compared to the calculated thermopower ..................................................... 264
Figure B-3: Electrical conductivity of constantan measured with HT System,

UHT System, and from Goodfellow ................................................................................ 264
Figure B-4: Room Temp Scanning Probe measurement on constantan wire ................. 265
Figure C-l: Diagram showing radiation losses in the HT System .................................. 267
Figure D-l: LabVIEW front panel for “Frequency Sweep Generator.vi” ....................... 274
Figure D-2: LabVIEW code for “Frequency Sweep Generator.vi” ................................ 275

xxiv

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Figure D-3: LabVIEW front panel for “Therm Properties of Connecting

Materialsvi” ..................................................................................................................... 276
Figure D-4: LabVIEW front panel for "Triangular Minimizing Method.vi" ................. 277
Figure D-5: LabVIEW code for "Triangular Minizing Method.vi" ................................ 277

Figure D-6: Front panel view of the LabVIEW program “Converting to Thermal
Circuit.vi” ......................................................................................................................... 278

Images in this dissertation are presented in color.

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Chapter 1: Introduction to Thermoelectrics Research

1.1 Introduction

Michigan State University (MSU) explores thermoelectric research to identify new
materials and measurement techniques and explore applications for these thermoelectric
materials. This research is a collaborative effort not only between departments at MSU
(Electrical and Computer Engineering, Mechanical Engineering, Chemistry, and Physics)
but also with the University of Michigan and Iowa State University. The goal of this
thermoelectric research, which has been guided by the firnding from the Office of Naval
Research (ONR), is to advance the scientific community’s knowledge of thermoelectric
materials, obtain a better understanding of how to manufacture the most efficient
thermoelectric material for high temperature applications, and to create a 1kW
thermoelectric power generation device for hot and cold side temperatures at 850K and
300K, respectively, with the highest efficiency. My role in this research includes:

0 to be a part of the team that tests and characterizes thermoelectric materials that

have been made at MSU

0 to identify new materials with good prospects of being used in thermoelectric

devices

0 to help better understand what makes a good thermoelectric material

0 and to determine how to use these materials to create a functional device for

power generation.
As a member of this measurement team I have not only used existing equipment at MSU
to characterize thermoelectric materials, but have developed a new transport

measurement system capable of measuring transport properties of materials over the

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temperature range of 25°C to 1000°C. Typical measurements include temperature
dependant thermopower, electrical conductivity, and thermal conductivity. In addition, I
have also investigated impedance spectrosc0py on thermoelectric materials to develop a
new measurement technique along with two theoretical models to describe the fi'equency
dependent behavior of thermoelectric materials. The three physical properties of
electrical conductivity, thermopower, and thermal conductivity determine the figure of
merit of a given sample. The transport measurement system described in this thesis
provides a capability to reach measurement temperature as high as 1000°C which was not
previously available in this laboratory. The development of a system capable of
measuring the frequency dependant behavior of thermoelectric materials along with the
described circuit based models for understanding these behaviors is unique to the
scientific community to the best of our knowledge. This has provided new investigative
techniques for measuring the figure of merit for faster, more reliable, and more accurate
measurements.

The uniqueness of the research into developing a new transport measurement
system for high temperatures is that high temperature properties of quaternary cubic
thermoelectric material, along with other materials developed at MSU, have been
obtained for the first time. Since these measurements will give the first insight into
thermoelectric properties at higher temperatures, the system is an important tool used to
investigate these new materials.

Finding the figure of merit for thermoelectric materials at MSU typically involves
measuring thermoelectric power and electrical conductivity at high temperatures while a

similar sample is measured for thermal conductivity elsewhere. The uniqueness of the

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research into investigating the frequency dependant behavior of thermoelectric materials
is that the figure of merit for these materials over a temperature range can be found
directly. The models developed for this research help to explain the frequency dependant
impedance behavior and can also be used to explain how a faster figure of merit test
could be performed on multiple samples. This system along with the relevant models is

an important tool in characterizing thermoelectric materials.

1.2 Thesis Outline

Inuoduced in the first part of the thesis is a brief overview of the history, theories
and fundamentals applied to thermoelectrics. These sections will outline the background
knowledge, which will be needed for the proceeding chapters. Descriptions of old and
new thermoelectric materials will be discussed along with various techniques of
characterizing thermoelectric materials and devices. The next sections describe the new
research done at MSU, which includes a new system for low temperature measurements
(Drift System), a new system for high temperature measurements (Ultra High Temp
System), and finally the investigations of impedance spectroscopy on thermoelectric
materials. Impedance spectroscopy measurements will lead to the development of two
models that describe the AC frequency dependant behavior of the thermoelectric
materials (RC One-Port Model and Thermal Transmission Line Model). Based on
investigations of the impedance, a final system is created for rapid figure of merit
measurements at room temperature of multiple samples simultaneously (ZT Machine).
The experimental results will be presented for all systems along with detailed analysis

performed on the frequency dependant impedance measurements.

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Chapter 2: Thermoelectric Fundamentals

2.1 Introduction

Thermoelectrics (converting thermal energy to electrical energy and vice versa) has
been a topic of research for many years. In everyday life, people are using refrigerators,
air conditioners, fans, and heat sinks to keep objects cool. Thermoelectrics provide
alternate ways to cool objects that may be more practical or effective. People also
generate enormous amounts of wasted heat energy from automobiles and industrial plants
which could be transformed back into useful electrical energy with the help of
thermoelectric generators. Converting waste heat back into useful power can have major
global impacts. For example, making trucks more fuel-efficient may reduce gas
consumption. Using less gas can lead to lower automobile emissions, which impacts the
atmosphere.

Thermoelectric (TE) modules are devices the can convert thermal energy from a
temperature gradient to electrical energy for power generation or vice versa (providing
electrical energy to the thermoelectric module to create a temperature gradient across the
module) for cooling applications. Power generation devices work similarly to commonly
used thermocouples, which produce a voltage that depends upon the temperature between
the tip and base of the thermocouple and the materials used in that thermocouple.
However, unlike a typical thermocouple used for temperature measurements,
thermoelectric modules for power generation can generate enough electricity to power a
watch from body heat, power onboard electronics of a satellite in deep space, convert

wasted heat from an automobile to power electronic systems and make the overall vehicle

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performance more efficient, and provide electricity from nuclear heat of a submarine in
deep waters without any moving parts or added noise.

With no moving parts, TE modules are rugged, reliable, and quiet. They can be
operated in any orientation and in zero gravity environments. For cooling applications,
another important feature is the ease with which a TB module can be precisely
temperature controlled, an important advantage for scientific, military, and aerospace
applications such as infrared detectors and laser diodes.

Thermoelectric research is the study of the conversion between thermal and
electrical energy [1,2]. Thermoelectric technology has been around since the 18008.
There are three main effects that appear in thermoelectrics: Seebeck effect, Peltier effect,
and Thomson effect. Thermoelectric material properties are governed by the figure of
merit, ZT, which is governed by the thermopower, (1 (also know as the absolute Seebeck
coefficient), electrical conductivity, 0', and thermal conductivity, K, of a sample, while T
is the absolute temperature [3]. Z has units of UK making ZT a unitless quantity. The
figure of merit, ZT, is extremely important for describing the thermoelectric performance
and will be discussed extensively throughout this paper. The equation for ZT is shown
below.

2
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This section will describe the three main effects for thermoelectrics. It will also
discuss another important equation that is used quite extensively in thermoelectric
research, the Wiedemann-Franz Law. This law identifies the relationship between

thermal conductivity and electrical conductivity for TB materials. Finally, thermocouples

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lhe Peltier Cr

militia] 5 (A a

file Pelti»

3r C(\

EFF ’ 0

New

clller hf

 

and thermoelectric module configurations (layout), properties, and applications are also

discussed.

2.2 Peltier Effect

After the discovery of the Seebeck effect, Jean Peltier discovered in 1834 that heat
is absorbed or liberated when an electric current passes through an interface between two
different conductors. A diagram of this effect is shown in Figure 2-1. The Peltier effect
is caused by the fact that a heat current in a homogeneous conductor, even at a constant

temperature, accompanies an electric current.

 

 

Heat,Q
Electric Current,l Electric Current]
——> ——>
;:;:;1;:::::;:::;:;:;:::;:;3:3:3:;:;:;:;:::::::;:;:;]
Material A Junction Material B

Figure 2-1: Peltier effect diagram

The Peltier coefficient, HA3, is directly related to the change in heat between two

materials (A and B), per electric current, I, as shown here.

“AB = £97 (V) (2.2)

The Peltier coefficient can also be related to the Seebeck coefficient times the
temperature of the junction.
11.43 = my -T (V) (2.3)

The Peltier heat, PQ, is related to the electric current by the Peltier coefficient as,

PQ 154mm! (W) (2.4)

Peltier also d3

$0 15 1116 LllFL‘L

2.1 Thomson

ln1854

reiersihle trar

 

Where the dire
to the manic
Pretiouslx ex

T55
W T:

1"
. r
a

Peltier also discovered that the effect is reversible. If the direction of current is reversed,

so is the direction of heat exchange at the boundaries of materials A and B. [4]

2.3 Thomson Effect

In 1854 a phenomenon discovered by William Thomson (Lord Kelvin) found that a
reversible transverse heat flow occurs into or out of a conductor of a particular metal
where the direction depends upon whether an electric current flows from the colder side
to the warmer or from the warmer to the colder side of a metal. Any temperature gradient
previously existing in the conductor is thus modified if an electric current is applied [5].

A diagram of this is shown in Figure 2-2.

AQ
I;

/ ‘ \
AT I! \\
f/ \t
F l
1 l
l
.i'
\
/

\ l /

\\ // “\l /
‘fi _ .,
\J/

Figure 2-2: Thomson effect diagram

The Thomson effect, y, is related to the Seebeck effect,

da
7 — :17 . T (V/K) (2.5)

01'

111a Thoma '

2.4 “leden .

Therm .-
phonons and ‘

9L.
henna] con. .

when 3 Sam .
lattice “ill V ‘-
Conductixit} :
mnifiblfilon‘
CO"“"lebUilOn

mmbmion.

he
hm Corr

4
‘;u “

 

T '
a(T) = [ETD-(1r (V/K) (2.6)
0

The Thomson coefficient relates the Thomson heat, FQ, and electrical current through,

FQ=g—%=—y-I-AT (W) (2.7)

2.4 Wiedemann-Franz Law

Thermal conductivity is the ability for a material to conduct heat. Both the
phonons and the charge carriers can conduct heat through the material such that the total

thermal conductivity will include electronic and lattice contributions as shown here.

Ktotal = “lattice + Kelectronic (wmthJ) (2-8)

When a sample is placed in a low temperature environment, the atoms in the crystal
lattice will vibrate at a lower intensity which can make the contribution of thermal
conductivity from the lattice very small or even negligible compared to the electronic
contribution. At sufficiently high temperatures, the lattice will vibrate so much that the
contribution of thermal conductivity from the lattice dominates the electronic
contribution. Between these two extremes, both mechanisms will contribute to the total
thermal conductivity. With thermoelectric materials, it is often possible to reduce one
component of the thermal conductivity without appreciably affecting the other material
properties.

For metals, the thermal conductivity is high, and those metals, which are the best
electrical conductors, are also the best thermal conductors. At a given temperature, the

thermal and electrical conductivities of metals are proportional, but raising the

h
conductit it}

where

 

 

Them

312111;

where x is 1

applies for

The
fi'tsrmal cc
3 Sample \

Ll.
.
A

rev“ '
HQ“ 11‘

temperature increases the thermal conductivity while decreasing the electrical
conductivity. This behavior is quantified in the Wiedemann—Franz Law shown below.

5 = L - T (word) (29)
0'

where

x = thermal conductivity (W/m°K)

0': electrical conductivity (S/m)

L = Lorenz number = 2.45x10'8 woK'2
T = temperature (K)

The value of this Lorenz number was found using quantum mechanics such that at

300K

L: K =7r2-k2

= 2.45 x10"8 (WQK'Z) (2.10)
0' ' T 3 - e2

 

where K is the Boltzmann constant (1.3807x10'23 J/K). This constant of proportionality
applies for temperatures above the Debye temperature, 09.

The Wiedemann-Franz Law is useful for estimating the temperature dependent
thermal conductivity of measured TE samples. For example, the thermal conductivity on
a sample with a certain crystal structure can be found experimentally using the flash
diffusivity-specific heat method. This thermal conductivity will include contributions
from both the crystal lattice and the electrons. A published sample of LAST (Pb-Sb-Ag-
Te) material had a thermal conductivity of 2.3 Wm'lK'l and electrical conductivity of
1850 S/cm at room temperature [6]. For LAST materials (degenerately doped
semiconductors), at some arbitrary temperature with mixed scattering, the Lorenz number
can be calculated as 2.28x10—8 WQK'2 [7]. The lattice and electronic contributions may

be decoupled to give the electronic contribution from Wiedemann-Franz as

relettmntt .

 

llattice I l“
is. measured

concentrati. -
contrihutior

2 1,. ,
WC'utdiLCl .1.

 

 

2.5 Thermo

Them:
research art-c
COD-ductors .

that 73% bee

fig" 1‘: 2‘

“electronic = L - 0' - T = 1.27 Wm'lK'l. Now the lattice contribution can be found as

Klam-ce = K1010] — “electronic = 2.3 —1.27 = 1.03 Wm'lK'1 . When another TE sample
is measured with similar composition and crystal lattice (but possibly doped at another
concentration), the electrical conductivity of the material will change. Assuming the
contribution from the lattice remains the same, the electronic contribution can again be

calculated and used in estimating the total thermal conductivity of the sample.

2.5 Thermocouples

Thermocouples are fundamental to thermoelectrics and are commonly used in
research and measurements. A thermocouple is made of any two dissimilar electrical
conductors such as copper and constantan. A type-E (chromel-constantan) thermocouple
that has been spark welded together is shown in Figure 2-3. There are eight NIST
standardized thermocouple types [8], which have been well characterized and are shown

in Table 2-1.

Chrome] Constantan

Figure 2-3: Type-E thermocouple spark—welded together using 25.4um in diameter wire.

10

llO'M‘W 61'. {:7 ~

thennoconn i,

I

In “hich 11 \t

1

The CF,

:3 15 d“ e:

 

Table 2-1: Thermocouple types and their corresponding Seebeck voltage

 

 

 

 

 

 

 

 

 

 

 

 

 

TYPO Materials Thermopower (pVIK) Temperature Range
at 25°C (°C)
N Nicrosil - Nisil 26.5 500 to 1000
T Copper-Constantan 41 0 t0 350
J Iron - Constantan 51.5 0 to 750
E Chromel - Constantan 61 0 to 900
K Chromel - Alumel 40.5 0 to 1250
Platinum 6% Rhodium — 800 to 1700
8 Platinum 30% Rhodium 0
Platinum - 0 to 1450
R Platinum 13% Rhodium 6
Platinum — 0 to 1450
8 Platinum 10% Rhodium 6

 

However, many other thermocouple combinations are available. Each type of

 

thermocouple has different features such as its voltage output sensitivity, the environment
in which it will work (vacuum or no vacuum, oxidizing or inert atmospheres, magnetic
fields, etc.), and the temperature range that it is appropriate for. Figure 2-4 shows a

configuration for a single ended thermocouple made of two different materials (A and B).

 

T1
Material A
T
+ O/ 2
VAB O/
- Material B

 

 

 

Figure 24: Single ended thermocouple

The ends of both thermocouples are thermally ground to T1 and T2. The voltage,
VAB, is developed based on the thermopowers of each material where,

72 T1 Tz T2
VAB= laA dT+ ja'B'dT: “CIA —aB)~dT= laAB dT
T1 T2 T1 T1

(2.11)

11

Herr. ant 1"

Seebeck of .‘

 

singleeneie-
end of the 11‘

used to Find

as long as b.

 

(tween the

‘4-
Fl 1 \5‘
A ki‘A; ‘1‘“?

:15
are U31“.

11

T1. v.7...
*kfj

j.“ .

I‘Aj ‘\“
£\‘1:\.“‘
.1

Here, aAB is used to represent the Seebeck of the thermocouple. See Table 2-1 for the
Seebeck of standard thermocouples at room temperature. To get an absolute temperature,
single-ended thermocouples can be used as long as the temperature at the measurement
end of the thermocouples is well known. A calibrated diode or platinum resistor can be
used to find this temperature. Extension wires can be used without any extra calculations
as long as both wires have the same thermopower and the same temperature gradient

between the ends of the wires. An example of this is shown in Figure 2-5.

 

 

 

 

 

 

 

 

T1 TR
Materral A /,_:....:...,,
Cu
1 + O (E
Vo trneter :

O C dJ-D/ M . 18 j T]
u atena ; .
L- _ _/

 

 

 

 

 

 

Figure 2-5: Typical thermocouple setup for temperature measurements

In this case, TR is a reference junction where the temperature is known and the extension
wires are both copper. T1 does not need to be known to find the junction temperature T].

This can be shown as follows,

TR TJ T R 71
Vmeter = jaCu {1T + Ia A dT+ Ia B dT + jaCu dT
T1 TR TJ TR (2.12)
TJ TJ
= {(0:14 -aB)dT = jaAB {1T
TR TR

From here, usually the junction temperature, T], is desired. The first step is to measure
the thermocouple voltage with its reference junction at TR and its measuring junction at
T), which was done above as Vmeter (now called V R] “voltage between reference and the

junction”). The next step to achieving this value is to compute the emf voltage of an ice-

12

point 10 0C.

NIST “her:

This equatit
tillage out;
the output \
the 11.1.3 can

compensate.

 

 

 

 

point (0 °C) compensated thermocouple at the temperature TR. This data is provided by
NIST where the representing equation is as follows,

VOR =F(TR) (V) (2-13)
This equation can be read “the voltage from 0°C to the reference temperature is the
voltage output function of the thermocouple evaluated at the temperature TR.” Plotting
the output voltage data versus temperature for the thermocouple and using a curve fit to
the data can be used to find this function. Next, compute the emf voltage of an ice-point

compensated thermocouple at T]. Here, the representing equations is as follows,

V0.1 = VRJ + VOR (V) (2.14)

Finally, the junction temperature, T], can be calculated from the ice-point calibration data
for the thermocouple as,

TJ = F (V01) (°C) (215)
Plotting the thermocouple data as temperature versus output voltage and using a curve fit
to the data can find this function.

Thermocouples are used extensively in the characterization of TE materials. They
are used in finding the temperature gradient that is placed across a TE sample for
thermopower measurements. Often, these same thermocouple wires are used to measure
the voltage produced by the TB material when a temperature gradient is established
across the sample. For this measurement, it is necessary to know the thermopower of the
measuring wires and to apply a correction to the measured voltage from the sample due

to the voltage developed by the wires themselves.

13

2,6 Seebecl

In 18:
meals as in

Thompson | .

conductor or
"town as tlt.
a? '\

that. The '_

conductor is

 

 

 

2.6 Seebeck Effect

In 1821, Thomas Seebeck observed the thermoelectric effect using two different
metals as in the thermocouple, which is the only way to observe the phenomenon. It was
Thompson (Lord Kelvin) who later explained the observed effect. A temperature
difference between two points in a conductor or semiconductor results in a voltage
difference between these two points. Alternatively stated, a temperature gradient in a
conductor or semiconductor gives rise to a built-in electric field. This phenomenon is
known as the Seebeck effect. The Seebeck coefficient quantifies the magnitude of this
effect. The thermoelectric voltage developed per unit temperature difference in a

conductor is called the absolute Seebeck coefficient, also known as thermopower.

E E
Tk Cold
4—— Temperature AT ——>
EF
1 > 1(5) H \ \

VoltageAV ———>
+ $ 9 o 9 $ :69 -

Hot + .e e c :9. .oe. 0°. _ Cold

+6 63 $'$°‘$-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2-6: Seebeck effect on an aluminum rod

For normal metals, i.e. an aluminum rod, when one end of the rod is heated relative
to the other end, the electrons in the hot region have more entropy and therefore have
greater velocities than those in the cold region (See Figure 2-6). The conduction

electrons around the F errni energy have a mean speed that has a small temperature

14

dependenci
{guard the
region and
continue UI
timer elec
sometime).

diiierenee i

3) content
hot side. T:
m is mis!

bemom“;

of,» x 51

 

 

dependence. This difference in electron energy causes a net diffusion from the hot end
toward the cold end. This diffusion leaves behind exposed positive metal ions in the hot
region and accumulates electrons in the cold region. The diffirsion of electrons will
continue until the electric field developed between the ends of the sample prevents any
further electron motion from the hot to cold end. At steady state (constant heat flow after
some time), the voltage difference across the aluminum rod due to the temperature
difference is called the Seebeck effect. The equation for thermopower is shown below.

dV
a - 2}? (V/K) (2.16)

By convention, the sign of or represents the potential of the cold side with respect to the
hot side. The coefficient a is also referred to as thermoelectric power even though this
term is misleading as it refers to a voltage difference rather than power. By integration of
thermopower, the voltage difference across the sample can be found as shown below.

T2
AV: ja-dT (V) (2.17)
T1

The average energy E ave per electron in a metal with the density of states

g(E) at E“2 is given by

2
3 57: kT
E T =—E 1+—— — 2.18
ave( ) 5 F01: 12 [E 0]] ( )

where Em is the Fermi energy at 0K and k is Boltzmann’s constant. The Fermi-Dirac
distribution extends to much higher energies when the temperature is raised so that the

average energy per electron is actually greater in the hot end.

15

For 3
the potenti;

So. {or met

For tf.

electrons in

XE. = 1 In.
with high-er

dlixbe from

normed meta

Scattered h.-

mfibie [0 at.

 

EIMOU min

 

 

For an electron to diffuse from the hot region to the cold, it has to do work against
the potential difference. This work done decreases the average energy of the electron.
So, for metals, the Seebeck coefficient is as follows,

_7I2k2T
2eEF0

~
~

 

(V/K) (2.19)

For the above explanation to be valid, some assumptions were made. First, the
electrons in the metal behave as if they were “free”. Second, the electron energy E =
KE. = 1/2m¢"‘v2 and the effective electron mass me“ is constant. Finally, the electrons
with higher energy have greater mean speeds and longer mean free paths so that they
diffuse from the hot to cold region. These assumptions only apply to what are called

normal metals (e.g. Na, K, Al, etc.).
i The diffusion of electrons from the hot to cold region assumes that the electrons in
the hot region have higher speeds. In reality, the interactions of the conduction electrons
with the metal ions, the lattice vibrations, and thus on how the conduction electrons are
scattered, have to be considered. Except for certain metals, the free electron theory is
unable to account for the sign of the thermoelectric effect. It has been found that the net
electron migration, hot to cold, or cold to hot, is determined by the energy dependence of
the electron concentration, n, the mean free path (MFP), A, and the mean scattering time,
2'. In those metals in which the MFP decreases strongly with the energy, electrons will
migrate from the cold to hot and the thermoelectric power is positive. By including the
energy dependence of the scattering processes, Mott and Jones [9,10] have derived the

following expression for the Seebeck coefficient,

16

there r is .1

charge tram. s

 

mkww.

leg. .\'i ). .-\

 

_7rzk2T
ZeEFO

~
~

 

x (mg (2.20)

where x is a numerical constant that depends on the energy dependences of various
charge transport parameters. This equation does not apply to metals in which electrons
can be scattered from one transport band to another transport band as in transition metals

(e.g. Ni). A list of thermopower values of some metals is shown in Table 2-2. [11]

Table 2-2: Thermopower of various metals

 

 

 

 

 

 

 

 

 

 

Metal Thermopower (uVIK)
at 25°C

Al -1 .66
Pb -1 .05
Pt -5.28
M0 5.6

Cu 1 .83
Ag 1 .51

 

2.7 Thermoelectric Modules

Thermoelectric modules behave similarly to thermocouples in that both have the
ability to convert heat energy to electrical energy and vice versa. However,
thermoelectric modules are typically made of degenerately doped semiconductors where
the charge carriers carry the heat from one end of the semiconductor to the other. The
modules are also typically made of many couples electrically connected in series (n-type
connected to p-type) (connecting many thermocouples together electrically in series
creates a therrnopile). This way, a module for power generation can convert enough
thermal energy to electrical energy to provide a considerable amount of power, where as

thermocouples do not. For cooling applications, the module can actively transfer enough

17

thermal 1‘
device.
.\l;

COFLIEL‘CIL'

‘.‘-. _.
-- ---

//-

Figure j

 

 

 

thermal energy from one side of the module to the other to make a functional cooling
device. Thermocouples are typically only used for temperature measurements.

Many thermoelectric modules consist of p-type and n-type semiconductors
connected electrically in series and thermally in parallel as shown in Figure 2-7 and
Figure 2-8. Figure 2-7 (a) shows a pn module used for cooling applications while (b)
shows the same device being used for power generation. By the Seebeck effect, heat
flow through this thermoelectric material will tend to move the charge carriers in the
same direction as the heat flow. Examples of thermoelectric modules for both power
generation and cooling applications are shown in Figure 2-9 where (a) shows an example

of a stacked module.

Heat Applied

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

|_.

Figure 2-7: PN Thermoelectric Modules. (a) Cooling applications. (b) Power
generation.

 

 

 

18

——————-——~~~——~—- ~ .___ — ~ ( old side ——~— , ,2 ., ~ ~~~~—~——~

Electrical Electrical
Current Current

 

 

Thermal
Flow

 

 

 

 

 

 

 

—> —> —> —>
Electrical Electrical Electrical Electrical
Current Current Current Current

_ ................. H 0t S i d e .................

Figure 2-8: Thermoelectric module consisting of many unicouples.

r. :
k. I . 1“:

   

(b)

Figure 2-9: Examples of thermoelectric modules. (a) is stacked module, (b) and (c) are
modules of difference sizes

This combination of p-type and n-type materials does not form a diode because the
semiconductors are highly doped causing the junctions to be ohmic. A diagram of this
behavior can be examined more closely if instead, we look at a connection between a
highly doped n-type semiconductor and a metal shown in Figure 2-10 where the work
fimction of the metal is smaller than the work function of the semiconductor. In Figure
2-10 (a) electrons are flowing from the metal to the conduction band (CB) of the
semiconductor. Current is carried by the electrons near the Fermi level, Epm, in the metal.
When the electrons cross over into the CB of the semiconductor, their energy is EC plus

average kinetic energy (KE). Therefore, there is an increase in the average energy per

19

electron in
entironme
Passing an
junction (1
Oldie mate

(hi) llCiti [(‘i

. Figure 2
absorption

electron in the contact region. The electron must therefore absorb heat fi'om the
environment (lattice vibrations) to gain this energy as it moves through the junction.
Passing an electron from the semiconductor to the metal results in a release of heat at the
junction (Figure 2-10 (b)). There is Joule heating which arises from the finite resistivity
of the materials and it is due to the conduction electrons losing their energy gained from

the field to lattice vibrations when they are scattered by such vibrations.

I I

__- q f-.- ,
++++++ 6. w...
‘ i l .
i L«.- >- f EC i j i ’55,].f. EC
EFITI FQ“V ’ ’ ‘ EFn EFm ,1 -- sic-“J ” ------ ’EFn

 

 

 

 

 

/ l i/ / i
VB ? iVB
i
/ ‘ /
L——~ 4———-— > -: -—-—- —--4— >
Ohmic Contact _ Ohmic Contact
' Region Region
Metal I n-Type Metal n-Type
Semiconduct Semiconduct
(a) (b)

Figure 2-10: (a) Current from an n-type semiconductor to the metal results in heat
absorption at the junction. (b) Current from the metal to an n—type semiconductor results
in heat release at the junction. [9]

The efficiency of a thermoelectric generator is titled efficiency, 7], while the

efficiency of a cooler is titled the coefficient of performance (COP), (6. TE devices can

20

'3 0‘”
file/1m”

533 “0:1;

 

 

be scaled without loss of efficiency making the COP derivable from a single TE couple.

The ideal efficiency for power generation (neglecting contact resistance) is as follows,

 

 

 

AT
T
,7 = _ Hot _ (Ideal efficiency) (2-21)
1 AT 4
2—-—- +
2 7H0! Z-THot_

 

 

The coefficient of performance for a thermoelectric cooler and its maximum efficiency

are shown below

apN-TCOId-I—é-Iz-R—K-AT
(15: (2.22)
2
apN-AT-I+I ~R

¢ =Tan-l(/I+Z.Tavg—\1)_l (223)
max AT-(/1+Z-Tavg+1) 2 '

The limit to the maximum efficiency is called “Carnot Efficiency”, which is the ratio of

 

 

the work to the input heat and is shown below.

__ AT
THot

 

77c (Carnot Efficiency) (2.24)

Thermoelectric modules cannot be made ideally. They will always suffer from at
least one major contributor, which is contact resistance between thermoelectric materials.
The equations below show how the percentage of contact resistance to the overall
resistance of an entire module can degrade the ZT of the module linearly. If we let R be
the total electrical resistance of a module and separate it into the resistance of the
thermoelectric materials (RTE) and the contact resistance (RC), and we let the contact

resistance be a percentage of the total resistance, the resulting ZT can be found.

21

2. 2.
ZT = a K = a K (2.25)
R (RTE + RC)

LetRC=x%-R

 

Then R = ———RTE
(1 — x%)

_a2-K
RTE

 

ZT - (1 — x%)

This formula shows that if you know the contact resistance and the resistance of the TB
materials, then you can determine what the ideal ZT value would be. Clearly, low
resistance contacts are very desirable and have a major part in research for making

thermoelectric devices. [12,] 3]

22

3.1 lntrod

 

This
.k .1 ..
tfmmLillL

descriptior

 

 

Chapter 3: History and Current Developments

3.1 Introduction

This section discusses the renewed interest in thermoelectric research. Efforts in
enhancing the figure of merit of these TE materials will be briefly described including
descriptions of common thermoelectric materials. Finally, measurement techniques for
characterizing TE properties will be given along with measurements currently being done

at Michigan State University.

3.2 Renewed Interest in TE Research

In 1954, Goldsmid suggested that bismuth telluride (BizTe3) alloys would make
good TE materials [14]. Over the years, BizTe3 has been one of the best known
thermoelectric materials with a ZT of about 1 near room temperature. Much effort has
been done to increase this ZT but without much improvement. A renewed interest in
thermoelectrics research (Early 19905) has been due to predictions of large improvements
possible through nanostructured materials due to quantum confinement of charge carriers
and the resulting modification of the band structure [15]. Materials with a ZT of about 4
or 5 are needed in order to compete with a compressor-based refiigerator, and a Z T of 2
could prove to be useful in many applications such as automobiles. However, any
improvement in ZT is expected to increase the number of applications of thermoelectrics.

Quantum confinement effects have been realized in thin film devices (TFD) and
have shown a great increase in efficiency. However, unlike traditional bulk grown

materials, TFDs still have challenges to overcome in order to be useful power generation

23

or coolii
gradient
Sh'OMl ii
proporti
required

SU'UCIUIK‘

FRYCSS

— '— — -——__h—H

 

or cooling devices. Such challenges include the ability to have large temperature
gradients across them and the need for improvement of manufacturing cost and time. As
shown in equation (2.21), the power produced from a TE generator is directly
proportional to the temperature gradient established. Therefore, higher gradients are
required to yield more power out. Bulk samples may use the benefits of quantum
structures found with TFD research but can be made without the complex manufacturing

process along with the ability to withstand higher temperature gradients.

3.3 List of TE Materials

The following paragraphs discuss many of the thermoelectric materials that have
been investigated over the years. This is a non-exhaustive list of materials and new
materials are still currently being discovered. Many of the materials can be used for
different operating temperatures and firnctions. It is also possible to combine different
materials in a segmented leg of a TE module so that each material is operated at its
optimized temperature range, which improves the overall efficiency of the TB module.
This list also helps to show the many ways thermoelectric performance can be enhanced
by adjusting the thermal conductivity of materials using quantum confinement, cage-like
structures, complex crystal lattices, etc.

One of the most commonly used thermoelectric materials is bismuth telluride
which exhibits a ZT~1 near room temperature. It is currently made in mass production
for cooling applications and for power generation. Usually, it is alloyed with antimony-

telluride (szTe3) which has the same rhombohedral crystal structure. The alloy helps

reduce the thermal conductivity to values as low as K=1 W/mK which is a significant

24

contribut:
I
is file 111::

well suite

ll-l"

SITUCIUIL’.

a good m.

l
“ith viii

 

 

Sili.‘
thermoele
10A IlUClt
SiGe can

msmOCi

efiici»

contribution toward achieving the high ZT value. The main disadvantage of this material
is the limited maximum operating temperature of ~470K. Therefore, this material is not
well suited for high temperature applications.

II—IV semiconductors such as PbS, PbSe, and PbTe have the cubic NaCl crystal
structure. PbTe is a narrow gap semiconductor often used in TE generators because it is
a good material for hot side operation around 700K. The standard alloy is Pb1-xSnxTe and
with x=0.25, the ZT is greater than 1 near 800K.

Silicon germanium (SiGe) alloys have been chosen for many radioisotope
thermoelectric generators since 1976 where they were first used in space in the SNAP-
10A nuclear reactor. In space, its spherical radioactive core serves as a heat source.

SiGe can be used up to 1300K without significant degradation and the cold side to the
thermoelectric material is maintained by heat fins where heat is flowing out into space by
means of radiation. Primary considerations for space applications are reliability and high
operating temperatures to take advantage of the T4 (temperature to the forth power)
dependence of radiator heat rejection rates. Therefore, high operating temperatures give
rise to higher temperature gradients which correlate to a larger output power and
efficiency.

At the other extreme, bismuth-antimony is an alloy for TB devices that operate at
low temperatures. The highest ZT for Bi-Sb is 0.6 and it is reached with 10-15% of Sb
alloying with Bi. This alloy exhibits a magnetothermoelectric effect where magnetic
fields can double the value of the ZT for a value greater than 1 near 200K.

The family of skutterudite compounds has also been of great interest recently.

Skutterudite is a naturally occurring mineral, COAS3, with an open, or cage-like structure.

25

  
 

Men 2111):-

thermal c.

material.
An. .

similar to

 

srraller 'g

isobutene.

 

tr) stallize
the cage-1i
low frequ.
hale (he [
M a mate
material 5

Ha.
MNi311 1

b). em 0

When atoms are placed into the interstitial voids, or cages, of these materials, the lattice
thermal conductivity can be substantially reduced compared to that of the unfilled
material. A ZT greater than 1 has been achieved in these materials at 700K.

Another open structure is found in the clathrates which have crystalline structures
similar to that of ice that occur when water molecules form a cage-like structure around
smaller ‘guest molecules’. Common guest molecules are methane, ethane, propane,
isobutene, normal butane, nitrogen, carbon dioxide, and hydrogen sulfide. Clathrates
crystallize in the cubic system rather than in the hexagonal structure of normal ice. When
the cage-like structure of these materials is filled with guest atoms, they strongly scatter
low frequency phonons by what is called “rattle” scattering. Low frequency phonons
have the highest group velocity and contribute the most to the lattice thermal conductivity
of a material. With high Seebeck coefficients and electrical conductivities, clathrate
materials are gaining interest for thermoelectric applications.

Half-Heusler alloys are cubic materials (MgAgAs type) with the general formula
MNiSn where M is a group IV transition metal (Ti, Zr, or Hf). Half-Heusler is formed
by removing the Ni atoms on one of the two Ni sublattices of the full Heusler alloys
(MNiZSn) and replacing them by an ordered lattice of vacancies. Half-Heusler alloys are

intermetallics and exhibit a high negative thermopower (-40 to —250 uV/K) and low

electrical resistivities to form materials with some of the highest power factors (320')
known. Unfortunately, they also exhibit a high thermal conductivity (~10 W/mK) and
several efforts are under investigation toward lowering the thermal conductivity without

significantly reducing the power factor.

26

Tell;
TAGS hm
TAGS-tsp.
TAGS-85.

materials.

 

a1 7001;. "l

 

 

 

meelanica
X C\\
fire) has e

densit) of

qui'll‘m t

(It

Tellurium (Te), Antimony (Sb), Germanium (Ge), Silver (Ag) alloys known as
TAGS have been used successfully in numerous space and terrestrial applications. Basic
TAGS-type materials have the general formula of (AngTe2)1-x(GeTe)x. TAGS-80 and
TAGS—85, 80% and 85% of GeTe respectively, are two of the most commonly studied
materials. TAGS-80 exhibits a ZT of ~1 .85 at 800K and TAGS-85 exhibits a ZT of ~1 .35
at 700K. TAGS-85 is the preferred TE material because it is more stable and has better
mechanical properties than TAGS-80 [16].

New efforts are being made using quantum dot superlattice (QDSL) structures.
They have been reported to show enhanced TE device performance due entirely to a high
density of quantum nanodots of PbSe composition embedded in a matrix of PbTe. These
quantum dots allow electron transport while decreasing the thermal conductivity.

Much of the research at MSU has been on materials called LAST (L = lead (Pb), A
= antimony (Sb), S = silver (Ag), and T = tellurium (Te)) for n—type bulk materials and
LASTT (extra T = tin (Sn)) for p-type bulk materials. These materials exhibit melting
points near 800°C and therefore target applications with hot side temperatures near
533°C (or 800K which is 2/3 of the melting point. The general formula AngHSbTesz
(with m=18 to be called LAST-18) is a family of n-type bulk cubic compounds with
complex composition which combine a set of desirable features, such as isotropic
morphology, high crystal symmetry, low thermal conductivity, and the ability to control
the carrier concentration. Members of this family can be optimized to produce high Z T
values (~2) at elevated temperatures. These compounds possess an average NaCl
structure. Other materials also being investigated that show promising high ZT values at

high temperatures are Ag-Sb—Pb—Se, Pb.Sb—Te-Se, Na—Pb-Sb-Te, and K-Pb—Sb-Te. In

27

addition 1.

quantum :1

Or;

sexera‘. e).

the best 2

aneed fo

Pi?” V \r-‘”
l\11‘." i“.

addition to the creation of the bulk materials, MSU is also investigating embedding
quantum nanodots of CdTe into a bulk sample of PbTe. [17]

Over the years, it is apparent that many materials have been investigated with
several exhibiting good thermoelectric properties. Figure 3-1 is a graph showing some of
the best Z T values obtained over a wide temperature range. The graph shows that there is
a need for improvement on thermoelectric materials if they are going to replace current

refrigeration technology by having average Z T values greater than 2.

