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THESS
z
2000

 

 

LIBRARY ‘
Michigan State
University

 

 

 

This is to certify that the

thesis entitled

INVESTIGATION OF THE NEW FAMILY OF CUBIC
CHALCOGENIDE COMPOUNDS

AmBanQZm+n FOR THERMOELEETRIC

APPLICATIONS
presented by

Stephan De Nardi

has been accepted towards fulfillment
of the requirements for

M.S. Chemistry

degree in

Major professor

 

 

 

S/V/Zfloo

 

0-7 639 MS U is an Affirmative Action/Equal Opportunity Institution

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE

DATE DUE

DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11m CJCIHCan-p.“

 

——~

INVESTIGATION OF THE NEW FAMILY OF CUBIC CHALCOGENIDE
COMPOUNDS AmBanQ2m+n FOR THERMOELECTRIC APPLICATIONS

By

Stephan De Nardi

A THESIS

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

MASTER OF SCIENCE
Department of Chemistry

2000

ABSTRACT

INVESTIGATION OF THE NEW FAMILY OF CUBIC CHALCOGENIDE
COMPOUNDS AmBuMszm+n FOR THERMOELECTRIC APPLICATIONS

By

Stephan De Nardi

A growing concern for environmentally friendly devices as well as a need for more
efficient materials, has revitalized recently the field of thermoelectricity. Several research
groups are investigating new compounds that could replace the established materials
BizTe3 and PbTe which have been used for several decades for thermoelectric
applications.

A new family of quartenary chalcogenides semiconducting compounds of general
formulae AmBanQzlm+n (where A is K or Ag, B is Pb or Sn, M is Bi or Sb and Q is S,
Se, or Te) was synthesized and characterized. Preliminary measurements show that these
narrow band gap semiconductors possess promising transport properties for
thermoelectric applications. A wide range of values have been observed for the
parameters of interest (the Seebeck coefficient, and the electrical and thermal
conductivity) depending on the elements chosen and the values of n and m. Among all the
systems investigated, KPmeiTelz was chosen for further optimization. The thermal
conductivity of this compound can be decreased significantly by increasing the mass
fluctuation in the structure via solid solutions. The introduction of Sn as chemical dopant
agent increased the figure of merit ZT. Significant differences between measurements of

the Seebeck coefficient on cold pressed pellets and ingots were observed and investigated.

TABLE OF CONTENTS

List of Tables. ...................................................................................................................... v
List of Figures ................................................................................................................... viii
Chapter 1: Introduction and Thermoelectric Concepts ....................................................... 1
1-1. Brief History of Thermoelectricity ..................................................... 2
1-2. Focus of this Research ........................................................................ 7
1-3. Concepts and Important Physical Properties ................................... 11
Performance of a Material ........................................................... 12
Electrical Conductivity (o) ......................................................... 13
Thermal Conductivity (K) ........................................................... 17
Seebeck Coefficient (S) ............................................................... 25
Other Important Properties and Notions ................................... 31
References .................................................................................. 42

Chapter 2: Investigation of the Thermoelectric Properties of the Family

of Cubic Semiconducting Quartenary Chalcogenidesr AmBanQ2m+n .............................................. 44
2-1. Introduction ...................................................................................... 44
2-2. Experimental Section ........................................................................ 48

Reagents .................................................................................... 48
Synthesis of AmBanQ2m+n Compounds. .................................. 50
Physical and Transport Property Measurements ....................... 52
2-3. Results and Discussion. .................................................................... 55
Synthesis and Crystallographic Data. ........................................ 55
(l) K/Pb/Bi/T e System .................................................. 55

(2) K/Pb/Bi/Se System .................................................. 59

(3) K/Pb/Bi/S System .................................................... 62

(4) Ag/Pb/Bi/Te System. ............................................... 65

(5) Other Systems. ......................................................... 67
Physical Properties. ................................................................... 69
(1) K/Pb/Bi/T e System ................................................... 69

(2) K/Pb/Bi/Se System .................................................. 71

(3) K/Pb/Bi/S System .................................................... 74

(4) Other Systems. ......................................................... 74
Transport Properties .................................................................. 76
(1) K/Pb/Bi/T e System ................................................... 76

(2) K/Pb/Bi/Se and K/Pb/Bi/S System. ........................ 84

(3) Ag/Pb/BiTe System. ................................................ 84

2-4. Concluding Remarks. ......................................................................... 90
References. ................................................................................................. 93

Chapter 3: Decreasing the Thermal Conductivity of KPbloBiTe 12 by Mass Fluctuation

via Solid Solution Experiments ........................................................................................... 94
3-1. Introduction ....................................................................................... 94
3-2. Experimental Section .......................................................................... 96

Reagents .................................................................................... 96
Synthesis .................................................................................... 96
Physical and Transport Property Measurements ....................... 97
3-3. Results and Discussion. ..................................................................... 97
Synthesis and Crystallographic Data ......................................... 97
(1) The Solid Solutions KwaBiTem‘Sx ....................... 97
(2) The Solid Solutions I(Pb10BiTe12.xSex ..................... 99
(3) The Solid Solutions KPbloBiSem‘Sx ..................... 101
(4) Solid Solutions of the Type
KPb 10Bi058b005T66SC6 ............................................. 102
Physical Properties .................................................................. 103
Thermal Analysis ......................................................... 103
Energy Gap .................................................................. 105
Transport Properties ................................................................ 107
(1) The Solid Solutions I<2Pb10BiTe12.xSex ................... 107
(2) The Solid Solutions KanoBiSenz-xSx ................................ 114
(3) Other Solid Solutions of KPbloBi1-bexTe6Se6 ...... 116
3-4. Concluding Remarks ........................................................................ 127
References ................................................................................................ 1 28

Chapter 4: Effect of Doping Agents on the Transport Properties of KPbloBiTe6Se6

and KPb10B1058b05T66866 .............................................. 129
4-1. Introduction ..................................................................................... 129
4-2. Experimental Section ........................................................................ 131
Reagents ................................................................................... l3 1
Synthesis ................................................................................... 131
4-3. Results and Discussion .................................................................... 132
Synthesis and X-ray Powder Diffraction Data ........................ 132
Energy Gap .............................................................................. 136
Transport Properties ................................................................. 138
(a) DOPEd KPbloBiTesses ................................................................. 138
(b) DOpCd KPbloBlo_5Sb0_5T€6se6 ................................ 143
4-4. Concluding Remarks ........................................................................ 148
References ................................................................................................ 150
Conclusion .................................................................................................................. l 5 l

Table 1-1.

Table 1-2.

Table 1-3.

Table 1-4.

Table 2-1.

Table 2-2.

Table 2-3.

Table 2-4.

Table 2-5.

Table 2-6.

Table 2-7.

Table 2-8.

Table 2-9.

LIST OF TABLES

Thermoelectric properties of n-type PbTe and BizTe3

at Optimum temperature (Tmax) .............................................................

Thermal conductivity at room temperature for different

type of materials ...................................................................................

Energy gap (eV) for some semiconductors. The nature of

the band gap is also reported (i.e. direct (i) or indirect (d)) .................

Different effective mass ratio for several different type of

semiconductors .....................................................................................

Known members of the system A’mBanQ2m+n

(With A’= Ag, Cu, Tl; B = Pb, Ge; M = Bi, Sb; and Q = S, Se,Te)....

Cell parameters of KanBiTen+2 members for different

experimental conditions .......................................................................

Cell parameters for selected members of the family
KanBiSen+2 (with n = l, 2, 3, 4, 5, 8, 10)

and KPmeiSn+2(With [1:1 , 4, 8) ...........................................................

Cell parameters for members of the KanBiSe2+n and

KanBiSm systems made by “flame” induced reaction ......................

Cell parameters for members of silver based systems .........................

Cell parameters of members of the K/B/M/T e system

(where B is Pb or Sn and M is Bi or Sb) ..............................................

Energy gap for members of the family of compounds

KP aniQn+2 ...........................................................................................

Seebeck coefficient (pressed pellets) and electrical conductivity
(ingots) for members of silver based systems at room

temperature ...........................................................................................

Room temperature electrical conductivity and Seebeck
coefficient for members of the K/B/M/T e system

(where B is Pb or Sn and M is Bi or Sb) ..............................................