 

 

 

  

——t— TlgBiTe’3 + p-TeAgGeSb
—<>— Zn43b3 -+- CeFe3 5CoO SSbm
—E— PbTe —V— Yb‘ ,iVCOJSb,“
+ Ce_ Fe_CoSb —O-— Eu- Co Sb _Ge
ll,“ .1 13 L142 4 1131 05
—+— TAGS-85 + CsBi4Te6
—l2— SiGe (n-type) —9— Bine‘
+ Ba_ Ni, . Co __Sb ——-— LAST
U 3 ‘J H.“ 3 a; 12
—-O— Bi-Sb LASTT
_
2 -l
d
1.5 -
P I
1 _
N r I
, .
0.5 -
o ‘ l l l l l I l l l J I

 

 

200 400 600 800 1000 1200
Temperature (K)

Figure 3-1: Best ZT values obtained for a variety of materials

28

3.4 Tecl

Tr.
is import
ummfli
electrical
and treat
effects as '
measurer
understar
made. I] _
det'ices.
meaSUIE t
andtech; ~

dlSafl'Van:

 

 

/

3.4 Techniques of Characterization

Transport measurements of TE materials has been a main focus in my research. It
is important to be able to identify materials with good TE properties. This is
accomplished by acquiring accurate temperature dependant data for thermopower and
electrical conductivity of the TE samples. Using existing TE measurement techniques
and creating new measurement systems requires the knowledge of the thermoelectric
effects as well as computer and electrical engineering skills. The goal of the
measurements is to not only identify high performance TE materials, but to develop an
understanding of the materials to a level where improvements upon the materials can be
made. These improvements will be used for developing the materials into ftmctional
devices. In the following paragraphs, I discuss various existing techniques developed to
measure electrical and thermal properties of TE materials as well as the measurements
and techniques currently being used in our lab. Studying the advantages and

disadvantages of these methods helps to design better measurements systems.

3.4.1 Steady-State Technique (Thermal Conductivity)

A common technique for low temperature measurements of thermal conductivity
(where heat radiated from the sample is much smaller than heat transported through the
sample) is the steady-state method [16]. With this technique, heat is applied to one end
of a sample for relatively long times in order to establish a steady state temperature

gradient along the sample. A diagram of the setup is shown in Figure 3-2.

29

 

9’—

fl

(1;

re

 

8)
supplied 1

K can the

A15 the C

 

 

Figure 3-2: Diagram of measuring thermal conductivity using the steady-state technique

By measuring the temperature gradient along the sample, the heat, Q, being
supplied to the sample, and by knowing the sample dimensions, the thermal conductivity,
K, can then be calculated. The equation for thermal conductivity is shown below where
A is the cross sectional area of the sample, L is the length between the temperature

measurements, and AT is temperature gradient Tl-Tz.

_ Q-L
K_—A-AT (3.26)

If the sample has high thermal conductivity, then the length of the sample should be
sufficiently greater than the diameter. This helps to create a larger temperature gradient
along the sample. For low conductivity materials, equilibrium times become very long so
the length to area ratio should be kept small. The disadvantage of this technique is the

long stabilization period needed for precision measurements.

30

3.4.2 Hal

1h.
thermorxi
rnaterials I
junctions
rnxrureri
method is
current pi
applyinga
induced a;
Cooling 3:

500d UCllo

 

[181. Thii

for the me

3.4.2 Harman Technique (Thermal Conductivity and Z T)

The Harman Technique [18] is a measurement of electrical conductivity,
thermopower, and thermal conductivity by utilization of the Peltier effect. Because TE
materials can create a temperature gradient when electrical current is flowing through the
junctions formed to the material, the need for a heat source is eliminated. This
measurement allows one to calculate all parameters of ZT. A special feature of this
method is that ZT is given in terms of the ratio of two voltages (voltage produced due to
current passing through a resistance and voltage produced due to the Seebeck effect). By
applying an electric current through a thermoelectric sample, a temperature gradient is
induced as caused by the Peltier heating at one end of the sample and a subsequent Peltier
cooling at the other end of the sample. There will also be Joule heating and thermal
conduction. From here, it is possible to find the 21' using the Harman technique circuit
[18]. This circuit (which uses 8 measurement wires connected to the sample) also allows
for the measurements of thermopower, electrical resistivity and contact resistance. This
technique is only feasible if the two voltages can easily be distinguished, which can be

challenging for low ZT materials.

3.4.3 Pulse Technique (T hermopower and Thermal Conductivity)

The pulse technique [19] is a method for measurement of thermopower and thermal
conductivity. It is very similar to the steady-state technique but does not require an
extremely long waiting time. This is an AC method used to avoid offset voltages; the
heater current, which is used to create a thermal gradient across the sample, is pulsed

with a square wave (See Figure 3-3 (a)). This method will produce piecewise exponential

31

the aver:
proportit
plotted 1 l
therrnopt

determin

1T [Ill

 

 

signals for the voltage across the sample (Figure 3-3(b)) and the temperature gradient
across the sample (Figure 3-3(b)). When the temperature gradient is small compared to
the average temperature of the sample, the voltage across the sample is directly
proportional to the temperature gradient across the sample. Here, AV versus AT can be
plotted (Figure 3-3 (d)) and the linear slope of the measurements used to determine
thermopower. This allows for a large accumulation of data points to more precisely

determine the thermopower.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I I I I I '7
E -
O _
g ‘ Heater Current (A): 0.0094 .
a . - ..
2 0 Volts
g - i— - -
L l I l l I —-i
Time
(a)
I I I f fi ‘I I f I
4 - -
Z .. g L ..' "
I- " . -'
4 5 - .° .
l L l l I - / l L 1
Time AT (K)
(C) ((0

Figure 3-3: Pulse technique example. (3) Plot of heater voltage vs time. (b) Plot of AV
vs time. (c) Plot of AT vs time. (d) Plot of AV vs AT.

32

B)
may slm
sample v
lsexcral '
this stea.
faster th;

etail in

By pulsing the heater on the sample (on and off) the overall sample temperature
may slowly rise due to Joule heating. However, the temperature gradient across the
sample will reach a steady AC function with constant amplitude after a short time
(several minutes). Because the temperature gradient and the voltage gradient maintain
this steady state AC function, thermal conductivity measurements can be made much
faster than the DC steady-state technique. The pulse technique will be explained in more

detail in later sections discussing the Drifi System and the Ultra High Temp System.

3.4.4 Modified Harman Technique (Z 7)

Continuing from the work of Harman, a modified technique [20] was developed to
again measure ZT by utilizing only the voltage components in the measurement. In this
technique, a switching square wave current source (positive to negative) is used in one
step of the measurement. First, a high frequency electrical current signal is put through
the sample to prevent the thermoelectric module from developing a temperature gradient.
Without a temperature gradient, the electrical conductivity of the sample can be measured
without contributions from the Peltier effect. The second part of the measurement
involves applying a DC electrical current source through the sample and measuring the
voltage across the sample to calculate the resistance. This will of course have
contributions from the Peltier effect and the finite resistance of the material. Using the
two measurements, one can now separate the voltage due to Seebeck and the voltage due
to the electrical resistance of the material. Knowing the DC and AC resistance of the

material allows for calculations of the figure of merit, ZT. This technique will be

33

heard

IllCIiSllICi‘

3.5 \lea

Mic

 

has man}

lhi‘SE m (11:

3165mm

de‘filorfi

discussed in greater detail in later sections involving impedance spectroscopy

measurements on thermoelectric materials.

3.5 Measurement Systems at MSU

Michigan State University typically works with bulk thermoelectric materials and
has many measurement systems to characterize the temperature dependent properties of
these materials (thermopower, electrical conductivity, and thermal conductivity). The
systems that are discussed here were used excessively throughout my research and do not
include all measurement systems available at MSU. These systems not only provided
measurement data on new materials, but were also used to help verify the new systems

developed during this research.

3.5.1 Room Temperature Electrical Conductivity Scanning Probe

A common system used to verify electrical conductivity measurements in the MSU
Electronic Materials PLD and Characterization Lab is the Room Temperature Scanning
Probe (RTSP) shown in Figure 3-4. To measure electrical conductivity of a sample, a
small current (typically ~10-50mA) is put through the sample via a Keithley Instruments
2400 current source. The current is a square wave function, 50% duty cycle, at
approximately 33Hz. The voltage is then measured along the sample either by using a
single probe and moving it along the sample in measured increments, or by simply
placing the array of ten pins on the sample and measuring the voltage at each pin (Figure

3—5). This system has three axes of motion (x, y, & z). The x and y direction allow the

34

user to pr
1
lowering .
purposes.
would ca.
second pi-
temperatr
mezsurerr

subtractin

 

 

done Ncr

along the

user to probe over the entire surface incrementally while the z axis is for raising and
lowering the spring loaded probes onto the sample. The switching of the current has two
purposes. The first is to keep the sample from establishing a temperature gradient, which
would cause an error due to the Seebeck voltage developing across the sample. The
second purpose is to cancel out any voltage offsets on the measurement wires due to
temperature gradients or diode effects. This is accomplished by taking a voltage
measurement for a positive current, taking a voltage measurement for a negative current,
subtracting the two measurements, and then dividing by two. This process is typically
done twenty times and the average of those values is used. By scanning the voltages
along the surface of a sample, the electrical conductivity can be found by plotting the
voltages versus the probe position and taking the slope (AV/Ax) as shown in Figure 3-6.
The slope can then be used along with the sample dimensions to find an average
electrical conductivity. This method is more accurate than the standard four-point probe
configuration because many points can be tested along the sample instead of just two.
Then, by knowing the sample dimensions, the resistance (R) of the sample is converted to

electrical conductivity (0') of the sample using the following equations.

 

I l
Ax
a = —-1—- length (S/cm) (3.28)
R area

35

Micrometers ,

10 probes

Sample
holder

 

Figure 3-4: Room Temperature Scanning Probe

 

 

Figure 3-5: Room Temperature Scanning Probe diagram

36

l

(-J

_l

(A,

a

( I
1.

r-)

r n

_ h .

(T) I
l

h)
()

1. l.
——

Voltage (V)
4 (h
“3 r 1

A
0
II. I

(71
in

L)
(I

I T:

610

Figure l
ShOlA'
indicate.j
plotted to

 

 

J.

 

 

 

 

 

 

 

 

 

.4
3510-4 . r r - 35104 I ' '
310 - l 310 . .
-4 - -4
2.5104 - - a 2.510 - .1
A -4
§ 210.4 - - .1 3’ 210 _ .
g 1.510 - "’ - 5’ '4
> 110 - - > -4
'5 - 110 I- -I
5100 - - -‘ -5
0105 - «I- ~ 510 " "
_510- l J L l I I
-50 0 50 100 150 200 -5 0 5 10 15
Data Point Index Position (m)

Figure 3-6: (Left) Each probe typically measures 20 data points. Here is an example
showing 9 probes each taking 20 measurements. (Distance between probes is not
indicated on this graph). (Right) Each probe takes the average measured voltage and is
plotted versus position. This slope is then used in the calculation of the average electrical
conductivity between the measured distances.

3.5.2 4-Sample System

This well established low temperature system (80-400K) at Michigan State
University, called the 4-Sample System, is automated to measure properties of
thermoelectric materials on four samples at one time in a high vacuum environment
(~5x10’5 Torr). The system is capable to measure the thermopower, electrical
conductivity, and thermal conductivity. The thermocouple used in this system is a Type-
T (copper-constantan) differential thermocouple for measuring the temperature gradient.
Separate wire leads are connected to the sample using indium or silver paste very close to
the same location as where the temperature gradient is being measured. Figure 3-7 shows
a diagram of a sample mounted in the 4-Sample system. The method and sample

configuration are a variation of the pulse technique. The sample stage is temperature

37

contrt llct

lower he

samp? a:
{BONE m -

discue .

(D
(2..

 

 

 

controlled using heaters connected to the stage. Liquid nitrogen (LN2) is then used to

lower the temperature of the stage.

 

 

 

Figure 3-7: Typical mounting of the thermoelectric sample in the 4—Sample System

This system proves to be extremely useful to measure the thermal conductivity of a
sample at low to room temperatures. A sample can start in the 4-Sample system and then
move on to the High Temp System for higher temperature measurements, which will be

discussed next.

3.5.3 High Temperature System (HTS)

The High Temperature System (HTS) [21] measures thermopower and electrical
conductivity from room temperature to 700K in a high vacuum environment (~5x10'5
Torr). This computer-controlled system was designed to measure the thermoelectric
power through a slope measurement technique, also called the pulse technique. Electrical
conductivity is measured in the standard four-probe configuration. This system was used
extensively to measure bulk thermoelectric samples. The HT System uses single ended

thermocouples, which are used in the thermopower and the electrical conductivity

38

 

IllCilSlIl'L‘T

3-8 uhii

 

i]:

at
erase t

measurements. An example of a sample mounted in the HT System can be seen in Figure

3-8 while Figure 3-9 shows the entire cryostat of the HT system.

 

Figure 3-8: Typical sample mounted in HTS

 

Figure 3-9: HTS Cryostat

The HT system uses heaters on the stage where the sample is mounted to adjust the

average temperature of the sample. The heaters are PID (Proportional Band, Integral,

39

)1

CL.

I."

 

Derivative) controlled so that the system stays at a maintained temperature while
measurements are being taken. The overall system is a good model for the development

of new measurement systems.

3.5.4 Device Testing System (DTS)

Systems that are used to measure thermoelectric properties of bulk samples
typically lack the capability of fully characterizing a thermoelectric device of various
sizes and types (single layer or stacked modules). The Device Testing System (DTS)
provides these capabilities [22]. This system measures device thermopower, resistance,
efficiency, and power out for varying load and gradient conditions. The DTS was
designed to place a large temperature gradient across a module by keeping the cold side
at room temperature and the hot side varying up to 900K. The DTS uses a method
adapted by Min and Rowe [23,24] to determine the figure of merit for non-short circuit
conditions including Joule effects due to Peltier current by testing under varied load
conditions. The calculation for Z T is shown below where AT open is the temperature
gradient across the module without any load. ATM is then the temperature gradient with
a load. T h and T c are the hot side and cold side temperatures respectively. R1404“).3 and

Rm are the resistances of the module and the load applied to the module respectively.

ATopen __1

AT
ZTave =+ Load (3.29)

2
[ RModule I 2 ' Th ]_[ RModuIe ] [Th " Tc J
RModuIe + RLoad Th + Tc RModule + RLoad Th + Tc

 

 

 

40

This system is also provides a large space to perform other experiments at room
temperature under high vacuum such as Z T measurements using an AC electrical
technique discussed in later sections describing impedance spectroscopy measurements
on thermoelectric materials. Figure 3-10 shows a picture of the DTS system and all of

the main components.

 

Figure 3-10: Picture of DTS

3.6 Properties of TE materials at MSU

Much of the thermoelectric material being manufactured and tested at Michigan
State University behaves very similar to each other. This is due to the fact that the

samples are degenerately doped semiconductors. The typical behavior can be seen by

41

examini
ofthe L

11
increase
reach a]
Houete

“roll-me

L~\S I m

 

 

 

examining the temperature dependant electrical conductivity and thermopower behavior
of the LAST (Pb-Sb-Ag-Te) and LASTT (Pb-Sb-Ag-Te-Sn) materials.

The thermopower of the LAST materials are negative, which indicates n—type, and
increases in magnitude with increasing temperature (Figure 3-11). Some samples will
reach a peak in thermopower and then begin to decrease in magnitude similarly to BlzTe3.
However, for high temperature applications, the thermopower doesn’t typically reach a
“roll—over” point until very high temperatures (>700K). The electrical conductivity of the

LAST materials decreases with increasing temperature (Figure 3-12).

 

O .IIII'IIIU'IIII'IIII'IIUI'I‘II'IIII'III

n-type LAST Samples

 

Thermopower (uV/K)
11)
O
O

-350

llllllllllllllllllllllllllllllllllllll-

 

 

lIII'lIII'IIII'IIIII'IIIIIIII'IIIIIIII

IIIIllllllIlllllllllllllllllllllllllLl.

0 100 200 300 400 500 600 700 800
Temperature (K)

 

Figure 3-11: Plot of thermopower versus temperature for n-type LAST materials

42

 

4
1-410 IIIII'IIII'IIII'IIII'IIIIIIIII'IIIIIIIII

1.2 104 n-type LAST Sample

         

110

8000

6000

4000

2000

Electrical Conductivity (S/cm)

IlllllllllllllllllllllllLLl

 

 

III III III III III III II
I I I I I I

 

0.
0 100 200 300 400 500 600 700 800
Temperature (K)

Figure 3-12: Plot of electrical conductivity versus temperature for n-type LAST
materials

The thermopower for the LASTT materials is positive, which indicates p-type, and
typically increases with increasing temperature (Figure 3-13). The thermopower can also
reach a maximum value and “roll-over” but for high temperature TE materials, this peak
in thermopower happens at very high temperatures (>600K). The electrical conductivity

for LASTT samples, like the LAST samples, decrease with increasing temperature

(Figure 3-14).

43

Igu

 

 

 

IIIIIIIIIIIIIIIIIIII’TIIIITI—I'IIIIIIIIII

    

      
   

300 p-type LASTT Samples
0'
:1"
250 5:.- . ' f.
..l. o .
0:... :' 0..
200 .in: /.. . .0": I
.-’ : .... no

Thermopower (uV/K)
3.
O

IIIIIIIII'IIII'IIII'IIIIIIIIIIIII‘

 

 

 

0 :IIIJIIIIIIIIIIIIIIIIIllllllll

0 100 200 300 400 500 600 700 800
Temperature (K)

 

Figure 3-13: Plot of thermopower versus temperature of p-type LASTT materials

 

5000 IIIIIIIIIIIIIIllIII'IIIIIIIIIIIIII'IIII
p-type LASTT Samples

1.

  

N W 43
O O O
O O O
O O O

—l
O
O
O

h'IIIIIIII'IIIIlIIIIlIIII
lllllllllllllllllllllll

Electrical Conductivity (S/cm)

a...
a a o u
IIIIIIIIIIIII'IIII IIIIIIL‘IIIJJ‘I-llllll

 

 

 

0 100 200 300 400 500 600 700 800
Temperature (K)

Figure 3-14: Plot of electrical conductivity versus temperature of p-type LASTT
materials

4J ln

condue
proxid.
measur
temper:

temper:

31mm l

lhne_[n
“as also

tempera

examiner

 

Chapter 4: Drift System

4.1 Introduction

For low temperature measurements on thermoelectric materials, a new system was
developed as part of this dissertation at Michigan State University called the “Drift”
System. This system measures electrical conductivity, thermopower, and thermal
conductivity of TE materials for the temperature range of 100K to 300K. This system
provided Michigan State with a second low temperature measurement system that could
measure four samples at a time. However, unlike the 4-Sample System, which uses PID
temperature control, the Drift System slowly, but continuously, rises (drifts) in
temperature from 100K to 300K while the system collects data. Allowing this system to
drift in temperature provides smooth data at the expense of not being able to take
multiple measurements at a single temperature.

The motivation of this system was to not only create another low temperature
system but to also experiment with new mounting techniques to reduce the mounting
time. Investigations on using a different technique for calculating thermal conductivity
was also examined. Finally, the concept of drifting the sample environment in
temperature (as opposed to controlling only the temperature of the sample stage) was

examined for improved measurements of the thermoelectric samples.

4.2 Drift System Setup and Mounting

The Drift System comprises of a rough vacuum pump and a turbo vacuum pump to

provide a high vacuum environment (1x1 0'5 Torr) for thermal isolation shown in Figure

45

 

toltage (
sample 1
7003 is

temper:

4-1. A current source meter (Keithley Instruments 2400) is used to supply power to the
sample heater for thermopower measurements as well as to supply current to the sample
for electrical conductivity measurements. Four nanovolt meters (Keithley Instruments
2182) are used to measure the voltage across the sample heater, two thermocouples, the
voltage developed across the sample when a temperature gradient is applied, and the TB
sample for measuring electrical conductivity. A switch system (Keithley Instruments
7002) is used to switch the measurement meters between four different samples. A
temperature-monitoring unit (N eocera) uses a calibrated diode to identify the temperature
of the sample stage. There is also the chamber for the samples to be measured. A picture
of the measurement equipment is shown in Figure 4-2. Finally, there is a computer using

LabVIEW software for instrument control and automated data collection.

Drift System
Chamber

LN; Dewer

 

Figure 4-1: Drift System chamber with LN; dewar and vacuum system

46

T.
irsicie.
hCI’E C0:
“1111 PII
helps 10

COEtrolli

 

 

 

 

 

Figure 4-2: Drift System measurement equipment

The measurement chamber is vacuumed sealed with the sample to be measured
inside. The chamber is cooled on the outside using liquid nitrogen (LNz). The advantage
here compared to the 4-sample system which uses an internal heater on the sample stage
with PID control is that this system has a much larger area of uniform temperature. This
helps to make the sample and its surroundings all at the same temperature instead of only
controlling the temperature of the stage. The outside of the chamber is placed in liquid
nitrogen approximately a third of the way up the chamber (Figure 4-1). The liquid
nitrogen is in a dewar and is allowed to slowly evaporate. As the liquid nitrogen
evaporates away, the level up the side of the chamber decreases causing the chamber to
slowly rise in temperature.

Each sample is mounted on its own gold plated stage using single ended
thermocouples (wire diameter = 25.4um) and a resistor as a sample heater for
measurements similar to the HT System. Figure 4-3(lefi) shows an example of a
mounted sample. The idea here was to allow each sample to be pre-mounted to a

portable stage under a microscope without interfering with the mountings of other

47

 

“gum

 

samples. This stage is much smaller than the one used in the 4-Sample system and
allows the experimenter to work in the entire space around the sample. The 4-Sample
system only allows for approximately 90 degrees of space around the sample.

Each stage has its own radiation cap, which is gold plated and screwed down onto
the stage (Figure 4-3(right)). This keeps the samples from radiating heat to each other.
This stage is then mounted to a larger main stage (Figure 4—4). This main stage is gold
plated and also has its own gold plated radiation cap to cover all four samples (Figure
4-5). The main stage is mounted to a stainless steel shaft, which has low thermal
conductivity. Along the shaft are radiation fins to reduce the thermal radiation flow
between the main stage and where the wire connections are made. This long shaft is then

inserted into a stainless steel tube where it is vacuum-sealed with a rubber ‘O’-ring. (See

Figure 4-6)

 

Figure 4-3: (Left) Individual sample stage with a sample mounted. (Right) Main stage
without radiation cap shown a four sample stages with their radiation caps on

48

 

Figure 4-4: (Left) Sample stage on main stage without radiation cap. (Right) Sample
stage on main stage with radiation cap.

 

"’4‘ ‘ ..

Figure 4-5: Main stage with radiation cap on.

49

 

 

 

 

Figure 4—6: Drift System main chamber (Left) and inside shaft with sample stages
(fight)

The wiring diagram for this system is shown in Figure 4-7. This diagram shows
how the four nanovolt meters and the current source are connect to each of the four
samples through the switch box. Voltages V1 and V2 are used to identify the hot and cold
side temperatures, respectively. V3 is the voltage between the copper wires of the
thermocouples for electrical conductivity measurements and to identify the voltage

developed across the sample during thermopower measurements.

50

Sample#l I H i i 1 Sample #4

O D A 1:) 3 ,3 ,'\ A A: h
\f’s «71,»- - ,1 Sample #2 Sample #3 \ i1}--- 7
_. ~42 _; f/ . V /A,: / f
95;“. - - >5”; ,9»- -
—— ‘ r V_jf x V K r I x V 3““ ‘\
'\/-O ‘1; , / \ I/ ,r _\ __,/\’—. .
: «*L °’ 5713' /4/’ 1 :
U ”‘s ~ \ . 9‘ 4 l f
' " v- 7; I L" T "‘~ I
\ \\
CH ;,- t /
A \F. \b. L
/
T U. ’ U; /
\. \\ //
\ ‘3 /
:\* :
\~ \
\
l \ ‘
A O ‘
Temperature
Sensing
Diode

 

Figure 4-7: Wiring diagram for mounting each sample

4.3 Drift System Automation

Once the Drift System is loaded with the desired samples, the chamber is cooled
down to the desired start temperature, and is then to be allowed to slowly rise in
temperature. A computer takes control of the measurement process via a personally
designed LabVIEW program. This program performs many tasks and is very similar to

the HT System software.

51

4.3.1 Tl

Al
togehher
The on ti
reach a s
before if.
gradient
The pmg
lfimpcrat
heater cu

Th.
Tll‘ical r
State “he
me“ 3131:
Calculate
IOUInca
measilrei
be r16Ces.

IE“Denir

4.3.1 Thermal Conductivity Measurements

All sample heaters are connected in series. The sample heaters are pulsed on an off
together to establish an AC steady state temperature function across each of the samples.
The on time of the heater must be long enough such that the sample being tested can
reach a steady state AC function where the temperature gradient reaches steady state
before the sample heater changes to the next state. It is important that the temperature
gradient stabilizes so that an accurate thermal conductivity measurement can be made.
The program keeps track of when the heater is turn on and turned off. By doing so, the
temperature gradient and voltage gradient measurements are separated by the state of the
heater current.

The Drift System employs a new technique for measuring thermal conductivity.
Typical measurements require the samples using the pulse technique to reach a steady
state where the temperature gradient levels off before the sample heater changes to the
next state. From here, the average max change in temperature gradient is used to
calculate the thermal conductivity of the sample. The temperature gradient with respect
to time approximates piece-wise exponential curves. It is possible to speed up the
measurement by identifying the equation for the exponential curves so that it would not
be necessary for the temperature gradient to level off in order to locate the max change in
temperature gradient.

Because the program can easily separate the temperature data for when the heater is
on and when the heater is off, it is possible to separate the piece-wise temperate gradient
data in to a rising exponential fimction (when heater is turned on) and a falling

exponential function (when heater is turned off). The data is then curve fit to an

52

 

exponentia|

313 COHSIZII

.315 t —) x
identifies
constant ‘
tern perm
is projcc
The diff

‘llfisam

AT

exponential firnction such as the one shown here using LabVIEW where A], A 2, and A3

are constants.

F(t) = A1 + A2 ~e(_A3 '0 (4.30)
As I -—> oo , the exponential term goes to zero leaving only the A] term. This term
identifies the temperature that the sample is approaching. The program solves for this
constant for both cases where the sample is either rising in temperature or falling in
temperature. An example of the curve fitting is shown in Figure 4-8 where the curve fit
is projected out further in time where the temperature is stabilized to a constant value.
The difference between these two constant values is the appropriate change in AT across
the sample for a given heater power. Using this method of finding AT provides a more
accurate calculation of the thermal conductivity of the sample. One reason for the
increased accuracy is that instead of just the last few data points being analyzed to
calculate AT, the entire heating/cooling profile is curve fitted. Using the entire curve
makes the calculation less susceptible to glitches in the data. It also helps reduce the

experimental measurement time.

 

 

 

 

 

 

 

 

2 ,_ I I I _ __I _ 2 _ I I I T I _
1.5 '- - 1 _5 r— u-
d
'- ’ I: I— -t
Q 1 l- I; 1
9.
O
0.5 I- I‘ 0.5 r- ‘ d
O P - o — \“~h—~ ——-.——-————q
I l l I l l L l l l
Time Time

Figure 4-8: Plot of AT for sample rising in temperature (Left) and falling in temperature
(Right) with the curve fits projected out further in time.

53

4.3.2 I

measurr
& the 1

sample

(’a

sanipl .
The sys
(current

the VOlL

4.3.2 Thermopower and Electrical Conductivity Measurements

The Drift System uses single-ending thermocouples (type-T) for the thermopower
measurements. The technique for calculating the thermopower of the sample is the same
as the HT System (slope-measurement technique). A resistor is placed on top of the
sample as the sample heater. Two thermocouples are placed along the length of the
sample. A diagram of a sample mounted for the Drift System is shown in Figure 4-9.
The system measures electrical conductivity in the same manner as the HT System
(current flipping technique). The current leads are attached to the ends of the sample and

the voltage probes are the thermocouple wires.

Heater

  

r..— .,

 

 

 

N\/’< T.

Figure 4-9: Diagram of sample mounted for Drift System

4.3.3 Program Description

As the system is slowly increasing in temperature, data is being continuously
collected on each sample. However, each sample is measured at a slightly different
temperature. The system will first select a sample to be measured, start pulsing the
heater, and then begins collecting data for thermopower calculations. The heater is then
turned off (on all samples). After a delay, electrical conductivity of the sample is made.

The temperature chosen for these two data points is that average temperature between the

54

start and
system rt
the poet
establish
automat

the desii

4.4 Ve

In this
autom;

boil 3

start and end of the thermopower/electrical conductivity measurement. From here, the
system moves on to the next sample and repeats the process. The program also monitors
the power into the heater for each sample and keeps track of what current is needed to
establish a 1°C across the sample for the thermopower measurements. Adjustments are
automatically made to the heater power to keep the temperature gradient within 20% of

the desired AT.

4.4 Verification of the System

The temperature versus time of a typical Drift System run is shown in Figure 4-10.
In this run, the minimum temperature was about 160K. At this temperature, the
automated data collection program was initiated while the liquid nitrogen was allowed to
boil away.

300

 

280- -t

240 ,

220

Temperature (K)

200

180

 

 

 

l l l
010 20 30 40 50607080
Data Point # (30min increments)

160

Figure 4-10: Plot of temperature versus time for the Drift System. Automated data
collection is started when the temperature reaches a minimum value.

This system used stainless steel as a reference material to test electrical

conductivity, thermal conductivity, and thermopower. The most important test for this

55

5) stem is I
gradient a.
the serum:
shows the
electrical c
plotted 3g.
experiment

stainless st

Electric-I Conductlvny (S/cm)

 

system is the verification of the thermal conductivity measurements. The temperature

gradient across the sample at 163K versus time is shown in Figure 4-11. This plot shows

the separation in the data for when the sample is heating up or cooling down. It also

shows the temperature gradient to be about 1K. Figure 4-12 shows both plots for

electrical conductivity and thermal conductivity versus temperature for the stainless steel

plotted against reference data. There is good agreement between reference data and

experimental data shown. This system was also able to obtain the thermopower of the

stainless steel and is shown in Figure 4-13.

Electrical Conductivity (Slcm)

 

 

 

Stainless Steel
1'2 l I I I
1 . .
Heating
0.8 -
g o
v 0.6% -I
i- 1)
<1 ..
0.4 u it .
1-‘1 .
Coolin
0.2 - 1% g -
o r r 1 WW

 

Time

Figure 4—1 1: Plot of AT versus time for heating and cooling of the sample.

 

IIthIH‘III 'UIYUUUIIIfjli'Ur‘

Reference 5
- - O- - Experimental 5

I"

C). (:-

“o

O

 

  

 

I'V'UI'U'VI'I

llllllllllll

O

I'I'U'l'.‘

4‘ ‘
x.‘

 

 

"I'II'
C.
llllllllllll

I
p
I
p
p
b
p
1-
I
n
-
I
n
I
I
I-
i-
in
I
I
-
I
1-
n
I-
-
p
I
I
p

a

 

O
S

200 300
Temperature (K)

400 500 600

Thermal Conductivity (WImK)

18

16

14

12

10

 

 

 

 

 

 

C
. .3? 0 Reference 1
.' o - - O- - Experimental 1
.l-lllllllJJlqulllllllllllll.
0 100 200 300 400 500 600

Temperature (K)

Figure 4-12: Thermal conductivity verification against stainless steel reference sample.
(Left) Plot of electrical conductivity versus temperature. (Right) Plot of thermal
conductivity versus temperature.

56

.4.
(II
F-

 

 

 

 

‘05 I I r
2
>
3 -1 r -
I. .0
d)
3
o
a.
o
E -15 -
G
.c
I'-
_2 r 1 l
100 150 200 250 300
Temperature (K)

Figure 4-13: Plot of thermopower of stainless steel versus temperature.

4.5 Limitations of the System

The Drift System performed well and was used to test many samples. However,
the mounting process for the samples proved to be much more difficult than anticipated.
In addition to the long sample mounting times, the system also did not reach low enough
temperatures. The goal was for the system to reach liquid nitrogen temperatures (~80K).
Attempts were made to increase the thermal conductance between the main sample stage
and the outside walls of the chamber that where submerged in the liquid nitrogen. Figure
4-14 shows the addition of aluminum foil to the main stage so that a thermal contact
could be made to the walls of the chamber. The addition of the aluminum did bring the
minimum temperature down to less than 130K shown in Figure 4-15 but did not reach the

goal of less than 100K.

57

fl

Flguri

 

Figure 4-14: Adding aluminum foil to make thermal contact to walls of chamber

Temperature (K)

 

 

20 40 6
Time (Hours)

Figure 4-15: Plot of temperature versus time of the Drift System after adding aluminum
to the main sample stage.

4.6 Conclusion

The Drift System was assembled and built for low temperature measurements of
TE materials. A personally designed LabVIEW program was created for automated data
collection. The ‘drift’ technique for TE measurements proved to be a viable method to
use and obtain smooth data. The technique was then applied to a new high temperature
system, which is discussed in the next section. A LabVIEW program was created to
curve fit the temperature profiles along the sample during thermopower measurements
for an improved thermal conductivity measurement. Further investigation is required for

lowering the minimum run temperature to at least 100K or below.

58

51 l

rnodu

70011

measr 3

extra;
lhene

Cfil '

theljl
condo
taupe
Plflic
hon‘u

Eiffel

(llamas

r0

he

it

 

Chapter 5: Ultra High Temperature Measurement System

5.1 Introduction

The thermoelectrics project is intended for high temperature thermoelectric
modules, which may go as high as 900K. The current HT system at MSU can reach
700K and then data is extrapolated up to higher temperatures. A system was needed to
measure thermoelectric materials at these higher temperatures to eliminate the need for
extrapolation of data, which can provide a false sense of the thermoelectric properties.
There is existing research on many systems [25-30]. Presented here is a system that can
measure thermoelectric materials from room temperature to 1200°C. This system, called
the Ultra High Temp System (UHT System), is used to find thermopower and electrical
conductivity on materials never before tested and up to and beyond the necessary
temperatures of 300K to 850K. It also employs the ‘drift’ technique discussed in the
previous section. This section describes the components of the system. A description of
how the measurements are performed along with verification of the system against a

reference sample is provided.

5.2 UHT System

The UHT System is comprised of a large furnace to control the average sample
temperature, a sample stage, measurement devices, and a computer for system control
and data acquisition. The sample holder with all electrical connections makes use of a
commercially available ProbStat by NorECs. The UHT System uses a minimal amount

of measurement equipment for the thermopower and electrical conductivity

59

11163511

descril

mount:

(II
L.»
L...
*

to creat
ohwm
S} stems
\dws

hwnfi
IRE“
rate of 1‘-
electrica
SlOVl'l} d
from the

head

measurements. Experiments are also performed under high vacuum. This section will
describe each of the components to the system along with how a sample is typically

mounted.

5.2.1 Furnace

The UHT System uses a large split tube furnace from ThermCraft (see Figure 5-1)
to create a large, uniformly distributed volume of heat around the sample. This technique
of surrounding the entire sample holder with a uniform heat is unique to this lab. Current
systems heat the sample stage while the surroundings are close to room temperature
values. This furnace is rated from room temperature to 1200°C. The power for this
heater is 208 VAC single phase (2 legs of a 3-phase network). The maximum current it
uses is 19.8 amps. The size of the furnace gives it a large heat capacity and will cool at a
rate of less than 2°C/minute. This slow cooling rate allows for thermopower and
electrical conductivity measurements to be taken while the overall sample temperature
slowly drifts down to a room temperature value naturally. This technique is different
from the High Temp System, which uses a small heater inside a vacuum chamber that is

set to a desired temperature and controlled using a PID controller.

60

0f the
Platir
C0015
temp.
increg
The c.
Tillie.
Vdue

Stile:

Panict

 

Figure 5-1: ThermCraft split tube furnace

A ThermCraft temperature controller, using PID connol, regulates the temperature
of the fumace (See Figure 5-2). Two S-Type thermocouples (Platinum -
Platinum/Rhodium) are placed into the center of the furnace to monitor temperature. The
controller uses on/off switching (pulse train modulation) to maintain the furnace
temperature. This temperature controller allows the user to adjust the rate of temperature
increase and decrease along with many other important features such as the PID settings.
The controller is not computer controlled making the system only semi-automated.
Typical measurements are performed by increasing the temperature to a desired max
value and then turning off the furnace to cool naturally. This is similar to the Drift
System however, unlike the drift system, the temperature can be maintained at a

particular level for multiple measurements.

61

l$¢€ Fight
pen leabi.
P101 ides .
€190 rical

tern} (Tall.
all)“ E “iii
high temp

aUTIC Sphi’,’

 

 

HIS“ I’UWIH

 

 

Figure 5—2: ThermCraft temperature controller

5.2.2 ProboStat

The UHT System uses an apparatus called a ProboStat purchased from NorECs
(see Figure 5-3). A ProboStat is a measurement cell for electrical properties and
permeability studies at high temperatures and in controlled atmospheres. The ProboStat
provides a long testing stage so that the sample can be inside the furnace while the
electrical connections to the testing equipment remain outside the furnace at a safe
temperature. The ProboStat uses S-type thermocouples (Platinum & Rhodium/Platinum)
along with platinum measurements wires. Platinum is used because it remains stable to
high temperatures without melting and without oxidizing in inert or non—inert

atmospheres.

62

 

Figure 5-3: NorECs ProboStat

The ProboStat was design to handle long-term temperatures less than 1200°C and is
used to measure a single sample. The base of the ProboStat is shown in Figure 5—4
which contains four Swagelok quick connects to 1/ 8” tubing. Two of the quick connects
are for inlet of gasses and two are for exhaust (or vacuum). There are three thermocouple
connections (only two are used for this measurement system) and six BNC electrode
connections (4 connections are used) are available with the option of being switched
either to isolated or ground). The housing of the base is made of nickel-plated brass.
The base unit can handle up to 120°C, however, the BNC cables are rated for only 70°C.
There is an option to either water or air-cool the top of the base unit, however, it has not
been necessary for this measurement system. The top of the base typically has a

temperature that does not go above 310K.

63

 

A (
Connectit
Connecti
them (0
Plain un
Cell insi
Platinm
5311301 i
milsur

Sample

Cooling

(water/air)
Thermocouple
connections
BNC
connections
Gas line
connections

 

Figure 5-4: Base of Probostat

A diagram of the base of the ProboStat is shown in Figure 5-5 to identify electrical
connections. The base unit comes with pre—marked labels next to the electrical
connections such as HC, HV, LV, and LC. We can ignore what the letters mean but use
them to identify the locations of the electrical connections. For example, a PT-103
platinum resistor (used as a temperature sensor) is placed at the base of the measurement
cell inside where the thermocouple connections switch between Platinum (or
Platinum/Rhodium) wires and copper wires. The current supplied to this temperature
sensor is supplied through the HC connection. The voltage measured across the sensor is
measured through the HV connection. LV is used to supply electrical current through the
sample and LC is used to supply electrical current to the sample heater (which will be
explained in later sections). The thermocouple attached to the “cold” side of the sample
is connected to the top thermocouple connections, while the “hot” side thermocouple is
attached to the lower thermocouple connection (shown in the diagram). The switches
that are shown in the diagram determine if the BNC cables are grounded to the base or

isolated. This system uses the isolated case.

_......_._. . ___.;.x

TC Cold" , "

 

 

TC Hot‘éjj , ,
Biank‘sf
\\
///
Probostat
HC PT-103 1011A current
HV PT—103 Measure Voltage
LV Sample Heater Current

LC Sample Current

Switches Keep flipped up
(isolated shields of BNCs)

 

 

 

Figure 5—5: Diagram for the base of the Probostat unit

5.2.3 Measurement Equipment

Electrical resistance and thermopower measurements involve measuring voltages in
the nanovolt range. This requires measurement equipment than can perform in this
range. Figure 5-6 shows the five pieces of equipment used for all of the measurements.
#1 is Keithley Instruments 2400 current source, which will provide current to the sample
and also current to the sample heater. #2, #3, and #4 are Keithley Instruments 2182
nanovolt meters. #2 measures the voltage across the temperature sensor as well as the

voltage across the sample. #3 and #4 measures the voltage of the hot side and cold side

65

them

CUITC

(In
.5.)

the

Pic

thermocouples respectively. #5 is a Lakeshore 1011A current source used to supply

current to the temperature sensor.

005.7? . ”

r-:-v05.uuul :- ~51.

-.a000:ooo . . g:

_ 0 _....1., .4

 

Figure 5-6: Measurement equipment

5.2.4 Vacuum Pump

The UHT System takes measurements under high vacuum. A Varian Task V70LP
(Rough and Turbo Pump Package) vacuum pump is used to pump down the ProboStat to
approximately 2X10‘5 Torr. However, the vacuum pressure can only be measured
between the pump and the ProboStat (not on the inside of the ProboStat). There is only a
1/8 inch copper tubing for the vacuum line into the ProboStat. Therefore, it is possible
that the vacuum pressure inside the ProboStat is higher than the measured values. A

picture of the vacuum pump is shown in Figure 5-7.

66

D.
electrical
CORDCCIL‘.
ProhoSta

COHDCCIIL

 

Found 10

V1

 

Figure 5-7: Varian vacuum pump

During the initial system tests, the vacuum pump was identified as a source of
electrical noise in the measurements of thermopower shown in Figure 5-8. The pump is
connected to the ProboStat via a metal hose. To electrically isolate the pump for the
ProboStat, a non-conductive clamp and ‘O’-ring was used to make the vacuum
connection. This considerably helped to reduce the noise, which was likely caused by a

ground loop situation.

1.3-.-
*L
#k 4,2“:
ALA h L 4

-wfi—fir~r 1 v

Volts (11V) r

444

{'0’

Time

Figure 5-8: Electrical noise in measurements due to vacuum pump connection

67

thiclnev
10 mount
10p ex en
|

B.-
|
appropn.
l
acetone 1.
|

an) resic'

For

[emitter -
”16am.

1

“map

int
\

 

5.2.5 Sample Mounting

The UHT System is designed to measure bulk TE samples where the width and
thickness is 3mm or larger and the height is 5mm or larger. Smaller samples are difficult
to mount with all the necessary wires and because the sample must support a heater on
top even in the presence of small vibrations (mostly due to the vacuum pump vibration).

Before a sample is mounted, it must first be prepared. Each sample is first cut to an
appropriate size using a diamond wheel saw. After the sample is cut, it is cleaned with
acetone to remove any dirt and mounting wax followed by a bath in methanol to remove
any residue from the acetone. The sample is then lightly polished with fine grit
sandpaper. This step can help remove and oxides that may have formed on the surface of
the sample. Once the sample is ready to be measured, the ends of the sample where the
current leads are attached are nickel-plated using electro-plating processes. This thin
nickel layer will help distribute the contact area to insure a uniform electric field
throughout the sample and it also acts as a diffusion barrier to help prevent the silver
paste that is applied later from diffusing into the sample. Dimensions of the sample are
then measured and the sample is ready to be mounted into the system.

For measuring thermopower and electrical conductivity, a heater is placed on top of
the sample, two thermocouples are placed along the length of the sample to measure the
temperature gradient, and current leads are placed on top and bottom of the sample for
measuring electrical conductivity. A diagram of the setup is shown in Figure 5-9 along

with a picture of a sample already mounted. '

68

11163.5

 

Tcmot)... -- l 321/)
TC(Cold)+Og 3 : 1* ”g: 2

 

Figure 5-9: Mounting a sample for measurement (TC = thermocouple)

The sample heater is a small platinum resistor typically used for temperature
measurements. The thermocouples are Type-S (Platinum - Platinum/Rhodium), 0.003
inch or 0.002 inch in diameter. This thermocouple is a good candidate for this
temperature range because it can handle the higher temperatures without oxidizing. The
current leads to the sample (1+ and I-) are platinum wires 0.003 inch in diameter. The

sample sits on an alumina stage. Colloidal silver pastes is used for all connections.

5.3 Electrical Conductivity Measurement

To measure electrical conductivity of a sample, a small current (typically +/-
lOmA) is put through the sample via the current leads and the platinum wires of the two
thermocouples measure the voltage across the sample creating a four point measurement.
The current is a square wave fimction, 50% duty cycle, at approximately 33Hz. The

switching of the current has two purposes. The first purpose is to keep the sample from

69

establisl
voltage

offsets 0
accompl
measure
by two.

used F r

then con

Fir.

 

Sfit“D at.

mph “
temp.

establishing a temperature gradient, which would cause an error due to the Seebeck
voltage developing across the sample. The second purpose is to cancel out any voltage
offsets on the measurement wires due to temperature gradients or diode effects. This is
accomplished by taking a voltage measurement for a positive current, taking a voltage
measurement for a negative current, subtracting the two measurements, and then dividing
by two. This process is typically done ten times and the average of those values is then

used. From there, by knowing the sample dimensions, the resistance (R) of the sample is

then converted to electrical conductivity (0') using the equation shown below.

0' = 1. length (S/cm) (5.31)
R area

 

5.4 Measuring Thermopower Using a Pulsing Technique

i -—~~+-— _ , IREF .
V1 1 '14::g,“ N». C” l— ‘Pthh Pt Res'sm": _V HEATER
__ _.__ , ‘f\..__C.u J.
V . —.—— — 8,,4- I .
3 2: * . ,_ Cu
.___._ ___.-. M/
_-_ ___ -- _ /'\ Cu
“___ ___- + ‘73‘ 'T' 1*
VZlit lEq‘ ’3; -_ T

 

 

 

Figure 5-10: Measurement setup

Figure 5-10 shows a diagram of the electrical connections in the measurement
setup where V1, V2, and V3 are measured by Keithley nanovolt meters, Cu stands for
copper wires, Pt for platinum, Pt/Rh for platinum/rhodium, and Tm: stands for reference

temperature which is found using a platinum resistor as a temperature sensor. To

70

measurc

ofi'. con:

a stable I

is apprw

tempera:
\‘Ollfigc v,
55518”) .1
[hf calm.
the them

between

 

 

measure the themopower of a sample, the heater on top of the sample is pulsed on and
ofl“, continuously causing the temperature across the sample to increase and decrease.
After some period of time, the difference in temperature across the sample will maintain
a stable periodic function with a constant offset (no drifi). The difference in temperature
is approximately 10K. It is this difference in temperature and voltage that is used in the
calculations of thermopower. The advantage of this technique is to be able to use many
data points for the calculation of thermopower. This technique eliminates any unknown
temperature gradients along the measuring wires. This also eliminates any D.C. offsets in
voltage on the measuring wires. This technique is currently used in the High Temp
System and is a modified version of the Maldonado technique [19]. The following shows
the calculations for V1 and V2 and how the difference between those two voltages equals
the thermopower of the thermocouples used multiplied by the temperature gradient

between the two thermocouples.

TH TR TH
V1= lSmmnm an<T>dT= HSPth(T)—SP1(T)ldT
T T T
R ” R (5.32)
T C TR TC
V2 = ISpm<T>dT+ lSpt<T)dT= flSPtRh(T)‘SPt(T)]dT
TR TC TR
TH TC
V1—V2 = flSPtRh(T)“SPt(T)]dT— [lemme—Spunk?”
TR TR
TH TR T C TR
= [STC(T)dT— [STC(T)dT— [STC(T)dT+ [STC(T)dT (5.33)
o o o o
T H
= [STC(T)dT
T C

71

Atthe s
l'scanh

VOllage ‘

 

 

 

TH TH
lSrc(T>dT erc<TA VGH‘I =STC(TA VG)'(TH -TC) (5.34)
TC TC

T1 + T2
2
2’ SSample (TH ) “ SSample (TC ) & S Pt (TH ) 3 S Pt (TC )

TH -TC << TAVG E

S Sample (T) and S pt (TH) are a constant.

V1 - V2 = STC (TH - TC) = STC (TA VG) - AT (5.35)

 

V1 - V2 =STC(TA VG)-AT (5.36)

 

 

 

At the same time the temperature gradient is being measured using V1 and V2, the voltage
V3 can be used to find the electrical voltage across the sample due to the thermoelectric

voltage developed by the sample. This derivation is shown below.

TH TC TR
V3 = IS“ (T)dT+ I SSample (T)dT-t I51); (T)dT
TR TH TC
T” TR TH TR TC
= I S p, (T)dT — j S p, (T)dT — jsSample (T)dT + [31), (T)dT _ jspt (T)dT
TH TH
= " ISSample (T)dT + I S Pt (T )6”
T C TC

(5.37)

WhenTH ‘TC << TAVG ETl—ZT—z—D STC(TH)zSTc(TC) Sfc(TH)isaconstant.

72

Ta

To

“l1:

COfist

Taking the sample thermopower, and platinum thermopower to be constant over the

small temperature gradient (T H -TC) gives

V3 = [Sm (TA VG) ‘SSample (TA VG )J-(TH — TC) (5.38)

 

V3 = [SPt (TA VG) - SSampIe (TA VG )J- AT (539)

 

 

 

To find the thermopower of the sample, AT from equation 5.36 (VI-V2) can be put into the

equation for V3 as shown below.
V3 = [SP1 (T A VG) - SSamp1e(TA VG )l' AT

V
SSampIe (TA VG ) = S Pt (TA VG) ‘ ZT—

 

 

 

 

 

V3
:5 T — 5.40
Pt( AVG) [ V1_V2 J ( )
STC(TAVG)
=SPt(TAVG)- 3 -STC(TAVG)
V1-V2
SSampIe (T A VG) = SP1 (TA Var-[V1 _3V2 )‘STC (T A VG) (5-41)

 

 

 

The Seebeck coefficient of platinum is known from reference data and the Seebeck
coefficient of an S-type thermocouple is provided by NIST. To find the thermopower of
the sample, one simply needs to find V3 / (Vl-Vz). Even though V3 is some exponential
function of time and V1-V2 is also some exponential function of time (non-linear), the

relationship between V3 and Vl-Vz is linear. This can be explained with the following:

T1+

 

When T H — T C << T A VG a T2 :> S Sample (T) is a constant. Therefore, the 2A??- is

constant.

73

 

will bc
best fit

(typt'ca

5.5 Prt

lab-VIE
COUU’Ollc

material

 

 

V3 is linearly related to Vl-V2, and when one is plotted versus the other, the result
will be linear line. By taking a best fit to this linear fimction and finding the slope of the
best fit, the relationship between V3 and (V 1-V2) is found using many data points

(typically 200-300 data points). An example of this will be shown in Figure 5-13.

5.5 Program Overview

The system is interfaced to a PC and the data collection is fully automated using
LabVIEW software. With the average temperature of the sample being independently
controlled, the LabVIEW program performs the following procedures to collect the TB

material properties of interest.

Pulse the sample heater for 3 minutes (approximately 2 pulse periods)
0 Get temperature of the base of the thermocouples using Pt Resistor

0 Convert measured resistance (R p, = V / I ) to temperature

using the following formula:

Temp(1ep,) = 30.098 + 2.3026 . R p, + 0.0012209 - R p,2

0 Get temperature of sample
0 Use base temperature and voltage of TCHOT to find temperature
of the sample
0 Start collecting voltages V1, V2, and- V3 for 2.2 pulse periods

0 Store data

74

 

The fror
below,

 

 

 

0 Main file contains all calculated values from measurements
(temperature, thermopower, electrical conductivity, power
factor, temperature gradient, etc.)

0 Separate files store the V1, V2, and V3 voltage arrays for each
measurement taken (This can be used for post processing later
if need be)

0 Stop pulsing heater, measure electrical conductivity of sample
(flipping current method) and store results into main file

0 Repeat this process after an arbitrarily set delay

The front panel view of the LabVIEW program for the UHT System is shown

below.

75

 

 

(Eii‘i‘é’fi‘ifimfwifiu
flat-a anew tools 20.... Wow deb

 

 

mfuomew ti
WEE-0000M) lE

 

 

 

 

 

Figure 5-11: Front panel view of the LabVIEW program for the UHT System

5.6 The Built System

The full system (except for the computer) is shown in Figure 5-12. An example is
provided of a typical measurement of the UHT system in Figure 5-13. Notice that even
though the voltages from the thermocouples are not at a steady oscillating function but
rather decreasing in time, the difference between V1 and V2 does remain a steady
oscillating function along with V3. This is again because the thermopower of the sample
is constant during the period of time the measurement took place and while the sample is

slowly drifting down in temperature. Also notice that when plotting V3 versus Vl-V2, the

76

 

results
minimi
chccltir
oxer tht
thermot

sample

 

 

results are linear, such a best-fit relationship between V3 and Vl-V2 can be used to help
minimize the influence of noise in the signals. Such a plot is also an excellent method for
checking that both the sample thermopower and thermocouples are relatively constant
over the temperature gradient used. If the temperature dependence of the sample
thermopower varies rapidly and nonlinearly, and a large temperatre gradient across the

sample is used, then the plot of V3 versus (VI-V2) would not be linear.

 

Figure 5-12: UHT System

77

5'7 Ver

Sample.

Support

arcing

 

V1 & V2 (VOltS)

 

.................

_ _A_._._A_—._4‘

_. a - . A a . n.‘..- t

V1- V2 (VOIIS)

V1- V2 (VOltS)

Figure 5-13: Typical data collected for UHT System

5.7 Verification of the UHT System

To test the system up to high temperatures, a platinum wire was used as a reference

sample. The wire gauge was 10 mil and was shaped in a way to stand by itself and

support a heater as shown in Figure 5-14. The electrical conductivity and thermopower

are in good agreement with reference data and are shown in Figure 5-15 and Figure 5-16.

78

 

 

2:85 950 .25

 

Elect. Cond. (S/em)

W...

Figure 5-14: Platinum wire reference

 

 

 

 

 

 

 

 

PlafinunMreReferenee Run
8-7-04
UHTSystem
1105 L T T T T : T T T T I T T T T I T T l T T T T T T T 7 T T fT l T I f1 T T T—T q
o
i S 0 Pt Wire Elect Cond. (Run #1) j
910‘ a . PtVVIre Elect. Cond. (Run #2) _
C 0 Reference from CRC Chem 8. Phys :
L .
810‘ L g
r- -1
710‘ l S
610‘ l -
510‘ f l
410‘ L ‘ '. Lest/:4. _]
. ~ . 204 i
310‘ — ‘ . 9 ., j
" t
t- -l
2104 h i l r r l 1 L441 r r .- l l r t #1 l l J r .L l r T l l J t r t 3 l r l l r
200 300 400 500 600 700 800 900 1000
FumaoeTemp(K)

Figure 5-15: Platinum wire electrical conductivity measurements

79

TEP ttV/K

lr.
comp“

Figttt‘e 5

 

 

Platinu'n Wire Reference Run

 

 

 

 

 

 

 

 

 

8-7-04
ll-ITSystem

'4 L 1 r t r fT r r r l . r t T T Y 1 r T l T 1 a r
i O PtVVweTEP (Run #1) j
«6 _ a PtWtreTEP(Run#2) ~
0 Reference Meas. Sci. Technol. 12 j

(2000254472 (Roberts)
.8 _ _.
'10 ’- A'ba.‘ _,
é b ‘Q‘M j..\ -
:1 thf}\ _.
h a -
t- -12 — 0 ~ . r
t— ‘ " L

-14 - 4.- ‘_ -
t “. l -
-16 ~ -
. g.

_18 r 1 1 1 l r 1 1 l l . r 1 1 l J 1 1 1 l 1 1 1 1 l r 1 r 1 l r 1 1 1 l 1 1 1 1

200 3CD 400 500 600 700 8(1) 900 1000
Furnam Term (K)

Figure 5-16: Platinum wire thermopower measurements

In addition to testing platinum wire as a reference sample, comparisons where
made between data collected by the UHT System and HT System. A LAST sample, with
composition Ago,76PblngTe2o, was tested and the results are shown in Figure 5-17 and

Figure 5-18. These results show an excellent agreement between the two systems.

80

 

Figun

“gun.

 

 

 

 

     

 

 

 

 

 

KF2228R3A1 (Agoonwastezo)
Ultra High Temp System
-100 . I I I I I I I I I l r I f I l I I I I l I I I I I I I I I .
-120 :; o UHT System (8/19/2004) .‘
I —0— HT System (8/4/2002) 2
g -140 _— -‘
> I I
3: -160 T. .1
b I 1'
O l' ..
g -180 L' 1
e : =
’200 '- c-
E : :
g . .
l- '220 T ‘ 1
I V p 2
.240 .. cf 73C; "
, he; ,
_260 h I I I I l I I I LI I I I I I I I I I I I I I I l I I I I ‘
300 400 500 600 700 800 900

Temperature (K)

Figure 5-17: Plot of thermopower versus temperature of a LAST sample showing good
agreement between the UHT and HT System

1600

1400

1200

1000

800

600

Electrical Conductivity (Slcm)

400

200

 

 

 
   
 

 

 

 

 

KF2228R3A1 (AgoJSPbmeTezo)

Ultra High Temp System

. I I I I l I I I I l I I I I I r I I I I I I I I I Ifi I I ‘
:_ o UHT System (8/1 912004) _
: —0— HT System (814/2002) :
s x a
.' 1
:. s .‘
I l l I I Fe 5&1) i.

300 400 500 600 700 800 900

Temperature (K)

Figure 5-18: Plot of electrical conductivity of a LAST sample showing good agreement

between the UHT and HT System

81

Many samples where tested using the UHT System and data on a new sample that
uses potassium in the TB material is shown in Figure 5-19 to provide another example of

the high quality data that is obtained from this system.

    

 

 

 

1000 I I I I I I I I I I I I l I I I I
1

A FPNK-OOZ (K0.86Pb215bT923) q -150
E 900 3
2 It
(I)
.. 800 J -180 3
=3 1 a
"3 700 .1 -200 3
a me. ——> . g
5 600 ;. . 2
2 ”’02- - 420 e
a "0,. <
o 500 -,
é 1 3
2 400 ‘0 1 -240
m e

'0 -1

‘e
300 1 l 1 1 l n I a n f.£j 1 ‘ _
400 450 500 550

Temperature (K)

Figure 5-19: Plot of a thermopower and electrical conductivity of a new TE material
using potassium using UHT System

5.8 Further Developments and Future Improvements

Upon further developments of the UHT System, with the help of lock-in amplifiers,
it was discovered that a significant amount of electrical noise was coming from the
furnace, which was due to the 60Hz oscillation in the power lines. When the sample was
maintained at a specific temperature, the fumace would be pulsing on and off and
ultimately caused an error in the electrical measurements. A high temperature shield
made of stainless steel foil was put around the ProboStat and electrically grounded.

Figure 5-20 shows the shield in place, which is over the quartz tube of the ProboStat.

82

 

ClCCU‘lc

 

 

Stainless
Steel Foil
Tube

 

Figure 5-20: Stainless steel foil that is grounded was used as an electrical shield to
eliminate noise being emitted fi'om the firmace.

The UHT System was adapted to be able to perform ZT measurements using AC
electrical impedance measurements discussed in the following sections. This was
accomplished by changing the center sample holder shaft so that four wires could be used
to dangle a TB pellet for measurements (see Figure 5-21). This measurement can only be
made with the UHT System because the surrounding temperature is modified, not the
sample holder like in the current HT System. This is another reason that makes the UHT

System a valuable asset to thermoelectric research at MSU.

83

 

Figure 5-21: Picture of UHT System adapted for ZT direct measurements by dangling a
sample in a high temperature environment

A future improvement to the UHT System is to add the capability of back-filling
the system with an inert gas such as argon. It has been experimentally discovered that
some samples are unstable and outgas at high temperatures in a high vacuum
environment. A solution to this would be to first remove the air in the system and then
either backfill with argon or possibly provide a continuous flow of argon into the system.
This will require a gas flow controller and research into the affects that the argon will
have on the thermopower and electrical conductivity measurements. In addition, the
background gas would not be suitable for the ZT measurement since it would cause a

thermal loss (thermally short the sample) and increase the error in this measurement.

5.9 Conclusion

The UHT System is a valuable asset to Michigan State University’s thermoelectric
research program by providing measurements of thermopower and electrical conductivity

of TE samples up to higher temperatures than previous systems. The unique design of

84

 

the 5}
which

smcc l

shoult‘

 

 

the system has allowed it to be adapted for high temperature ZT direct measurements,
which is discussed in the following sections. This system has been continuously active
since its completion where it has been used to measure a large number of samples and

should continue to contribute valuable data in the fixture.

 

85

 

in) est
incluc
here i:
an AC
utilizit

mOJU”

 
  
  
  
  

range 1'
Collect
H0“E\

10 Calc'

Chapter 6: Impedance Spectroscopy of Thermoelectric Materials and Devices

6.1 Introduction

Measurements of assembled thermoelectric modules commonly include
investigations of the module’s output power versus load resistance. Such measurements
include non-ideal effects such as electrical and thermal contact resistances. Research
here is to analyze the frequency dependent impedance of thermoelectric modules. Using
an AC electrical measurement, a model for a thermoelectric module can been developed
utilizing electrical circuits for both the thermal and electrical characteristics of the
module.

Preliminary measurements were taken at room temperature over the frequency
range of lmHz to SOOHz using lock-in amplifiers. From such measurements, the data
collected fi'om commercially available modules can be used for the extraction of ZT.
However developing a model to explain the frequency dependent impedance can give rise
to calculating the thermal conductivity and thermal capacitance of the module as well.
This measurement technique can then be applied to finding ZT of modules at higher
temperatures.

The extraction of ZT is extremely important when creating thermoelectric
materials. Currently, the accepted method for determining the ZT of a sample is by
measuring the temperature dependant data for electrical conductivity and thermopower
on the same sample while another sample of the same composition is measured for
thermal conductivity. Two samples are required since the required geometry for the
sample used in thermal conductivity measurements is vastly different than the required

geometry for the electrical conductivity and thermopower measurements. This method

86

 

6.2 I

mOdulk

OfIhe I.

816 fan

 

 

 

 

could lead to a false sense of ZT. It would be extremely beneficial if the temperature
dependant ZT for high temperatures could be found directly. This section will describe
the setup and the measurement process for collecting the fiequency dependant impedance

of thermoelectric materials and devices.

6.2 Existing Research in Scientific Community

There has been a limited amount of research published on observing and modeling
the dynamic behavior of thermoelectric materials [31—43]. There were three main articles
which did have some insight into this area of research. The first source of material was
fiom Paul Gray. He published a book on The Dynflric Behavior of Thermoelectric
ngjgg in 1960 [44]. This book used extensive mathematical derivations on
thermoelectric dynamic behavior in the time domain but it lacked in the ability to apply
the equations to experimental data. The next important article came from J. A. Chavez
[45]. He published an article called “SPICE model of thermoelectric elements including
thermal effects” in 2000. This model used an electro-thermal model to describe TE
module behavior in the time domain. The model did not include any thermal capacitance
of the TB material and it did not wok in the frequency domain. Finally, a third article by
Stefan Dilhaire called “Determination of ZT of PN thermoelectric couples by AC
electrical measurement” published in 2002 [46] did show frequency dependant data of a
single TE couple attached to copper blocks. The article also provided an AC model using
a thermal analysis but lacked in evaluating TE modules and investigations up to high
temperatures. However, the article provided a good motivation to further investigate an

AC model that would include modeling of complete TE modules, single pellet

87

 

63F

a DC i
one sit
This h
current
device
Voltagi
multip
be app

Oflhe:

 

 

 

measurements, and simple unicouples with research into measurements at high

temperatures.

6.3 Frequency Dependent Experimental Measurement

A thermoelectric (TE) module is an active device. This can be shown by applying
a DC voltage source across the input terminals of the device causing heat to move from
one side of the TE module to the other to form a temperature gradient across the module.
This heating and cooling is due to the Peltier effect. The heat flow is proportional to the
current passing through the device. When there is a temperature gradient across the
device, a voltage is developed due to the Seebeck effect. This voltage opposes the

voltage source applied to the TE module and is equal to the Seebeck coefficient, on,

multiplied by the temperature gradient, AT. The electrical behavior of the TE module can
be approximated by the circuit shown in Figure 6-1, which shows an electrical resistance

of the material, R, in series with a dependent voltage source due to the Seebeck effect.

VSource —O
9 W
a - AT (V)

Figure 6-1: Electrical circuit describing the electrical properties of a TB module

 

This model shows that the impedance of the TB module is dependent on the temperature
gradient across the model. One way to find the electrical resistance of the model would
be to use an AC electrical source oscillating at a frequency where the temperature

gradient could not be established. This would cause the dependent voltage source to

88

l
approu

frequc'.
allows
of the t
intercs

freque

 

lna

mOd

approach zero leaving only the electrical resistance. As the AC source approaches zero
frequency (DC), the overall resistance increases due to the Seebeck voltage source. This
allows one to separate the voltage due to the Seebeck effect from the electrical resistance
of the material. This technique can be used to find ZT [47], however, here we are
interested in the behavior of the impedance as the frequency transitions from a high

frequency down to low fiequency (approaching a DC value).

6.4 Experimental Setup

Using two 7165 DSP Lock-In Amplifiers, a frequency sweep can be performed on
a TE module using the setup shown in Figure 6-2. One Lock-In is used to provide the
AC source voltage signal and to measure the phase and magnitude of the voltage across a
sense resistor for calculating the current going through the TB module. The second

Lock-In measures the phase and magnitude of the voltage across the TB module.

 

‘ TE Module

 

 

 

 

 

VSOUI'CC

 

 

 

Figure 6-2: Experimental setup for AC measurements

The TE module is suspended by the wires connected to the terminals of the device
in a vacuum (IE-6 Torr) so that these wires are the only thermal connection between the

module and the measurement equipment. The wires should be small in diameter and long

89

 

enoug

gTL‘ZilC

 

mmnu
tenfic
unoug
cantw
modul
the re.
Inagni

coordi

 

No“. l

ph&§3é

mOduI.

 

 

enough so that the thermal resistance of the measurement wires is orders of magnitude
greater than the thermal resistance of the TE module. The sense resistor is assumed to
maintain a constant value throughout the frequency sweep. This assumption has been
verified using an impedance analyzer. Using a small AC voltage so that the current
through the TE module is about 10mA(RMS), the phase and magnitude of the impedance
can be calculated from the measured phase and magnitude of the voltage across the TE
module. Starting with the algebra of complex numbers, if 2 equals the impedance, a is
the real component, b is the imaginary component, 0 is the phase angle, and r is the
magnitude, then the following shows the representation of impedance in rectangular

coordinates or cylindrical coordinates.

Algebra of Complex Numbers [48]:

z =a+jb
Rez=a
lmz=b
a=rcos€
b=rsin6 (6'42)

2 =r(cos0+jsin6)
ejg =cos€+jsin6

z=r-ej6

Now let the phase and magnitude of V1-V2, as 03mg and vsem, respectively. Also, let the
phase and magnitude of V2 as 62 and V2, respectively. Then the current into the TB

module is as follows.

90

‘- ‘3 "43. :n‘ .g ‘1'. "5‘; l ‘ :
:rrwr-‘vwverl -. '. " “ - . .. .

"' '- ...
- t. mum-i.- nu}1t.;‘

I
e
. O
t
he
r
,‘_-
. 9"
9
‘ .‘
.§ ‘
'1‘.
0.39
&;
.';
i.’
a :
.
‘ I
?.z
3".
1I
.
I
t‘;
-I
- Y
‘ l
.g!
'4“
' 4

or; u- " co .u} -=.. ' L... f.
L - keuttwflfliyfirw. :.

' 3'!

o
. p .‘ 4 2 "I
, .*vasw--_+-

 

 

New.

From

and ti.

are US;

 

The Si;

amplit'

few n.

C.

 

jgsense

 

 

i IN = Vsense 3e
Rsense (6.43)
= Vsense ‘C°S(gsense) + j ' Vsense ' Sin(9sense)
Rsense

Now, the impedance of the module, z, can be found as follows.

 

z _ vz -ej62 _ vz °cos(92)+j-vz ~sin(t92)

1IN 1IN

'6
___ Rsense ‘V2 .8] 2 (644)

 

. jgsense
”sense e

Rsense . V2 . ej(62 _6sense)

 

Vsense

From the above equation, the magnitude of the impedance of the module is:

Rsense . V2 (6.45)
Vsense
and the phase of the impedance is:
192 — 656,138 (6.46)

6.5 Lock In Amplifier

To measure frequency dependant impedance of TE materials, Lock-in amplifiers
are used to get the phase and magnitude of the impedance in a noisy environment where
the signal levels can be very low. The following is a description of how Lock-in
amplifiers are very useful for this measurement.

Lock-in amplifiers are used to detect and measure very small AC signals down to a

few nanovolts. Accurate measurements may be made even when the small signal is

91

 

 

obscu
techni

a spec

refere

at 1le
noise .
l00ltl~
1000)
noise 1
a Q=1
kHz '1;

andth

 

r Efefer
The [85

 

fuflcrit

obscured by noise sources many thousands of times larger. Lock-in amplifiers use a
technique known as phase-sensitive detection to single out the component of the signal at
a specific reference frequency and phase. Noise signals at frequencies other than the
reference frequency are rejected and do not affect the measurement to a certain degree.
Why use a lock-in amplifier? Consider an example signal that is a lOnV sine wave

at 10kHz. Amplification is required to bring the signal above the noise. A good low

noise amplifier will have about 5 nV / x/Hz of input noise. If the amplifier bandwidth is

lOOkHz and the gain is 1000, the output can be expected to be 10 uV of signal (10 nV x

1000) and 1.6mV of broadband noise (5 nV / \le x 3/100kHz x 1000). The signal to
noise ratio will be too low to make any measurements. If a bandpass filter is applied with
a Q=100 centered at 10kHz, any signal in a lOOHz bandwidth will be detected (10

kHz/Q). The noise in the filter pass band will be 50 uV (5 nV / 3/Hz x 3/100Hz x 1000)

and the signal will still be 10 uV. Still, an accurate measurement cannot be made, even if
fitrther gain is used because the signal to noise ratio is too low. Now use an amplifier
with a phase-sensitive detector (PSD). The PSD can detect the signal at 10kHz with a
bandwidth as narrow as 0.01 Hz! In this case, the noise detection bandwidth will be only

0.5 [4V (5 nV/x/Hz x 3/0.le x 1000) while the signal is still 10 uV. The signal to

noise ratio is now 20 and an accurate measurement of the signal is possible.

What is phase-sensitive detection? Lock-in measurements require a frequency
reference. Typically an experiment is excited at a fixed frequency and the lock-in detects
the response from the experiment at the reference frequency. In the diagram below, the

reference signal is a square wave at frequency (or. This might be a sync output from a

function generator. If the sine output fiom the firnction generator is used as a source, the

92

 

rcspor
lsio '

{N

and (2
signal
diagra

ShOtVF

UShtg;

WaVES

 

 

response might be the signal waveform shown below. The signal is

Vsig -sin(a),. -t + gsig) where Vsig is the signal amplitude, a), is the signal fi'equency,
and asig is the signal’s phase. Lock-in amplifiers generate their own internal reference

signal usually by a phase-locked-loop (PLL) locked to the external reference. In the
diagram below the external reference, the lock-in’s reference and the signal are all

shown. The internal reference is VL -sin(a) L ct + emf)-

Reference
1
asig
i n l _
S g a /, \ (7 y/ \\ // \\\
1
\ / \ + //'1' \ /
gref
Lock-in /'“»\ 4 )/ /, ,-_\
/ \‘, 1" \ {.I' ‘1
x", f,“
V \.--_,/ \\_/

Figure 6-3: Lock-in signal example

The Lock-in amplifies the signal and then multiplies it by the lock-in reference
using a PSD or multiplier. The output of the PSD is simply the product of two sine

anCS.

=_.Vsig.VL.cos([a)r —a)L]-t+gsig—0ref)— (6.47)

'Vsig 'VL -cos([a),. + 0L1" + asig + gref )

Nli—INv—I

93

 

 

 

The
0the
tilts:
(1), 1

filter

This

phase
gref
if 9 is

We

 

mUllip

 

The PSD output is two AC signals, one at the difference frequency (a), — (0L) and the

 

other at the sum frequency (a), + a) L ). If the PSD output is passed through a low pass
filter, the AC signals are removed. Normally, this would remove everything, however, if
(0,. equals a) L , the difference frequency component will be a DC signal. In this case, the

filtered PSD output will be

VPSD 2 ° Vsig 'VL 'COSWSig — gref ) (6-48)

1
2

This is a very nice signal. It is a DC signal proportional to the signal amplitude.

6.5.1 Magnitude and Phase

The PSD output is proportional to Vsig -cos(6) where 6 = (QM-g - gref ). Bis the
phase difference between the signal and the lock-in reference oscillator. By adjusting
Bref we can make theta equal to zero, in which case we can measure Vsig (cos(0) = 1).
If Bis 90°, there will be no output at all. A lock-in with a single PSD is called a single-
phase lock-in and its output is Vsig - cos(6).

Adding a second PSD can eliminate the phase dependency. If the second PSD

multiplies the signal with the reference oscillator shifted by 90°, i.e.

VL - sin(a) L -t + gref + 900 ) , its low pass filtered output will be

1
V =——-V° -V -sin(t9' —-6 )
PSD2 2 szg L szg ref (6.49)

Vpsnz = 'Vsig °sin(¢9)

94

 

Nov» *

sint (f

 

6.6 l

reSis

\

Now we have two outputs, one proportional to cos(6) and the other proportional to
sin(6) . If we call the first output X and the second Y

X = Vsig -cos(6)
. (6.50)

These two quantities represent the signal as a vector relative to the lock-in reference
oscillator. X is call the ‘in-phase’ component and Y the ‘quadrature’ componenet. This
is because when 19:0, X measures the signal while Y is zero. By computing the

magnitude (R) of the signal vector, the phase dependency is removed.

 

R = \[(X2 + Y2) = Vsig (6.51)

R measures the signal amplitude and does not depend upon the phase between the signal
and lock-in reference. A dual-phase lock-in has two PSD’s, with reference oscillators 90
degrees apart, and can measure X, Y and R directly. In addition, the phase q between the

signal and lock-in reference, can be measured according to;

e=tan‘1(Y/X)

6.6 Example Data using Tellurex Module

The experimental data of the impedance of the commercial Tellurex [49] TE
module for power generation is show in Figure 6-4. Notice that for low frequencies, the

resistance of the module is much larger than at high frequencies.

95

 

7 l

6.5

 

    

6 5 5 5 4
5 4

Amaze—CV 93:25.59:— 232

s
3

30

 

Mag Impedance (Ohms)

 

 

 

 

 

 

 

 

7 I I I I I 5
. kMagnitudel
6-5 ' r. Phasel i
L.“ — 2 — — 7'7 -1 O
6 .3 .7 t
'7. .J , g
5.5 - . - -5 g.
"c
5 - o g.
4 - -10 8
.5 '- Q A
4 - 4 q
4 -15
3.5 - ~ -
o e e ekrc1_++.a+.‘ H)
3 l l J l I _20
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

Figure 6-4: Magnitude and phase of the impedance of a Tellurex TE module

      
 

Under Vacuum
Atmospheric Pressure

 

5.5

P
J- at

5"
at

U!
IIII'IIII'IIII'IIII'IIII'III&
O

Magnitude Impedance (0)

 

31
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

Figure 6-5: Plot of magnitude versus frequency for high vacuum and atmospheric

conditions

96

 

 

 

6.7 An

Neglect

The hea

The volt:

The figure

 

 

6.7 Analysis of the Data

Neglecting radiation losses, the figure of merit, ZT, of the model is:

2.

 

- T (6.52)

The heat flow, Q, and the thermal conductivity can be equated to this:

Q = a - T - I
__ Q .Iength (6-53)

 

— AT area
The voltage across the terminals of the model equals:

V=R0-I+a'-AT
a-AT
I

 

V
RTotal = 7 = R0 + (6.54)

_ length
R0 ~area

The figure of merit, ZT, can now be found to be:

ZT=a2- length _ AT-area

 

R0 ~area a-T-Iength-I
_a-AT

 

(6.55)

 

 

a - AT
1 (6.56)
RAC(AT—>O) = R0

 

RDC =R0+

R
ZT = JE — 1 (6.57)
RAC

97

 

6.8 .110 rt

 

All)
. I
measunn:
This secti.

|
module. a

 

6.8.1 Sin‘

diagramc
ends 0f t
Configu;
low “111
are [her
temper

“913%

6.8 More Sample Measurement Setups

Along with measuring commercial thermoelectric modules, investigations on
measuring the ZT of other thermoelectric materials and configurations have been made.
This section describes the setup for measuring ZT on single TE pellets, a pn inline TE

module, and unicouples or multicouple modules.