11

18

36

4o

47

59

62

63

65

67

71

86

89

Table 2-10.

Table 3—1.
Table 3-2.

Table 3-3.

Table 3-4.

Table 3-5.

Table 3-6.

Table 4-1.

Table 4-2.

Table 4-3.
Table 4-4.
Table 4-5.

Table 4-6.

Table 4-7.

Table 4-8.

Physical and transport properties for members of different
systems .................................................................................................

Cell parameters for solid solutions of KPbloBi'l“e12.Sex .......................
Cell parameters for solid solutions of KPbloBiSe12-xSx .......................

Cell parameters, energy gaps, recrystallization and melting
temperatures (Tcryst and Tm), for members of the system
KPbloBi1.bexTeGSe6 ............................................................................

Room temperature Seebeck coefficient (on pressed pellet)
and electrical conductivity (on ingot) for solid solutions
KPbloBiT612-xSex ..................................................................................

Room temperature Seebeck coefficient (on pressed pellet)
and electrical conductivity (on ingot) for solid solutions
KPbIOBise]2-xSx ....................................................................................

Room temperature Seebeck coefficient (on pressed pellet)
and electrical conductivity (on ingot) for solid solutions
KPbloBi]-bexT66366 ............................................................................

Cell parameters for doped KPbloBiTe6Se6 with different agents .........

Correspondence between weight and atomic percentages of
concentration for different doping agents of KPbloBiTe6Se6 ...............

Cell parameters for Sn doped KPbloBio_5Sbo.5Te6Se6 ...........................
Energy gaps for KPbloBiTeGSeg doped with Ag and Sb ......................
Energy gaps for KPblOBinSbOjTCfiseé doped with Sn ........................

Transport properties for KPbloBiTe6Se6 doped with Ag, Sb, Sn
measured at our lab (0 measured on ingots and S on cold pressed

pellets) ..................................................................................................

Electrical conductivity of KPbloBio,5Sbo_5Te6Se6 doped with
various amount of Sn (measured on cold pressed pellets and
on ingots) ..............................................................................................

Effect of annealing on the transport properties of pressed
pellets of KPbloBio5Sb05Te6Se6 doped with 0.15 % Sn ......................

vi

92

100

102

106

109

115

116

134

135

135

138

138

144

145

147

Table 4-9. Seebeck coefficient and electrical conductivity at room
temperature for KPbloBio.5Sbo_5Te6Se6 doped with various
amount of Sn ....................................................................................... 148

vii

LIST OF FIGURES

Figure 1-1: The two principal effects in thermoelectricity:
(a) Seebeck effect used in power generation and
(b) Peltier effect used in refrigeration technology ..............................

Figure 1-2: Figure of merit for the best thermoelectric materials:
n—BiSb, BizTe3, PbTe, LaFegCoSblz, n-SiGe, and CsBi4Te6 ..............

Figure 1-3: NaCl crystal structure type of "AmBanszfl. compounds
with A, B, M, on the Cl- atomic sites and Q on the Na+ sites ............

Figure 1-4: Variation of the conductivity as a function
of temperature for different materials .................................................

Figure 1-5: (a) Intrinsic and (b) extrinsic semiconductor ......................................

Figure 1-6: (a) p-type doped and (b) n-type doped semiconductor .......................

Figure 1-7: Lorentz factor L0 as a function of the reduced Fermi level

and different scattering process (s) .....................................................
Figure 1-8: Thermal conductivity and the different scattering processes

involved ..............................................................................................
Figure 1-9: Three phonons interaction. (a) Normal process

and (b) Umklapp process ....................................................................

Figure 1-10: Seebeck coefficient behavior for different types of materials ............
Figure 1-11: Seebeck measurement showing a maximum at the point A ...............

Figure 1-12: Calculation of an energy gap using absorption spectroscopic
data ......................................................................................................

Figure 1-13: (a) Direct transition process and (b) absorption coefficient
showing a abrupt absorption edge with an energy increase ................

Figure 1-14: (a) Indirect transition involving a phonon and (b) absorption
coefficient showing a slower increase with energy ............................

Figure 1-15: Carrier concentration behavior for a semiconductor as a function
of temperature ....................................................................................

viii

Figure 1-16: Effect of the effective mass on the electronic band ............................ 39
Figure 2-1: Research methodology ........................................................................ 46
Figure 2-2: X-ray powder diffraction patterns of (a) KPbgBiTem,

(b) KPbBiTe3,(c) KszBiTe4 (using flame reaction),
(d) KPbloBiTe 12 (e) impurity phase in KszBiTe4, and

(1) calculated BiTe .............................................................................. 57
Figure 2-3: X-ray powder diffraction patterns of (a) KPbgBiSes, (b) PbSe,

(c) KszBizses, and (d) calculated BiSe ............................................. 60
Figure 2-4: Cell parameter variation in the system (KBiSe2)1.,((PbSe)x ................ 61
Figure 2'51 X-ray powder diffraction patterns of (a) KPbgBiSlo and (b) PbS ....... 64
Figure 2-6: Cell parameter variation in the system (KBiSz)1.,‘(PbS)X .................... 64
Figure 2-7: X-ray powder diffraction pattern of AngloBiTelz ............................ 66
Figure 2-8: Cell parameter variation in the system (AgBiTe2)1.,((PbTe)x ............. 66
Figure 2-9: X-ray powder diffi'action pattern of KSnBiTe; ................................. 68

Figure 2-10: Optical absorption spectrum of KPbloBiTelz
showing the energy gap ...................................................................... 70

Figure 2-11: Variation of the energy gap as a function of x for the system
(KBISCz)1-x(PbSC)x .............................................................................. 72

Figure 2-12: Optical absorption spectrum of KPbsBiSe7
showing the energy gap ...................................................................... 72

Figure 2-13: (a) Optical absorption spectrum of KPbloBiSelz.
The band gap of the compound is masked by mid gap energy
levels. (b) No band gap appear after annealing of the
sample for 24 h at 400 °C .................................................................... 73

Figure 2-14: Optical absorption spectrum of KPbgBiSlo
showing the energy gap ...................................................................... 73

Figure 2-15: Optical absorption spectrum of KPbsste7
showing a broad tail ............................................................................ 75

ix

Figure 2-16: Seebeck coefficient as a function of temperature for
members of the system KanBiTen+2 synthesized using

“flame” reaction (cold pressed pellet measurement) ......................... 78
Figure 2-17: Seebeck coefficient and electrical conductivity for KPbBiTe; .......... 78
Figure 2-18: Seebeck coefficient measurement of KPbgBiTelo and

KPbloBiTelz (ingots) ........................................................................... 80
Figure 2-19: Thermal conductivity of KPbgBiTelo and KPbloBiTelz (ingots) ....... 80
Figure 2-20: Electrical conductivity of KPbgBiTelo and KPbloBiTeu (ingots) ...... 81
Figure 2-21: ZT versus T for KPbgBiTelo and KPbloBiTen ................................... 81
Figure 2-22: Charge carrier concentration for KPbgBiTelo and KPbloBiTelz as a

function of the temperature ................................................................. 83
Figure 2-23: Temperature dependence of the mobility of samples of

KPbgBiTem and KPbloBiTelz .......................................... 83
Figure 2-24: Seebeck coefficient for KPmeiSlz (cold pressed pellet) .................. 85
Figure 2-25: Seebeck coefficient for AngloBiTelz (cold pressed pellet) ............... 85
Figure 2-26: Electrical conductivity of AngloBiTelz (measured on ingot) ........... 87
Figure 2-27: Seebeck coefficient for AngmBiTen (measured on ingot) ............... 87

Figure 3-1: X-ray powder diffraction patterns of (a) KPbloBiTe3sg,
(b) KPbloBiTe389 after annealing, (c) KPbloBiTe98e3,
(d) KPbloBiSe339, (e) KPbloBio.sSbo.sTees€6, and

(f) KPbloBiTelz (showing for comparison) ........................................ 98
Figure 3-2: Cell parameter variation for the solid solutions

KPbloBiT612-xSex ................................................................................ l 00
Figure 3-3: Cell parameter variation for the solid solutions

KPblOBise]2-xSx .................................................................................. 102
Figure 3-4: Cell parameter variation for the solid solutions