6.8.1 Single Sample ZT Measurements

A single sample of thermoelectric material can be measured for ZT using the setup
diagramed in Figure 6-6. In this diagram, there is a sample with electrical contacts at the
ends of the material. The setup shows four wires attached to a TE sample, labeled a, in a
configuration that will include the contact resistance between the wires and the sample
but will not include the electrical resistance of the measurement wires. The four wires
are then thermally grounded to a reference temperature. This is typically room
temperature. At the location of the thermal reference, the wires may change materials to
copper wires, which will go to the measurement equipment. A voltage source is shown
in the figure to provide the power for the measurement; however, a current source may
also be used. If a voltage source is used, a sense resistor of a known value is placed in
series with the source in order to calculate the current flowing through the sample. For
room temperature measurements, wires labeled a may be Copper wires that are very
small in diameter such as 25 pm. For high temperature measurements, the wires may be
Platinum. It is important that the wires have a low thermal resistance. It is also
important that the thermopower of the measurement wires is very low compared to the

sample being tested. When this is true, the therm0power of the wires can be neglected

98

 

 

 

 

without a
resistance
accompli:
contacts 1
The hi gh

There \t'il

Sam

For:

bem‘een ti,
as the One
measufi‘m.

HOWEVER .

 

high

“ 10 10M

completch

“‘9 Voltag.

even Spark

 

without acquiring a significant error in the measurement. Except for the small thermal
resistance of the measurement wires, the sample is thermally isolated. This is
accomplished by hanging the sample by the measurement wires so that there are no other
contacts to the sample and also by placing the sample in a high vacuum environment.
The high vacuum is used to eliminate thermal loss due to conduction and convection.

There will, however, still be losses due to radiation.

Sample

 

Figure 6—6: Single TE pellet for ZT measurements including contacts

For measurements of single TE pellets which do not include contact resistance
between the measurement wires and the sample, a four point configuration is used such
as the one diagramed in Figure 6-7. For high frequency measurements and DC
measurements, the placement of the probes will not effect the measurement of ZT.
However, the AC measurement of the impedance as the frequency is transitioned from
high to low frequency will be affected by the placement of the probes. This will be
explained in later sections. The sample, which is dangling during the measurement, is
completely supported by the wires at the ends of the sample which supply the current.
The voltage measurement probes can either be carefully soldered on, silver pasted on, or

even spark welded on.

99

 

Sam]

Fiat

Ad

sample 31/

The1

 

platinum P"

The

clecmbEll c

 

Of the COm .

 

 

 

 

 

 

 

 

 

TH ‘l—_ CU (___
, 1-—-.
a Cu
/
Sample I. + e
a Cl] V
\ O "
TV ___. cu

 

Figure 6-7: Single TE pellet for ZT measurements in four-point configuration

A detailed diagram with dimensions (using variables) is shown in Figure 6-8 for the

sample size and voltage probe locations.

 

 

 

 

 

 

 

 

If L/ X fl]
L
L
1* ‘l
l 1
TC l l TH
.. V +
L
1‘ AT 4
L J
F AT/x 'I

Figure 6-8: Detailed view of a single TE pellet connection

The thermopower of constantan is low enough that the thermopower of the
platinum current leads will affect the measurement. Therefore, the thermopower of the
platinum must be known and corrected for.

The schematic of the setup is shown in Figure 6-9 where a representation of the
electrical circuit and thermal circuit is provided. Figure 6-10 shows the equations for all

of the components presented in Figure 6-9.

100

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

apt "TI

T Rthpt 4 Rthpt3 Rthptl "

 

 

 

 

 

 

 

 

 

Thermal Circuit

 

 

V3 V2
_. V4 V1 +

RPt-elec4 RPt-elecl

 

 

Figure 6-9: Electrical and thermal model of setup

101

 

 

TH TH
V1= [art-dT VA= [apt-dT QA=QB=Qc=asample-1-T
TR Tx” 1 1
“H TxC RthA = R’hsarnple '(1“;);
V2 = IaPt '5” VB = Iapt -dT 1
TR TxH “'73 = Rthsample ;
TxC TC 1 1
V3 = [apt -dT VC -.- IaPt -dT R’hC = R’hsample ’(1-;)'(1-;)
TR TIC
1 1
TC RA = Rsample (Li—1:);
V4 = [apt ~dT
1
TR RB = Rsample ’ _
x
1 1
RC =Rsample‘ 1“ '1‘—
x n

 

 

Figure 6-10: Equations for Figure 6-9

The measured voltage across the constantan wire can be calculated using the

schematic from Figure 6-9 and is shown below.

TX” ] TIC TR
Vmeasured = IaPt 'dT + I'Rsample ';+ [asample 'dT+ IaPt 'dT
TR TX” TxC

Tx
1
= flaPt “asample)'dT+ I'Rsample ; (6.58)

 

~ (“Pt ’asample)' AT + I ‘ Rsample

~

x x

102

 

 

 

Assum i 1‘.

the temp

ZT Oflht-

 

fOHOVVS

Assuming the wire thermal resistance is much larger than the sample thermal resistance,

the temperature gradient across the sample can be approximated as follows.
AT e (ample - apt )- I . T . Rthsample (6.59)

ZT of the tested material is found from the basic equations shown below.

2
“sample ’0' sample .

 

 

 

 

(ZT) = T (6.60)
sample "sample
Qzasample ‘T'I (6-61)
K = _Q_ . l_eng_th_ (6.62)
AT area
2 length AT-area
(ZT) = “sam le ' ° 'T
sample p Rsample ~area “sample 'T '1 -length
_ a l 2 1 AT
— sam e ' '
p Rsample “sample 'T ' I
_ “sample , AT (6.63)
Rsample ' I

_ asarnplez 'R’hsample . T

 

Rsarnple
The measured values for RDC and RAC can be calculated below

(“Pt "asample ) AT + Rsample
x-I x

 

RDC =
(6.64)

Rsample

RAC(AT—>0) = x

Now the ZT that is measured can be calculated from using the Harman technique as

follows.

103

 

The abox
measured

Oflhesan

 

11

 

RDC
ZT = — — 1
( )measured R A C

 

x-I x

Rsample
x

_ (“Pt —“sample)' AT (6 65)
— Rsample ' I .
(“Pt — “sample)’ (“sample _ “Pt ) I ' T ’ R’hsample

Rsample ' 1

[(“Pt ' “sample)’ AT + Rsample]
-1

 

 

 

_ (“Pt ’“sampley 'R’hsample ~T

 

Rsample
The above equation shows that how the thermopower of the platinum wire affects the
measured ZT value. A correction must be made to the measured ZT to get the actual ZT
of the sample by introducing a correction factor as follows.

(ZT) = (Z “measured - Correction

sample

2 )2
a -Rt 6: —a -Rt
sample hsarnple ~T ___ ( Pt sample hsample ~T . Co ection

Rsample Rsample

 

 

 

“sample

(“Pt ’ “sarnple)2

 

Correction

 

 

 

(6.66)
The above equation indicates that in order to correct for the thermopower of the
measurement wires, the thermopower of the sample must be known. This may not

always be the case. However, typically, samples measured by MSU have large

104

thermopower values in that the thermopower of the platinum voltage probes can be

neglected.

6.8.2 Inline PN Module

To create a full working thermoelectric module, p-type and n-type materials must
both be used. Typically the thermoelectric properties as a function of temperature are
different between the two types of materials. It is important to test how both materials
will work together when combined as a function of temperature. A convenient way to
test the combination of the two types is to place them in an inline configuration shown in
Figure 6-11 and Figure 6-12. A pn inline module is simply a p-type and an n—type TE
sample connected together in a straight line. The two materials are bonded together using
a material such as silver paste, solder, or something that will diffuse into both samples to
hold them together. In this configuration, the module has the least number of contacts, 1
(n-type sample bonded to p-type via bonding material). Contact resistance directly
effects ZT measurements so by reducing the contacts, the overall contact resistance is
reduced and the measured ZT is closer to the actual ZT of the module if there were no
contact resistance. The inline configuration also provides a simple and efficient way to
make the module. The two TE materials can be placed in a vacuum-sealed quartz tube
with the bonding material in between and some added weight to hold the two materials
together while it is place in a furnace for the diffusion of the three materials.

Figure 6-11 shows a diagram of the inline module setup which will include the
contact resistance between the measurement wires and the sample. Figure 6-12 shows

the diagram of the setup where it is in a four-point probe measurement configuration such

105

 

 

that the 1
materials
increases
opposite.
the samp
hot tempt
sample el
depender
depend o
the bond
elL‘Ctrical
the inline
rePresent
rnOdule 13
639h of th
measurerr

reach the

 

 

that the voltage leads do not included any contacts except the bond between the two
materials. In both configurations then ends of the module will both tend to either
increases or decrease in temperature while the bond between the two materials will do the
opposite. Because the materials will have different properties, it is likely that the ends of
the sample will not be at the same temperature. The diagram shows this by showing two
hot temperatures, Tm and Tm. This is because, even though both samples have the
sample electrical current flowing through them, the heat flow through each sample is
dependent upon the thermopower. The temperature at the ends of each sample will
depend on both the heat flow and the thermal conduction of the material. For modeling,
the bond between both samples will be forced to have the sample temperature. Using an
electrical circuit to model the thermal behavior, Figure 6-13 shows the thermal circuit of
the inline module where a current source represents heat flow and the electrical resistance
represents thermal resistance. As long as the temperature gradient along the inline
module is much smaller than average temperature of the module, the thermopower along
each of the samples can be assumed to be constant. With a constant thermopower, the
measurement of ZT should be not affected by the fact that the ends of the sample do not

reach the same temperature.

106

Sample

p-type

 

Figure 6-11: Inline TE module including contacts

Sample

Tc

  
 

T112

Figure 6-12: Inline TE module in four point probe configuration

Figure 6-13: Inline module with thermal circuit overlay (DC steady state)

 

107

Inline modules are useful for testing ZT using impedance spectroscopy but because
of the configuration, the module is not firnctional for other applications. This module can
not be tested in MSU’s Device Testing System (which also measures ZT) to verify the
results. The ZT measured can be compared to the individual measured properties of each

material along with the contact resistance to calculate the predicted ZT value.

6.8.3 Unicouples and Multicouple Modules

Described here is the setup for measuring unicouples and multicouple modules in
the standard configuration (electrically in series, thermally in parallel). Figure 6-14
shows the diagram of the setup for measuring a unicouple or a multicouple module. The
setup uses four wires to eliminate the resistance of the measuring wires but will include
all the non-ideal effects in the module, including contact resistance of each connection.
In Figure 6-14, where a unicouple is being measured, there will be four non-ideal
contacts in the module that will affect the ZT of the module. This ZT measurement will
be the actual ZT of the complete module. Unlike the inline module, the thermal circuit
(shown in Figure 6-15) is in parallel instead of in series. The temperature across each of
the samples will be the same. However, in this case, the heat flow in each sample will

not be solely determined by the individual samples.

108

Sample TH

    

TC

Figure 6-14: Unicouple TE module for ZT measurement

 

 

 

Figure 6-15: Typically unicouple module with thermal circuit overlayed (DC steady
state)

The advantage of this setup is that the ZT measurement is performed on a
functional module that can also be tested in the Device Testing System for cross

comparison.

109

6.9 System Program

A LabVIEW program was designed to conduct the impedance measurements of the
thermoelectric materials. The program controls the setup of the Lock-in amplifiers and
collects the data from the Lock-in amplifiers to be organized and stored into a text file for

fitrther analysis.

110

Chapter 7: RC-One Port Method

7.] Introduction

There has been research on DC electrical measurements and modeling of TE
modules by Chavez [45] and AC electrical measurements by Dilhaire [46]. Proposed
here is applying an RC-One Port analysis method [50] to provide a simple model that will
effectively describe the behavior of a TB module. The first approach to developing a
model is to assume that thermal and electrical circuit elements of the module can be in
lumped quantities. This approach will provide an overall thermal conductance and
thermal capacitance of the module if the average module Seebeck coefficient is known.
The model proposed here provides a simple equivalent circuit, which can be analyzed
using an electrical simulator such as SPICE. This model makes use of the magnitude and
phase of the electrical impedance measured by the lock-in amplifiers at the input
terminals of the module and includes fitting parameters of the total electrical resistance,

thermal conductance, heat capacitance, and module Seebeck coefficient.

7.2 Development of RC One-Port Model

The RC One-Port model is a model that is based on the impedance of an RC
(resistor, capacitor) circuit using a one-port analysis. The model is developed after
collecting experimental data on the impedance of a commercially available
thermoelectric module. The thermoelectric module is treated like a “black box”. From

the experimental data, the thermoelectric module appears to be a passive device. It is the

111

experimental data that leads to comparing a thermoelectric module to the impedance of a

passive RC circuit.

7.2.1 Comparing Data to Simple RC Circuit

The experimental data collected of the impedance of the commercially available
thermoelectric module has similar characteristics to an RC circuit, shown in Figure 7-1.
In this figure, Z(s), represents the impedance of the circuit in the s-domain. By
inspection of the circuit, the impedance of this circuit will be high and constant for low
frequency values (R1+R). For high frequency values, the impedance will be low and
constant (R). This behavior is the same as the experimental data collected on the

thermoelectric module.

 

 

 

 

 

41 R
O—‘i C] 0%—
___W—-
21s) R1
C}

Figure 7-1: RC circuit

The equation for the impedance in the 3 domain of the circuit shown in Figure 7-1 is

shown below where the imaginary value 31—1 = j and a) is frequency in radians per

 

second.
s=jw
6:231 (rad/s) (7.67)
Z(S)—R (S+(l)z) ( )
( mp)

112

The equation for the impedance is in terms of the poles and zeros. This indicates

that there is a zero and a pole in the impedance function at (02 and (up , respectively with

both the pole and zero being nonnegative and simple. The magnitude and phase of the

impedance function in the fiequency domain is shown here.

 

 

|Z(a))| = 9A - R - (7.68)
(0p 2
1 + [1]
“’p
Z phase (0.)) = tan—1(1) + tan—1 [2] (7.69)
(”z (”z

The experimental magnitude resistance data is curve fitted to the equation for the
magnitude of the impedance for the circuit shown in Figure 7-1. This step can be
accomplished by using the Levenberg-Marquardt algorithm in LabVIEW to determine
the least squares set of coefficients that best fit the set of input data points (X,Y) as
expressed by a nonlinear function y=f(x,a) where a is the set of coefficients. The results
of the curve fitting are display in Figure 7-2. Using the results from the curve fit, the
phase of the impedance is then calculated and also plotted with the experimental data in
Figure 7-2. By inspection, the experimental data fits extremely well to the impedance

equation for the chosen RC circuit.

113

 

 

 

 

 

 

 

10 + I I I‘I—TIII' I I I II‘III' I I I IIIII‘ I I I IIIII o
' I. . I -
I - I
I« .I q
9 " l. I
A - I '- -5
m .
E 8 " I I
.c ,
9’ ' ' - -10 3
8 7 T m
S i I I Ex ' ntIM itude ' g
+0 " I - A
6.... -   A. we; :9: I e
g _ g I._ , .. urve agn u e _‘ _15 9
05 . '\ I I I Experimental Phase 1
g 5 '- \ . - * ~Curve F'rt Phase ,
2 ’ t
- -20
J
4 - \\I.- '4
: “.mkH , e—e ‘
3 p I I ILIIIII l I 1 III-II I I I IIIIIl I I I IIIII‘ -25

 

0.001 0.01 0.1 1 10
F requency(Hz)

Figure 7-2: Curve fitting experimental data to an impedance equation of the circuit
shown in Figure 7-1

The curve fitting routine in LabVIEW provides the values for the pole and zero along
with the resistance, R, directly, which is shown here for the experimental data in Figure
7-2.

86,, = 27t-(O.064 Hz) (rad/s)
(op = 272' - (0.037 Hz) (rad/s)

R = 3.49 ((2)
To determine the values for R 1 and C1, the First Foster Technique [51] is used and is
described below.
The First Foster Technique can be used to determine an RC circuit that satisfies a
real rational impedance function where the poles and zeros are simple, line on the

negative real axis, and alternate with each other, the first critical frequency (pole or zero)

114

being a pole. For this situation, the general form of the impedance as a function of s is
shown here where H , K , and 0' are all real constants with 0' representing a critical

frequency.

K " K-
Z(s) = H+——O-+ 2—1— (7.70)
S i=ls+0i

The general equation can then be written in terms of the critical frequencies as:

H-(s+0'21)-(s+0'22)...
(s+0p1)-(s+0'p2)...

 

Z RC (3) = (771)

Using the above equation, the values for the RC components, shown in Figure 7-3, can be

found as follows:

H = Z(s)ls_m
K0 = S ° Z(S)Is=0

13.- = (s +0020)!

s=—a,°

 

 

 

 

 

 

 

C =— C =—
1 1 Kl n Kn
C0-K— Jl ll
0 ll ll
O—H———0 0— — — —<l o—I\/\/—
—W— R =H
Z(s) K] n °°
R1=— R":—
01 0'”

 

 

Figure 7-3: First Foster Technique circuit

This technique can be directly applied to the RC circuit representing the
thermoelectric module. First, the impedance of the RC circuit is written in terms of the

critical frequencies.

115

2(3):%.R.(1+S/wz).(—l+—Slfw—)_
p p (7.72)
= R-(wz +5)

(0) p + 3)
Using the formulas from the First Foster Technique, the values for H, K0, and K1

are found and shown here.

H=R
K0=0
K1=R°(a)z —a)p)

Now the RC components of the RC circuit for the TB module are found and shown in

 

 

 

 

 

 

 

Figure 7-4.
C1 1
11 C =
1r Roo=R 1 R-(mz—wp)
Q——4> 41—w—
R1
___.W—
Z s
() Rl—R.(a)z_a)p)
0 mp

Figure 7-4: Using First Foster Technique for TB Module

Another approach to determining the values for R1 and C1 is to analyze the circuit
in the 5 domain where the impedance of the capacitor will be 1/(s - C1) and manipulate

the impedance function until it shows a resistor in series with another resistor in parallel
with a capacitor. With a few manipulations of the equation, the values for C1 and R, can

be found as shown here.

116

 

 

R-(s+wz)_s-R+a)z-R

Z(s)=
(s+a)p) s+wp

- 3.134.502 .R+[R-(s+wp)-R'(S+wp)l

 

s+a)p

{‘92—pr

R-(mz—arp)1 s-cop }
K 3‘01? 7

[..M].[.M]

(0p S

A

”’p

=R+

 

 

-R

 

 

=R+M=R+R1//C1
R1+C1

 

 

R - (a) — a) )
where C} = 1 and R1 = z p
R - ((02 -— a) p ) a) p
Using the curve fitting routine in LabVIEW for the data collected shown in Figure
7-2, the values for R1 and C1 are shown here.

R1 = 2.63 Q
C1 = 1.65 F

It is interesting to note the value for C]. There are not any known capacitances in a
thermoelectric module (except for small parasitic capacitances) and typically, an
electrical capacitor with a value of 1.65 farads would be very large. The thermoelectric
module is effectively storing energy similar to a capacitor. If the thermoelectric module
was in a “black box”, the user could assume that the “black box” would have this large

capacitor inside.

117

Up to this point, the experimental data has been fitted to an entirely electrical RC
circuit. However, the thermoelectric module obviously has a thermal characteristic. The
next task is to identify where the thermal properties come into play with the RC circuit.
To begin, first start with the steady state circuit for the thermoelectric module, which
includes the electrical resistance and the Seebeck dependant voltage source shown in

Figure 7-5.

Figure 7-5: Steady state thermoelectric model

The impedance of this circuit is shown in Figure 7-6. The impedance of the steady state
thermoelectric model and the impedance of the RC network can be compared. Because
the Seebeck dependant voltage source has a negligible effect at high frequencies, the
electrical resistance of the module can be set equal to the series resistor found in the RC
circuit. This leaves the parallel combination of R1 and C1 to be related to the dependant
voltage source. R1 and C1 must be a representation of the thermal behavior of the TB
module that affects the impedance due to the Seebeck effect, which is discussed in the

next section.

118

Impedance —> I a-(TH—TC)/I

 

 

 

Figure 7-6: Comparison of impedance between circuits

7.2.2 Thermal Impedance

The next task is to relate this electrical impedance of the RC circuit to a thermal
impedance [52] of the thermoelectric module. Relating R1 and C1 to the dependent

voltage source due to the Seebeck effect, the following is found:

 

 

 

“'(TH_TC)=R1//C1= R1
'IN (R1 ~C1-S+1) (7 73)
R -i °
(TH—Tc): 1 1”

a-(Rl-C1-s+1)
Thermal impedance can be represented by the temperature gradient across the sample
divided by the heat flow, Q. For the thermoelectric module, the heat flow can be defined

by a - i [N °Tavg . Substituting the relation found for the temperature gradient into the

thermal impedance equation, the new equation for the thermal impedance is as follows:

119

AT_ TH—TC
Q a'iIN°Tavg
_ R1

 

 

Z Thermal =
(7.74)

 

This can be rewritten into a familiar form of a capacitor in parallel with a resistor, which
is shown here.

1

ZThermaI = 1
C1oa2-Tavg-(s+ )

= 1 (7.75)

2
a -T
+___ avg
R1

 

 

 

S'Cl 'az 'Tavg

1

 

5 ' CThermal + _—
RThermal

The values for RThermal and C Thermal shown here do not represent an electrical

resistance and capacitance, but rather a thermal resistance and capacitance where the
values for these components are:

CThermal = a2 'T avg ‘Cl

R (7.76)
RThermal = Tl.-
a ' Tavg

Notice that C Thermal and RThermaI are both related to the Seebeck coefficient, a. This
indicates that the Seebeck coefi'rcient must be known in order to solve for the thermal
resistance and capacitance. From here, the thermal capacitance and thermal conductance

of the module can be calculated. It would also be possible to find the thermal

conductance if the thermal capacitance is known instead of the Seebeck coefficient.

120

Figure 7-7 shows the related equivalent circuit found in the above equation to the

impedance of the Seebeck dependent voltage source.

 

 

 

 

 

 

 

CTHllfftMAL
1 l ‘
0—0
——W— E Z (s) Oar . AT
Z(s) RTHERMAL ,- IN
C I

Figure 7-7: Thermal impedance related to electrical impedance

7.2.3 Final Model

The final AC model for the thermoelectric module is shown in Figure 7-8. In this
model, the dependent voltage source can be called a temperature dependent voltage
source. The following equation also shows how using only the poles and zeros of the
impedance can also give ZT of the module.

ZTJACHI
RAC

 

 

 

= 0” (7.77)

121

 

A

<1? CTHERMA Ll RTHERMAL
a - iIN - TAM T

'

 

 

 

Thermal Circuit

-.-.-.-.-a-------«-n-.-«-.-o-.---.-.-.-------.-----.-.---o-o-----.-.-----n---..

A
V

R
V a a ° I ' AT
SOURCE

Electrical Circuit

C)

 

 

 

Figure 7-8: AC thermal-electrical model for a TB module

From the Tellurex website [49], the Seebeck coefficient for this module is
approximately 0.04604 (V /K). The module consists of 254 pellets, and the size of each
pellet is 1mm by 1mm by 1.4m. With this information the thermal resistance and

capacitance can be calculated. The results are shown in Table 7-3.

Table 7-3: AC TEM model results

 

 

 

 

 

 

 

 

 

 

Seebeck of Module (V /K) 0.04604
Number of Pellets in Module 254
ZT 0.75
Electrical Conductivity (S/cm) 1.02E+03
Seebeck of 1 pellet (V/K) 1.81E-04
Thermal Conductivity (W/m-K) 1.33
Thermal Resistance of Module (K/W) 4.14
Thermal Capacitance (W's/K) 1.075

 

 

122

7.2.4

Thar

progr.

panel

 

 

t . ( I
6 1.. ! ytoe 2 01... Y 562

It

.. ..< ___ 4 I. .

313 3.2:

I4..l

 

7.2.4 Final Program for Analyzing Data

The curve fitting program using this RC one-port method was created in LabVIEW.
The program first takes the data that was collected by a previously explained LabVIEW
program that controlled the impedance measurement experiment. A picture of the front

panel view of the program is shown in Figure 7-9.

 

Figure 7-9: Front panel view of the RC One-Port Method LabVIEW program

123

7.3 Circle Plot

Another possible approach to analyzing the impedance data of the thermoelectric
module is to plot the imaginary impedance versus the real impedance, also know as the
Nyquist plot. For a thermoelectric module that behaves like the RC circuit, this plot will
create a semi-circle. The Nyquist plot is different than the Bode plot in that the Nyquist
plot shows visually the relation between the real and the imaginary impedance.

However, the disadvantage is that the dependence on frequency is lost.

Why does plotting the imaginary versus real give a semi-circle? First, let’s look at
the real and imaginary components of the impedance function for the simple RC circuit.
Let x equal the real components and y equal the imaginary components as indicated here.

x = Re[Z(s)]

(7.78)
y = 11an (3)]

In order for a circle to be made, the real and imaginary components must satisfy the
equation for a circle shown below where A (the x offset) and r (radius of circle) are not

dependant upon frequency.
(x — A)2 + y2 = r2 (7.79)
The equation for the impedance is as follows with s = j a) and a) = 279" ,

Z(s): (s+a)p)

 

(7.80)

The fiequency at the zero of the impedance function is:

a) _ l _ R1+Rm
Z (R1//Rm)'Cl R1°Rm‘Cl

 

(7.81)

The frequency at the pole of the impedance function is:

124

1
a) =
p R1 “C1

 

(7.82)

Substituting the above equations back into (7.80) and writing the equation in terms of real

and imaginary components is shown below.

R-{S+RRI;R"£']
Z(s): 11m 1
s+ --
l Rl'Cl]
R+R )
R[...1 ".11 1
= Rl'Rm'Cl R1-C11

1 1 ‘
s+—— s——-——-
R1-C1 R1-Cl)

R 2 {—Rm +Rm+R1].s_ Rm+R_1_

 

 

 

 

 

 

 

'S + ___—___.
_ m R1'C1 Rr-Cl (R1-C1)2
2 1
s _______
(RI-C1)2
(R1'C1)2°Rm'(j'w)2+(Rm'C1XR1)'(f'w)‘(Rm+Rl)
(RI-Cllz-(j-w)2-l
=(R1'C1)2°Rm-w2+Rm +R1 + ., 412-0140 (7.83)
(R1.C1)2.a12+1 (R1-C1)2-a)2+1
= Re[Z(s)]+ ,- - Ile<s>l

 

 

 

The values for the real and imaginary components for this impedance function can

be used to satisfy the circle equation where A and r are not dependant upon the fiequency

as shown here.

125

 

Fron
the C1
be R
can b
frequc

b)" lTnt

This ff:
CUn-e l

‘5 react

 

 

2 2
R12-C12-Rm-w2+Rm+R1_2-Rm+R1 + -R12'C1-a) _[1 R1]2
R12-C12-a12+1 R1-C12-(02+1

2
k V /T \VJLYJ

x y r

 

 

(7.84)

From the above equation it is clear that the radius of the circle is 0.5 - R1 . The center of

the circle lies on the x-axis at 0.5 - (2 - Rm + R1). The far most left side of the circle will

be Rm while the far most right side of the circle will be Rm + R1 . The peak of the circle

can be used to identify the capacitor value. This can be explained by identifying the
frequency that gives the maximum absolute imaginary impedance. This is accomplished

by finding when the derivative of y is zero.

 

 

i=0
da)
_d_ —R12-C1-a) _0
d0 R1-C12-a)2+1
2 2 2
R -C -(o —1
R12-C1-12 12 2 =0 (7.85)
R1 -C1 '0) +1
R12-C12-w2=1
a) k" 1
ea _—
p R1-C1

This frequency is the same as the pole of the impedance function, a) p . Therefore, a

curve fitting circle fit must be used to identify the frequency where the peak of the circle
is reached. Once that is found, the capacitor value can be calculated as follows.

1

C1 =—-—————
R1""peak

(7.86)

126

An example of the Nyquist plot is shown with experimental data in Figure 7-10
along with a curve fit to the data that was performed using LabVIEW. The figure

identifies the direction of increasing frequency.

 

Rm RI+RM

v I v v vv I va v I v v v vva—fiwlrv

   
 
 
  

 

Circle Curve F'rt

 

0 Experimental I

 

  
     

Imaginary

Impedance (0) -0.8 L C,=1/(co peak-R1)

l

 

 

A l A A I I l A A l A A A A I A A I a l A A A A

3 3.5 4 4.5 5 5.5 6 6.5
Real Impedance ((1)

)—
p

 

Figure 7-10: Imaginary versus real impedance plot

127

Chapter 8: Thermal Transmission Line Model

8.1 Introduction

A second approach to modeling a TE module is to model the thermal properties as
a distributed thermal resistance and capacitance spread throughout the length of the
material using a Thermal Transmission Line Model (Thermal TLINE). This approach is
similar to using transmission line theory with electrical cables long enough to propagate
an electrical wave. This model, although more complicated than the RC one-port model,
can provide a more realistic and detailed description of the thermal and electrical
behavior of the module. This is because the model separates out the individual thermal
components of the module such as: the thermoelectric pellets, the nickel traces for the
interconnects, and the alumina plates attached to the top and bottom of the module. The
model provides insight on the effects of thermally grounding one side of the module. The
motivation for investigating the use of transmission line theory was the inability of the
RC One-Port model to explain the impedance behavior found experimentally with inline

modules and single TE pellets.

8.2 Thermal Dynamics

The TE module is composed of thermoelectric material, nickel traces, and ceramic
end caps as shown in Figure 8-1. These components (because of their length) must

propagate thermal energy through them (heat transfer is not instantaneous).

128

 

 

Thef.

 

 

Ceramics

 

 

'\ /'

Nickel
Figure 8-1: Components of a TB module

 

 

(Din I (Dom
Tin Tom

 

 

 

L
Figure 8-2: Thermal dynamics of a 2-D material

The following variables will be used for the explanation of thermal dynamics.

1 = thermal conductivity
p = density
c = specific heat
CD = heat flow
T = temperature

L =length
A=Area

To being the analysis, first look at the thermal dynamics for a one-dimensional case
[53]. Figure 8-2 shows a two dimensional diagram for the thermal dynamics of a
material with a given length, L. The equation for temperature throughout a material of
length L is a second-order linear differential equation (SOLDE) both dependent upon

space (x) and time (1) shown here.

129

 

 

For tl

DC\K C

Lat 92

 

me he

 

2 .
5_Z=P_E.5_T f0r0<x<L (8.87)

The heat flow through the material is represented by the following equation.

6T
<I>=—/1-A-—— (8.88)
6x

For the purposes of the analysis, the assumption will be made that T = 0 for t = 0 . It is

possible, with the help of Laplace transform, to rewrite the SOLDE for temperature so

. . . . . . ,1
that 1t rs based only on space (not on trme). To 51mplrfy the notation, let a = — so the

.0 ' 0
new equations are now:
2
fl = 1.27: (339)
6x2 a at
(Dz—l-A-a—T (8.90)
6x
Let Band (15 be the Laplace transform of T and (D respectively, where s = j a) .
oo
6(x, s) = 1T(x,t)e(‘s’)dt
O (8.91)
(X)
¢(x,s)= j¢(x,t)e(’s’)dt
0
The new equations are now only dependent on position and are shown below.
2
£2 = 3.19 (8.92)
63:2 a
69
= —/1-A-— 8.93
¢ ax ( )

130

 

initi

bclo

vshe1

By ir

This 1‘. I

 

 

 

A solution for Bean now be found. By existence and uniqueness of solutions with given
initial conditions, there is always exactly one normalized pair of solutions which is shown
below (K 1 and K2 are constants)

6(x) = K1 .cosh(,B - x) + K2 -sinh(fl - x) (8.94)

where

82 = (8.95)

S
a

By imposing the following boundary conditions,

 

0 =6x=0
m ( ) (8.96)
60u1=9(x=L)
K1 and K2 canbe solved for in the following way:
6in=K2
l9 =K°sinh ~L +K -cosh -L
out 1 (16 ) 2 (.6 ) (8.97)
¢in:"l'A'.B'Kl
(tout=l-A-fl-(K1~cosh(,6-L)+K2-sinh(,6-L))
1
9- =cosh(,B-L)-6 +—-sinh(,6-L)-¢
m out Mfl out (8.98)

¢in = M16 ' 3&1th ‘ L) ' gout + 0051416 ' L) ' ¢out

 

 

 

The above pair of equations for the Laplace of temperature and heat flow into the
sample is written in terms of the Laplace of temperature and heat flow out of the sample.
This form for the equations will become apparent in the next section where the thermal
dynamic equations will be compared to the Telegrapher’s equation from transmission line

theory.

131

83 C

dmui
tmmS“
(U), c

byas

bflou

imped

 

8.3 Comparing Thermal Dynamics with Transmission Line Theory

An electrical transmission line is a distributed parameter network as opposed to a
circuit, which consists of lumped elements. A model for a small segment of a
transmission line is shown in Figure 8-3 which consists of resistance (R), conductance
(G), capacitance (C), and inductance (L) all as units per length such that multiplying them

by a small distance, Ax, gives the appropriate units.

 

Transmission Line

 

 

 

Figure 8-3: Transmission Line Model

Equations for the voltage and current going into a transmission line are shown
below where VL and IL are the voltage and current across a load, Z0 is the characteristic

impedance, and yis the propagation constant.

 

y = ,/(R + sL)(G + sC) (8.99)

R+sL
Z =,/ 8.100
0 G+sC ( )

Vin(x') = VL -cosh(7-x')+ 1L ~Z0 ~sinh(7-x')

 

8.101
Iin(x')=—E14-sinh(7-x')+IL ~cosh(7-x') ( )
0

132

The equations above are known as Telegrapher’s equations and can be directly compared
to the temperature and heat flow equations found with the thermal dynamic equations,

which are shown again here.

1 .
gin = out ’003h(16'14)+m'¢0ut -srnh(/3 'L)

¢in = M75 ‘ gout -sinh(,8 ' L) + ¢out 'COSh(.5 ‘ L)

(8.102)

The relation between the thermal dynamics in Laplace form and Telegrapher’s equations

can be shown be letting the following equalities be true.

gout = VL
¢0ut = 1L
.6 =7

 

 

s-pc _
,1 _J(R+sL)(G+sC) (8.103)

_l_=z

up 0
l _ /R+sL
“ZS,“ G+SC

Using the above equalities, an electrical representation of a thermal circuit can be made

where the values for R, C, G, and L are as follows.

 

 

 

R271; (m’l)

CZPCA (m4) (8.104)
6:0 (111“)

L=0(m4)

 

The relations shown above can be justified. R is the thermal resistance per unit of
position. C is the heat capacitance per unit of position. G represents a thermal loss due

to thermal conductance. However, a sample that is heated and in a vacuum (neglecting

133

radiation losses) will remain at that temperature and will not cool down. Therefore, it is
justified to find that G = 0. L represents a thermal inductance. Heat flow is a diffusion
process and there is no known thermal inductive component. Therefore, it is also

justified to find that L = 0.

8.4 Applying Thermal Transmission Line Model

By converting the thermal properties of a sample into an equivalent electrical
circuit, the transmission line equations may be used to describe the thermal properties of
thermoelectric modules. This can also be applied to inline modules as well as single TE

pellets.

8.4.1 Thermal TLINE Model for Commercial Module

The thermal transmission line model can now be applied to each of the elements of
the thermoelectric module shown in Figure 84. Due to the Peltier effect, an alternating
heat flow source will be modeled as an electrical current source. Voltages V1 and V2 in

this figure indicate temperature at their locations.

V1 V2

Ceramic Nickel TE Nickel Ceramic
Pellets

ZLEFI‘ ZPELLETS ZRIGHT
Figure 84: Applying Thermal TLINE model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

134

The equation for finding the temperatures indicated by V; and V2 are shown below
using a condensed notation and are found using super-position. In this case, Z stands for
the thermal impedance.

V1 = i ' (ZPellets With ZRight ) ll ZLeft _ li ' (ZPellets With ZLeft )// ZRight l@ V1

V2 2 -i . (Z Pellets with Z Left)” Z Right + [i ' (Z Pellets With ZRight)” ZLefi l@V2

(8.1 05)
By knowing the dimensions and the thermal properties of the ceramics and the nickel
traces used on the TB module, a fit to the data can be achieved using LabVIEW software.
Figure 8-5 shows a picture of a commercially available TE module created for power

generation that was used to test the Thermal TLINE model.

Figure 8-5: Commercially available TE module

The dimensions and thermal properties for the module are separated into the three main
components: the ceramics, the nickel traces, and the TB pellets and are shown in Table

8-1.

135

 

whicl

 

 

Table 8-1: Commercially available TE module component properties

  
 
 

    
   

Specific Thermal

Heat

 
 

Length Width

The values shown in Table 8—1 are used in the Thermal TLINE model using a setup file,

which is shown in Figure 8-6.

 

 

Figure 8-6: Setup LabVIEW vi for commercially available TE module

136

Using the information on the TE module and using the Thermal TLINE model
along with the RC One-Port model to fit the data, it can be seen in Figure 8-7 that the
Thermal TLIN E model fits well to the experimental data For this sample, both the
Thermal TLINE fit and the RC One-Port fit match the data. However, the RC One-Port
model indicates that the thermal capacitance of the module is 1.09 Ws/K without being
able to identify where the thermal capacitance is from. The Thermal TLINE model
indicates that the thermal capacitance of the TB material alone is 0.67 Ws/K with a
thermal resistance equal to 4.07 W. Thermal capacitance of the nickel traces on one
side of the module equals 0.39 Ws/K with thermal resistance equal to 0.018 W. The
thermal capacitance of the larger ceramic plate is 1.81 Ws/K with thermal resistance of
0.02 W. Finally the thermal capacitance of the smaller ceramic plate is 1.64 W/sK
with a thermal resistance of 0.02 W. These values are lumped element values and it is
the entire layout of the thermoelectric module that determines the overall capacitance of
the module. However, it is useful to identify how the thermal capacitance of the TB

pellets compares to the other components of the module.