KpbloBil-beT66866 ............................................................................ 103

Figure 3-5: DTA of KPbloBi0258b0jsse6S6 showing the recrystallisation
and melting temperatures .................................................................... 104

Figure 3-6:

Figure 3-7:

Figure 3-8:

Figure 3-9:

Figure 3-10:

Figure 3-11:

Figure 3-12:

Figure 3-13:

Figure 3-14a:

Figure 3-14b:

Figure 3-15:

Figure 3-16:

Figure 3-17:

Figure 3-18:

Figure 3—19:

Optical absorption spectrum of KPbloBio_5Sbo.SSe686
showing a band gap ............................................................................. 106

Seebeck coefficient for KPbloBiTeuSe (batch a)
measured on cold pressed pellet ......................................................... 108

Thermal conductivity for KPbloBiTenSe before and
after correction .................................................................................... l 1 1

Radiative losses as a function of T3 .................................................... 111

Seebeck coefficient and electrical conductivity for

KPmeiTenSe (ingot) ........................................................................ 112
Seebeck coefficient showing a minimum for

KPbloBiTel ISC .................................................................................... 112
Figure of merit ZT for KPbloBiTel lse ............................................... 1 13

Seebeck coefficient of solid solution
KPbloBiSe12.xSx (cold pressed pellets) ................................................ 1 15

Thermal conductivity for the solid solutions
KPbloBi1.bexTe68e6 (on ingots and before correction) ..................... 120

Thermal conductivity for the solid solutions
KPbloBi1.bexTe5Se6 (on ingots and after correction) ........................ 121

Electrical conductivity for the solid solutions
KPbloBil-bexTe6$e6 (ingots) .............................................................. 122

Seebeck coefficient for the solid solutions
KPbloBi1-bexTe6Se6 (ingots) ............................................................. 123

Seebeck coefficient for the solid solutions
KPbloBil-bexTe6SE¢5 (pellets) ............................................................. 124

Seebeck coefficient for the solid solutions
KPbloBi1.bexTe6Se6 (ingots and pressed pellets) .............................. 125

Figure of merit ZT for the solid solutions
KPmei1-bexTe6Se6 ........................................................................... 126

xi

Figure 4-1:

Figure 4-2:

Figure 4-3:

Figure 4-4:

Figure 4-5:

Figure 4-6:

Figure 4-7:

Figure 4-8:

X-ray diffraction powder patterns of
(a) KPblOBiTe6sefi doped with 0.1 weight % of Sn and
(b) KPbloBio,5Sbo_5Te6Se6 doped with 0.23 atomic % of Sn

substituted for Bi ................................................................................

Optical absorption spectra of
(a) KPblOBiTe6Se6 doped with 0.1 weight % Sn and
(b) KPmeiasSbojTeésee doped With 0.05 % SD and

showing a broad tail ...........................................................................

Seebeck coefficient (on cold pressed pellets)for KPbloBiTe6$e6

doped with different doping agents. ..................................................

Seebeck coefficient of KPbloBiTe68e6 doped with

0.1 weight % of Sn (ingot) .................................................................

Thermal conductivity of KPbloBiTe6Se6 doped with

0.1 weight % of Sn (ingot) .................................................................

Radiative losses versus T3 for thermal conductivity of

KPbloBiTe68e6 doped with 0.1 weight % Sn (ingot) .........................

Electrical conductivity of KPbloBiTe68e6 doped with

0.1 weight % of Sn (ingot) .................................................................

Seebeck coefficient of KPblOBinSbOjTefiseé doped by
excess of various amount of Sn on Bi sites

(a) measured on cold pressed pellets and (b) on ingots ......................

xii

133

137

140

141

141

142

142

146

Chapter 1

Introduction and Thermoelectric Concepts

It would be too long here to list the numerous applications that thermoelectric
materials (TE) can produce. From inertial guidance systems in aerospace industry, to
wine coolers, military night vision equipments, laser diode coolers, hypothermia blankets,
blood analyzers, or whipped cream dispensers in restaurants], the impact of this
technology in our lives is important. The necessity of developing better thermoelectric
materials lies not only in technological needs but also in the growing concern on global
warming and the increasing demand on environmentally friendly devices. Today, more
people than ever are concerned about pollution and warming effects. As an example,
during the third World Conference on global warming, one of the major points of
attraction was thermoelectric materials that can generate power from waste heat 2.

Thermoelectric materials can also be used for refrigeration purposes. A new class
of isostructural conductive compounds of formula AmBanQ2m+n where A is an alkali
metal or silver, B lead or tin, M bismuth or antimony, and Q a chalcogenide was studied is
this Thesis and showed particularly promising thermoelectric properties. They are
narrow band gap semiconductors and possess different physical properties, depending

not only on the elements chosen but also on the value of m and n.

The aim of this research was to explore this wide family of compounds and to
optimize selected members in order to enhanced the figure of merit ZT that is defrned as:

ZT=(S (:2 T) /x Eq.(1-1)

Where S is the Seebeck coefficient, 6 and K the electrical and thermal conductivity

respectively, and T is the absolute temperature.

l-l. Brief History of Thermoelectricity

The history of thermoelectricity began more than 150 years ago when Thomas
Seebeck 3 (1822) and Jean Peltier 4 (1834) discovered the thermoelectric phenomenon.
During this time period numerous investigations on the interaction between an electric
current and'a magnetic field, that was first discovered by the Danish physicist Oersted,
were carried on by numerous scientists like Laplace and Ampere, just to cite a few.
Around the same time period that Faraday found electromagnetic induction, Seebeck
noticed that a small flow of electrical current was generated when a difference of
temperature was applied to the junctions of two dissimilar conductors (see Figure 1-1a),
referred later in this work as the therrnoelements. This phenomenon is known as the
Seebeck effect, the first of three fundamental effects in thermoelectricity, and it is mainly

used today in spacecraft power generation 5(such as Voyager I and II).

Based on Seebeck’s discovery, a French watchmaker, J. C. Peltier, found that heat
was liberated or absorbed at a rate Q, depending on the direction of a current passing
through two different conductors (see Figure 1-1b). He showed that this effect was
reversible, proportional to the intensity of the current applied as well as independent on
the size of the thermoelements, making it different form the well-known effect named
after Joule. This constitutes the basic effect used in refrigeration and it can be expressed
according to Eq. (1-2) 6:

Q = TIJ Eq. (1-2)

Where J is a flow of current and TI is the Peltier coefficient.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_ /
\
_J_ __r_
T T-AT
A A u A
T+AT __ T+AT
B B
___._l
(a) (b)

Figure 1-1: The two principal effects in thermoelectricity: (a) Seebeck effect used in

power generation and (b) Peltier effect used in refrigeration technology.

The explanation of this phenomenon was not demonstrated until Lenz, in 1838, froze a
drop of water placed at a junction of bismuth and antimony rods after changing the
direction of the current.

Finally, the third important effect of thermoelectricity was formulated by
W. Thompson (Lord Kelvin) who demonstrated, in 1854, some 30 years after Seebeck's
reports, that reversible heating and cooling was also created through a single conductor
when a current flow was applied to it. He was able to establish the relationship between
the Peltier coefficient and the thermoelectric power on as 6:

Q = aTJ=lTJ Eq- (1-3)
In fact, the association of the Thompson and the Peltier effects give rise to the Seebeck
effect 7.

A century elapsed before research in this field really started. The initiator of the
rebirth of interest toward thermoelectric phenomena was Ioffe 8 (195 7) when he observed
that doped semiconductors were the best TE materials. Until then, the compounds
investigated were mostly metals, but because of their poor Seebeck coefficient and their
large thermal conductivity, the interest in thermoelectric applications was limited. Ioffe’s
find led to numerous measurements on several compounds, and to the discovery of the
best thermoelectric materials used to date: bismuth and lead telluride, as well as their

antimony alloys 9’ '0.

After a period of disinterest, due to the impossibility of further optimization of
the compounds found, and the failure to discover better ones, funding revitalized research
programs at the beginning of the 80's, mainly because of technological and scientific
advances in other fields and because of the need to improve the efficiency of materials
used in cooling devices; thermoelectric cooler efficiency being only 10% of Carnot cycle,
but thermodynamic laws applied on thermoelectric phenomena show that achieving 100%
is possible ”.

Nevertheless, even with only 30 % of the efficiency of Freon-based refrigerators
TE devices created niches markets due to their reliability. For example in LR. detector
technology, where the expected lifetime of a detector is 10 years, the small size of TE
devices allows their integration into compact optical systems ‘2. Because TE materials
can also be used as power sources (due to the Seebeck effect), research to find new
materials such as (GeTe)1_,((AngTe2)x ‘3 (commonly called TAGS) were extensively
carried on. Unfortunately, diffusion of Ag in the samples under the action of heat, created
instability and short lifetime (of the devices based on these materials. Applications
included power generation for remote installations used in space exploration and
petroleum industry. Once again, for such application the first requirement of the devices
is reliability over efficiency.

Today, different optimized compounds are used depending on the working
temperature range needed for the device. Figure 1-2 gives a summary of these

thermoelectric materials according to their range of use. As we can see from this figure,

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there is a need for new compounds possessing good properties below and around room
temperature. It is important to note that any material with a figure of merit superior to 1
will have possible industrial applications.

The interest in thermoelectricity is not recent but the need for new materials is
increasing. There is great effort for developing new compounds that could surpass the
properties of bismuth telluride that leads the market for the last 30 years. Taking into
account the difficulty of “frnding” the right compound, and optimizing it, long term
planning is necessary and collaboration between physicists and engineers is the key to
success. Such collaborations have been the paradigm in which the approach in this work

has been developed.

1-2. Focus of this Research

Toward the need for developing new TE materials, investigations on different
systems have been carried out by several research groups. TAGS (tellurium-antimony-
germanium-silver) 13, skutterudites 15, half-Heusler alloys 18, clathrates 19, and quantum
wells 20 are some systems that have been actively investigated. Metallic compounds
typically have a small thermopower and a large thermal conductivity as already
mentioned, therefore the use of semiconductors, as shown by Ioffe 8 constitute a better
choice.

Our research group has been involved for several years in research on ternary and

quartenary bismuth chalcogenide systems. Several promising compounds have been

discovered. Such new materials include for example BaBiTe3 2‘ and CsBi4Te6 17. The
latter one possesses a value of ZT equal to 0.8 at room temperature making it as good as
the best Bi2.,‘Sb,(Te3.ySey alloys. Promising quartenary compounds have also been
synthesis such as K1_xSn5-xBin-xSe22 22 and A1+XM'4-2xBi7+xSe15 23 (with A=K, Rb; M'=Sn,
Pb).

In addition, materials having complex composition and structure may possess
complex electronic structure and may have a high thermoelectric power as well as low
thermal conductivity. Therefore we investigated the system of isostructural
semiconductive compounds having for general formula: AmBanQ2m+n , where A is an
alkali metal or silver, B is lead or tin, M is Bismuth or Antimony, and Q is S, Se, or Te.
This system crystallizes in the cubic face centered NaCl structure type with Fm 3m for
space group. Crystals of KPbBiTe3 were first discovered using a flux method 24 by Dr.
D.-Y. Chung. The structure was solved and as shown on Figure 1-3, the chalcogenides
occupy the anionic positions, while the cations are disordered in the Na+ sites.

The reasons our attention was attracted on this family of quartenary compounds
can be summarized as follows:

0 As mentioned, complex structures might give rise to complex electronic band
structures that could be easily “tunable” in order to obtain enhanced
properties.

0 By choosing heavy elements such as Bi, Te, and Pb, we expect low phonon

frequencies and therefore low thermal conductivity 25 .

 

Figure 1-3: NaCl crystal structure type of AmBanQ2m+n compounds with A, B, M on

the Cl' atomic sites and Q on the Na+ sites.

0 One system highly investigated is M2Q3 (with M=Sb, Bi ; Q=S, Se, Te) 26.
These optimized compounds are good TE materials, and since M and Q can be
integrated in the general formula of our compounds, we expect good
thermoelectrical properties as well .

0 As previously mentioned, our research group has investigated many ternary
and quartenary compounds such as BaBiTe3 21, CsBi4Te6 ‘7, KBi6_33S.027,
KzBissrs 27, a‘B'KzBisseB 28, K2.sBis.sser4 28, 1334131631313 29, Buzpszisscrs 29,
and Al+be4-2be7+xSe15 (A=K, Rb) 29. The ternary system K/Bi/Se 30 has also
been investigated and all these compounds showed promising properties.
Since only bismuth-antimony telluride and bismuth antimony alloys are
widely used today tend to confirm that Bi plays a decisive role in the
enhancement of thermoelectric properties. It is important to note that its
contribution is not well understood at the present time.

o A quartenary compound should have very low thermal conductivity especially
if it exhibits mass fluctuation in the lattice.

0 Due to their high polarizabilities, the use of heavy elements such as Pb, Bi,
Sn, Sb, Se, and Te should give rise to compounds with large dielectric
constants that would create a strong screening of the impurities and therefore

increase the mobility of the carriers.

10

Because of these considerations, the investigation of this new family of
compounds is justified. The starting goal of this work was to obtain new TE compounds
that could be used around room temperature, with the hope of being able to “tune” the
band gap and to maximize the dimensionless figure of merit ZT, by varying the
composition of the compounds.

The material of reference in any TE research is BizTe3 and its alloys. Our goal is

to surpass some or all of its transport properties summarized in Table 1-1 and to achieve

a ZT greater to 1.

Table 1-1. Thermoelectric properties of n-type PbTe and BizTe3 at optimum

temperature (Tmax).

 

Compound Tmax (K) 0(S/cm) S(p.V/K) K(W/m-K) ZT Mp (°C) Ref.

 

i BizTe3 400 800-1000 i210 1.4-1.6 0.8-1.1 585 *

PbTe 650 360 -180 1.1 0.70 1197 31

 

*data provided by Marlow Industries Inc.

1-3. Concepts and Important Physical Properties
In order to understand how to optimize materials for applications, let us take a

closer look at the different variables that constitute the figure of merit ZT (see Eq. 1-1):

11

 

the electrical conductivity, the thermal conductivity, and the Seebeck coefficient. These
important parameters are affected by energy gap, carrier concentration, and effective

mass.

Performance of a Material

Because we need a tool to compare different thermoelectric materials, the figure of
merit Z was introduced; often the dimensionless figure of merit ZT is used instead, where
T is the absolute temperature. This dimensionless variable is proportional (see Eq. 1-1)
to the square of the Seebeck coefficient S (uV/K), to the electrical conductivity 6( S/cm),
and to the inverse of the thermal conductivity K (W/m-K). It is important to note that
these three parameters are not independent and their values are determined by the details
of their electronic structure, and by the scattering and number of charge carriers.
Therefore, by modifying one property, one can affect the other in the wrong direction.
Usually when increasing the electrical conductivity the Seebeck coefficient decreases, and
vice versa. Therefore, a subtle equilibrium must be found in order to achieve
optimization. As we can see from Eq. 1-1, in order to increase the figure of merit ZT, we
must decrease the thermal conductivity, while increasing or keeping constant the two

other parameters. This can be achieved by doping, and/or by preparing solid solutions.

12

Electrical Conductivity a

A semiconductor normally exhibits thermally activated electrical conductivity that
increases with rising temperature. There are two types of electronic semiconductors,
intrinsic and extrinsic, depending on the presence of impurity levels in the forbidden
energy gap. The dependence of the conductivity as a function of the temperature for
different types of materials is shown in Figure 1-4.

Metals (curve a) have very high conductivity, typically above 2000 S/cm that
decreases as the temperature increases. Instead, semiconductors (curve b) exhibit a
conductivity that rises with temperature but the magnitude is much lower than for a
metal, and typically in the range of 10'5 to 2000 S/cm depending on the band gap.
Insulators have conductivity inferior to 10'7 S/cm.

(a) Intrinsic Electronic Semiconductor.

If a semiconductor does not have impurities, its energy diagram can be represented
as Figure 1-5a. As the temperature increases, electrons from the valence band where they
were engaged in bonding orbitals, are excited to the conduction band where they can move
freely. As they leave the valence band, holes are created and left behind. Under the
action of an electric field, the holes move in the opposite direction of the electrons present

in the conduction band.