137

Flgu

 

8.4.2 ”I

5 5 5 4
5 4.
eoEfiunzz awayEméé

5
3

 

6 I I I

e Experimental Data

 

 

 

 

9. 5.5 ----- RC One-Port Fit
3 Thermal TLINE Fit
1::
5 'u
3 =-
q; n
a. a
E 45 0
- 3
e: m
g 4 E
r.-
s.
a 3.5
E
3 I I I l I _20
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

Figure 8-7: Experimental data, RC One-Port fit, and Thermal TLINE fit to data for
commercially available TE module

8.4.2 Thermally Grounding One Side of Module

 

 

 

 

 

 

 

6.5 I I l I l
6 ‘L”~° 0 e . 0 Experimental Data _
0 Transmission Line Fit
8 5.5 - ' .
5 .
B 5
8 .
_g 4.5 - . _
8
E 4 - ' .-
3_5- .'Oee‘ee'ee'e‘eeeee'eeeé'e'eeee _
3 r r r r 1
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

Figure 8-8: Curve fitting thermal transmission line model

138

An advantage of using the Thermal TLIN E model is that the effects of thermally
grounding one side of a commercially available TE module can be observed and it is
possible to investigate how well the thermal ground is achieved. Figure 8-8 shows data
and the Thermal TLINE fit for a different TE module than the one used in Figure 8-7.
This module was dangling in a high vacuum environment. Figure 8-9 shows how the
data should be theoretically shifted in frequency for this module thermally grounded on
one side compared to the module that was not thermally grounded on either side. Figure
8-10 shows experimental data of the module that was thermally grounded to a heat sink
using thermal grease compared to the theoretical ideal case. Notice that the experimental
data in Figure 8-10 does not agree with the data predicted by the transmission line model.
However, the model allows the user to change how it is grounded. For example, instead
of an ideal thermal ground, a thermal resistance of 10K/W to ground was used on one
side of the module in the Thermal TLINE Model to simulate a theoretical poor thermal
ground. The new data predicted by the model, shown in Figure 8-11, agrees. well with
the experimental data and indicates that a poor thermal ground was established between

the TB module and the heat sink.

139

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.5 l l l I I
6 ll ‘ 5' 0 0 e . 0 Experimental Data
’ e 7 7 Transmission Line Fit "
0 (Thermally Grounded)
3 5.5 - ' -
§ .
is“: 5 ‘ . ‘
8
g, 4.5 - . -1
a
as
2 4 - ° .
I
3.5- 'O‘Oeeeeeeeee‘ee‘ieeeeieee ‘
3 1 1 1 1 1
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)
Figure 8-9: Ideal thermal ground one side of TE module
6.5 I I l I I
6 ‘1"- !- 0 Experimental Data
0 . (l’hennally Grounded) "
. Transmission Line Fit
. (Thermally Grounded)
8 5.5 " 7 a
5 I
B 5
E .- u
8 .
,3 4.5 - -
a .
2 4 _ . .
3.5- ....‘OOOO-eoeeeo......'_..1
3 1 1 1 1 1
0.001 0.01 0.1 1 10 100 1000

Frequency (Hz)

Figure 8-10: Compare ideal thermal ground with experimental data

140

6.5 I I l I T

 

 

 

 

 

 

 

6 l1.- .. o 0 Experimental Data .J
’ , (Thermally Grounded)
e Tranmission Line Fit
. (Poor Thermal Ground)
g 5.5 - . ..
B
E. 5 - 0 .
% .
a 4.5 " -l
'E
g0 e
2 4 _ . .
I O
3.5- ..‘-0-O%O+e—eooogroooeoe "
3 l J I 4 1
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

Figure 8-11: Theoretical poor thermal ground compared to experimental data

The Thermal TLINE Mode] provides much more detailed analysis of the
commercially available TE module than the RC One-Port model. It was able to identify
where the thermal capacitance and resistance of the module was located along with the
corresponding values. The fit to the data was comparable to the fit using the RC-One
Port Model. However, the Thermal TLINE Model was able to explain the data collected

after attempting to thermally ground one side of the TB module.

8.4.3 TTLM for Inline PN Module

It is important to test materials created by MSU that will be used in the fabrication
of a large thermoelectric module. AC frequency measurements were made on an inline

module where the n-type sample was LAST (Lead, Antimony, Silver, Tellurium) and the

141

p—type material was LASTT (Lead, Antimony Silver, Tellurium, Tin) bonded together
with antimony and without ceramic end caps (see Figure 8-12). This inline module
happens to be tested at 600K. Alter analyzing the impedance spectroscopy data on this
inline module, the Thermal TLINE model is a better fit to the data than the RC-One Port

Model (see Figure 8-13).

 

Figure 8-12: Inline TE module using LAST material

 

 

 

 

 

 

 

 

 

 

0.015 . . x
‘. . ..
0 Experimental Data
0014 _ _ Transmission Line Fit _
- ----- RC Impedance Fit
0
E
.2 0.013 -
8
M
D
E
-— 0.012 -
En
:3
2
0.011 _
001 I I l I
0.001 0.01 0.1 1 10 100

Frequency (Hz)
Figure 8-13: Comparison between Transmission Line Model and RC-One Port Model

142

The experimental data shown in Figure 8-13 shows an interesting behavior as the
frequency goes from low frequency to high frequency measurements. Towards the lower
frequencies, the impedance behaves similar to the RC One-Port model. However, at high
frequencies, the data has a much smoother bend in impedance than the RC One-Port
Model. This shape for the data can be expected because the inline module is behaving
like a single transmission line with only one source at one end of the line. This is due to
the fact that there is not a thermal capacitance at the ends of the module (no ceramics). A
possible temperature profile along the length of the inline module (using a low frequency
electrical current that is close to the pole of the impedance function) is shown in Figure
8-14. The voltage probes are towards the ends of the inline module where the

temperature profile will approximately be in phase with each other.

 

Figure 8-14: Possible temperature profile at one instance in time along the length of an
inline pn TE module using a low fi'equency electrical current that is close to the pole of
the impedance function

The inline module temperature profile approaches the behavior of an electrical
transmission line with a single source at one end and grounded at the other. This can be

seen if the inline model is thermally grounded at the ends of the sample as shown in

143

Figure 8-15. Thermally grounding the ends of the sample shorts out the Peltier Heat flow

source at the ends of the sample leaving a thermal circuit shown in Figure 8-16.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N-Type P-Type
QQ) 92$ 93$
TLINE TLINE
Q1=an'l'Tavg Q2=anp‘I'Tavg Q3=ap'I'Tavg
Figure 8-15: Thermal circuit showing the thermally grounded ends of an inline pn TE
module
N-Type P-Type

 

 

 

 

 

 

 

 

Q2
TLINE TLINE

v

 

 

 

 

 

 

 

 

QZ = anp ' I ' T avg
Figure 8-16: Thermal circuit showing the simplified schematic of Figure 8-15

For another inline module example that closer resembles a reference sample, an n-
type and p-type pellet was removed from a commercially available module and bonded
together with a solder in the inline configuration shown in Figure 8-17. The overall
length of the module is about 3mm. Due to the lack of space (pellet dimensions are 1mm
x 1mm x 1.4mm), the voltage probes are at the ends of the sample and will include
contact resistance. The data, shown in Figure 8-18 shows a sharp change in impedance at
low frequencies and a smooth change in impedance at the higher frequencies (again,
which is unlike the RC circuit equivalent). However, the Thermal TLINE model agrees

well with this behavior and the percent error between the data and the two models is

144

shown in Figure 8-19 indicating the Thermal TLINE model is a better fit. The data also
shows that the frequencies where the magnitude of the resistance transitions from low to
high values is at a higher frequency than the full commercially available module. This is
expected because there has been a reduction in heat capacitance at the ends of the module
by not included the nickel traces or the ceramic end plates. The ZT for this inline module
was found to be 0.74. This value is most likely lower than the full module because of

contact resistance.

 

3 .22mm

Figure 8-17: PN inline module consisting of Bi2T63 from commercially available
module and bonded together using woods metal

 

 

  
 
 

 

  

 

 

 

 

0.065 I 1 1 1 r 10
A 0 Experimental Data
9'; 0.06 ----- RC One-Port Fit _ 5
8 Thermal TLlNE Fit
: (1055 -
a '0
g 0 3
c; (105 m
E 0
a, 0.045 -5 8'
g (a
fig 0.04 v
8’ 0035 -10
:E .

0.03 ' "'l ' I 4 '15

0.01 0.1 1000 10“

1 10 100
Frequency (Hz)

Figure 8-18: Plot of a pn inline module consisting of Bi2T63 from commercially
available module showing magnitude and phase of the impedance versus frequency

145

 

 

 

8 r W I I I

6 - —0— RC One-Port Fit -
4 _ + Thermal TLINE Fit _
2

0

% Error to Curve Fit

 

 

 

-8 I I I I I

1 10 100 1000 104
Frequency (Hz)

 

Figure 8-19: Percent error

8.4.4 Thermal TLINE model for single pellet measurements

lrnpedance spectroscopy measurements have been made on single samples of
thermoelectric material created by MSU. An example is shown here using a singe p—type
pellet created by MSU with a chemical composition of NaongzoSbMTezz shown in
Figure 8-20. Here the voltage probes are within the ends of the sample so contact
resistance is not included in the measurement. The magnitude and phase of the
impedance for this sample is shown in Figure 8-20 along with the RC One-Port fit and

the Thermal TLINE fit.

 

Figure 8-20: Single TE pellet of p-type material (Nm,ngzoSbo,6Te22)

146

 

 

 

 

 

 

0.025 ~ - l L I T
a 0 Experimental Data z 10
v (_— ----- RC COG-Port Fit
3 Thermal TLINE Fit
: fi .0
g 0.02 o _ 0 =-
Cl 0 9
Q I m
E ——‘—> a
— - -1o ""
8 e
3 0.015 — 3
3
g) o ‘ -20
«I
E \_

0 01 ' 1 ' J 1 _30
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

Figure 8-21: Plot of single TE pellet showing magnitude and phase of the impedance
measurements of a p-type sample (N a0.8PbZOSb0.6Te22)

 

 

 

 

 

 

10 . . . 1 . .
—0— RC One-Port Fit
.. 8 ' +TherrnalTLlNE Fit
E 6
0
Z
5 4
s
g 2
t
H 0
,\°
-2
_4 l l l I I
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

Figure 8-22: Percent error

The data for a single pellet shows a dip where the zero critical frequency would be.
This dip in the data is also predicted by the Thermal TLINE model and is due to probe

position and the thermal wave developing along the length of the sample. When the

147

 

-1

probes are at the ends of the sample, the thermal wave at the ends of the sample are
always 90 degrees out of phase. But, when the probes are within the ends of the sample,
this is not the case. Figure 8-23 shows a possible temperature profile along the length of
the sample using a fiequency that is close to the pole of the impedance function. Figure
8-24 shows a possible temperature profile along the length of the sample at the fi'equency

where there is a dip in the magnitude resistance data.

Temp
4

N-Type

    

Figure 8-23: Possible temperature profile at once instance in time along n-type sample
using a low frequency (close to the pole) voltage source across sample

Temp

 

Figure 8-24: Possible temperature profile at one instance in time along n-type sample
using a frequency where the dip in the data is created

148

A LabVIEW program was develop using the Thermal TLINE model to indicate the
temperature profile along the length of the sample at a given frequency. Figure 8-25 and
Figure 8-26 show the temperature profile along the length of the sample at the frequency

where there is a dip in the impedance versus frequency data for two instances in time.

 

Figure 8-25: LabVIEW program using Thermal TLINE model to indicate temperature
profile along the length of the sample at an instance in time where the ends of the sample
are at the maximum difference. The frequency of oscillation is at a value where there is a

dip in the magnitude versus frequency data

 

5
i
l

Figure 8-26: LabVIEW program using Thermal TLINE model to indicate temperature
profile along the length of the sample at an instance in time when there is a thermal wave.
The frequency is at the value where there is a dip in the magnitude versus frequency data.

149

8.5 Development and Curve Fitting to the Thermal Transmission Line Model

The development of the Thermal TLINE Model involved incorporating many
options in the program after impedance spectroscopy data is collected on a TE sample.
First, it must include the sample dimensions and optionally the probe positions. Next, the
analysis must work with the different types of TE samples such as a full TE module, an
inline module, or a single TE pellet. It must also accept different setup configurations
such as dangling the sample, thermally grounding one side of the sample, and including
the thermal properties of other possible materials in the module such as nickel traces and
ceramic end caps. Next, the program needs to be able to curve fit the data to find the
appropriate probe positioning. The probe positioning will account for the dip in the data
in single pellet measurements. The program must then be able to finally curve fit the data
(which involves adjusting the capacitance of the TB material) to find the lowest mean-
square-error (MSE). Once that data is curve fitted, output files are created for
documentation purposes.

The development of the Thermal TLIN E Model first involved creating a program
that would simulate the AC behavior of an electrical transmission line in the frequency
domain. Once this was established, the model was used to simulate thermal behavior in
the fiequency domain. Next, to establish a starting point for quickly estimating the
electrical resistance, thermal resistance, and thermal capacitance of the thermoelectric
samples, the RC One-Port Model is incorporated into the program. Finally, two curve
fitting routines are developed to adjust the voltage probe positions and find the correct
capacitance value to establish the lowest MSE between the model and the experimental

data.

150

8.5.1 Development of AC model for Electrical Transmission Lines

The first step in the development of the Thermal TLINE model was to simulate the
transmission line model for electrical transmission lines. A schematic of using a
transmission line in a circuit is shown in Figure 8-27 where an alternating voltage source

(V s) that has a source resistance (R5) is attached to a transmission line that has a load

impedance (RL).

 

Rs
n A
T.) V
Vs . . .
+ Transmrssron Line + R

Vm Vom L
A I'\

U

 

:X

 

Figure 8-27: Electrical circuit schematic using a transmission line

The equations for the transmission line used in Figure 8-27 are the Telegrapher’s

equations, which are again shown here.
Vin (x) = VL ~cosh(7~x) + [L -ZO -sinh(7-x)

8.106
lin(x)=:—f)'3inh(7'x)+11,-cosh(7'x) ( )

The user starts by knowing the values of the transmission line (R, G, C, and L) in
units per length along with the total length of the line. The user also inputs either a
current or voltage source along with a source resistance. Finally, the user inputs the load
impedance and the test frequency. For instance, to test an RG-58 cable, the user can
input an AC source voltage of magnitude 1 volt, a source resistance of 50 Q and a load

impedance of 50 Q. The line parameters for an RG-58 cable 1 meter long are as follows:

R = 19.4mQ, C = 98.4252pF, G = 0 Q", and L = 246.063nH. A test frequency of

151

300MHz is chosen. The program first calculates the propagation constant (7) and the
characteristic impedance (20). The impedance into the transmission line can be found as
follows where l is the total length of the transmission line.

Z- =20 ZL+Z°'ta“h(7'l) (3.107)
'" ZO+ZL -tanh(7-I)

 

The open circuit impedance (Z i0 ), where Z L —> oo , is found using the following.

20

Z - = —— 8.108
10 WW) ( )
The short circuit impedance (Z is ), where Z L —+ 0 , is found using the following.
Zis = 20 -tanh(7-l) (8.109)

The program divides the transmission line up into 100 pieces. By doing so, the program
can calculate the voltage and current into each piece using Telegrapher’s equations. This
can be used to map out the magnitude of the voltage and the phase of the voltage along
the length of the transmission line.

This program also calculates the expected resistance, capacitance, conductance, and
inductance values of the transmission line when terminated with a short-circuit and an
open-circuit. Using a short circuit test, the resistance and inductance can be found using

the following two equations respectively where a) is the frequency radians.

R =Re[ZiS] (8.110)
L=ELZLSJ (8.111)
(0

Using an open-circuit test, the conductance and capacitance can be found as follows.

G = Re[—i—] (8.112)

i0

152

Li
C=Im[i (8.113)

a)
Figure 8-28 shows the front panel view of the LabVIEW program that models the AC
characteristics of a transmission line. The program plots out three graphs. The first
graph is the magnitude of the voltage along the length of the transmission line. The
second graph plots out the phase of the voltage along the transmission line. The third
graph plots out the real voltage across the transmission line at the moment in time when

the voltage source (or current source) is at the magnitude and phase that the user set.

 

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Figure 8-28: Font panel view of the LabVIEW program modeling transmission lines

153

Another program was created to test the transmission line program by performing a
frequency sweep and observing the magnitude of the impedance of the transmission line
with a given load versus frequency, the characteristic impedance versus frequency, and
the propagation constant versus frequency. Again, a model of an RG-58 cable was used
for this test. The main test here was to verify that the impedance of the RG-58 cable
would remain 50 (2 over the fiequency sweep which it does and can be seen in Figure

8-29.

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dependence for the transmission line program. This figure displays an example of testing
an RG-58 cable.

154

8.5.2 Incorporation of RC One-Port Program

The impedance spectroscopy data always should provide a constant resistance for
frequencies below the pole and above the zero. The difference between the multiple
module configurations is the transition from low to high frequencies between the critical
frequencies. The RC One-Port model can estimate the resistance values that will give the
constant resistance values at the appropriate locations. For this reason, the RC One-Port
model is incorporated into the Thermal TLINE model. This provides a good starting
point for the user. From here the user can tweak the resistance values obtained fi'om the
RC One-Port model to get a better fit to the data. Once the resistance values are
acceptable, the next step is to identify the correct probe position and the thermal

capacitance value.

8.5.3 Curve Fitting the Probe Positioning

The dip in the data shown in Figure 8-21 is due to the probe position when
measuring a single TE pellet. The Thermal TLINE program has the option of searching
for the best probe position that will provide the lowest MSE between the curve fit and the
experimental data. This curve fitting routine divides the sample into many pieces and
then tries all possible combinations for the probe positioning (assuming that the probes
are placed on both sides of the middle of the sample). Afier all combinations are test, the

probe positioning that results in the lowest MSE is chosen.

155

With the probe position specified as shown in Figure 8-30 where L1 is the total
length of the sample and L1 and L2 represent the distance from the left and right side of
the sample, respectively. The positions are then converted to the percentage of the

overall length of the sample.

 

L1 L2
Figure 8-30: Diagram of probe positioning

The nansmission line model must include the entire sample, not just the sample between
the measurement probes. The values for the electrical resistance, thermal resistance, and
thermal capacitance must be known for the entire sample that is measured. This is
calculated by knowing the percentage of the total sample that is being measured and
using this to increase the component values as follows.

Total Value = W (8.1 14)
% of Sample Tested

Using the total values for the electrical resistance, thermal resistance, and thermal
capacitance, the Thermal TLINE model is applied as if the probes where at the ends of
the sample. This model divides the sample into 100 pieces and calculates the complex
temperature at each location. By superposition, the difference between the two probe
locations can be found using the complex temperatures at the appropriate locations. An
example of the program is shown in Figure 8-31. This figure shows what the data would

be if the probes were at the ends of the sample or at the user specified locations.

156

 

 

 

 

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Figure 8-31: Front panel view of the LabVIEW program "TLineTE Materialvi"
showing the results of probe positioning

8.5.4 Curve Fitting for Heat Capacitance

After the probe space is determined and the values for R1 and Rm are identified, the
next step is to find the capacitance that will best fit the experimental data. The goal is to
curve fit to a function where the capacitance has a non-linear effect on the mean-square-

error (MSE) between the curve fit and the experimental data. A technique based on the

157

 

Nelder-Mead simplex algorithm [54] was used to provide a fairly fast and easily
programmed method for finding the optimal capacitance value.

The Nelder-Mead simplex algorithm, first published in 1965, is an enormously
popular direct search method for multidimensional unconstrained minimization. This
algorithm has become one of the most widely used methods for nonlinear unconstrained
optimization. The Nelder-Mead method attempts to minimize a scalar-valued nonlinear
function of n real variables using only function values, without any derivative
information. This method may not be the fastest method (See Powell’s method),
however, this simplex method is frequently the best method to use if the motive is “get
something working quickly” for a problem whose computational burden is small.

A simplex is a geometrical figure consisting, in N dimensions, of N + 1 points (or
vertices) and all their interconnecting line segments, polygonal faces, etc. In two
dimensions, a simplex is a triangle. In three dimensions, it is a tetrahedron. This method
is designed for multidimensional minimization where the algorithm starts with a guess,
that is, an N-vector of independent variables as the first point to try. The algorithm is
then supposed to make is own way downhill through the complexity of an N—dimensional
topography until it encounters a (local, at least) minimum. The goal is to continuously
change the size of the volume of the simplex and diminish it until it is small enough to
contain the minimum value of the function within the desired accuracy. The operations
of the changing simplex involve contraction, expansion, and reflection to determine new
simplex corner points by linear combinations of selected existing corner points. More

details can be found in reference [54].

158

In this case of finding the optimal capacitance that gives the lowest MSE to a
specified accuracy, the problem is only l-dimensional. The simplex algorithm has been
modified to take into account that the MSE and the capacitance values are never negative.
An example of finding the capacitance value that will give the minimum MSE is depicted

in Figure 8-32 where the MSE is simply some function of capacitance, C.

MSE

 

Figure 8-32: Example MSE function versus capacitance values

The algorithm begins by making two guesses for the capacitance value. The first
guess comes from the capacitance value found by using the RC One-Port model which

will be called C1 . This capacitance value is then used in the Thermal TLINE Model and
the MSE is calculated, called M1. The second guess for the capacitance value is C2 ,
where C2 = C1 -1.1 . C1 is applied to the Thermal TLINE Model where the MSE, M 2 ,

is found. The idea of the algorithm is to quickly surround the optimal capacitance value
by the two guesses and then decreases the ‘distance’ between the two guesses to narrow
in on the optimal value.

Because the MSE never becomes negative, the direction of increasing or decreasing

the capacitance value must be kept track of, which uses the variable X. Also, the

159

improvement or degradation of the MSE is kept track up using the variable, T, where a

value of 1 indicates improvement while 0 indicates degradation. For increasing or

decreasing the next capacitance value by a specific factor, the variable Y is used. This

algorithm is an iterative process, which begins with the initial two guesses. The two

guesses are compared along with the corresponded MSE values. For the next two

guesses, C1 next will be the previous best guest, and C 2 next will be the calculated next

guess to try. A truth table, found in Table 8-2, provides the logic for determining the

variables Tum, X, Y, and Z based on the criteria: T, C1>C2, and M1>M2. ,

Table 8-2: Truth table for curve fitting routine

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T C1>C2 M1>M2 Next T X Y Z

O 0 0 0 1 -1 .2 C1
0 0 1 1 -1 -1 .2 C2
0 1 0 0 -1 -1 .2 C1
0 1 1 1 1 -1 .2 C2
1 0 0 O 1 41.2 C1
1 O 1 1 -1 -0.2 C2
1 1 0 0 -1 -0.2 C1
1 1 1 1 1 -0.2 C2

 

 

 

From Table 8-2, the value for the next C1 guess is the best guess fi'om the previous tries.

C'1 next 2 Z

The value for the next C2 is found using the formula shown here.

{CZnext = X'Y'GCI "CZDTZ for CZnext > 0
C2next = 0.4' Z

otherwise

(8.115)

} (8.116)

The truth table also provides formulas for Tum, X, and Y which are shown here.

160

O for M1 <M2

T = 8.117
next {I for M1>M2 ( )

X:{1 for (C1>C2)69(M1>M2)=false (8.118)
—1 for (C1>C2)€B(M1>M2)=true
={—1.2 for T=false (8.119)
—0.2 for T=true

From here, the algorithm can then be programmed into LabVIEW where it can interact
with the existing models also programmed in LabVIEW. The iteration terminates when
the difference in the mean-square-errors between the first and second guess is less than
lE-S. This algorithm is not optimized for speed or efficiency but does provide a curve
fitting routine that is relatively fast and achieves the desired accuracy for the purposes of

the Thermal TLINE model.

8.5.5 Final Program

The front panel view of the LabVIEW program for the Thermal TLINE fitting is

shown in Figure 8-33.

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Figure 8-33: Front panel view for the TLINE curve fitting LabVIEW program

8.6 Thermal Imaging

It is well known that applying electricity through a thermoelectric material will
cause a temperature gradient to develop. A good way to show this phenomenon is by
applying electricity to a TB material and observing the temperature profile with the use of
an infrared camera [55]. The use of an infrared camera will also help to verify the
dynamic behavior of switching the polarity of the electrical current through the sample

over time.

162

Long, 15mm, samples of p-type (ETP9) and n-type (ETN75) materials were made
by MSU and arranged into the configuration shown in Figure 8-34. The TE materials
were bonded together and to the nickel strips using a commercially available, low
temperature, “woods metal” solder. The TE module was then placed on a alumina plate
for support. A picture of the actual device is shown in Figure 8-35 (A). The TE samples
are very shiny. This shine will cause errors in the measurements of temperature with the
infrared camera because of various reflections from the surroundings and there are
different emissivity values for the n-type, p-type, and nickel traces. To eliminate the
shine and make everything at the same emissivity value, the setup was painted black
using non-electrically conductive paint (See Figure 8-35 (B)). Next, the TB module is
then placed inside a box where it is also painted black (See Figure 8-36). The experiment
was conducted at room temperature at atmospheric pressure. The infrared camera that

was used is shown in Figure 8-37.

 

15mm

 

    

_“

Figure 8-34: TE module setup for thermal imaging

163

   

(3)
Figure 8-35: (A) Picture of TE module. (B) Same device painted black

 

Figure 8-37: Infi'ared camera

The electricity applied to the TB module was a square wave pulse with a frequency
of 0.1Hz. A picture was taken at each second for a duration of 10 seconds and is shown

in Figure 8-38. Each picture has a graph of the temperature profile along a line placed on

the p-type sample These thermal images provide good evidence of a thermal wave
developing in the TB material as predicted by the thermal transmission line model. It is
also important to note that there appears to be electrical current crowding happening at
the corners of the pn interfaces because of the arrangement of the TE pellets. The effects

or pros and cons of current crowding are only noted and not discussed in this thesis.

 

 

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Figure 8-38: Thermal images

166

8.7 Comparing ZT Direct Measurements to Using Individual Measurements

ZT calculations are typically done by measuring the individual components of ZT
(electrical conductivity, thermopower, and thermal conductivity). Measuring ZT directly
through the impedance measurements of the TB materials have been compared to the
standard method and show excellent agreement. An example is shown using a LAST
sample (Ago,43Pb.ngi,2Te20). Figure 8—39 and Figure 8—40 show the temperature

dependant data for electrical conductivity and thermopower of this sample.

 

 

 

 

 

A

E

2 1200

m

V

3? 1000

>

"3

3 800

'2:

8

U 600

E

-: 400

H

O

.2

m 200 L l I l l l
300 350 400 450 500 550 600 650

Temperature (K)

Figure 8-39: Plot of electrical conductivity versus temperature for Ago_43Pb13Sb1_2Te20

167

 

-100

-120

-140

-160

-180

Thermopower (uV/K)

-200

 

 

 

 

—220
300 350 400 450 500 550 600 650

Temperature (K)
Figure 8-40: Plot of thermopower versus temperature for Ago,43Pblng1,2Te20

The electrical conductivity and thermopower at 300K is 1240 S/cm and -102.2
uV/K. The thermal conductivity of the sample was measured by calculating the power
supplied to the heater and dividing it by the temperature gradient across the sample
(taking sample dimensions and temperature probe spacing into account). This assumes
that all of heat generated by the heater flows through the material and radiation loss is
neglected. Using this method at 300K, the thermal conductivity of this sample was
found to be approximately 2.12 W/m-K. The resulting ZT at 300 K is then 0.18.

By performing a impedance measurements of the same sample, the ZT is found
directly with a value of 0.19 (see Figure 8-41). This shows excellent agreement between

the two different methods of obtaining ZT.

168

 

 

 

 

 

 

 

 

 

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A 0 Experimental Data A 2
g 6 ----- RC One-Port Fit
m 520 10 - (_— Thermal TLINE Fit
0 .
g a 0 'u
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g ———> 2 2
3 48010‘3 ' g
3 8
.2
C
s - -4
3» 46010
S
440105 ' ‘ -6
0.001 0.01 0.1 1 10 100

Frequency (Hz)

Figure 8—41: Plot of magnitude and phase of the impedance versus frequency for
Ago.43Pb183b1.2T€20.

Another example is shown using Ago,29Pb)3.6)Sbo,23Te)9. The plot for the

temperature dependant electrical conductivity and thermopower data for this sample is

 

 

 

 

 

shown in Figure 8-42.
1400 I I I l l l 140
A . A9029" I’11:.1515"0.287"19
g 1200 \ EQE74R1P253BotA_01_ HT a -150
5:; \ Measured by Adam Downey ;
a 1000 . ., 4426/2005 '1 "80 «an
.E. '-\ -200 e
‘5 o .3
'3 800 .. \«_ _220 g
8 1
g 600 .. ( T— ’240 E
'l: K
g -260 V
"' 400 I-
“ -280
200 l l -300
300 350 400 450 500 550 600 650

Temperature (K)

Figure 8-42: Plot of electrical conductivity and thermopower for LAST sample
Ag0.29Pb18.6ISbo.28T€19

169

Assuming the lattice contribution to the thermal conductivity at room temperature
is 1.3 W/m-K, and by identifying the room temperature value for electrical conductivity
to be 1295 S/cm, then the electronic contribution to the thermal conductivity is 0.886
W/m'K, making the total thermal conductivity about 2.19 W/m-K. The thermopower at
this temperature is -l37 pV/K making the ZT at 300K to be 0.333. A plot of the
impedance versus frequency is shown Figure 843, which indicates a ZT of 0.33 for this

sample. Again, this shows excellent agreement between the two methods of obtaining

 

 

 

 

ZT.
Ag Pb Sb Te
0.29 18.61 0.28 19
,3 EQE74R1 P253BotA
2.4 10 I f l I
-i 10
A 2.2103 I- --: _p, a “Viz; wfi—a _ 0
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‘ . zr = 0.33 a
5‘ - -40
e: _3 g
g 1.6 10 ..
wig—m - -50
1.4 10-3 l l I l -60
0.001 0.01 0.1 1 10 100
Frequency (Hz)

Figure 8-43: Plot of magnitude and phase of the impedance versus frequency for
Ago.29Pb18.613b0.28T619

170

Chapter 9: ZT Measurements at High Temperatures

9.1 Introduction

It is very desirable to be able to measure ZT on thermoelectric materials directly up
to high temperatures (800K). For temperature dependent measurements up to these high
temperatures, starting at room temperature, the UHT System was used with very little
modifications. Only four platinum measurement wires are needed for this measurement
along with using the Lock-in amplifiers instead of the Keithley nanovolt meters.

This section will discuss the effects of radiation losses for this particular
measurement. It will also evaluate the thermal losses due to the thermal conduction of
the measurement wires. Example measurements of TE Materials from MSU will be

shown.

9.2 Evaluation of Radiation Losses

Radiation losses are a major factor in the calculation of thermal properties of
materials at high temperatures. Radiation happens when there is a temperature difference
between the sample and the environment. Optical phonons within the sample can emit
photons which carry energy away from the sample. More states within the optical
phonon band are occupied at higher temperatures, and radiation increases. It is important
to investigate how large a factor radiation plays into the calculation of ZT. One
measurement in the calculation of ZT is using the high frequency AC signal applied to
the sample to get the electrical conductance of the sample without any Peltier effects.

This should not create a temperature gradient across the sample; rather the sample should

171

remain at the same temperature as the surrounding environment. If the sample should
rise in temperature due to Joule heating, the entire sample should rise in temperature
evenly. This would cause heat to radiate from the sample but would not affect the
measurement of electrical resistance. The other measurement for calculating ZT is to use
a very low frequency signal, which can be approximated as a DC signal, that would cause
a linear temperature gradient profile along the length of the sample. The hot side of the
sample will be slightly higher in temperature than the environment causing heat to be
radiated from the sample. The cold side of the sample will be colder than the

environment allowing heat to be radiated into the sample. A diagram of this is shown in

Figure 9-1.
Radiation Radiation
<———— ————>
P 1
‘—
Ts

P2

—>
-———>

 

Figure 9-1: Diagram for the steadyI state Tanalysis of radiation losses for applied DC
current

This effect happens at all temperatures, however, radiation is related to temperature
to the fourth power. The equation for the power of the heat radiated versus temperature

is shown here.

172

P=e-0'-A-(T4—TS4) (W) (9.120)

Where

A = Radiative area (m2)
P = Power radiated (J/s)
e = emissivity (e = 1 for blackbody)

0' = Stefan - Boltzmann constant (5.6703 - 10’8 W/m2K4)
T = Temperature of radiator (K)

Ts = Temperature of surroundings (K)

To examine the situation shown in Figure 9—2, assume that the temperature gradient
across the sample is 1 °C or less. The analysis here does not include Joule heating due to
contact resistance and assumes the emissivity is not a function of temperature. Also, it is
assumed that the temperature profile along the length of the sample is linear in position as

shown in the following equation.

TH = max temp hot side

TC = min temp cold side
L = Length

AT = T H - T C

T(x)=A—T-x+[Ts——A—7;) (K) (9.121)
L 2

This assumption will prove to be reasonable by the end of this section. Divide the sample
into four regions as shown in Figure 9-2 where the sample has been separated into two

halves along with also separating the ends of the sample from main body. Now the

power being radiated from the sample in each of the four regions can be solved for.

173

 

Region 1 Region 2 Region 3 Region 4

TC TC TH TH
P. ‘

 

17X

 

 

 

Figure 9-2: Sample divided into four regions. Linear temperature gradient along the
length of the sample.

Neglecting the end caps (regions 1 and 4), the power being radiated along the
length of the sample is shown here.

a=wMM
b = thickness

19de &3 (x) = e - a - 2 - (a +b)-(T(x)4 — T54) (W) (9.122)

Using the chosen temperature profile along the length of the sample, the equation for

power radiated now becomes:

4
Prad2&3(x)=e-0'-2-(a+b)- (if-HP J33] —TS4 (W) (9.123)

Taking the derivative of the power radiated will indicate if the power radiated is linearly

proportional to the position along the sample.

174

17"

 

4
d d AT AT 4
Eprad2&3(x)=:d; e-a-Z-(a+b)- (7°x+(T ‘7]] —TS ]

(9.124)

 

= e'a'zja‘ib) -[AT-(2-x—L)+2-T_, -L]3 -AT

L
Typically for this measurement, the temperature gradient across the sample will be kept
small (below 1°C) which will allow the following to be true:

When the above statement is true, the derivative of the power radiated now becomes:

iPradU)“ (0+b)°

3
13.0162 ~AT 9.125
dx 3 ( )

 

The above equation shows that the derivative of the power radiated is not dependant upon
the position. This indicates the power radiated is linearly proportional to position in
regions 2 and 3. This is helpful in that the radiation loss will affect the entire length of
the sample evenly without altering the linearity of the temperature profile.

Now the total power radiated from each region of the sample can be solved for.

The total power at the end of the sample on the cold side, region 1, is as follows:
_ _ 4 4
fi—e-a-a-b-(Hx—O) —Ts ) (W) (9.126)

The total power on the cold half of the sample not including the end of the sample, region
2, is as follows:

L/2
1E2= j9°0'2°(a+b)-(T(x)4—TS4)-dr (W) (9.127)
0

The total power on the hot half of the sample not including the end of the sample, region

3, is as follows:

175

L
P3: je-a-2-(a+b)-(T(x)4—Ts4)-dx (W) (9.128)
L/2

The total power at the end of the sample on the hot side, region 4, is as follows:
P _ _ 4 4
4—e-a-a-b-(T(x—L) —TS ) (W) (9.129)
For the measurement of ZT, the difference in power being radiated from the hot

side compared to the cold side must be known. This will give an effective power

radiated. This can be done as follows:

Pradefir =(P3 +P4)-(11 +P2) (W) (9.130)

1
Pradefl. =Z'e'O-‘AT'TS°

9.131
(L-ATZ~(a+b)+8-L°TSZ-(a+b)+a-b-(4-AT2+16-T52) ( )
Again, the following assumption is made:
AT2 << T32
When the above statement is true, the effective power radiated is:
Pradefl e 2-e-o-AT-Ts3 -(L-a+L-b+2-a-b) (W) (9.132)

Using the temperature gradient and the effective power radiated from the sample, an
effective radiation resistance can now be found to be:

_ AT _ AT
efl Pradefir Zieo-AT-Ts3'(L-a+L-b+2'a'b)

 

Rm; (9.133)

1
eff 2-e-a.TS3-(L.a+L-b+2-a-b)

 

Rrad (K/W) (9.134)

Therefore, for small AT , the effective radiation resistance is not dependant upon AT .

176

9.2.1 The Effect of Radiation on ZT Measurements

The simplest way to include this new radiation resistance is to go back to the RC
One-Port Method and place this added resistance in parallel with the thermal resistance of

the sample due to conduction. Instead of AT across the sample being

AT = a ' I'Tamb “RThermal (9-135)
The new AT will be

RThermal . RRad (9.136)
RThermal + RRad

 

ATnew = a'I'Tamb '

The ZT measured, which includes radiation, can be calculated by

a - ATnew

9.137
R0,] 1 )

ZTRad =

Let Z Tideal be the ZT value without radiation losses. Then the percent error between

the ZT with radiation losses compared to the ZT without radiation losses is as follows:

 

 

 

 

 

. _ A _
Percent Error = ”“1901 Zde 100% = T ”new 100%
ZTideal AT
Rthermal ' Rrad
R _
: thermal Rtheraml + Rad 400%
Rthermal
R
Percent Error = [1— rad ]-100% (9.138)
Rthermal + Rrad

If RThermal = R Rad , then the ZT measured will be exactly half of the correct value

(50% error).

177

9.2.2 Example Calculation (MSU TE Materials)

Currently for the thermoelectrics project at MSU, TE pellet dimensions arc: length
= 7m, width = 5m, and thickness = 5m. For high temperatures, assume that thermal
conductivity of the sample is about 1 W/mK (this is reasonable based of many thermal
conductivity measurements). It has been found experimentally that there is an
improvement in the ZT measurement by making the sample smaller, which involves

cutting the pellet in half to the dimensions shown below.

Table 9-1: Sample specifications

le Dimensions
m

m

m

 

 

henna! Cond. (WImK) 1
Thermal Resistance (KNV) 333.33

 

 

 

 

 

The emissivity of the samples are unknown so a value of 1 (worst case scenario) was
used in this example. With this sample size, plots were created to estimate the amount of
radiation loss and what the thermal resistance is due to radiation. An example of the
temperature profile along the length of the sample at 300K is shown in Figure 9-3.