13

 

b
L

 

 

 

 

7A 104 .— a-Metal

E E

:2 3 -

E: 10 g

3E 2

g 10 F b-Semioonductor

“:3 E

a w' ;—
c-Insulator

lPrrr—T—Irerllrrrlrrrrlrrrrlrrrr

0 100 200 300 400 500 600

Temperature (K)

Figure 1-4: Variation of the conductivity as a function of temperature for different

materials.

 

 

 

 

 

 

 

 

Conduction
Band
Energy I: In .
. purity
Gap ' E9 ‘ Level
Valence
Band

 

   

Figure 1-5: (a) Intrinsic and (b) extrinsic semiconductor.

14

This creates an electrical conduction that is expressed in Siemens per centimeters (S/cm)

and can be written as 32:

 

o 6 ”Eg E (1 4)
= ex . -
° ZkBT q

where 00 is the limit of the conductivity at high temperature, E8 is the energy gap, k3 the
Boltzmann constant, and T the absolute temperature. It is important to note that for
industrial applications, extrinsic semiconductors are used because their conductivity can
be precisely controlled through doping. In practice, all semiconducting materials are

“extrinsic” since they are either adventitiously or intentionally doped.

(b) Extrinsic Electronic Semiconductor

The values of the conductivity can be greatly increased by the addition of small
controlled amount of impurities in the pure semiconductor. The band diagram can be
represented as Figure 1-5b. Impurity levels have been created in the forbidden energy
gap by addition of these dopants. Two cases are then possible.

0 If the impurity added has one electron less than the element in the system that it
replaces, the later will provide the missing electron for the partial covalent bond
(Figure 1-6a) leaving a moving hole behind. We therefore obtain a p-type doped
material and the conductivity is equal to o = (50 exp. (-Ep/kBT) where 0'0 is the limit of

the conductivity at high temperature, and Ep the energy level of the impurity added.

15

o In the case where the element added has one electron in excess, this electron will move
freely in the crystal since it cannot be integrated in covalent bonding (Figure 1-6b).
The system is then said to be n-type, and o = 00 exp.(-En/kBT) where En is the energy

level of the impurity having one electron in excess.

 

Conduction Band

 

 

 

 

 

i i i lnpurity level

o o L—' lmpuritylevel

 

 

1‘ 1‘ 1
5'6 b—o o m F05 _0 60—10 0 o
.; Electron
Valence Band . 3 Hole

 

 

 

 

 

 

(a) (b)

Figure 1-6: (a) p-type doped and (b) n-type doped semiconductor.

The electrical conduction can also be expressed as a function of the mobility (see Eq. 1-5)
which is a proportional coefficient between the average drift velocity vd of the charge
distribution and the applied field E”.

o = Neun + Penp Eq. (1-5)

16

where N and P are respectively the number of electrons and holes moving in the system
expressed in number per cm‘3, and tin and up the mobility of the negative and positive

charge carriers expressed in cmZN-sec.

Thermal Conductivity (K)

The value of the thermal conductivity of a compound plays a decisive role in its
possible use as a thermoelectric material. Because the value of ZT is inversely
proportional to the thermal conductivity, a low value is necessary (see Table 1-2). From
these data, we can see that metals possess the highest thermal conductivity values while
the lowest are found for insulators. Semiconductors lie between.

The thermal conductivity of a material is mainly the sum of two components: the
lattice (phonons) KI, and the electronic part K33“).

K=Kc +r<l Eq. (1-6)
In this equation, we have neglected the bipolar contribution that is due to the
simultaneous movement of electrons and related holes, only important in the intrinsic
region of the semiconductor.

For an intrinsic undoped semiconductor, the thermal conduction will be mainly

due to the lattice contribution. As electrons (or holes) are added to the system, the

electronic contribution rises since the electrons (or holes) act as carriers of heat.

17

Table 1-2. Thermal conductivity at room temperature for different type of materials 33(3).

 

 

 

 

 

Compound KRT (W/m°K) Compound KRT (W/m-K)
Metals Semiconductor
copper 400 BiZSe3 2.4
Ag 430 Se 2
Te 3
Semimetals PbSe 1 .7
Bi 8.5 PbTe 2.3
Sb 18 PbS 3.0
GeTe 1-3
Other CdS 20
Glass 0.8
Concrete 0.9

 

Nevertheless, they also serve as scattering centers for the phonons (quanta of
lattice waves) that will diminish the mean free path A. of the heat carriers, and as a
consequence diminish the lattice thermal conductivity. It is understandable that
predictions on the evolution of the thermal conductivity are therefore challenging since the

addition of a dopant has a double effect on K.

(a) Electronic Thermal Conductivity

This contribution, due to electrons (or holes) that carry heat in the system, is
insignificant at very low doping level but become more important as the number of charge
carrier increase. The electronic participation of the thermal conductivity is given by the
Wiedemann-Franz law as a function of the electrical conductivity 0', the absolute
temperature T, and the Lorenz factor L0 in the approximation where only one band

18

 

contributes to the transport properties 33“).

k 2
x, = [—3-] Loo’I‘ Eq. (1-7)

The Lorenz factor is dependent upon the scattering mechanisms that occur in the
system, and upon the level of doping. It has a wide range of variation: from a value of 2
in the case where an acoustic scattering mechanism is dominant, to a value of 4 for a
ionized impurity scattering mechanism (see Figure 1-7) 33“”.

The reduced Fermi level I; is introduced as: §=EF / kBTwith B; being the energy
measured at the band edge. The problem is then reduced to determining the appropriate
value of L0 for the system studied. Nevertheless, values converge to n2/3 for high carrier
concentration, in other words, for high doping level. This value is the one usually used in

calculations.

19

\wo

 

 

 

Figure 1-7: Lorentz factor L0 as a function of the reduced Fermi level and different

scattering process (3).

20

(b) Lattice Thermal Conductivity

In a crystal, atoms can vibrate around their positions and give rise to standing or
traveling vibrational waves through the lattice. These normal modes of vibration have
characteristic frequencies. Phonons are defined as the quanta of excitation of these normal
modes of lattice vibration that are created. As impurities are introduced, the normal
modes of vibration are altered or new ones are created. If a temperature gradient is built,
the phonon distribution deviate from the equilibrium and a flow of heat is generated.

The lattice thermal conductivity follows a T3 law at very low temperatures, and a T'1
law 33“) (see Figure 1-8) at temperature higher than the Debye temperature. These
dependencies can be explained by an Umklapp three-phonon scattering, and boundary
scattering mechanism 34. A three phonon interaction is created by the anharmonic nature
of the crystal potential and can be simply described in Figure 1-9a 34, where two
longitudinal phonons, represented by the wave vectors q, and q; interact to produce a
third one (q3). In terms of conservation of energy, this is described as : (1)3 = w1+w2.
The conservation of the momenttun give us q1+ q; = q; (normal process). In fact, the
phonon momentum can be changed in some cases and we have the new expression:

(11 + ‘12 = (13 + G
(where G is the reciprocal lattice vector) as shown in Figure 1-9b.

Therefore depending on the value of G, two cases have to be considered:

21

°2° If G = 0, the total phonon momentum is conserved. The flow of phonon will
continue independently of the temperature. Since the mean free path it stays
unchanged, no thermal resistance is created.

60 In the case of Ga: 0, the mean free path is altered and a thermal resistance is created.
This generates a maximum in the thermal conductivity at the boundary between the T3
and the UT dependence (see Figure 1-8).

Leibfreid and Schlomann (1954) 35 derived the following equations that can
account for the behavior of the lattice thermal conductivity as a function of the

temperature, if we assume that an Umklapp process takes place:

x. = x0 f(®D/ T) Eq. (1-8a)
At high temperature, T > OD f(®D/ T) = (99/ T Eq. (1-8b)
T 3 6
While, when T< OD f(®D/ T) = [—] expL—i) Eq. (1-8c)
OD bT

To this effect, we have to add the boundaries scattering, at low temperature, and
the exponential rise of the lattice thermal conductivity (in Eq. 1-8c) is changed to a T3
law. The prediction given by the UT law at high temperature (from Eq. 1-8b) is in good
agreement with the experimental values if the volume and the pressure are kept constants.