Similar profiles will exist at higher temperatures.

178

Temperature Profile

300.6

 

300.4

300.2

300.0

299.8

Temperature (K)

299.6

 

 

 

299.4 .
0 0.001 0.002 0.003 0.004 0.005 .

Ele

Figure 9-3: Temperature profile at 300K where AT = 1

The effective radiated power versus a small range of ATs for various surrounding
temperatures is plotted and shown in Figure 9-4. The effective radiation resistance versus
DT for various surrounding temperatures is plotted and shown in Figure 9-5. Finally, the
plot of effective radiation resistance versus surrounding temperature (for small ATS) is

shown in Figure 9-6

179

 

 

 

 

 

 

 

MRS
g 0.0204 .00
g e 'INNK!
3 a. ' 400K
g 0.0151 ,0 I’
g .0 -' Asoox.
: o I' l
g .0 l.- Ioamx
‘5 0010 o’ .I' ‘I-700K
é o. I'- a... ' flux
0 o I .00 ~9
I? 0005 ’ l' o"
m . I 0.... .0 ‘AA“‘

9 e
I... A“AA‘.......QO :
0mm “‘IIII-II.. I
0 1 2 3 4 5
DflhT

 

Figure 9-4: Effective radiated power versus AT for a specific example

 

B’fective Radiation Resistance (KM!)

 

 

 

 

 

1.
E450“ IIIIIIIIIIIIIIIIIIIIIIII
1':4flmr
‘ l
Igaam. lmmK!
. r
F ASOOKI
=2flm4 l
g IommKl
I g 2000* oooooooooooooooooeooooooo I‘m“;
: ‘E 1500‘ 'oeooxIl
i 5 1000i AAAAAAAAAAAAAAAAAAAAAAAAAI M“ I
I 0
j 5 gm ooeoeeoooooeeoooeoeoeooe
1 “J o '0'..."".""""."" I
0 1 2 3 4 5 '
‘ umar

Figure 9-5:

180

Thermal resistance due to radiation for specific example

8

Radiation Resistance (KIW)

 

8

333

2500 -
2000 .
1500
1000

Reeletanee (KIW)

 

 

 

300

Figure 9-6: Radiation resistance versus temperature for specific example (AT is small)

Figure 9-5 and Figure 9-6 illustrates how the thermal resistance due to the radiation
loss compares to the thermal resistance of the sample through conduction that was
calculated in Table 9-1. For high temperatures, they do fall into the same magnitude

range (above 500K, both values are below 1000 K/W). This will dramatically affect the

ZT measurement.

If a comparison of measuring ZT at 700K between the ZT including radiation

compared to the ZT without radiation is made, the percent error can be found to be as

follows:

Percent Error (at 700K) = (I —

400 500 600
Temperature (K)

370
333+370

181

)-100%z47%

 

This indicates that for material properties chosen, there is potentially an enormous error
because of radiation in the ZT measurement for this sample. Here the measured ZT value

would be 47% less then values indicated in literature.

9.2.3 Example Calculation (Small Constantan Sample)

ZT has been measured of constantan wire. Will radiation effect this measurement
if the sample size is small? In the range of 300K to 800K, the thermal conductivity of
Constantan ranges from 20 to 40 W/mK. For this example, chose an average value of 30
W/mK to be constant over the temperature range. The emissivity of a constantan metal
strip is e = 0.09 [56]. This example will use a small cube of constantan with the
following dimensions: length = 6m, width = 0.5mm, and thickness = 0.5mm. With
these dimensions, the thermal resistance due to conduction is 800 K/W. The same linear
temperature profile that was used in the previous example will be used here. The
effective radiation resistance is plotted versus surrounding temperatures and is shown in
Figure 9-7. This plot shows that even at 800K, the thermal resistance due to conduction

is much smaller than the effective radiation resistance of the sample.

182

Radiation Resistance (KIW)

1000000

 

1 00000

Resistance (KM!)

 

 

1 0000
300 400 500 600 700 800

Temperature (K) i

 

Figure 9-7: Effective radiation resistance versus temperature where AT = 1

If a comparison of measuring ZT at 700K between the ZT including radiation

compared to the ZT without radiation is made, the percent error can be found to be as

follows:

_ 44000
800 + 44000

 

Percent Error (at 700K) 2 [I ]-100% = 1.79% (9.140)

This indicates that the ZT measured with radiation losses is 1.79% lower than the

expected ZT from literature values.

9.2.4 Can a Correction for Radiation be made to the calculation?

The radiation resistance can be assumed to be in parallel with the thermal resistance

due to conduction.

183

 

a(a.1_TamboRThermal'RRad]

 

 

- AT R + R
ZTRa d = a R new : Thermal Rad (9.141)
0 — I R0 - I
Let X be the correction factor.
ZT Rad ‘ X z ZTIdeal
X = RThermal + RRad :1 + RThermal (9°142)

 

RRad RRad

From here, it is clear that more information about the TB material, such as the
thermal conductivity, is still needed in order to get the ideal ZT value. MSU does
measure the thermopower of the sample, which may be enough information to use with
the ZT measurements and extract the thermal conductivity. The ZT measurement would
also require the emissivity to be a known value. This may be accomplished by painting
the sample black to make the emissivity equal to ~l . However, a lower emissivity value
would be preferred. This shows that radiation effects at higher temperature can adversely
effect this measurement. This also suggests that coatings could help ZT values at higher
temperatures where radiation losses outweigh conduction losses. This topic will need

firrther development and is not discussed here.

9.3 Thermal Conductivity of the Measurement Wires

For high temperature measurements, a TB sample is mounted in the UHT System
so that the material is suspended by two of the measurement wires that attach to the ends
of the sample. The wires are stuck to the stage using silver pasted. Small diameter

platinum wires (dia = 0.001 inch) are used to mount the sample. The wires must have a

184

 

thermal resistance that is much higher in magnitude than that of the sample. If the
thermal resistances are comparable, then the ZT measurement will be inaccurate. Figure
9-8 shows a typical MSU TE sample being mounted in the UHT System. The wires are
at least 1cm long before they are thermally grounded to the stage. The stage is assumed
to be at the same temperature as the fumace. Heat will flow from the stage to the cold
side of the TE material, and it will flow from the hot side of the TB material to the stage.
Here, an example will be given to approximate the thermal resistance of the measurement

wires and determine if they cause a significant error in the ZT measurement.

TE Sample

 

Stage

(B)

 

(A)
Figure 9-8: (A) Sample mounted in UHT System for ZT meter measurements. (B)
Diagram of the sample dangling from the measurement wires attached to the ends of the
sample.

185

The thermal conductivity at 700K for Platinum is ~72 W/mK. The wires attached
to the ends of the sample are the shortest at about 1 cm in length. With the wire diameter

at 25.4 pm, the thermal resistance of this wire is about

 

Rpm," =i(m'K]- 0'01 m e274,000 5 (9.143)
P‘ 72 W (25.4E—6]2 m2 W
7!. ___——
2

Table 9-1 shows that a typical MSU TE sample would have a thermal resistance of about
333 W. This is three orders of magnitude smaller than the resistance of the wires.
Therefore, thermal losses up the measurement wires can be neglected for this
measurement.

ZT measurements are also taken at room temperature using copper wires. The
wires in this case are also 25.4 um in diameter but the thermal conductivity is 401
W/mK. The wires for these measurements are at least 2 cm in length. The thermal

resistance due to this wire is as follows.

 

Rpm," =_—__1 {—m’K]. 0'02 m e100,000 5 (9.144)
C“ 401 W (25415—112 m2 W
”a ___—___.
2

Here, a typical MSU TE sample thermal resistance would again be about 3 orders of
magnitude less then the measurement wires.

Finally, for a ZT measurement on constantan wire at room temperature, the thermal
resistance of a 508 um diameter constantan wire that is 6 mm in length and with thermal

conductivity of 22 W/mK would be

186

 

 

 

1 m - K 0.006 m K
2 J

W (50813-6 m2
7t- _—

Here, the resistance of the constantan sample compared to the measurement wires of
copper is only two orders of magnitude difference. This can lead up to a 2% error, which
is still tolerable for this measurement. However, these types of calculations must be
made in order to insure that the ZT measurement is accurate when measuring a sample

and any temperature.

9.4 Example Measurements of Z T up to Higher Temperatures

Direct ZT measurements have been made at higher temperatures. This was
accomplished by suspending a single TB in the UHT System and setting the temperature
to higher values in the range of 300K to 700K. The UHT System would be raised to a
desired temperature and allowed to stabilize for at least one hour. Monitoring the
electrical resistance of the sample could identify temperature stabilization. The TE
samples that are tested typically have strong temperature dependence for electrical
conductivity and when the electrical resistance of the sample stabilizes, it is assumed that
the temperature of the system has stabilized.

Presented here are three examples of comparing ZT direct measurements to using
the standard technique of measuring each component of ZT individually. All examples
show that the ZT direct method deviates from the standard method more and more as the
temperature increases to the higher temperatures. The discrepancies in the data are likely

due to radiation effects. The first example shows a direct comparison between using the

187

standard method for obtaining ZT and the ZT direct method. It is shown that the ZT
direct method does not reach as high of ZT values as the standard method. The second
example shows that the ZT direct method may be less susceptible to radiation than the
standard method, where thermal conductivity (including radiation loss) is measured by
knowing the heater power on top of the sample and the temperature gradient across the
sample (the assumption is all heat flows through the sample). The final example uses p-
type SiGe sample. In this example, using a reference emissivity value for SiGe helps to

correct the ZT data collected by the AC technique.

9.4.1 Comparing ZT measurements Using AngSbTe Sample

The sample, EQE74R2P253TopC (Ago,39szo,MSbo,27Te2)) was measured using the
ZT direct method at several high temperatures. It was then compared to an estimated ZT
values obtained by the standard method. The temperature dependant data for electrical

conductivity and thermopower of this sample is shown in Figure 9-9.

188

 

 

 

 

 

 

A90.39""20.134$bo.27“"21
EQE74R2P253TopC
A 1800 I I I I I I -140
g 1600 - -160
i 1400 180 Q
.E: 1200 . -200 g
g '6
E 1000 .4 -220 3
CD
5 800 - -240 {:4
'5 <
.E 600 - -260 5
§ 400 - -280
[a]
200 I I I -300
300 350 400 450 500 550 600 650

Temperature (K)

Figure 9-9: Plot of electrical conductivity and thermopower versus temperature for
EQE74R2P253TopC

The thermal conductivity was estimated assuming the same lattice contribution to thermal
conductivity as the sample published in science for the LAST materials (KF2242R3C
AgogrngingTezo). The temperature dependant total thermal conductivity of this
published material is shown in Figure 9-10 along with the polynomial curve fit to the
data. The temperature dependant electrical conductivity of this sample was measured and
is shown in Figure 9-11 along with the polynomial curve to fit the data. From here, using
the Wiedemann-Franz Law were the Lorenz number is estimated to be 2.28E-8 WQK’2
(discussed in Chapter 2 and in reference [7]), the lattice contribution to this total thermal
conductivity can be found using the electrical conductivity and is shown in Figure 9-12

along with the curve fit to the data.

189

 

 

 

 

 

 

 

 

 

 

 

AgO.86Pb18$bTeZO
KF2242R3C
2.6 .
2 4 Y = MD + er + M8‘x8 + M9‘x9
' MO 49392
g 2-2 M1 0009072
g 2 M2 334059-06
5 13 M3 2.5846e-09
a .
.5 15 R2 0.99927
4'
1.4
1.2

1
300 350 400 450 500 550 600 650 700
Temperature (K)

Figure 9-10: Plot of measured thermal conductivity versus temperature of KF2242R3C

 

 

 

 

 

 

 

 

 

 

[6]
Ag0.86pb185b1’920
KF2242R3C

“ 2000
E l . Y = M0 + M1'x + M8'x8 + M9‘x9
a 1 M0 7729.9
3* 150° 1 M1 -3o.911
:5 . rnz (l043962
‘g 1 M3 -2.1641e—05
2 100° 1 R2 0.9992
0 u
c) .
ig 500 I
t: .
H
0 I:
2
m lillljlllllllllllllllllllllllllllllllll

 

 

300 350 400 450 500 550 600 650 700
Temperature (K)

Figure 9-11: Plot of electrical conductivity versus temperature for KF2242R3C

190

A90.8¢s"b183bT"20

 

 

 

 

 

 

 

 

 

 

 

KF2242R3C

Y = M0 + M1‘x + M8'x8 + M9‘x9

M0 4.9392

A M1 0026696

E M2 7.3818e—05

~ M3 -9.7649e-08

5 M4 4.9341e—11
Q

2 R2 1
1::
2

2

 

0.7
300 350 400 450 500 550 600 650 700
Temperature (K)

 

Figure 9-12: Plot of calculated lattice contribution to thermal conductivity versus
temperature

By assuming this lattice contribution to the thermal conductivity and knowing the
electrical conductivity of this sample, we can again apply the Wiedemann-Franz Law to
obtain an estimated thermal conductivity of the sample with will be used in the standard

ZT calculation.

191

Pb Sb Te

A90.39

 

20.64 0.27 21

EQE74R2P253TopC

2.4 IIIiIlIIII'IIIIlIU‘I'IIIIIIIYYIIVY‘.

8 2-2 .- 1
iii : 1
.§ 2 .- ':
*6 : :
a 1.8 _- 1
>9 : :
g 1.6 -_- 1
3 : :
_1.4 "' u-
S I 2
I312 1 J
3 : :1
1 hllllllllllllllllllllllllllllllllll.

 

 

 

300 350 400 450 500 550 600 650
Temperature (K)

Figure 9-13: Plot of calculated thermal conductivity versus temperature for
EQE74R2P253TopC

The sample, EQE74R2P253TopC, was also measured for ZT directly using the
impedance of the sample at multiple temperatures. The results of the frequency sweep
are shown in Figure 9-14. A plot of the ZT calculations using both methods is shown in
Figure 9-15. These data show that ZT direct method measures lower values than the
standard method. It also shows that the deviation between the data increases with
increasing temperature. It is assumed that this discrepancy between the two methods is

caused by inclusion of radiation losses in the ZT direct method.

192

 

 

 

 

 

 

 

 

A90.39""20.643bo.277°21
EQE74R2P253TopC
0'03 I I I —I I i
A 0.025 .700K
C: A A A
I: A
g 0.02 I- 600K A
no 4) . . . . . ‘
8. o A
g 0.015 I 500K 9 A A A A ZT=0.70
0 IIII. o. AAAAA AAAAAA
'3 l I o zr—— 0.78
.. 0.01 . °oo¢oooooooooo
ED . 27 = 0.67 I
g lllllllllllll
0005 .3021: O O O 27‘: 035
."'OOooooooooo'ooo
o I I l I
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

Figure 9-14: Plot of direct ZT measurements using magnitude impedance versus
frequency at multiple temperatures for EQE74R2P253TopC

 

 

 

 

A90.39Pb20.645bo.27“21
EQE74R2P253TopC
1 h I U U ' I I I ' I l I I ' U I ' ' U I I I I I I l U I U ' d
0.8 - . -
I . I
I . d
0.6 - "
l- : :
N . I
0.4 '- "
I C I
I l
0.2 - "‘
o I I l l I ll L l l l l l l L. I l I l l l l I l l l I 14 ‘
200 300 400 500 600 700 800

Temperature (K)

Figure 9-15: Plot of ZT versus temperature. (Line) Estimated ZT using standard
measurements of electrical conductivity, thermopower, and thermal conductivity. (Dots)
Direct ZT measurements using impedance of the sample

193

9.4.2 Comparing Radiation Losses using PbTe with Nanoparticals of PbS

The second example uses a PbTe structure with nanoparticals of PbS. The

frequency dependant impedance data for multiple temperatures is shown in Figure 9-16.

This sample was then measured in the HT system for temperature dependant data for

electrical conductivity and thermopower as shown in Figure 9-17. The system also

measured the thermal conductivity of the sample (including radiation affects) by

measuring the power to the sample heater and measuring the temperature gradient along

the length of the sample (assuming all heat produced flows through the sample). This

data is shown in Figure 9-18.

The rapid rise in thermal conductivity measurements is due

to the radiation losses, which have a temperature dependence of T3.

 

 

 

 

 

- 0
Pbo.955"0.05Te PbS 16/o
JAE143P226-B 0
®QXQd- ' bfiggfiafiaflgfia
a '9 L] «.1 C ‘2); _ -
A 0.015.... 958 . 3 5
g 14.986mQ <> ‘ . -‘ f ‘ ' .1,
o ' :13 ‘ G 2'
U ‘ ‘ 3. m
= -. f . a
a .. . .
a E ‘ - -10 5'
g 0.01 - ’ :3 ZT = 0.694 @ 600K .5
5 \ 3....-999-09-9 9-9 9-09 8.
Q I- I - I 3 a 1:. 8343511152 E
a 7.9844mQ I. ’ - -15 n
g S g 21“ = 0.57 @ 500K 5:
50 0.005 - ill-.I-Ill-II-I II III 3
5 50929de _20 ‘5
ZT = 0.24 @ 300K
" ' "' “’ "' O-o e-e 0-0 a o-o e-e 0-0 0-0 0
111634“) 1.7474mQ
0 7 l l l l I _25
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

Figure 9-16: Plot of high temperature direct ZT measurements using magnitude

impedance versus fiequency.

194

 

Pbo.9ss"o.05T°'Pbs 1 6%
JAE143P226-B

 

3000 I I T I T l l .80
A B -1 400
E 2500 .— “L
g 2000 I- .\-. L. - _140 a
’5 -. E- »——> 8
3 1500 - “7 x: " 46° 3
= ’ . “2 a
5 +———'~ ‘ ”:33 - -180 1
a 1000 - 0 "i U E
.0 L‘\_ -. .1 -200 \
5 . ‘1 U»: 5
E 500 it"‘No- B‘s .. .220
m " e-..”
.4 .240
1 1 1 1 1 1 1

 

 

 

0
250 300 350 400 450 500 550 600 650
Temperature (K)

Figure 9-17: Plot of electrical conductivity and thermopower versus temperature for
JAE143P226-B

 

 

 

 

PhD-”SnofisTe-Pbs 16%
JAE143P226-B
I T 1 l l I I
2.4 - -'
x A
E a
:3 2.2 - . -
1: .
:g 8 z .
u 5 \‘~ ,/
5 '5 2 — I" .1
1: fl o”
5 a 5 ’
“a,“ ,
E-‘a’ 1.8 . -
=
E L'L
1.6 h 1
J_ _1 1 1 1 1 1
250 300 350 400 450 500 550 600 650
Temperature (K)

Figure 9-18: Plot of measurement thermal conductivity (including radiation losses)
versus temperature for JAE143P226—B

The ZT measured for both methods is shown in Figure 9-19. This data shows that

room temperature measurements agree but high temperature measurements disagree with

195

 

 

the ZT measuring using the direct method having a higher value. Although it is assumed
that both techniques suffer from radiation losses, here it indicates that the radiation effect
may have less of an impact on the ZT direct method that using the standard method. It is
the radiation effect that prohibits thermal conductivity measurements to be made in this

fashion. However, using the ZT direct method may prove to be useful in that the effect is

less in this method.

 

Pbo.958l‘lo.05Te-Pbs 16%
JAE143P226-B
1 F I I I I I I
g 0.8 — 4
O
-J o
g 06 - -
Hg. 3395.53.38
N '3 D '
I: 0.4 - :1 ' -
é .
.E’. i
g 0.2 - -

0 1 1 1 1 1 1 1
250 300 350 400 450 500 550 600 650
Temperature (K)

 

 

 

Figure 9-19: Plot of ZT versus temperature. (Squares) ZT calculated using the standard
method. (Circles) ZT direct measurements from impedance of the sample.

9.4.3 Testing ZT of p-type SiGe and Correcting for Emissivity

The third sample tested for high temperature ZT measurements was a p-type
Singezz sample provided by Ames Laboratory at Iowa State University. Platinum wires

were resistively welded to the sample shown in Figure 9-20(a). The sample was then

196

 

 

 

suspended in the UHT System as shown in Figure 9-20(b). A digital flipping technique
(discussed in a later chapter) was used to collect resistor versus frequency at various
temperatures and is shown in Figure 9-21. The electrical resistivity of this sample was
compared to the data provided by Ames Laboratory and is in excellent agreement as

shown in Figure 9-22.

 

:. ~L '
‘ -
~4sfir-r-x‘»

 

(a) (b)
Figure 9-20: (:1) Si7gGe22 Sample with platinum wires (dia = 0.003 inch) resistive
welded to sample. (b) SiGe sample suspended in UHT System.

197

Slnee22 (Ames Labs)

UHT System using Digital Flipping
"3012006 A. Downey

 

 

 

 

25 r I I

20 '- -
Cl
5 900K
0 800K
8 M 700K
.2 I—Ik—i—o- 600K
8
n: W 500K

10 ' 400K "

M 300K
5 1 1 1 1
0.001 0.01 0.1 1 10 100
Frequency (Hz)

Figure 9-21: Resistance versus frequency at various temperatures of Si7gGe22

2.4

 

: Experimgtal

2 iuAmes Lab ' —— I:

1.84 — .e - .—~n— _,

)
_N
N

 

1.6 ._- ~ * - 7.0---- i L, ._
1.4 (w ~~ ~.D~ ,, k L, , i
1.2 .. a. — a 7

1.
300 400 500 600 700 800 900 1000 I

Temperature (K)

Resistivity (Ohm-cm
u

 

 

 

Figure 9-22: Measured resistivity of Si73G622 sample compared to Ames Lab
measurements

198

 

 

By taking the RDc/RAC and subtracting one, the uncorrected ZT value of the sample
can be found. The first correction to the ZT value is to account for the thermopower of
the platinum measurement wires as discussed in previous sections where the
thermopower of both the sample and the measurement wires must be known. This then
compared to reference data for p-type SigoGCZO data [57] due to a lack of data published
for Singezz. The results are shown in Figure 9-23 where it is again clear that the
measured ZT value deviates from the traditional ZT measurement method at the higher
temperatures due to radiation loss. However, a correction can be made to the ZT value
by taking into account the sample dimensions and the emissivity of SiGe. A highly
doped sample of SiGe was published to have an emissivity value of 0.7 over the
temperature range tested [58]. When this value is used along with the correction method
discussed previously, the data more closely matches reference data as shown in Figure
9-24. There is still a slight deviation at the highest temperature tested which could be due
to surface roughness, emissivity value changing versus temperature, or the fact that the

reference data is for SigoGCzo

199

 

 

 

 

 

_— c’SESrre'c‘t chT/Ieasuréfifinivwe?
‘ p-SiGe Reference i ‘
13 Raw Collected ZT i

 

 

0.7
0.6 A _. __ -L‘L“

 

 

0.5 LA 1 ‘i
0.4 #_.;L
0.3

0.1 4 9 -L , I

 

 

 

300 500 700 900
Temperature (K) i

 

Figure 9-23: ZT values measured versus temperature compared to p-type SisoGezo. This
plot shows the raw ZT value collected and the ZT correct for the measurement wires.

__ IEiGéReféEfi’ce ‘

 

 

 

 

 

l
‘ , oZT Comected for Radiation i
l 0.7 L* — ,_,,_,_ ******
. 5.- L _- _ ___, __-__
0 ‘ A
w—_m—3r_
O
0.4 — v ___fi; fi — 4
n O
0.3 —— A * 0 ¥ — — _—
1 02 -emwmroe e — e he )
0.15—9h_“e__e_
l
00¢F
300 500 700 900
Temperature(K)

Figure 9-24: Measured ZT of Si7gGe22 that has been corrected for radiation losses using
‘ an emissivity value of 0.7

200

 

Chapter 10: ZT of Constantan

 

10.1 Introduction

There are many researchers involved in thermoelectrics, however, an accepted
reference material with high ZT values has not been established for confirming
measurements of thermopower and ZT. One possible reason for this is the difficulty in
manufacturing identical thermoelectric samples. This presents difficulties in verifying 1'
new techniques for investigating thermoelectric material properties except by having a
sample measured by many different companies in a “round-robin” approach.
Thermocouples, however, have been well characterized and their output voltage versus
temperature has been published by NIST (National Institute of Standards and
Technology). Presented here is a suggestion to use constantan (copper 55%, nickel 45%),
which is used in a Type-T and Type-E thermocouple, as a reference material because it
has a relatively high thermopower and low thermal conductivity compared to other
thermocouple materials (copper, iron, chrome], alumel, platinum). By using published

data from various sources, it is possible to calculate the ZT of constantan. The ZT is

 

large enough to be measured by the ZT meter and can be used as a reference material.

10.2 Establishing Constantan as a reference material

NIST provides the output voltage versus temperature for a Type-T thermocouple
where one material is copper and the other material is constantan (See Figure 10-1). The
thermopower of a Type-T thermocouple can be found by taking the derivative of this

output voltage with respect to the temperature shown in Figure 10-2. The thermopower

201

 

of a thermocouple is equal to the difference in thermopowers of each of the wires shown
in equation the equation below. In this case, copper has a positive thermopower and
constantan has a negative thermopower.

S Type T = SCopper — SConstantan (10.146)
The thermopower of copper has been published by Roberts [59] where the data and
polynomial curve fit to the data is shown in Figure 10-3. This data is used to extract the
thermopower of constantan shown in Figure 10-4. This thermopower of constantan can
be used as a reference for other systems that measure thermopower directly such as
MSU’s High Temperature (HT) system [21]. See Appendix B for thermopower and
electrical conductivity measurements made with MSU’s HT System. The electrical
conductivity of constantan is 52 uflcm according to Goodfellow with temperature
coefficient of +/-0.00002 (K'l). The thermal conductivity of constantan comes from two
published sources, one for low temperature values [60], and the other for high
temperature values [61] (see Figure 10-5). The figure of merit, ZT, for constantan can
now be found using equation the equation below and the results are shown in Figure

10-6.

ZT=a "’1 (10.147)

 

202

 

 

 

N
U"!

0
300 350 400 450 500 550 600 650 700

Temperature (K)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 Y = M0 + M1‘x + M8*x" + M9‘x9
: M0 -52.523572
A 20 -l
> . M1 0758629334
E, : M2 -0.00496786397
d
g, 15 4 M3 1.71724575e-05
g 1 M4 -2.75241767e-O8
g : M5 -2.66892886e-12
«5 1° 1 M6 9.15755819e-14
9 1 M7 -1.61535312e—16
3 5 ; M8 1.24985525e-19
: M9 -3.79293207e-23
- R 0999999999
"' I—____—.l

Figure 10-1: Output voltage for Type-T thermocouple from NIST

(1065

(106

(1055

AmV/AT

(105
(1045

(l04

lllllllllllllllllJllllu

 

300 350 400 450 500 550 600 650 700

 

 

Temperature (K)

Figure 10-2: Thermopower of Type-T thermocouple from derivative

203

5"
or

Y = M0 + M1‘x + M8‘x8 + M9‘x9
0183706027
000596025885
-3.93945306e-07
3.89026595e-15
0999992681

 

UI

 

P
or

 

 

A

 

 

w

Thermopower (uVIK)
p w
01 UI

N

 

1.5 '
200 300 400 500 600 700 800 9001000

Temperature (K)

 

Figure 10-3: Thermopower of copper from Roberts (squares) with curve fit on top (line)

  

  

 

  
  
  
  
  
  
  
  
  
  
   

 

 

 

 

 

 

 

 

 

 

 

 

-35
I Y=MO+M1'x+... M8‘x°+M9‘x9
: M0 -996.557489
2 '40 1 M1 13.9463863
a : M2 -0.0801583144
E .45 1 M3 0000222554832
; . M4 -2.45151607e-07
g 3 M5 -2.17858754e-10
° ‘50 1 M6 9.67057136e-13
g : M7 -1.11899956e-15
'15 _55 _- M8 5.37574211e-19
- M9 —7.46944001e-23
60 H R 0999999984

300 350 400 450 500 550 600 650 700
Temperature (K)

Figure 10-4: Thermopower of constantan based on published thermopower of copper
and NIST data for Type-T thermocouple

204

Thermal Conductivity (W/m-K)

.5
O

 

u
or
I

u
C
l

N
01
l

N
o
l

 

15

Y=M0+M1'x+... M8‘x°+M9‘x9

 

25.1070348

 

00329667566

 

-0.0032442501

 

3.984124076-05

 

-2.299365728—07

 

7.63354855e-10

 

-1.5345749e-12

 

1 .846305416-15

 

-1.22465673e-18

 

3.44812305e-22

 

 

l l I I l J

 

 

0

100 200 300 400 500 600 700
Temperature (K)

0999682374

 

Figure 10-5: Thermal conductivity of constantan from two published sources

21'

 

 

 

Y = M0 + M1‘x + M8*x° + M95?

 

0.0426568885

 

0.00562630239

 

-8.228572256-05

 

4.57839727e-07

 

-1.154681Se-09

 

8.001596466-13

 

2.55604704e-15

 

-6.7589713Qe-18

 

6.39615537e-21

 

-2.246215168-24

 

 

 

 

0.12 I l l l
M0

0.1 - - M1
M2

0.08 I- - M3
M4
M5

0.06 - - M6
M7

0.04 - - M8
M9
R

002 I l l l

200 300 400 500 600 700

Temperature (K)

Figure 10-6: Calculated ZT of constantan

205

0. 999999999

 

10.3 Measurement of Constantan

A small sample of constantan wire was used measured using the single TE sample
configuration shown in Figure 10-7. For high temperature ZT measurements, the Ultra
High Temp system was utilized. Because of the higher temperatures, platinum wires are

used for the current leads and voltage leads connected to the sample.

Pt TR

 
  

     

.. .a-v'--- .
. l.wm-.-.
nu... ‘
'- .u
a,» 5 .

 

Cu

 
  
  

Sample

I
+—

+

v i

 
 

  
 

Cu

3...,“

  

Pt

4 iu’ "- t-t-‘I-I-"é‘i '

Pt

I ‘,._ ‘7‘5‘ 5"“ “31-3.7, '.’ .

    
  
 

 
  

Tc

 

Figure 10-7: Setup for single TE pellet

A detailed diagram with dimensions (using variables) is shown in Figure 10-8 for

the sample size and voltage probe locations.

L/x

 

 

 

 

 

 

 

 

k 4
L

L

r 'l

I I
Tc I I TH
- V +

L

1' AT ’i

 

L J
F AT/x 1

Figure 10-8: Detailed view of a single TE pellet connection

206

The thermopower of constantan is low enough that the thermopower of the
platinum current leads will affect the measurement. Therefore, the thermopower of the
platinum must be known and corrected for. Published data on the thermopower of

platinum is shown in Figure 10-9 along with the polynomial curve fit.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'4 I I I I r I
. Y= M0+M1“'x1-...M8"x"-1’M9"x9

A 45 - - M0 118724984
1 I
\ M1 -2.10073889
a, _8 _ I _ M2 00167153763
3 I I M3 -7.86175678e-05
3 10 _ I . || M4 2.35649658e-07
8. I H M5 464450512e-10
° I H M6 6.00944332e-13
E -12 - I -
a . M7 4.920710678-16
15 . M8 2.31451138e-19

‘14 ' I ' M9 4.76770298-23

R 0999999716 ||
-16 1 1 1 1 1 L

 

 

200 300 400 500 600 700 800 900
Temperature (K)

Figure 10-9: Thermopower of platinum from published data (Roberts)

The schematic of the setup is shown in Figure 10-10 where a representation of the
electrical circuit and thermal circuit is provided. Figure 10-11 shows the equations for all

of the components presented in Figure 10-10.

207

 

 

 

 

 

 

 

 

 

 

 

 

 

 

apt-~TI

 

 

 

 

 

 

 

 

Thermal Circuit

 

 

 

 

 

Figure 10-10: Electrical and thermal model of setup

208

 

 

 

V1: Iam-dT VA: [apt-d7" QA=QB=QC=asample-I-T
TR TXH 1 1
V2 = [apt -dT VB = Iapt -dT 1
TR Tx H R’hB = R’hsample ;
TXC TC 1 1
V3 = [apt -dT VC = IaPt ~dT R’hC = R’hsample '(1‘;]'(l';]
TR TIC
1 1
TC RA =Rsample‘ 1“ '—
x n
V4 = Iapt -dT
1
TR RB = Rsample ”—

X

1 1
RC = Rsample '[1_“]'(1‘_)
x n

Figure 10-11: Equations for Figure 10-10

 

 

The measured voltage across the constantan wire can be calculated using the

schematic from Figure 10-10 and is shown below.

Tx H TxC TR
Vmeasured = [apt ~dT + I - Rsample -—1£+ Iasample ~dT + [apt -dT
TR Tx H TxC
Tx
= flaPt -— “sample ) 0'?" + I - Rsample -$ (10.148)

 

~ (“Pt "'asarnple)'AT + I ' Rsample

~

x x

209

Assuming that wire thermal resistance is much larger than the sample thermal resistance,

the temperature gradient across the sample can be approximated as follows.

AT z (“sample ’“Pt )1 'T' R’hsample

ZT of the tested material is found from the basic equations shown below.

“sample2 '0’ sample . T

 

(Z T)sample : ”sample

Q=“sample'T°1

Q length

_ AT area

 

2 length _ AT - area

 

(ZT)sample : “sample '

 

 

: asarnplez . R 1 . AT
sample “sample 'T ’ I

_ “sample 'AT

— Rsample '1

2 .
_ “sample 'R’hsample -T

 

Rsample
The measured values for Roe and RAC can be calculated below

a —a ~AT R
RDC = i Pt sample) + sample

 

x-I x

Rsample
RAC(AT—>O) = _—

(10.149)

(10.150)

(10.151)

(10.152)

(10.153)

(10.154)

Now the ZT that is measured can be calculated from using the Harman technique as

follows.

210

 

 

 

RDC
ZT = —— —1
( )measured R A C

 

x-I x

Rsample
x

(“Pt — “sample ) AT

[(“Pt '“sample)'AT + Rsample]
—1

 

 

 

 

= (10.155)
Rsample ’ I

_ (“Pt ’“sample)'(“sample -“Pt )‘I’T'Rthsample

_ Rsample ‘1

_ (“Pt ‘“sample)2 “R’hsample ~T

_ Rsample

The above equation shows that how the thermopower of the platinum wire affects the
measured ZT value. A correction must be made to the measured ZT to get the actual ZT
of the sample by introducing a correction factor as follows.

(ZT) (ZT)measured ~Correction

sample :

 

 

2 P
a ° Rt CZ - a ' Rt
sample hsample . T ( Pt sample hsample . T . C 011

Rsample Rsample

 

“sample

(“Pt ‘ “sarnple)2

 

Correction =

 

 

 

(10.156)
The above equation indicates that in order to correct for the thermopower of the

measurement wires, the thermopower of the sample must be known. This may not

211

always be the case. However, typically, samples measured by MSU have large
thermopower values in that the thermopower of the platinum voltage probes can be

neglected.

10.4 Experimental Results

Constantan wire was tested for ZT using the Ultra High Temp system. A picture of

the mounted sample is shown in Figure 10-12.

714213859, .
. r” ”613,“:

 

Figure 10-12: Mounting constantan wire for ZT measurement

 

 

 

0 i 1.44 i 4.50 5.69 i
.06 5.00 '6.38

Figure 10-13: Constantan wire (dia = 0.02” = 0.508mm) probe spacings

212

 

 

Several sample temperatures were investigated, and once thermal stabilization was
achieved, a frequency sweep for impedance measurements was initiated. The results of
the magnitude and phase of the impedance at various temperatures are shown in Figure

10-14 and Figure 10-15.

0.0079

I
0.0078 - K

0.0077 -

 

 

 

  

 

 

0.0076

 

0.0075

0.0074 1-

0.0073 -

Mag Impedance (Ohms)

0.0072- .gssssssg

 

 

0.0071 4 ' ' ' i

0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

 

Figure 10—14: Magnitude of impedance versus frequency at multiple temperatures

 

213

 

Phase Impedance (deg)

-3

 

 

1

 

 

 

 

 

 

(1001

01“

OJ

Frequency (Hz)

10

100 1000

Figure 10-15: Phase of impedance versus frequency at multiple temperatures

By knowing the thermopower of the constantan wire and the platinum, the

correction factor can be found and is shown in Figure 10-16 with the polynomial curve

fit.
1.65

I I I I Y=M0+MPXLUM$f+Myf
3 1-6 "' M0 -11.5835284
8 M1 017105912
E 1’55 ' Ii M2 0000927986297
'3 1 5 _ M3 2.47244562e-06
.2 ' || M4 -2.58138734e-09
g 1_45 - |[ M5 -2.35767787e-12
= M6 9.334039e-15
3 1.4 - M7 -9.27187619e-18
1;; M8 2.97000378e-21
0 1.35 - M9 2.58485063e-25
R 0999999993

13 I I l =

 

 

 

 

  

  

 

 

  

 

  

 

  

 

  

 

  

 

  

 

  

 

 

 

 

 

 

 

 

 

 

200 300 400 500 600 700
Temperature (K)

Figure 10-16: Correction factor for measuring constantan using platinum wires

214

Using the correction factor and the measured impedance measurements of the constantan

wire, the ZT was found and is shown in Figure 10-17

 

 

 

 

 

 

0'14 l l I I l
9 Experimental
.. O -
0‘12 —— Reference /
g ,0
1: /
+3 m/
g 0.08 - / -
o /
li— . //
o
1.. 0.06 - / -
N /
o '/
o_o4 .. / -
0.02 I I I I I
200 300 400 500 600 700 800

Temperature (K)

Figure 10-17: Experimental results for measuring ZT of constantan

215

Chapter 11: Rapid ZT Measurements

11.1 Introduction

ZT measurements using the AC impedance sweep requires measurements at very
low frequencies. If the samples are too long or have too large of a thermal conductivity
and thermal capacitance, this can cause the frequency range of the experiment to be
below the range of the measuring equipment. This section will discuss the option of
changing the sample dimensions in order to shift the frequency range up to a high range.
This will not only help the measurement equipment, but it will also help speed up the
measurement time by not requiring as low of a frequency measurement.

Frequency shifting will be helpful for rapid ZT measurements, however, there is
still more that can be done to increase the speed of a ZT measurement. One possibility is
to measure ZT based on the phase of the impedance alone. This section will describe
how the phase of the impedance can be used to calculate ZT. Furthermore, it will show
how the maximum phase angle of the impedance over the appropriate frequency range
can also be used to calculate ZT. If measurements are measured at this frequency of
maximum phase angle only, the time required for ZT measurements can be dramatically

decreased.