Using these equations, we can justify the T 3 rise of the thermal conductivity by

considering Eq. (1-8b) and the UT at higher temperature from the Eq. (1-8c).

22

 

'o. Umklapp + impurity

i , '. scatteringl/T dependance
>4 ’ .°

3 Boundary

L .’ scattering

; ..- T3 dependance
.w r L r L r r r J r r 1 l

 

 

Temperature (K)

Figure 1-8: Thermal conductivity and the different scattering processes involved.

 

 

 

 

 

Ky KY
Q2 92
V q1 q1
Kx Kx

/

(l3 / <13
/
5/
G
(a) (b)

Figure 1-9: Three phonons interaction. (a) Normal process and (b) Umklapp process.

23

(c) Radiative Losses
This important phenomenon is common to all materials. Photons passing through
a material will give rise to thermal radiations. The contribution due to this effect was

formalized by Genzel 36:

Kphown, = (139) Gon2T30t" Eq. (1-9)

where 00 is the Stefan-Boltzmann constant, n the refractive index of the material and or
the absorption coefficient. The radiative losses follow a T3 law as seen in Eq. (1 -9).

Bhandari and Rowe pointed out that this contribution is appreciable for tellurium,
selenium, and the lead chalcogenides. Therefore, we can expect to find this part in the
measurement of the materials presented in this dissertation.

During the analysis of the thermal conductivity data, the photon contribution need
to be subtracted since the value of Kphomns depends on the shape of the samples measured
and is not an intrinsic property of the material. In order to obtain K of a certain sample
without the photon contribution, the following methodology is adopted:

1 - The electronic contribution is calculated using the Wiedemann-Franz law and

subtracted from the experimentally measured thermal conductivity. Let us call K'

the remaining thermal conductivity contribution.

24

2 - At high temperature, typically superior to 150 K, a l/T fit is applied to the
appropriate part of the K’ plot (see Figure 1- 8). The difference between the fit
and K’ give the radiative contribution K photons.

3 - K. is then obtained by keeping the values of K’ at low temperature and by using
the value given by the fit at higher temperature.

4 - The total thermal conductivity without the contribution from radiative losses
is then obtained by adding the lattice and the electronic contribution.

5 - In order to verify that the rise in the original plot of the thermal conductivity at
high temperature is due to radiative losses, Kphowns is plotted against T3. A good
linear fit act as proof of the hypothesis developed, since the contribution from
radiative losses should vary linearly with T3, see Eq. (1.9).

In the following work, the photon contribution was subtracted as indicated above.

Therefore, plots of the thermal conductivity before and after corrections will be presented

for each measurement made if radiative losses are presents.

Seebeck Coefficient (S)

As soon as a new compound is synthesized, the first property measured is the

Seebeck coefficient since it is squared in the equation for ZT. It is a relatively simple

measurement that can be done on semiconductors and, in addition to the value of S at

different temperatures, the measurement of this property gives also other valuable

25

information on the material such as its class (metal, insulator, semiconductor), its doping
state (n-type, p-type), and sometimes its energy gap.
The Seebeck coefficient can be in a simple way be viewed as being the measure of

the "heat" per carrier over the temperature.

_ "heat" per carrier
Charge per carrier times T

 

Boltzmann transport theory lead to understanding of the Mott equation:

= n_2 kgr d1no(E)) _
8 [3X 6 I (E 5:12. Eq.(110)

 

where 0(E) is the electrical conductivity depending on the band filling (the Fermi energy
EF). If we consider the electronic conductivity being independent of the energy, 0(E) is
then proportional to the density of state at E and S is a measure of the difference of the
electrical conductivity above and below the Fermi surface. It is important to note that the
Seebeck coefficient is inversely dependent upon the carrier concentration 37 of the dopant

since it is dependent on the reduced Fermi level i by:

, 3/2
S = (EB—X; + s — 5) and § is related to n by n = {wilt—Bi] exp(§).
e

26

However, because the carrier concentration affects only slightly the thermal
conductivity, it is possible to enhance the figure of merit by optimizing S and 0 through
changes in the carrier concentration. Nevertheless, if 6 became too large Wiedemann-
Franz law predicts that the thermal conductivity will rise considerably. As a rule of

thumb K increases of about 0.7 W/m-K with an increases of o of 1000 S/cm.

(a) Trend of S

The plots of Figure 1-10 show the behavior of S for different type of materials as
a function of the temperature. Therefore, by looking at the value and the shape of the
curve, one can tell if the measured sample is a metal, an insulator, or a semiconductor.

For a metal, S decreases as the temperature decrease in accordance to the relation

between S and T38:

S~ Q- E (1-11)
eEF q.

where e is the charge of the canier and tap the Fermi level. The value of kB/e being
approximately 87 uV/K, S must be much inferior to it, since for a metal the transport take
place within kBT. On the contrary, for a semiconductor, the absolute value of S increases
as the temperature decreases based on Eq. (1-12). In the case where only one type of
carrier is present, a value superior to 87 uV/K is expected 38.

(fail...

~ W .. (1&1 (2:33)] Eq. (1-12)

27

 

Finally, among other possible behaviors, some narrow band gap semiconductors
can exhibit a combination of metallic and semiconductors behavior. The thermopower in
this case may be reminiscent of either a metal or a semiconductor, or may even be nearly

temperature independent depending on the size of the bang gap and the degree of doping.

(b) Sign
The sign of S is a simple and safe way to find what kind of carrier is predominant
in a compound in a given range of temperature. The Seebeck coefficient can be written
as a function of a difference of potential over a difference of temperature as in Eq. (1-13).
S=AV/AT Eq.(1-13)
A negative Seebeck coefficient indicates that the compound is n-type, meaning
that the majority of the carriers are electrons. When measuring the Seebeck coefficient, a
temperature gradient is applied to a material and a cold (Tc) and hot (Th) sides are
generated. The electrons move from Th to Tc because electrons on Th have higher kinetic
energy than those on the cold side (i.e. kinetic theory of gases). As a consequence, a flow
is established from Th to Tc creating a negative charge build up on Tc, and a current is
generated form Tc to Th in order to avoid more charging on Tc. This creates charge
separation between Th and Tc and the generation of a voltage difference AV. If the
material is n-doped the created voltage is negative and because of Eq. (1-13), S is also
negative. In the case of the compound has a majority of hole carriers (p-type), a similar

flow is generated with holes moving from Tc to Th. Nevertheless, the potential created

28

will be in opposite direction of the one created by electrons and the sign of S will be
positive. Seebeck measurement is an effective, fast and easy way to determine the type

of the majority carriers.

(c) Energy Band Gap

Often, the behavior of semiconductors is slightly different from what described in

 

(a). Because of the existence of two different regions (extrinsic and intrinsic), S I does
not vary linearly. As the temperature rises, extrinsic carriers are exited from impurity
states. This allows the gap between the Fermi level and the appropriate band to increase ,
which enhanced the absolute value of the Seebeck coefficient. As soon as the temperature
is large enough, carriers coming from impurities reach a saturation level and electrons-
holes pairs across the band gap are excited (intrinsic region), creating opposite carriers and

therefore I S 1 decreases, because S is the sum of the contribution due to the electrons and

the contribution due to the holes (see Eq. 1-14).

_ aeSe + OhSh

S Eq. (1-14)

If we plot S as a function of the temperature, Figure 1-11, the Seebeck coefficient
pass through a maximum. The energy gap of the semiconductor can then be estimated
based on Eq. (1-15) 39:

Eg .~. 2eSmameax Eq. (1-15)

29

 

600 _

 

 

 

AA A 0 Metal
2 500 _ A A 0 Narrow Band Gap Semrconductor_
A A ' a

Z. . Semiconductor .

t- A 4
V 400 '— A AAA 1
‘E " AA 1
o A
”-1 .- A AA 4
2 "' AA A A “
g 300 ‘— AAAA -‘
(3 : ... ...... :

O O.

r O O i
g 200 H. . 00.. _
in r 000 "
8 r .0 0 OOO ‘
m 100 _ . 00000 —

l- . 00 O O 3

l' . O O O

l. 00

_. 0000

0.00.1; ..rr..r.1..rrr.rr.1.11.1.r..
0 100 200 300 400 500 600
Temperature (K)

Figure 1-10: Seebeck coefficient behavior for different types of materials

700

 

180
160 L

140 _

S (NV/K)

120 L
100 L

80’—

 

l

A l I l l

A (Tmax=350, Smax=163)
© .