11.2 Frequency Shifting by Sample Dimensions

Measuring the ZT of thermoelectric materials requires very low frequency
measurements. This is due to the fact that TE materials have very low thermal

conductivity values. When measuring a large commercially available thermoelectric

216

 

module such as one from Tellurex, the alumina plates on the module account for most of
the heat capacitance and this also lowers the frequency required to measure the
impedance. It is approximately the product of the thermal resistance and the thermal
capacitance of the module that determines the frequency range need for the measurement.
A potential way to increase the frequency range of a Tellurex module would be to
remove the Alumina plates. When measuring single pellets, unicouple, or multicouple
modules made at MSU, it is the thermal resistance and thermal capacitance of the
material that drives the frequency range. In this case, the sample dimensions can be
altered to increase the frequency range of the impedance to a more time saving range. To
simplify this analysis, a lumped element model will be used for the single pellets. This
allows for calculations to be made using the RC one-port method. The results from this
analysis will be good enough to describe how the frequency range can be shifted up so
that measurements can be made faster. In some cases, this will also help to keep the
range in a workable range for the measurement equipment.

It has been shown for the RC One—Port model that for the circuit shown in Figure
7-1, R1 depends on the thermal resistance, thermopower, and the ambient temperature,
while C 1 depends on the heat capacitance, thermopower, and ambient temperature shown

here.

C1 : CThermaI

2
a '7an (11.157)

2
R1 = “ 'Tavg ' RThermal
The pole of the impedance function, (0p, determines the approximate lower

frequency point where measurements at frequencies lower than this point should give a

217

 

constant value for the magnitude of the impedance. The pole is related to R1 and C; as
shown here and can also been shown that it is simply related to the thermal resistance and

heat capacitance of the material.

 

 

 

= rad/s
p R1 °C] ( )
= 1 (11.158)
2 C
“ 'Tavg RThermal Yz'hermal
a ’ Tavg
1
a) = (rad/s) (11.159)
p RThermal ' CThermal

In order to make sure that a sample can be measured in the frequency range of the
measurement equipment, the sample dimensions can be adjusted to increase (up.

Thermal resistance depends on the length and cross sectional area of the sample
while heat capacitance depends on the volume of the sample. Figure 11-1 shows an
example of the effects on changing the sample size where we let r be the thermal
conductivity and c be heat capacity. The product of thermal resistance and heat
capacitance of the sample is examined. Figure 11-1 (a) and (b) show that changing the
cross sectional area of the material does not change the time constant, 1. However, when
the sample length is reduced, as shown in Figure 11-1 (c), the ris dramatically reduced.
The equation below shows that ris inversely related to the square of the length of the

sample. Therefore, reducing the sample length in half will increase the frequency by

four.

218

 

1
r = —
RTherm 'CTherm

 

 

 

= 1 1 (11.160)
[r.__6118fh;).(c.leng,h_widm. thickness)
wrdth-tluckness
__1_
r-c-(length)2
‘2 2
‘ length 4
I RTherm=r'—=r-—-——
( ) area 2-2
a
4 CThem=c-volume=c.2.2.4
Ta = RTherm 'CTherm =16rc
Rmem] =r'length =r.i
(b) area 4.4
CTherm =C-Volume=c-4.4.4
Tb = RTherrn 'CTherm = 16rc
length 2
R :r‘ : .—
Therm area r 2.2
(C)

 

CTherm =c-volume=c-2-2-2

V '——-— z'cszherrn'CTherm=4":

Figure 11-1: Adjusting sample dimensions to change the frequency range of the
impedance.

If TE materials are improved by reducing the thermal conductivity, sample sizes

will need to be smaller in order to keep the dynamic impedance behavior within the

219

 

frequency range of the measurement equipment. The limiting factor with this will be

placing voltage probes along the length of “the sample without interfering with each other

for a four-point measurement.

 

 

 

 

 

 

 

 

0.016 ' -,- 0
' . “1%:W‘i\
00155 $4.862” -1
A 0’4.)
93 0.015 " . -2 g
3 a
5 0.0145 \ - -3 2.
8. —O—- Long Sample 5
E 0014 -—l— Short Sample - 4 E.
7. g
'5 0.0135 - -5 8
'5 mm 3
g: 0.013 ' —6 £
2
0.0125 -7
“H.”
0.012 I I 1 1 -8
0.001 0.01 0.1 1 10 100
Frequency (Hz)

Figure 11-2: Example of long versus a short sample showing that the minimum phase
occurs at a higher frequency of a short sample versus along sample.

11.3 Phase Angle with Simple RC Circuit

 

11
11 Rm

 

 

 

 

O—-0 1 ii——J\/\/~———
__W—‘
Z (5) R1
CF

Figure 11-3: RC circuit

The evaluation of using the phase of the impedance begins by looking at a simple

RC circuit that was used in the RC One-Port method. The real and imaginary

220

components of the impedance have been solved for in a previous chapter and the result is

shown again here.

Z(s):(R1'C1)2'Rm'“’2+Rm+Rl+ .. —R12'C1'(0
= Re[2(s)]+j-Im[Z(s)]

 

The phase of the impedance can now be found using the arctangent of the imaginary

components divided by the real components, which are shown below.

 

 

 

 

(
6(s)=tan—l Im[Z(S)])
\Re[Z(s)l
( -R12'Cl'0) \
o o 2
(9(a)):tan—l (R21 C])2 6;) +1
(RI-Cl) -R,,,-a) +19,,,+Rl (11.162)
K (RI'CI)2'(02+1 J

 

 

-1 —R12°Cl'(l)
:tan 2 2
(R1 -C,) -R,,, -a) +11", +111

Now that the phase of the impedance function is found in terms of frequency, the

minimum phase (absolute maximum phase angle) can be found by taking the derivative

of the phase function and solving for where it equals zero.

2
d d _ —R ~C-a)
—6l(a))=—tan1 2 l '2
dw dw (RI-C1) .me +Rm+R1

_ RIZ'C]'(Rm'602°R]2°C12—Rm—Rll

103-(62.111 -C,)4 +2-(R,,,-ro-R1-Cl)2 +2-11,,,.a)21113"-C12 +Rm2 +...
2°Rm 'R1+R12 +0)2 °R14 'Clz

(11.163)

221

 

 

 

Finding where the derivative equals zero is as follows:

d

(171)

6(w)=0—>(Rm-wz-R12-C,2—R,,,-R1)=0 (11.164)

Now the frequency that will give the absolute maximum phase angle can be solved for

and is shown here.

 

6] = R1+Rm
”’1 max Rm'Rlz'Clz

Applying this result back into the phase function will give the solution for the absolute

(11.165)

 

 

maximum phase.

 

 

 

 

 

 

 

 

 

 

{ \
R +R
_Rlz-C1.\/R IRZ’ZZ
R1+Rm —1 m' 1 - 1
6 = :6 =
m 1 1 (RI-CIV-Rm- 2 2+Rm+R1
2
[9| rum-1 1. R1
max 2 Rm'(Rl+Rm)
(11.166)

The above equation can be rewritten to find |9| max in terms of ZT where ZT has been

shown to be

ZT=—— (11.167)

Using this ZT, we find the magnitude

222

 

 

 

 

 

 

 

 

 

161 ‘11- R12
max 2 Rm'(Rl+Rm)
( )
2
Rm2 (El—+1] (11.168)
x m 7
=_ —1 1. _ZT2_
2 (ZT+1)

A computer math program was used, such as MathCAD, to solve the above equation to

give:

 

ZT = —2 - tanflalmax )[— tanQHlmax)i \[tan266|max)+1] (11.169)

Since ZT is not a negative quantity, we can neglect one of the terms above to give:

 

ZT = —2 . mqglmax) [_ tanQ6|max )+ \/tan2 Mm“ )+ 1] (11.170)

Now ZT has be solved in terms of |6| max . If one is measuring the circuit shown in

Figure 11-3 which is similar to the circuit model of the Tellurex module, one only needs
to locate the absolute maximum phase and take a measurement at this frequency. Of
course, the first time a thermoelectric module is tested, a full fi'equency sweep would be
desired which can take several hours. But once a module has been characterized and the
frequency of absolute maximum phase angle can be approximated, only a few

measurements about this point will be needed, which might only take several minutes

223

 

 

 

instead of hours. A plot is provided to show ZT versus maximum absolute phase angle in

Figure 11-4.

 

 

 

 

 

2 IIIII!IIIIIIITIIIITITTIIIIIII

1.5— —

h- -1

L -

E ‘r 1

0.5- _

F -l

)— .1

l. ..

0PIIIIIIJIJLIIIIIIIIIIIIIILI ‘

-30 -25 -20 -1 5 -1 0 -5 0
MaxPhase(deg)

Figure 11-4: ZT versus max absolute phase angle for RC circuit equivalent

11.4 Phase Analysis for Thermal TLINE model

Many thermoelectric devices do not behave exactly like the simple RC circuit such
as single pellets, unicouples, and modules with only a few couples. These devices
behave more like the Thermal TLINE model. In this case, the absolute maximum phase
angle cannot be used to determine the ZT directly. The following will show why.

Three different measurements where simulated using LabVIEW where all three
samples would have the same ZT value. The first was a sample that exhibited the circuit
shown in Figure 11-3. The second and third were samples that behaved like the
conditions explained in the thermal transmission line model (TTLM) where the

measurement probes were at the ends of the sample and with the measurement probes not

224

at the ends of the sample respectively. It can be shown by computer simulations that
plotting the phase versus fiequency indicates that each measurement has a different
absolute maximum phase angle. The sample with the probes at the end with TTLM
characteristics shows the least maximum absolute phase angle. Next in order is the
sample representing the RC-circuit. The sample with the highest maximum absolute
phase angle is the one with the probes not at the ends of the sample. The frequency at
this maximum absolute phase angle is not of interest at this point because this does not
influence the ZT of the material. It can also be shown that after plotting the phase versus
log frequency (Figure 11-6) for the three measurements, the area under the curves for all
three measurements is approximately equal for a given ZT value. The exact areas under
the curves for the transmission line circuits could not be found because values used in the

simulation become large enough that they reach the limitation of the software.

 

I Full Length (T LINE)
Using Probe Spacing (TLINE)

 

Phase(deg)

 

 

 

 

10'5 0.001 0.1 10 1000
Frequency (Hz)

Figure 11-5: Phase versus Frequency. Absolute maximum phase angle is different for
the three measurements even though the ZT value is the same.

225

 

 

 

 

0 Full Length (T LINE)
El Using Probe Spacing (T LINE)

 

 

 

 

 

 

 

 

5
0 - M, - “9945766693
A c:
U) - - " ‘7
g 5 Area under the curve
3' _10 _ L. .5“ Full Length = -24.8333
3 i” : Using Probe Spacing = -24.8977
E -15 .. raga RC Model = -24.8916
- 95 1
_25 1 1 1 1 1 1 1 1
-4 -2 0 2 4
Log (Frequency)

Figure 11—6: Phase versus Log Frequency. Area under the curve for all three cases is
approximately equal for a given ZT value.

11.4.1 Area Under the Phase Plot

What is the area under the curve? Since the areas for all three cases appear to be

 

approximately equal, only mathematically calculate the area under the curve to the RC
circuit. This will prove to me much simpler than the calculations using transmission line

theory. First, start with the equations for the magnitude and phase of the RC circuit.

2
072 . (“z

|Z(w)|=;o—— R- 2 (11.171)
P
1+[fl]
mp

thmm) =tan“‘[;)“’—]+tan“[5:"—’] (11.172)

 

 

 

226

l
a) :
p R1'C1

 

(11.173)
(0 _ R1 +Rm
2 R1 'Rm'Cl

Integrating the phase with respect to the log of frequency can be very challenging.
However, the use of standard techniques for plotting magnitude and phase as shown
below in a Bode plot can be employed. In such plots, at low frequency values where the
capacitance is considered to be open-circuit, the magnitude is a straight, horizontal line.
This line continues up until the frequency of the pole. At this point, the line bends
downward at a slope of -20dB/decade. This continues until the line reaches the
frequency of the zero. At this point, the capacitor is considered to be short-circuited
which gives a constant magnitude as frequency increases. The phase can be separated
into two plots (one for pole and one for the zero) that will be added together to get the
final result. The first plot of phase will look at the pole of the impedance function.
Starting from low frequencies, the phase begins at an angle of 0°. Then at one decade
before the pole of the impedance function, the angle decreases at a rate of —45°/decade.
This line will continue until it reaches one decade past the zero of the impedance function
where it will level off at ~90°. The second plot is of the zero of the impedance function
where again it starts at 0° at the low frequencies. When the frequency reaches one
decade before the zero of the impedance function, the phase angle increases at a rate of
45°/decade. The phase will increase until one decade past the zero of the impedance
function is reached where it will remain at 90°. The addition of the two plots is then
highlighted and shown in Figure 11-7. For this particular example, the phase made an

isosceles triangle. This does not have to be the shape. It could turn out to be a trapezoid.

227

 

 

 

It should also be noted here that this technique is simply an approximation to the actually

phase and magnitude but it should still help in the understanding and calculation of the

area under the phase versus log frequency plot.

 

 

   

121‘
(”pole
(”zero

. - I ~—~«‘--*|—09co
26...... '2 11 ° .1 2 3

Z

2 : ‘ ”We

-1- -- __1_4__4Az--—»Logm

Figure 11-7: Phase and Magnitude plots versus log frequency
From Figure 11-7, the area under the phase plot can visually be calculated, which is

shown here.

Area = —[log(a)p) — log(a)z )]- §

(11.174)
=—£-lo fl
2 Rm

From the plots shown and the equation above, it is clear that the area is independent of

log frequency and the thermal capacitance.

228

11.4.2 Applying a Correction to the Absolute Maximum Phase for ZT Calculations

The equation for the area can then be used to correct for the maximum phase angle.
This is accomplished by first collecting a full frequency sweep across the sample to get a
ZT value which identifies the values for R1 and Rm This firll sweep will also identify the
maximum absolute phase angle. Because the integration of phase with respect to log
frequency is the same for RC circuit model and the Thermal transmission line model, the
theoretical maximum phase angle can be calculated for the sample as if it were behaving
like the RC circuit model. To correct the phase so that the formula for finding ZT using
the phase for the RC circuit model can be used. Let X be a correction factor to the

measured phase.

 

|9|
= :“RC model (11.175)
l lmax'ITLM
So that
16' measured 'X = lgicorrected (11'176)

Now the formula for ZT can be used as follows.

 

ZTGB' corrected ): -2 ° tanQHI corrected ) I} tanqfll corrected )+ Jtanz «6| corrected ) + 1]

(11.177)

Now the maximum phase can again be used to find the ZT of the sample.

229

 

 

Chapter 12: Measuring Resistance of a TE Module using Alternating Digital Pulses
at Various Frequencies

12.1 Introduction

The modified Harman technique has shown that finding the AC resistance and DC
resistance of a TE module can be used to find the ZT of the module. A commercially
available Z-meter has been developed by RMTLTD [62] that uses a high fi'equency
digital square wave signal for the AC resistance and a low frequency digital square wave
signal for the DC resistance of the module. My investigations have been performing a
full frequency sweep of the module using a single harmonic sine wave. This technique
requires the use of lock-in amplifiers for identifying the magnitude and phase of the
impedance and can take a considerable amount of time to perform the experiment. Here,
the investigation is to examine the resistance of the module using alternating digital pulse
(5 0% duty cycle) at various frequencies and to learn under what conditions this technique
can be used for obtaining the ZT of the module.

Pulsing the current through the sample will introduce harmonic frequencies into the
module, which may affect the measurement. This method of measuring resistance will
not include the phase of the impedance. This section will explain the experimental setup,
the automated data collection program, and the results of the experiments. Finally, the
results will show that using digital square wave signals can be used to obtain the ZT of

thermoelectric materials under certain conditions.

230

 

12.2 Automated Program

The experiment uses a commercially available TE module for power generation
and is utilized at room temperature. Measurements where taken for the module exposed
to atmosphere as well as in a high vacuum environment. A four—point probe method was
used for the resistance measurement.

The experiment uses the same technique that is used to measure electrical
conductivity of the TE samples already discussed where a digital current source is flipped
positive and negative at a high frequency. Before each flip of the current source, the
voltage across the module is recorded and used for the calculation of resistance. Here,
the modification of this process is that the duration of the current pulse is increased to
create a lower frequency of flipping. This is accomplished by placing a delay (in
seconds) between when the current pulse is switched, and when the voltage is measured.
Immediately after the voltage is measured, the current source is flipped and the procedure
is repeated. A part of this work, a LabVIEW program was created to perform this
experiment which interfaced with a Keithley 2400 current source and a Keithley 2182
nanovolt meter. The front panel to the user interface of the LabVIEW program is shown
in Figure 12-1. This program allows the user to enter the amplitude of the current, the set
of delay values, and the number of measurements for each set of delay values. It then
records the calculated resistance value of the module at each frequency. It is important to
note that although exact delay values where used, there were additional delays from the
measurement equipment that were not taken into account. Therefore, the exact
frequencies are not precisely know for this experiment and only trends in the data from

high to low fi'equencies should be examined.

231

‘ ""7"".‘"." r

 

EwaqmmyMchuevrogmnanonipmr
E59 Edi gperate 10015 Browse flndow l-Jeb
-E§:@ll3ptAppicatanort ”iii-11:17“ : :

Digital Flipping Resistance Measrrements H‘
Mano. Downey

 

  

Flam
I Testingjl .txt
Path

 

 

i"E C:).Documents and SettingstAdamtDesktoptLow Frequency
‘ Measurements

Current Output
garner

a of Readings
2‘110

I of
Measuemerts

_,....

f? 20

1111

 

 

 

 

 

 

 

 

_sl 1' ' " ' ' w 1:»: ..

 

Figure 12-1: Front panel view of LabVIEW program for automated data collection of
the resistance of the TE module for various frequencies.

12.3 Room Temperature Measurements in Atmosphere

Experiments on the module were done at room temperature in atmospheric
conditions. Figure 12-2 shows a plot of the measured resistance versus frequency for
multiple current values (lmA - 80mA). The expected results showing a ZT value of

~0.71 for this module are when electrical currents are lower than 30mA. The lower ZT

232

 

value is due to thermal conduction losses from the atmospheric conditions. Between 30
and 40mA, the measured resistance of the module begins to deviate from expected results
and increases with increasing current values. Resistance measurements from lOOmA to
260mA are shown in Figure 12-3. This plot shows the continued deviation in resistance
measurements from the expected results. A plot is created in show the resistance value
versus current level at multiple frequencies and is shown in Figure 12-4. This plot is
convenient to identify what frequencies are affected by the increase in current level. The
data that has been presented here shows that in order to get a proper ZT value of the

module, the current used for the experiment must be 30mA or less.

300K in Atmosphere

 

0,:

0'1

Resmtance (Q)
.9
h 0'!
llIi'lllI—ITIII'Illl'lliililll'llll
1
.1
'/

 

 

3.5

 

2.5 1 ' ‘ '
0.001 0.01 0 1 1 10 100 1000

' Frequency (Hz)

Figure 12-2: Plot showing resistance measurements of a module in atmosphere using
multiple current values (lmA - 80mA).

233

 

E" i I

 

300K in Atmosphere

 

 

 

 

6 .
)-
: A __9— 100mA
5.5 9- —Ei— 120mA
E —<—»—— 140mA
: —a— 160mA
a 5 - +180mA
3' I +200mA
o : +220mA
5 45 - + 240mA
jg Z —+—2eomA
1" I
8 4 -
3.5 L if .4 .. __
)- ......
3 : 1 ~ -
0.001 0.01 0.1 1 10 100 1000
Frequency (Hz)

Figure 12-3: Plot showing resistance measurements of a module in atmosphere using
multiple current values (100mA - 260mA).

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
   

300K in Atmosphere —9— 5005+0 (Hz)

 

 

 

 

 

 

 

I I I f fl I I f j T 1 I ‘-- __8—250E+0 Hz
I I I A 'X—X"XEX“'X ' ——e—167E+0in;
7 a a 5 5 .: +45.5E+0(Hz)
f.’ ’ ‘: —o— 23.8E+0 (Hz)

. )1 1 ‘ ‘ _' + 9.8E+0(Hz)
4 , ,1 j _ ___,H + 4.95E+0(Hz)
a m. A 3 + 2.49E+0(Hz)
;' (I A“! _ _ k : —1z1— 998E-3(Hz)
u / fl. . —12— 50015-3 (Hz)
5 g + + + + + + + . ——Zi—— 25015-3 (Hz)
:5 gun-l : —<>— 12515-3 (Hz)
in 4.5.5.. A. 4 A A A 1 1 . —8.— 83315-3 (Hz)
g r” : ;&§§!—,! r r r r r : + 62.5E-3 (HZ)

3-6 were. :.9179“1£fi£=5§=y3§1!5§3 . —4— 505-3012)
e r: g = 5‘55 :8: '5: =25 ’5” T"- :1 =9” —= ” . + 33.3E-3 (HZ)

3.2 ”E! .1 —{>—— 2513-3 (Hz)
3 : + 12513-3 (Hz)
2.8 l J 14L 1 l l l l l LLLLI l L l l l l l l l I: ———v—_ 8'33E-3 (HZ)
—1:1— 4.175-3(1-12)

0 0.05 0.1 0.15 0.2 0.25
Current (A)

Figure 12-4: Plot showing resistance measurements of a module in atmosphere at each
fiequency versus multiple current values (lmA - 260mA).

234

 

 

 

12.4 Room Temperature Measurements in High Vacuum

The same experiment was repeated on the module except in this case; the module is
place in a high vacuum environment (1x10'6 Torr). This time, the measured ZT of the
module is ~0.77. This is in good agreement with expected ZT of this power generation
device at room temperature. This ZT value can be clearly identified using currents up to
50mA as shown in Figure 12-5 and Figure 12-7. Using current levels higher than 50mA
results in a deviation in the resistance plot from expected values as shown in Figure 12-6.
Again, a plot of resistance versus current for multiple frequencies is created to show the
behavior of the resistance for the module using currents up to 500mA (Figure 12-8). The
data presented here shows that accurate ZT measurements can be made when current

values are 50mA or less.

6 5 300K in High Vacuum

 

Resistance ((2)
.4- .01
0'! 0| 01

A

IIIIlIIIIIIIIIIIIII'rrIIIIIII'I'II

 

P"
or

 

 

3

0.001 0.01 100 1000

0.1 1 10
Frequency (Hz)

Figure 12-5: Plot showing resistance measurements of a module in high vacuum using
multiple current values (lmA - 50mA).

235

 

 

300K in High Vacuum

 
   
   
       
   
   
   
   
    
 

 

 

 

 

6.5»
I
6 L —e—— 60mA
- —51—— 80mA
I —6— 100mA
5.5 '- ;< 120mA
a : ——+—— 140mA
j; 5 :_ —-£x—1SOITIA
u . —O— 180mA
S : W \ + 200mA
35 4,5 '. —+— 250mA
W i
g .
4 :-
:
3.5 :—
3 ' ‘ =
0.001 0.01 0 1 1 10 100 1000

' Frequency (Hz)

Figure 12-6: Plot showing resistance measurements of a module in high vacuum using
multiple current values (60mA - 300mA).

 

300K in High Vacuum

 

——e—— 5005+0 (Hz)
-—13—— 2505+0 (Hz)
—6—- 1675+0 (Hz)
——><— 45.55+0 (Hz)
—+—— 23.85+0 (Hz)
——5— 9.85+0 (Hz)
——o—- 4.955+0 (Hz)
—I——- 2.495+0 (Hz)
—+— 9985-3 (Hz)
+ 5005-3 (Hz)
+ 2505-3 (Hz)
—4:1— 1255-3 (Hz)
+ 83.3E-3 (Hz)
—121— 62.5E-3 (Hz)
—12— 5053 (Hz)

 

 

0'!

 

1"
or

 

Resistance (0)

#1

 

 

 

 

 

3 5 “-------- + 3335-3 (H2)
1— 5‘,==.-_==—é9'——:——JJ—:_=—_—=LJF...=M=T—w,;w =~ . ti} 25E_3 (Hz)
: ) —ik—— 12.5E-3 (Hz)
3IIIIJIIIIIIIIIIILIIIIIIJ .8.33E’3(HZ)
0 0.01 0.02 0.03 0.04 0.05 _zg— 4475-3 (Hz)
Current (A)

 

Figure 12-7: Plot showing resistance measurements of a module in high vacuum at each
frequency versus multiple current values (lmA - 50mA).

236

 

 

 

  
    
   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   

300K in High Vacuum ~ 50090 (Hz)

x/

l I I I I I I I I I I I I I I I I I I I i l 250E+O (Hz)
: 167E+0 (Hz)
——:-<-— 45.55+0 (Hz)
—+— 23.8E+0 (Hz)
——-£3— 9.35+0 (Hz)
—o—- 4,955+0 (Hz)
+ 2,495+0 (Hz)
—o— 998E-3 (Hz)
+ 50053 (Hz)
—v— 2505-3 (Hz)
——0— 12553 (Hz)
—51— 83.3E-3 (Hz)
- 03‘- 62.55-3 (Hz)
——51—— 505-3 (Hz)
—12— 33353 (Hz)
+ 255-3012)
+ 12.55-3 (Hz)
+ 8.33E-3 (Hz)
——5— 4.1753 (Hz)

 

\l
.1
cl
1
1

 

 

.09
OI
IIII'IIII

 
  
     

O)

‘l .1
‘h .1
‘I r

01

P.
ammo:

 

 
 
 
 

Resistance (0)
H

II IIIIflIII

.0)
or

\-
v
I
I

 

ljllllllllllJlllllllllll

0.1 0.2 0.3 0.4 0.5
Current (A)

0)

 

C)

Figure 12-8: Plot showing resistance measurements of a module in atmosphere at each
frequency versus multiple current values (lmA - 500mA).

12.5 Monitoring the Voltages

The voltages across the module was examined versus time for several frequencies
and current levels to identify any unexplained behavior due to using digital square wave
signals. Using a small current value of 10mA, three delays of 1, 2, and 15 seconds where
tested and the results are shown in Figure 12-9, Figure 12-10, and Figure 12-11,
respectively. These plots show expected behavior for the resistance of the module. For
short delays, the Peilter effect does not contribute as much as for long delays. This can
be seen in the plots where the voltages rises and falls exponentially are much more
apparent for longer delay values. The jump in the voltage as the current is flipped is due
to the finite resistance of the module. For larger current values such as 140mA and

500mA, the voltage behavior was also as expected (a jump with the current is flipped

237

 

 

followed by an exponential rise or fall). There was no indication of noisy data to explain

the results shown above where high current values affect the ZT measurement.

 

 

High Vacuum

Dangling Module

Delay: 1 sec

0.04 Current: 10m?
0.03 l l q A q -
0.02 I I '3

E 0.01 I h l i I I ’ _
:2 0.01 l ”i ‘l f‘ I ::
:2: 1 .1 \l k
-0.04 :

 

0 150
5Data Index (time)00

Figure 12-9: Plot of voltage versus time across TE module using a 1 second delay and

Figure 12-10:

 

 

10mA.
High Vacuum
Dangling Module
Delay: 2 sec
Current: 10mA
0.04
A 4 ! -
0.02 : 1..
g l l
0 1 "
s 0 * -
% :
> .
-0.02 ’1 V’U \ 1
-0.04 r .1
0 50 100 150

Data Index (time)

Plot of voltage versus time across TE module using a 2 second delay and
10mA.

238

 

 

 

High Vacuum
Dangling Module

 

 

Delay: 15 sec

Current: mm

0.05 ._ ,

’ l

q

' ‘

0.04 ‘ ‘ .1

1 : ~ : l :

0.02 ¢ 1 .-

; l t ‘ t 1 -
g l i . i -
.3 ° '1
g + J + l -
002 7, 1 1 -
O b "
b ‘o u
004 t \
-0.06 - i

0 150

50 100
Data Index (time)

Figure 12-11: Plot of voltage versus time across TE module using a 15 second delay and
10mA.

High Vacuum
Dangling Module
Delay: 15 sec
Current: 140mA

(15

Voltage (V)

 

 

100 150

50
Data Index (time)

Figure 12-12: Plot of voltage versus time across TE module using a 15 second delay and
140mA.

239

High Vacuum
Dangling Module
Delay: 20 sec
Current: 500mA

 

 

 

4 I

3 . 1 -:

2 l l ‘ .‘

,0 l 1 l 1

o 9 1

A O ‘ -

a 1 l 3 | . ‘ :

a 0 l l l .3

H u

g o $ Q 3

> '1 'o 5 1 i 1

‘. l '1 ) '1 :

O I

-2 1
.4

0 50 100 150

Data index (time)

Figure 12-13: Plot of voltage versus time across TE module using a 20 second delay and
500mA.

12.6 Conclusion

Based on experimental evidence, it is viable to use a digital square wave current
signal to obtain the ZT value. For measurements taken in atmosphere, there must be a
correction factor applied to the ZT value obtained to account for thermal losses due to
conduction and convection. For both high vacuum or atmospheric conditions, careful
considerations must be made on the amplitude of the current used. Current values must
be kept small. The errors in the resistance measurements for high current values are
likely due to the Joule heating at the electrical contacts between to the TB material. By

using small current levels, the effect of Joule heating is dramatically reduced

(Q=i2-R)-

240

Chapter 13: ZT Machine

13.1 Introduction

In searching for the best thermoelectric material, many variables are present in the
manufacturing process such as chemical composition, cooling rate profile, cold and hot
pressing of the samples, environment conditions, etc. This leads to a vast number of
samples being made in order to optimize each variable in the process. These process
variables affect the strength of the materials, the brittleness, and of course the
thermoelectric properties. In the beginning of large-scale production of the TB materials,
the heating/cooling profiles along with chemical composition were changed to give
samples that did not contain voids and cracks and were robust enough to handle for

measurements. An example of a scaled up LAST material were cracking occurred is

shown in Figure 13—1.

 

Figure 13-1: Picture of 100g ingot of LAST material sliced up into 5mm thick coins.
This picture shows the cracking in the sample throughout the ingot and is affected by the
cooling profile.

From this point, the materials are investigated for hardness and electrical conductivity.
Based on typical measurements of good TE materials, higher electrical conductivity
warrants higher ZT performance. For a given TE crystal structure, the thermal properties

due to the crystal lattice will remain approximately the same for different doping levels.

241

The TE crystal can be doped with different concentrations of impurities to adjust the
electrical conductivity. The Wiedemann—Franz Law states that the thermal properties due
to the electrons increases linearly with increasing electrical conductivity. Because the
thermal properties due to the crystal lattice remains constant for the multiple doping
levels, the ZT of the material can increase with increasing electrical conductivity.
Measurements on electrical conductivity alone are not enough to determine a trend in
thermoelectric performance against the different variables. It is also possible that a brittle
sample will outperform a strong, non-brittle sample. It has been determined that
measurements of ZT at room temperature would be an important measurement to add to
the existing one for screening out good TE materials from the bad. For example, based
on previous measurements, a good n-type material for this project would have a ZT>0.2
at room temperature. Once this is achieved, the samples can then be measured for
temperature dependant properties in other systems at MSU. In addition of measuring ZT,
rapid measurements are needed to increase the throughput of TE development. For a full
frequency sweep using lock-in amplifiers, it would typically take approximately 16 hours
per sample to measure (not including sample mounting time). A faster method can be
employed for measuring ZT because this ZT measurement does not have to be as
accurate as the AC full frequency sweep. For this measurement, only a single low
frequency measurement and a high frequency measurement is needed to calculate ZT.
The transition from high to low fiequency is not needed. The lock-in amplifiers can be
removed from the measurement and replaced by a Keithely 2400 source meter and 2182
nanovolt meter. The lock-in amplifiers provided a large reduction in noise for the

electrical measurement; however, removing the lock-amplifiers will allow many samples

242

to be measured at the same time. By removing the lock-amplifiers and not performing a
full frequency sweep, this system can measure 16 samples of LAST material (5mm x
5mm x 7mm) in less then 4 hours. Having this system meets a reasonable goal of
screening approximately 30 samples per week. This will help in the development of
manufacturing good TE materials by providing a fair amount of feedback to the
developers.

This section will describe a new system at MSU for measuring the ZT and
electrical conductivity of 16 TE material samples at one time. The method for the
measurement will be explained along with a computer program overview. The
assembled system will be shown and finally, example data is provided included data from
a commercially available TE module that is used as a reference sample to verify the

accuracy of the system.

13.2 Method of Measurement

This system uses an existing technique called the Modified Harman Technique
[63]. This technique simply states that ZT can be found by measuring a high fiequency
resistance (RAG) such that no temperature gradient is established and a low frequency
resistance (RDC) such that the electrical current is effectively DC. With these

measurements, ZT is found as follows.

”5529—1 (13.178)
RAC

Previous impedance spectroscopy measurements on the TE materials have helped

in the development of this system. For example, small copper wires can be used at room

243

temperature to provide current to the sample and for the measurement probes as long as
the wires have a much higher thermal resistance than the sample being measured. Using
wires with low thermal resistance will reduce the accuracy of the ZT measurement. The
wires connected to the ends of the sample must cover the entire end of the sample to
insure a uniform electric field across the sample. The end contacts must also be a
reasonably low thermal resistance. High resistance contacts, especially if one contact has
a different resistance than the other, can cause an uneven joule heating at the contacts and
again reduce the accuracy of the ZT measurement. Finally, AC measurements are needed
to examine the transition from high frequency to low fi'equency resistance values so that
the phase of the impedance can also be examined. However, for just looking at high
frequencies and low frequency measurements where the resistance values do not change
for a small change in frequency, a square pulse may be used. This is also based on
experimental evidence. Experimentally, it has been found that using small electrical
currents through the sample (~10mA) can provide a good ZT measurement. High current
values (>100mA) have been found to give an error in the ZT measurement. It is
extremely beneficial to use a square wave pulse for rapid ZT measurements. Using a
square wave pulse for the current eliminates the need for the lock-in amplifier (assuming
the signal to noise ratio is at a reasonable level). This also eliminates the time that the
lock-in amplifier takes to “lock” on to the signal.

All 16 samples are connected electrically in series. Each sample is thermally
isolated from each other by using long wires connected between the samples, which are

mounted to a metal disk that acts as a thermal grounding point.

244

13.2.1 Mounting Current Leads

All of the 16 samples are mounted as shown in Figure 13-2. Copper wires that are
about 3cm long are used to dangle the sample in a vacuum fi'om a thermally grounded
location. The wires going to the ends of the sample are first attached to a thin copper foil
that covers the entire end of the sample. The copper foil is then soldered to the sample

using “woods metal” solder.

  
   

Thermal Ground
——>

Copper wires
—>

 

Copper foil /

Woods metal solder

TE Sample

Figure 13-2: Diagram of TE sample mounted for ZT measurements

13.2.2 Mounting Voltage Probes

Resistive welding is being used to connect copper wire voltage probes to the TB
materials for electrical conductivity measurements. This technique is very useful since it
is fast, easy to precisely place a contact point, creates a very small contact, and makes a

strong contact that will not fall off. An example of a resistive weld is shown in Figure

245

13-3, and Figure 13-4, and Figure 13-5. Other techniques of attaching voltage probes
involves either soldering the wires to the sample, which is a little challenging to get a
small solder spot, or by silver painting the wire to the sample, which is very difficult to
get a strong bond without making the contact are large (~1-2mm). Figure 13-5 shows
that the contact are is not much larger than the diameter of the wire. There is also no spill

over like there can be with silver paint.

 

Figure 13-3: Copper wire (0.003" in diameter) welded to a LAST TE material (5mm x
5mm x 7mm)

246

 

Figure 13-4: Close-up of Figure 13-

 

Figure 13-5: Microscopic image of copper wire welded to LAST sample showing the
small size of the contact area
Resistance welding uses the resistance of the parts in the current path to generate

heat energy for welding. Bulk resistance is a function of sample geometry and resistivity,
which is a material property. Contact resistances occur at the contact between the
electrode and the sample and normally includes the following two contributions:
constriction resistance and film resistance. When two metal surfaces each with a certain
roughness are brought into contact, the real contact are of the mutually deformed
asperities is much smaller than the apparent area as long as the normal pressure is below

the yield stress of the sofler material. When a current runs through the interface, the

247

current flow lines bundle together passing through the separated conducting spots of real
contact. This constriction of the electric current by the contact spots reduces the volume
of the metal used for electrical conduction locally at the interface, hence giving rise to a
resistance named the constriction resistance. The film resistance is due to less-
conductive surface films such as oxides, oil and water vapor, etc.

With a short pulse of electricity that comes from a commercial spark welder
(HotSpot shown in), the contact resistance heats up enough to melt the thermoelectric
material. With slight pressure, the copper wire moves into the melted material. When
the pulse is done, the melted material cools and it bonded to the copper wire. It has been
experimentally found that a 15-volt charge can be placed in line with the wire (0.003”
diameter copper), the thermoelectric sample, and a 2-ohm resistor to get a good strong

contact between the copper and the TE material.

 

"wt—"—

Figure 13-6: HotSpot thermocouple welder

13.2.3 Measurement Process

The ZT Machine system is setup for two separate sets of measurements, the high

frequency and the low frequency. For all measurements, the current (I) through all of the

248

samples is a square wave function ( F (t) ) with a 50% duty cycle. The function oscillates
between a positive and negative value, a, which is typically around 10mA. This function
is plotted in Figure 13-7. Another firnction, G(t), defines the time when a voltage
measurement is taken. For all measurements, the current through the sample is constant
for a specified length of time. At the end of the of this time period, a voltage
measurement is taken. When the measurement is complete, the current switches to the
negative value where the process is repeated.

For high fi'equency measurements (roughly 33Hz to 1H2), each sample is measured
for 10 periods at each frequency before switching to the next sample. The technique for
this measurement is the same as the flipping method used in all MSU systems for
measuring electrical conductivity. Before the current is flipped, a single voltage
measurement data point is collected and recorded. The voltage for the negative current is
subtracted from the voltage for the positive current and then divided by two. This gives a
single resistance value for one of the ten periods. Once all samples have been measured
over the high frequency range, the system switches to take low fiequency measurements.
For this measurement, after the current has maintained a particular value for the specified
length of time, and average of 10 voltage measurements are made on each sample before
the current is switched to the negative value. This is accomplished by using a 7002
controller with a switch card inside to allow the nanovolt meter to switch between
measuring each sample. Each frequency is measured using 4 cycles of F (t). It is this

measurement method that saves time for measuring ZT of many samples.

249

F0) 4)

 

 

v
N

 

 

 

 

 

Ga) A

—---——-—--—--—--(-—--4
----—---—-—---—----4

-—--——---i

I 2 t

v

 

Figure 13-7: Plot of current through sample and measurement locations

13.3 The Assembled System

The assembled system consists of a Keithley 2400 current source meter, a Keithlely
2182 nanovolt meter, a Keithley 7002 controller, a computer using LabVIEW to
automate the measurements, a vacuum pump, and the measurement chamber. The
measurement chamber is the Drift System that has been modified. Figure 13-8 shows the
inside of the measurement chamber held up with a ring stand where 16 samples are
mounted for ZT measurements. Eight samples are mounted on a ring towards the top of
the chamber (also shown in Figure 13-9) and another eight samples are mounted at the
bottom of the chamber (also shown in Figure 13-10). The samples are mounted to a
circuit board with pins that plugs into another circuit board with sockets. Each
removable circuit board holds two samples. This allows the samples to be mounted with

care under a microscope before loading them into the chamber.

250

 

 

Figure 13-8: Assemble ZT Machine (Inside view with 16 samples mounted)

251

 

Figure 13-10: Bottom 8 samples mounted in ZT Machine

252

 

13.4 Example Data

Example data has been provided to show how the system performs. A Marlow
Industries small thermoelectric module was used as a reference material for testing the
ZT machine. The module uses 34 Bismuth-Telluride pellets with nickel traces and
Alumina plates that make the overall size of the module: 6.6mm by 6.6m by 2.16mm

(See Figure 13-11)

 

Figure 13-11: Small TE module from Marlow Industries

The data for this sample is shown in Figure 13-12. Before a measurement is taken,
it is unclear where the critical frequencies will be for the module. Therefore, many
fiequencies are sampled. This allows for a clear indication of the high frequency AC
resistance, RAc, and the low frequency measurements, Roe. The transition between RAC
and RDC should be ignored for now because a square wave pulse was used for the
measurement. The square wave pulse consists of many frequencies and may give rise to
a large error if one was to analyze the data for the transition frequencies. From the graph,
the values for RAC and RDC can be observed and the calculation of ZT can be measured

using Harman’s formula.

253

 

_x
CD

 

 

 

 

l l I I I
c f0 0 0
1.6 - ..
g
a) 1.4 I- . H
o
r:
g ZT~O78
'5 1.2 I- ~ ' -
a: e
n:
1 _ -
J_ . o . .
0.8 r r r r 1
0.0001 0.001 0.01 0.1 1 10 100
Frequency (Hz)

Figure 13-12: Resistance versus frequency plot for BizTe3 Marlow Industries TE
module

Data fiom a single pellet of LAST material has been tested and an example of the
data is shown in Figure 13-13. This shows that the system will work for measuring the

ZT of the thermoelectric pellets created at MSU for rapid analysis.

254

 

 

 

 

l I l l l
_ O o e O o _
g - ..
o
o . .
r:
5
O .. ..
'3
g .
- ' e e e e-
l 4 J g I
0.0001 0.001 0.01 0.1 1 10 100
Frequency(Hz)

Figure 13-13: Resistance versus frequency for single LAST pellet

PbTe+Sb (16%) - JS15706-2
Measured by A. Downey

 

 

 

 

 

_3 12I27I2005 ZT Machine after HT Run
3 O 9 9 9 ZT at 300K ~ 0.07 J
1.410' -
3‘ c
13? a? 3 7.5 in siftemromms a
E 13810-3 - E". 7 c
.1: g g —> a 0.14 e-
9 .5 .5 .1012 a
'0 e- .
8 1.3610‘3 - 9 53 6 _a_ '31
g 0 . 5.5 ‘0‘1 a:
g -3 g .3 5 - 0.08 §
3 1.3410 - 03 .-
3 0 4.5 10.06 O
0! I- 5 300 400 500 600 700 g
3 V Temperature (K) v
13210 - g
9
9 g g 1
1310-3 L L i 1
0.001 0.01 0.1 1 10 100
Frequency (Hz)

Figure 13-14: Resistance versus frequency for single pellet PbTe+Sb(16%). Here, ZT
value is 0.07. HT System gets the same ZT value using measured thermal conductivity at
room temperature.

255

13.5 Conclusion

The system has been able to measure the ZT of 32 samples in one week at room
temperature. At this speed, many samples where tested of the LAST materials to help
identify potentially good TE materials. A plot showing the ZT values of a generous
amount of LAST samples is shown in Figure 13-15. From here, samples with ZT values
greater than 0.2 were then tested for temperature dependant thermopower and electrical
conductivity. The data also suggests that increasing the electrical conductivity of the
materials tends to increase the ZT of the material. Overall, this system will prove to be

very useful in the development of making and screening TE materials.

 

 

 

 

0'3 .I l I l I
O
0.25 - ° -
0.2 - -
C
'- 015 - 'o ’ ° -
N u
’ C C . .
C
0.1 -. C C '-
C O
C C
.0.
0.05 - e. ..
0
0L 1 I I I I
0

500 1000 1500 2000 2500 3000
Elect. Cond. (Slcm)

Figure 13-15: Plot of room temperature ZT values for many TE samples of LAST
composition where different compositions and heating/cooling profiles where used in the
manufacturing process.

256

 

2 ‘U'YYUI'T‘IIlitrjt‘fi'TIIIIIIUUVr

 

 

 

 

. LAST-18 .
‘15 - -
_ .ETN-16 (LAST-18)
_ Data from 21‘
Machine .
- ' 0 . LAST-18 -
1— 1 . Kosuga et al 2005 -
Pd -* -

 

 

 

320 400 480 560 640 720 800 880

Temperature (K)

Figure 13-16: Plot of temperature dependant ZT values for LAST materials and PbTe.
This shows how the ZT results compare at room temperature.

257

 

Chapter 14: Conclusion/Future Work

14.1 Conclusion

Advancements in thermoelectric research have been made by the development of
new thermoelectric measurement systems and thermoelectric modeling discussed in this
thesis. Some of these advancements include using a thermal drifting technique during
thermopower measurements, measurements of thermopower and electrical conductivity
at higher temperatures, and the investigations of measuring ZT directly both at room
temperature and high temperatures. The performance and validation of each of the
systems developed have been presented by testing reference materials. With these new
systems, more confidence in the measurements of thermoelectric materials can be had by
measuring a thermoelectric sample in multiple systems as a cross check. The analyses of
measuring ZT directly lead to the creation of the ZT Machine. This system has proved to
be very useful in the rapid analysis of thermoelectric samples in searching for the optimal
synthesis technique.

A list of contributions to the thermoelectrics measurement laboratory at MSU

includes the following:

Major Contributions

0 Drifi System
0 Assembly of the system
0 Design of the automated computer control via LabVIEW
0 New curve fitting technique for measruing thermal conductivity
0 Testing and validation of the system

0 Ultra High Temp System
0 Assembly of the system
0 Design of the automated computer control via LabVIEW
0 Testing and validation of the system

258

- ZT Meter Using AC Method
0 Assembly of the system
0 Design of the automated computer control via LabVIEW
0 Testing and validation of the system

0 ZT Machine Using Digital Pulses
0 Assembly of the system
0 Design of the automated computer control via LabVIEW
0 Testing and validation of the system

0 Other LabVIEW Programs
0 RC-One Port Model with curve fitting
0 AC Transmission Line Model
0 Thermal Transmission Line Model with curve fitting

0 H3LT (Hogan’s Heroes High & Low Temp) System
0 Assembly of the system
0 Design of the automated computer control via LabVIEW
0 Testing and validation of the system

0 Measurements of Thermoelectric Materials
0 Thermopower (80K to 900K)
0 Electrical Conductivity (80K to 900K)
0 Thermal Conductivity (80K to 400K)
0 ZT Direct (300K to 800K)

Minor Contributions

0 Room Temperature Scanning Probe
0 Made software improvements

0 Enhancement of Impedance analyzer LabVIEW program
0 Modified program for more functionality

0 Room Temperature Thermopower Measurement System

In addition to the above contributions to the thermoelectrics research at MSU, this

work has also been presented to the scientific community through an oral presentation

and publication of the RC One-Port model at the 24th International Conference of

259

Thermoelectrics [64]. The Thermal TLIN E model was orally presented with publication
at the Fall 2005 Materials Research Society (Materials and Technologies for Direct
Thermal-to-Electric Energy Conversion) [65]. Finally, data collected through our
collaboration with the MSU Chemistry Department has been published for the

investigation of new bulk materials [66,67,68,69,70,7l ].

14.2 Future Work

There are many opportunities for future work and some have already begun. One
topic of interest is more experiments with direct ZT measurements at high temperatures
to reduce radiation losses. One study is the effect of different coatings around the TE
sample. Another is to measure temperature dependant emissivity of a sample to calculate
radiation losses in ZT measurements at high temperatures. Also, include a study on how
surface roughness affects radiation loss of these TE samples. Incorporated with this work
would be to also expand on the Thermal TLINE model to include radiation losses.

Another future study would be to add more automation to the ZT Machine to
reduce the sample preparation/mounting time. When massive quantities of
thermoelectric materials are being made for large power generation devices, an
automated ZT measuring system would prove to be very useful in this industrial type
application for rapid analysis.

More investigations are being studied on finding the optimal chemical formula and
the TB material synthesis process in which the ZT machine is being used to get larges

amounts of statistical data. This data can be used investigate patterns to identify trends in

260

the manufacturing process which would be used to improve the performance of the TE
materials.

Finally, new systems developed will be used to study segmented thermoelectric
legs of a module. Investigations of measuring ZT directly under large temperature

gradients will be needed for these types of modules.

261

Appendix A: Properties of Materials

Table A-1: Thermal conductivities of various materials

Conducti ' /mK
erial °C 125 °C 5 °C
latinum l 1

18.5
.024

ickel

tainless Steel

robeum 3.7
ilver 29
A1203 35
Nitride 175-190

 

Table A-2: Emissivity values of various materials

 

 

 

 

 

 

 

Material Emissivity
Carbon Black Paint NS—7 0.88
Aluminum (Commercial Sheet) 0.09
Buffed Copper 0.03
Copper with thick oxide layer 0.78
Constantan metal strip 0.09
Nickel Polished 0.072

 

 

 

 

262

Appendix B: Constantan Wire

3.] Introduction

Constantan wire was used as a reference material. The thermopower and electrical
conductivity was tested on a constantan wire sample (dia = 0.015”) in MSU’s HT System

from 300K to 700K.

82 Setup

Figure B-l (a) shows constant wire shaped in a manner to be able to support itself
along with a platinum resistor heater on top. Figure B-l (b) shows the wire now mounted

in the HT System using two Type-E thermocouples.

 

Figure B-l: Constantan wire (a) mounted in HT system (b) for thermopower and
electrical conductivity measurements

263

B.3 Results

-35

 

 

 

 

 

 

 

 

I I I I I
Calculated
S? '40 - I Experimental -
3
a -45 I- -l
i
O -50 I- u:
E
o
S
*- -55 - .1
‘60 I I I J I
200 300 400 500 600 700 800
Temperature (K)

Figure B-2: Thermopower of constantan found experimentally using MSU’s HT System
and compared to the calculated thermopower

 

 

 

 

 

 

 

 

 

3
2410 I I I I I
A 3 --O--HTSystem
g 2310 - --I--UHTSystem "
9. 3 Goodfellow Reference
5210 - -
g 3
g 2110 - : _____ .__-._-- ..
W
o 3 I“
15 2010 - I!
'z 3
13' 1910 - .i
“'5 3
1810 L I I J I
200 300 400 500 600 700 800

Temperature (K)

Figure B-3: Electrical conductivity of constantan measured with HT System, UHT
System, and from Goodfellow

264

 

 

  
       

‘5 Constantan ere (dia - 0.064“)
300 10 I I f I I I
250 1045 _ Electrical Conductivity .
o = 19420 (Slcm)
.5
E 200 10 ..
g a
g 150 10 a
’5 c
> 100 10 a
.5
50 ‘10 .1
0
0 10 ‘ I I i I

 

 

    

 

-2 o 2 4 6 8 1o 12
Position(mm)

Figure 84: Room Temp Scanning Probe measurement on constantan wire

265

Appendix C: Radiation Losses of Sim’s HT System and
High Temperature ZT Measurements

C.l Introduction

This Chapter gives details for radiation losses attributed to Sirn’ HT System as well
as High Temperature ZT measurements using an AC technique. Calculated radiation
losses can become very complicated because of the many unknown variables (emissivity,
exact temperature of surroundings, etc.). This chapter explores a reasonable approach to
calculating the approximate radiation losses and provides an insight to the effects of

radiation for small temperature gradients across the sample.

C.2 Evaluation of Radiation Losses

Radiation losses are a major factor in the calculation of thermal properties of
materials at high temperatures. Radiation happens when there is a temperature difference
between the sample and the environment. It is important to investigate how big of a
factor radiation plays into the calculation of ZT. A diagram of a sample mounted in

Sim’s HT System is shown in Figure 01.

266

 

. . P
Radiation m"

 

 

Radiation Radiation
¢ : \
<—— ———>
>~Prad2
‘—_
‘—
.2

 

 

Figure C-l: Diagram showing radiation losses in the HT System

This figure shows a sample with a heater on top which is in a high vacuum
environment (IE-5 Torr). The sample is also covered by a cap which will be assumed to
be the same temperature as the stage the sample is mounted to. From the diagram, there
are two main sources of radiation loss. One is radiation from the sample heater and the
other is the sample itself radiating heat. These two sources of radiation can be analyzed

separately and then added together to get the total radiation loss from the setup.

Radiation Equation
Radiation losses happen at all temperatures, however, radiation is related to
temperature to the fourth power. The equation for the power, in Watts, of the heat

radiated versus temperature is shown here.

P=e-0'-A-(T4—TS4) (W) (0.179)

267

Where we let

A = Radiative area (m2)
P = Power radiated (J/s)
e = emissivity (e = l for blackbody)

0' = Stefan — Boltzmann constant (5.6703 -10'8 W/m2K4)
T = Temperature of rdiator (K)

TS = Temperature of surroundings (K)

Radiation of Sample Heater

Calculating the radiation loss from the sample heater alone is explained here. The
heater is assumed to be at the temperature AT for the entire surface. The radiative surface
area of the sample heater is the entire surface minus the area where the heater is in
contact with the sample. Therefore, the radiative surface area of the sample heater is as

follows.

A H = radiative surface are of the heater

a = width of sample

b = thickness of sample (C. 1 80)
AH =2-(LH 'WH +LH 'TH +WH -TH)—(a-b)

Prod] (x) =eH -a'-AH ~(T(x)4 —TS4) (W)
P (x)=e -0-A -AT-(4-T3+6-T2-AT+4-T -AT2+AT3) (
rad] H H s s s W)

(C.181)

When AT << TS is true, the above equation can be approximated to the following.

Pradl(x)zeH~0-AH-AT-(4-Ts3) (W) (C.182)

Radiation of Sample
To examine the effects of radiation on only the sample, assume that the temperature

gradient across the sample is 1 °C or less. Also, assume that the temperature profile

268

along the length of the sample is linear to position with the equation shown here. This
assumption will prove to be reasonable by the end of this section.

AT pro be = Temp gradient between measurement probes

Lp = Distance between measurement probes
L = Length of sample
AT = Temp gradient across entire sample

T (x) 2 Temp along length of sample versus position (x = 0 to L)

AT = 1L; - ATpmbe (K) (C.183)

T(x) = LET— - x + T, (K) (C.184)

Neglecting the ends of the sample, the power being radiated along the length of the
sample is shown here.

A S = Radiative surface area of sample (do not include ends of sample)

Pm, (x) =es «Ms (T004 434) (W) (0.185)

Using the chosen temperature profile along the length of the sample, the equation for

power radiated now becomes:

AT 4 4
Prad2(x)=es'0"As'[(T'X+Ts) "Ts ] (W) (C186)

Taking the derivative of the power radiated will indicate if the power radiated is linearly

proportional to the position along the sample.

269

4
d d AT
Epradz (30:; es'U'As‘[[T'x+Ts] ‘Ts4] (C187)

_ es '0'4’AS

L4 [AT-x+TS-L]3-AT

 

Typically for this measurement, the temperature gradient across the sample will be kept
small (below 1°C) which will allow the following to be true:

AT << TS

When the above statement is true, the derivative of the power radiated now becomes:

(1 As 3

The above equation shows that the derivative of the power radiated is not dependant upon
the position. This indicates the power radiated is linearly proportional to the position.
This is helpful in that the radiation loss will affect the entire length of the sample evenly
without altering the linearity of the temperature profile.

Because the temperature along the length of the sample is not constant, the power
radiated must be integrated over the length of the sample. Now the total power radiated
from the sample can be solved for as follows.

a=width
b=thickness
As =2-a-L+2-b-L=2-L-(a+b)

L
Pradz = les-a-Z-(a+b)-(T(x)4—Ts4)-dx (W) (C.189)
O
L AT 4
Pradz = les-a-2-(a+b)-[(T-x+TS) —TS4]-dx (W) (C.190)
0

270

Pradz 2e, ~0-%-(a+b)-L-(AT3 +5-AT2 T, +10.AT-TS2 +10-TS3) (W)
(0.191)

When AT << TS is true, the above equation can be approximated as follows.

Pmdz zeS-a-4-(a+b)-L-(Ts3) (W) (0.192)

Now, the total effective radiation power is the sum of power radiated from the

heated plus the power radiated fiom the sample as follows.
Pradefir : rad] + Pradz (0193)

When AT << TS is true, the total power radiated can be approximated as follows.

Pradeff “[eH 'U'AH .AT.(4.TS3):I+|:eS .o-.4.(a+b)-L.(Ts3)] (0194)

=4-a-AT-Ts3 -(AH ~eH +L-es -(a+b)) (W)
Using the temperature gradient and the effective power radiated from the sample, an

effective radiation resistance can now be found to be:

AT _ AT
Pradefl 4-a-AT-Ts3-(AH-eH+L-es-(a+b))

 

 

Rmdefl = (0.195)

1
‘77 4oa-TS3-(AH-eH+L-es-(a+b))

 

Rmd (C.196)

So for small AT , the effective radiation resistance is not dependant upon AT.

271

C.3 Comparing Radiation from ZT measurements and Sim’s HT System

For comparing the radiation loss of Sim’s HT System to the radiation loss of high
temperature ZT measurements using an AC technique, the following equation was used

for the radiative power loss of the ZT measurement.
PdeTefl z 2-es -0'-AT-TS3 ~(L-a+L-b+2-a~b) (W) (0.197)

Using the temperature gradient and the effective power radiated from the sample, an
effective radiation resistance can now be found to be:

AT _ AT
PradZTefl 2-es-a-AT-TS3-(L-a+L-b+2-a-b)

 

RdeTefl = (C.198)

1
2-eS-a-TS3-(L°a+L-b+2-a-b)

 

RradZTefl = (K/W) (0199)

For a comparison of the effective radiation conductivity between the sample and
the environment, an example sample was chosen and is shown in the next page. The
emissivity for the sample and the sample heater was chosen to be 1. A small temperature
gradient was used in this analysis. For this specific example, the HT system radiation
loss was more than 3 times greater than if the sample was measured using the AC

technique for ZT measurements.

272

 

 

 

MathCAD File:

 

Heater Sample
Dimensions (m) Dimensions (m)
Lh := 0.0041 L := 0.0075
Wh := 0.00487 W := 0.00225
Th := 0.00067 T := 0.002825
Emissivity eh := 1 Probe Spacing (m)
PS :2 0.002906
Radiative Surface area of heat
Excluding spot touching sample. Emissivity es := 1
Ah := Lh-Wh-Z + Lh-Th-2 + WhaTh-Z — W-T Radiative Surface Area

As := 2-L-W + 2-L-T

Temperature Gradient across

Temperature of Surroundings (K) Sample

Ts := 300,310.. 700 20 L
Stefan Boltzmann Constant (W/m"2K"4) ddT := 070" 20 dT(ddT) := F-ddT
S

0' := 5.6703108
PradHT(Ts,ddT) := 4-o-dT(ddT)-Ts3-(Ah-eh + L-es-W + L-es-T)
PradZT(Ts,ddT) := 2-es-o-dT(ddT)-Ts3-(L-T + L-W + 2-W-T)

PradHT(Ts,ddT). L

kradHT(Ts,ddT) :=
dT(ddT) W-T

 

PradZT(Ts,ddT). L
dT(ddT) W-T

kradZT(Ts,ddT) :=

 

 

mamas,”
see
kradZT(Ts,l)
BBB

Radiation Conductivity (W/mK)

 

 

 

 

300 400 500 600 700

Ts
Temperature (K)

 

 

 

273

Appendix D: Useful Programs

D.1 Frequency Sweep Generator (Program)

There have been many times when a series of frequency test points where needed
such as the AC impedance spectroscopy test or even when analyzing the data in
LabVIEW. A LabVIEW program was created to generate a list of test frequencies by
indicating the minimum frequency, the maximum fiequency, the number of total test
frequencies, and finally, the sweep mode (linear or logarithmic). A picture of the front
panel to the program is shown in Figure D-l. The LabVIEW code can be seen in Figure

D-2.

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274

 

 

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Figure D-2: LabVIEW code for “Frequency Sweep Generator.vi”

 

D.2 Thermal Properties of Connecting Materials (Program)

For the creation of the Thermal TLINE model, a program was created to input the
standard properties of the thermoelectric module or TE material. This program allows the
user to input the dimensions of the ceramic plates and the nickel traces along with the
corresponding thermal properties. The program also allows the user to adjust the wire
impedance of the current leads attached to the sample. The number of pellets used in the
module is inputted here. Finally, the user selects the measurement configuration, such as,
is the sample a single TE material that is dangle or thermally grounded on one side, is the
sample an inline module that is dangling or thermally grounded on one side, or is the
sample a full module that is either dangling, thermally ground on one side, or one side
has a thermal resistance to ground. A picture of the front panel to this program is shown

in Figure D-3.

275

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Figure D-3: LabVIEW front panel for “Therm Properties of Connecting Materials.vi”

B.3 Triangular Minimizing Method (Program)

For curving fitting data to the Thermal TLIN E module, a triangular minimization
technique was used but in only one dimension. The program keeps track of three items:
the initial guesses of the answer, the corresponding MSE for those guesses, and a toggle

to show if the guesses have been improving or degrading. The output of the program

276

then makes a decisions on what the next guess would be to minimize the MSE. A picture
of the front panel to this program and the LabVIEW code is shown in Figure D-4 and

Figure D-5, respectively.

 

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Figure D-5: LabVIEW code for "Triangular Minizing Method.vi"

277

D.4 Converting Impedance Properties of a TE module to Actual Properties

A program was created to convert the measured impedance properties of a
thermoelectric module and convert it to the actual properties of the module such as ZT,
thermal resistance, thermal conductivity, thermal capacitance, Seebeck coefficient of a
single pellet (on average), electrical conductivity, and heat capacity (if the mass density is

known). Figure D-6 shows the fiont panel view of the LabVIEW program.

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Figure D-6: Front panel view of the LabVIEW progam “Converting to Thermal
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278

[1]

[2]
[3]
[4]

[5]

[6]

[7]

[3]

[9]

[10]

[11]

[12]

[13]

References

A. F. Ioffe, Semiconductor Thermoelements and Thermoelectric Cooling.
Infosearch Ltd. 1957.

G. Mahan, "Good Thermoelectrics," Solid State Physics, vol 5.1, 1998.
H. J. Goldsmid, Electronic Refrigeration. New York: Plenum, 1964.

S. O. Kasap (2001), Thermoelectric Eflect in Metals: Thermocouples. [Online].
Available: http://Materials.Usask.Ca

J. Chen, Z. Yan, "The influence of Thomson effect on the maximum power output
and maximum efficiency of a thermoelectric generator," J. Appl. Phys, vol. 79, no.
11, 1996.

K. F. Hsu et al., “Cubic Ang(m)SbTe(2+m) Bulk Thermoelectric Materials with
High Figure of Merit,” Science, vol. 303, 2004, pp. 881-821 .

J. Short, S. Loo, S. Lal, K.F. Hsu, E. Quarez, M.G. Kanatzidis, T. Hogan, “Hall
Effect Measurements on New Thermoelectric Materials”, Mat. Res. Soc. Sym.
Proc., Vol. 793, 2004, pp. 323-332.

G. W. Burns, M. G. Scroger, G. F. Strouse, M. C. Croarkin, W. F. Guthrie,
"Temperature-Electromotive Force Reference Functions and Tables for the Letter-
Designated Thermocouple Types Based on the ITS-90," Natl. Inst. Stand Technol.
Monograph I 75, 1993.

S. O. Kasap, Principles of Electrical Engineering Materials and Devices, Revised
Edition. Boston: McGraw-Hill, 2000.

N. F. Mott, The Theory of the Properties of Metals and Alloys. New York: Dover
Publications. 1936.

H. J. Golsmid, J. W. Sharp, "Estimation of the Thermal Band Gap of a
Semiconductor from Seebeck Measurements," J. Electronic Materials, vol. 28, no.
7, 1999.

A. Suzuki, Y. Hasegawa, T. Komine, H. Morita, H. Shirai, Y. Ishikawa,

"Investigation of physical and electric properties of silver pastes as a binder for
thermoelectric materials," Rev. Sci. Instrum, vol. 76, 2005.

E. F. Chor, J. Lerdworatawee, "Quasi-Two-Dimensional Transmission Line Model
(QTD-TLM) for Planar Ohmic Contact Studies," IEEE Trans. Electron Devices,
vol. 49, no. 1, Jan. 2002.

279

 

[14] H.J. Goldsmid, “The use of semiconductors in thermoelectric refrigeration,” Bri. J.
Appl. Phys, vol. 5, Nov. 1954.

[15] L. D. Hicks, M. S. Dresselhaus, “Effect of quantum-well structures on the
thermoelectric figure of merit”, Phys. Rev. B, vol. 47, no. 19, pg. 727-731, 1993.

[l 6] R. Taylor, CRC Handbook of Thermoelectrics, ed. D. M. Rowe, CRC Press, Inc.,
1995.

[17] M. G. Kanatzidis, et. al., "Thermoelectric Materials: Solid State Synthesis," Naval
Res Rev, vol. 48, no. 4, 1996.

[18] T. C. Harman, J. H. Cahn, and M. J. Logan, “Measurement of Thermal
Conductivity by Utilization of the Peltier Effect,” J. Appl. Phys, vol. 30, no. 9,
Sept. 1959.

[19] O. Maldonado, “Pulse method for simultaneous measurement of electric

thermopower and heat conductivity at low temperatures”, Cryogenics, vol. 32, no.
10, 1992.

[20] T. C. Harman, J. M. Honig, J. Appl. Phys, vol. 13, 1962, p. 440.

[21] S. Loo, Transport Characterization of New High Temperature Quaternary
Thermoelectric Materials and Devices, Ph.D. Thesis, Michigan State University,
2003.

[22] J. Short, A New System Debeloped to Characterize Thermoelectric Devices for
Power Generation Applications, Master Thesis, Michigan State University, 2005.

[23] G. Min, D. M. Rowe, and K. Kontostavlakis, “Thermoelectric figure of merit under
large temperature differences,” J. Phys. D, vol. 37, 2004, pp. 1301-1304.

[24] G. Min, D. M. Rowe, “A novel principle allowing rapid and accurate measurement
of a dimensionless thermoelectric figure of merit,” J. Meas. Sci. T ech., Vol. 12,
2001, pp. 1261—1262.

[25] F. Chen, “Low-frequency ac measurement of the Seebeck coefficient,” Rev. Sci.
Instrum, vol. 72, no. 11, 2001, pp. 4201-4206.

[26] A. T. Burkov, A. Heinrich, P. P. Konstantinov, T. Nakarna, K. Yagasaki,
“Experimental set-up for thermopower and resistivity measurements at 100-
1300K,” Meas. Sci. T echnoI., vol. 12, 2001, pg. 264-272.

[27] A. L. Pope, R. T. Littleton, T. M. Tritt, "Apparatus for the rapid measurement of

electrical transport properties for both "needle-like" and bulk materials," Rev. Sci.
Instrum, vol. 72, no. 7, July 2001, pp. 3129-3131.

280

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[3 7]

[3 3]

[39]

R. T. Littleton IV, et. al. , "High Temperature Transport Probe for Thermopower
and Resistivity Measurements," Materials Research Society Symposium
Proceedings, 1998.

Z. Zhou, C. Uher, "Apparatus for Seebeck coefficient and electrical resistivity
measurements of bulk thermoelectric materials at high temperature," Rev. Sci.
Instrum., vol. 76, 2005.

M. Putti, M. R. Cirnberle, A. Canesi, C. F oglia, A. Siri, "Thermopower
measurements of hi gh-temperature superconductors: Experimental artifacts due to
applied thermal gradient and a technique for avoiding them," Phys. Rev. B, vol. 58,
no. 18, Nov. 1998.

R. Buist, "A new methodology for testing thermoelectric materials and devices,"
Proc. H Int. Conf on Thermoelectrics, Oct. 1992.

P. J. Talor, W. A. Jesser, F. D. Rosi, Z. Derzko, "A model for the non-steady-state
temperature behavior of thermoelectric cooling of thermoelectric cooling
semiconductor devices," Semicon. Sci. T echnol., vol. 12, 1997, pp. 443-447.

D. Kondratiev, L. Yershova, "TE Coolers Computer Simulation: Incremental
Upgrading of Rate Equations Approach, " Proc. 6'“ of the Eur0pean Thermoelectric
Society, Sept. 2001.

G. K. Ottarsson, "A Ladder Thermoelectric Parallelepiped Generator," Proc. 21‘"
Int. Conf. on Thermoelectrics, May 2002.

P. G. Lau, R. J. Buist, "Temperature and Time Dependent Finite Difference Model
of a Thermoelectric Pellet and Couple," Proc. XV Conf. on Thermoelectrics,
Pasadena, California, USA, 1996.

V. Milanovic, M. Hopcroft, C. Zincke, M. Zaghloul, K. Pister, "Modeling of
Thermoelectric Effects in Planar Micromachined Structures Using SPICE,"
Proceedings of Therminic Int. Workshop, 2000.

P. Turkes, "Thermal Network Calculation for Level-3 Compact Models," Infineon
Technologies AG, Application Note AN -PSM-12, Aug. 2001 .

H. Sasaki, K. Takahashi, B. Inglis, M. Klonz, "A Numerical Simulation of
Thermoelectric Effects in Single-Junction Thermal Converters," IEEE Trans.
Instrumentation and Measurement, vol. 48, no. 2, April 1999.

K. Takahashi, M. Sasaki, B. Inglis, M. Klonz, "AC-DC Voltage Transfer Difference
Due to Seebeck Effect in Thermal Converters," IEEE Trans. Instrumentation and
Measurement, vol. 48, no. 2, April 1999.

281

[40]

[41]

[42]

[43]

[44]

[45]

[46]

[47]

[43]
[49]
[50]

[51]

[52]

[53]

G. Snyder, J. Fleurial, T. Caillat, "Supercooling of Peltier cooler using a current
pulse," J. Appl. Phys, vol. 92, no. 3, 2002.

B. Lwo, K. Tseng, C. Kao, L. Lu, "Over-Temperature Forecasts on Electronic
Packages Through a Transient R-C Model," J. EIec. Packaging, vol. 122, 2000, pp.
42-47.

R. J. Buist, P. G. Lau, "Theoretical analysis of thermoelectric cooling performance
enhancement via thermal and electrical pulsing," Proc. of 15th Int. Conf. on
Thermoelectrics, Pasadena, California, March 1996.

T. A. Al-Obaidi, H. J. Goldsmid, "Determination of the Thermoelectric Figure of
Merit from Thermal Conductivity Measurements," Energy Conversion, vol. 9,
1969, pp. 131-132.

P. B. Gray, The Dynamic Behavior of Thermoelectric Devices. New York: The
Technology Press of The Massachusetts Institute of Technology and John Wiley &
Sons, 1960.

J. A. Chavez, J. A. Ortega, J. Salazar, A. Turo, M. J. Garcia, ”SPICE model of
thermoelectric elements including thermal effects”, Proceedings of the I 7th IEEE

Instrumentation and Measurement Technology Conference 2000, vol. 2, May 2000,
pp. 1019-1023.

S. Dilhaire, “Determination of ZT of PN thermoelectric couples by AC electrical
measurement,” Proceedings of the 21‘" International Conference on
Thermoelectronics, 2002.

H. Iwasaki, S. Yokoyama, T. Tsukui, M. Koyano, H. Hori, S. Sano, "Evaluation of
the Figure of Merit of Thermoelectric Modules by Harman Method," Jpn. J. Appl.
Phys, vol 42, 2003, pp. 3703-3708.

B.P. Lathi, Signal Processing & Linear Systems. Berkeley Cambridge Press, 1998.
Tellurex Corporation (2006, April). Available: http://www.tellurex.com/

G. M. Wierzba. (2002). ECE 831 Class Notes. Michigan State University. East
Lansing, MI. [CD-ROM].

W. Chen, Passive and Active Filters Theory and Implementations, John Wiley &
Sons, 1986.

M. Lenz, G. Striedl, U. F rohler, Thermal Resistance - Theory and Practice.
Infineon Technologies AG. 1999.

D. Maillet, Thermal Quadrupoles' Solving the Heat Equation through Integral
Transforms, John Wiley & Sons, Nov. 2000.

282

[54]

[55]

[56]

[57]

[58]

[59]

[60]

[61]

[62]

[63]

[64]

[65]

[66]

J .A. Nelder, R. Mead, "A Simplex Method for Function Minimization", Computer
Journal, vol. 7, 1965, p. 308.

P. M. Mayer, R. J. Ram, "Cross-plane Thermoreflectance Imaging of
Thermoelectric Elements," Materials Research Society Symposium Proceedings,
vol. 886, 2005.

K&K Associates, Thermal Connection. (2006, April). [Online]. Available:
http://www.tak2000.com/data2.htm#surffin

C. Vining, “Thermoelectric properties of pressure-sintered Si0.8Ge0.2
thermoelectric alloys,” J. Appl. Phys, vol. 69, no. 8, April 1991.

P.J. Tirnans, “Emissivity of silicon at elevated temperatures,” J. Appl. Phys, vol.
74, no. 10, Nov. 1993.

R. B. Roberts, F. Righini, R. C. Compton, Phil. Mag, vol. 52, 1985, p. 1147.

B. Sundqvist, “Thermal diffusivity and thermal conductivity of Chromel, Alumel
and Constantan in the range 100-450 K,” J. Appl. Phys, vol. 72, no. 2, 1992.

S. Sasaki, H. Masuda, H. Kou, and H. Takahashi, “A Transient Heating Technique
for Measuring the Thermal Diffusivity of Metals,” International Journal of
T hermophysics, vol. 19, no. 1, 1998.

V.Volodin, G. Gromov, D. Kondratiev, A. Ogryzko, A. Rogov, L. Yershova, "Z-
metering Developmen ", Proceedings of 2002 X anniversary Forum on

Thermoelectricity, 2002.

H. Iwasaki, M. Koyano, H. Hori, “Evaluation of the Figure of Merit on
Thermoelectric Materials by Harman Method,” J. Appl. Phys, vol. 41, 2002, pp.
6606-6609.

A. D. Downey, T.P. Hogan, "Circuit model of a thermoelectric module for ac
electrical measurements," Proceedings of the 24th International Conference on
Thermoelectrics, Clemson, South Carolina, June 2005, pp.79-82.

A. D. Downey, E. Tirnm, P. Poudeu, M. G. Kanatzidis, H. Shock, T. P. Hogan,
"Application of Transmission Line Theory for Modeling of a Thermoelectric
Module in Multiple Configurations for AC Electrical Measurements," Materials
Research Society Symposium Proceedings, vol. 886, 2005, pp. 425-430.

P. F. Poudeu, J. D'Angelo, A. D. Downey, R. Pcionek, J. Sootsman, Z. Zhou, O.
Palchik, T. P. Hogan, C. Uher, M. G. Kanatzidis,"Effects of Antimony on the
Thermoelectric Properties of the Cubic Pb9.6SbyTe10-xSex", Materials Research
Society Symposium Proceedings, vol. 886, 2005, pp. 195-200.

283

[67] J. L. Short, J. D’Angelo, A. D. Downey, M. A. Pajor, M. G. Kanatzidis, E. Timm,
H. Schock, T. P. Hogan, "Characterization of Thermoelectric Power Generation

Modules Made from New Materials," Materials Research Society Symposium
Proceedings, vol. 886, 2005, pp. 309-315.

[68] J. D'Angelo, J. L. Short, A. D. Downey, M. A. Pajor, E. Timm, H. Schock, M. G.
Kanatzidis, T. P. Hogan, "Investigation of Low Resistance Contacts to Pb-Sb-Ag-
Te (LAST) Materials for Module Fabrication," Materials Research Society
Symposium Proceedings, vol. 886, 2005, pp. 317-322.

[69] T. P. Hogan, A. D. Downey, J. Short, J. D'Angelo, E. Quarez, J. Androulakis, P.
Poudeu, M. G. Kanatzidis, E. Tirnm, K. Sarbo, H. Schock, "Progress on the
Fabrication and Characterization of High Efficiency Thermoelectric Generators,"
Materials Research Society Symposium Proceedings, vol. 886, 2005, pp. 487—492.

[70] J. Androulakis, K. F. Hsu, R. Pcionek, H. Kong, C. Uher, J. D'Angelo, A. Downey,
T. Hogan, M. G. Kanatzidis, "Nanostructuring and High Thermoelectric Efficiency
in p-Type Ag(Pb1-ySny)meTez+m," Adv. Mater, 2006, in press.

I

[71] P. Poudeu, J. D'Angelo, A. D. Downey, J. L. Short, T. P. Hogan, M. G. Kanatzidis,
"High Thermoelectric Figure of Merit and Nanostr'ucturing in Bulk p—type Na]-
bemeyTem+2," Angew. Chem. Int. Ed, 2006, in press.

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