.
rrlrrrlrrrl

j

l

1

 

 

6O . r
280

Figure 1-11: Seebeck measurement showing a maximum at the point A

300

320

340

360 380 400

Temperature (K)

30

420

Because for wide band gap materials, Tmax is superior to 150 °C, this way of
calculating Eg only works for narrow band gap semiconductors.

In conclusion, the measurement of the Seebeck coefficient should be the first
measurement made. The interpretation of the data can give valuable information about the
properties of the material such as its type, the type of the charge carriers involved in the
electrical conduction and even in some cases its band gap. Multiple measurements should

be made for the same material to insure reproducibility.

Other Important Properties and Notions

(21) Energy gap

As described above, the band gap of a semiconductor can be measured from the
analysis of Seebeck experiments if |S| passes through a maximum. It can also be obtained
from conductivity measurements using Eq. (1-4), but the most reliable way to obtain it is
optically. Analysis of the spectrum recorded can give us the value of the band gap as well
as its nature i.e. direct or indirect.

After data are collected using an infrared or solid state UV/V is spectrometer (see
chapter 2 for more details), the absorption (or/S) is calculated from the reflectance data

using the Kubelka-Munk function 40: or/S = (1-R)2/ 2R, where R is the reflectance at a

31

given wavenumber, or the absorption coefficient, and S is the scattering coefficient. The
value of the band gap is then given by the intersection point between energy axis at the
absorption offset and the line extrapolated from the linear portion of the absorption edge
as shown in Figure 1-12.

In a direct band gap, the energy (hv) and momentum (q) of the photon are enough
to excite an electron from a lower to a higher energy state (see Figure 1-13a). For such
transition, the spectrum shows an abrupt change in the absorption edge (Figure 1-13-b).
A linear variation of the square of the absorption coefficient as a function of the energy is
characteristic of a direct band gap (see Eq. 1-16) 4‘.

or(hv) = A(hV-Eg)m Eq. (1-16)
with A is a constant proportional to the effective mass of electrons and holes.

In an indirect band gap the momentum of the photon is not enough to allow the
transition and a third particle is involved: a phonon (Figure 1-14a). The threshold in an
indirect transition, as seen in Figure 1-14b, is less abrupt than in a direct transition since
the probability of the transition occurrence is decreased by the necessity of having
involved a third component. Because a phonon can be absorbed or emitted, the equation
similar to Eq. 1-16 is more complicated.

or (hv) = or,(hv) + or, (hv) Eq. (1-17)
where ora(hv) is the absorption when a phonon is absorbed and 0t¢(hv) when a phonon is

emitted; A is a constant 4‘.

(hv—Eg +113.)2

, h = A'
M V) exp(Ep /(k,T))-1

 

Eq.(1-18)

32

(hv — E, — 15,.)2

“C(hv) = A. 1- exp(-Ep /(k,r))

 

Eq. (1-19)

Therefore the use of a plot of 0t(hv) at a certain power versus the energy hv in
this scenario is not possible.

A last case to consider is the case of a heavily doped indirect semiconductor. Here
the momenttun is conserved through electron-electron scattering and a plot of the square
of the absorption coefficient versus the energy should give a linear fit according to Eq. (1-

20).

or(hv) = C(hv - 13g - 1))2 Eq. (1-20)

C and D being two constants 4"

Lovett 42 defines a narrow band gap semiconductor when the value of its band gap
is less than ten times kBT (0.26 eV). Table 1-3 give a list of some materials with their
corresponding band gaps. It is important to note that for thermoelectric materials the
band gap should be high enough to avoid the creation of minority carriers that would

decrease the thermopower S.

33

 

   
  
  
 

 

 

T— ................
r
h-
m r-
\ +
d .—
r-
’ Eg=o.25ev
r
pil+11411111LL11111111LLJILIJLIILLllllLi

 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Energy (eV)

Figure 1-12: Calculation of an energy gap using absorption spectroscopic data.

34

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E
Conduction Band - g 5 =
.
Eg g ............
r
Photon '5 ~
4 E‘ i ..............................................
o _ . . _
.8 i i 2
> <» I
0 1 k L— ....... g , .a...............n............... ...............
ValenceBand in.” U“ “.1411 1
Energy (eV)
(a) (b)

Figure 1-13: (a) Direct transition process and (b) absorption coefficient showing

abrupt absorption edge with an energy increase.

 

C.B.

 

Phonon

 

Photon,

vv

/ Transition

Absorption

/

\/

 

 

 

 

 

 

 

V.B.
Energy (eV)

 

(a) (b)

Figure 1-14: (a) Indirect transition involving a phonon and (b) absorption coefficient

showing a slower increase with energy.

35

Table 1-3. Energy gap (eV) for some semiconductors. The nature of the band gap is also

reported (i.e. direct (i) or indirect (d)) 43.

 

 

 

 

Semiconductor Energy Gap Semiconductor Energy Gap

0 K 300 K 0 K 300 K
AgCl 3.2 i InSb 0.24 0.18 d
AlAs 2.3 2.16 i HgTe -0.3 d
BizTe3 0.16 i PbS 0.29 0.35 d
C (diam) 5.4 i Sn 0 0
CuBr 2.94 SnTe 0.3 0.18 d
CdSe 1.84 1.74 d PbTe 0.19 0.3 d
InAs 0.43 0.34 d PbSe 0.17 0.27 d

 

 

(b) Charge Carrier Concentration

The carrier concentration is defined as the number of charge carriers of a certain
type per unit volume. This concentration shows different properties for different
materials. For metals, n is independent of the temperature which explain the decrease of
the conductivity that follows the behavior of the mobility due to the increase in the
scattering probability. For semiconductors n is a function of the temperature and
increases exponentially as T increases.

A typical plot of the carrier concentration as a function of temperature is shown
in Figure 1-15. Three distinct regions are present. At low temperature (high T‘l), only

few carrier are exited to the conduction bands. As the temperature increases thermal

36

excitation allows more transitions until a saturation plateau is reached (called exhaustion).
When the temperature is increased further, the intrinsic carriers are excited and we observe
a large increase of 11. As West44 noted, it is important to try to obtain the larger
temperature range possible for the exhaustion part, making the device performance stable

over large temperature range.

 

 

 

log n
Intrinsic
Exhaustion
—\Extrinsic
1 / T

Figure 1-15: Carrier concentration behavior for a semiconductor as a function of

temperature.

The figure of merit ZT is a function of the Femri energy. The Fermi energy is in
turn a function of the carrier concentration, carrier effective mass and the temperature.
Nevertheless, the thermal conductivity depends little on n, at least until a certain level.
The Seebeck coefficient is a function of 1/1n(n). Therefore, it is the conductivity that can
be optimized by controlling the carrier concentration introduced as impurities, and

through it the figure of merit.

37

It has been demonstrated that for an intrinsic senriconductor the product NP (see
Eq. 1-20) is a constant (N and P being the concentration of electrons and holes
respectively). Therefore when introducing one type of charge carrier in the system, the

concentration of the other type is adjusted to keep the product constant 45.

3 E
NP = {$352) [mcmh3’2eXp[k frD Eq. (1-21)
1‘ B

For extrinsic semiconductors, optimization of the transport properties is reached

 

 

for a certain number of charge carriers; if more charge carriers are added, the properties of
the materials deteriorate. For small band gap semiconductors, 11 should be in the range 46 of
1018 cm'3 and 1020 cm'3. If the charge carrier concentration is too high then the electronic
part of the thermal conductivity would increase considerably which is undesirable for TB
applications.

The role of carriers and their concentration is not fully understood but some basis
exists and the “goal of the game” is therefore to introduce the right amount of dopant (the

right carrier concentration) in order to optimize ZT.

(c) Effective Mass (m*,, m*h)

An electron in a vacuum when submitted to an electromagnetic field will have a
thermal velocity depending on its mass mo. If the electron is moving in a crystal, it will
feel the periodic electric field due to the presence of the atoms in the crystal. If the

electric field is E and v the velocity of the electron, then:

38

-eE=mv Eq.(1-22)
(Newton’s law Force = mass * acceleration)
with v = (3 k3 T / m )”2 Eq. (1-23)
In the case of a free electron, m is equal to m, (9.1 10'31 kg) in the equation of the
velocity. The effective mass m* is defined as the mass that the electron possesses when

moving in the crystal under E, and is equal to 47:

dze -1
*= h2 —— E .1-24
m [are] q( )

The denominator term is the “curvature” of the electronic structure band
considered. Therefore if m* is large i.e. if the carriers are heavy, the band will be less

disperse than for light carriers (see Figure 1-16)

Light In“

Heavy m*

 

 

 

Figure 1-16: Effect of the effective mass on the electronic band.

39

Electrons and holes have different effective masses when present in different materials
since they are submitted to different atomic parameters and lattice potentials. Table 1-4
shows different values of m*h and m*e. As we can see, these values vary notably from
material to material, which will give different velocities and create different electronic band
curvatures.

The role of the effective mass of electrons and holes in the enhancement of the
figure of merit ZT is not fully understood. Bhandari and Rowe37 suggest that a high m"‘c

and m*h/ m"‘c might increase ZT .

Table 1-4:. Different effective mass ratio for several different type of semiconductors.

 

 

 

Semiconductor m," /m m,“ lmo Semiconductor me“ lmo mh“ /mo

type type

(IV) Si 0.23 0.12 IV-Vi PbS 0.25 0.25
SiC 0.60 1.20 PbSe 0.33 0.34

III-V Ale 0.30 0.40 PbTe 0.22 0.29
InSb 0.01 0.18 II-IV MgZSi ....... 0.46

II-VI CdTe 0.14 0.37 II-V CdSb 0.16 0.10

 

Data from page 234 of reference 7

In summary, it has been shown that many physical properties have to be

considered in order to fully understand the mechanism by which the figure of merit ZT

40

 

can be optimized. Great attention is given to the measurement of the Seebeck coefficient
due to its importance in the formulation of ZT. Nevertheless, each term of this equation
is important and often large value of the thermal conductivity counterbalances large S.
However, as it has been demonstrated for BizTe3, K can be decreased by preparing
appropriate solid solutions, and the electrical conductivity increased by introducing the
right amount of charge carriers through doping, leading to optimum ZT for this material.

We hope to accomplish the same goal for the materials described in this dissertation.

41

References

9:59!”

>19

10.
ll.
12.
13.
14.
15.
16.
17.
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19.
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M. Rowe, Thermoelectric News, 1998, 12

T.J. Seebeck, ABH. Preuss. Akad. Wiss., 1822-1823, 265

J.C. Peltier, Ann. Chim. Phys., 56, 1934, 371

G.L. Bennett, “Space Applications”, in CRC Handbook of Thermoelectrics, Ed.
by D.M. Rowe, 1994, 515

AF. Ioffe “Physics of Semiconductor”, Ed. Academic Press Inc. New York, 1960
DD. Pollock, “Therrnoelectricity Theory, Thermometry, Tool”, Philadelphia,
ASTM, 1985, 111

AF. Ioffe, “Semiconductor, Therrnoelements and Thermoelectric Cooling”,
Infosearch Ltd., London, 1958

H. Sherrer, S. Sherrer, “Bismuth Telluride, Antimony Telluride, and Their Solid
Solution”, in CRC Handbook of Thermoelectrics, Ed. by D.M. Rowe, 1994, 211
V. F ano, “Lead Telluride and Its Alloys”, in CRC Handbook of Thermoelectrics,
Ed. by D.M. Rowe, 1994, 257

MG. Kanatzidis, F .J . Disalvo, Naval Research Reviews, 4, 1996,14

A.W. Allen, Supplement to Laser Focus World. March 1997

EA. Skrabeck, D.S. Trimmer, “Properties of the General TAGS System”, in CRC
Handbook of Thermoelectrics, Ed. by D.M. Rowe, 1994, 267

TM. Tritt Science, 272, 1996, 1276

BC. Sales, D. Mandrus, R.K. Williams, Science, 272, 1996, 1325

CB. Vining, “Silicon Germanium”, in CRC Handbook of Thermoelectrics, Ed. by
D.M. Rowe, 1994, 257

D.Y. Chung, T. Hogan, P. Brazis, M. Rocci-lane, C. Kannewurf, M. Bastea, C.
Uher. M.G. Kanatzidis, Science, 287, 2000, 1024

K. Mastronardi, D. Young, CC. Wang, P. Klalifah, R.J. Cava, Appl. Phys. Lett.,
74, 10, 1999, 1415

C. Uher, J. Yang, S. Hu, Mat. Res. Soc. Proc. 545, 1999, 247

H. Scherrer, Z. Dashevsky, V. Kanster, A. Casian, I. Sur, A. Sandu, Mat. Res.
Soc. Proc. 545, 1999, 99

D.Y. Chung, S. Jobic, T. Hogan, C.R. Kannewurf, R. Brec, R. Rouxel, M.G.
Kanatzidis, J. Am. Chem. Soc., 119, 1997, 2505-2515

A. Mroztek, D.Y. Chung, T. Hogan, M.G. Kanatzidis, submitted for publication
K.S. Choi, D.Y. Chung, A. Mroztek, W. Brazis, C.R. Kannewurf, M.G.
Kanatzidis, submitted for publication

A.C. Sutorik, M.G. Kanatzidis, Prog. Inorg. Chem, 43, 1996, 151

G.D. Mahan, Solid State Phys, 51, 1998, 81

(a) M.J. Smith, R.J. Knight, C.W. Spencer, J. Appl. Phys. 23, 1962, 2186-2190
(b) L.R. Testardi, J.N. Bierly, F.J. Donahoe, J.Phys. Chem. Solids. 23, 1962, 1209
(C) CH. Champness, P.T. Chiand, P. Parekh, Can. J. Phys. 43, 1965, 653

(d) Y.M. Yim, E.V. F itzke, J. Electrochem. Soc., 115, 1968, 556

42

27.

28.

29.

30.
31.

32.

33.

34.

35.

36.
37.

38.

39.
40.

41.

42.

43.

44.

45.

46.

(a) M.G. Kanatzidis, T.J. McCarthy, T.A. Tanzer, L.H. Chen, L. Iordanidis, T.
Hogan, C.R. Kannerwurf, C.R. Uher, B. Chen, Chem. Mater., 8, 1996, 1465

(b) B. Chen, C. Uher, L. Iordanidis, M.G. Kanatzidis, Chem. Mater., 9, 1997,
1655

(a) D.Y. Chung, K.S. Choi, L. Iordanidis, M.G. Kanatzidis, J.L. Schindler, W.
Brazis, C.R. Kannewurf, B. Chen, S. Hu, Chem. Mater., 9, 1997, 3060

(b) T.J. McCarthy,S.P. Ngeyi, J .H. Liao, D. DeGroot, T. Hogan, C.R. Kannewurf,

M.G. Kanatzidis, Chem. Mater., 5, 1993, 331

D.Y. Chung, L. Iordanidis, K.S. Choi, M.G. Kanatzidis, B. Kor. Chem. Soc., 19
(2), 1998, 1283

B. Aurivillus, Acta Chem. Scand., A37, 1983, 399

TC. Harman, J.M. Honig, “Thermoelectric and Therrnomagnetic Effect and
Applications”, Ed. McGraw-Hill, 1967, 290

JP. Suchet, “Electrical Conduction in Solid Materials”, Ed. Pergamon Press
LTD., 1975, 23

GM. Bhandari, D.M. Rowe, “Thermal Conduction in Semiconductor”, Ed. Wiley
Eastern Ltd., India, 1988 (a) p3, (b) p1, (c) p186, (d) p62, (e) p114

C. Kittel, “Introduction to Solid State Physics, Third Ed., J. Wiley & Sons, Inc.,
1966, 190

G. Leibfreid, E. Schlomann, Nach. Akad. Wiss. Gottingen, Mat. Phys. Klasse, 4,
1954, 71

L. Genzel, Z. Physik, 135, 1953, 177

GM. Bhandari, D.M. Rowe, “Optimizaton of Carrier Concentration” in CRC
Handbook of Thermoelectrics, Ed. by D.M. Rowe, 1994, 43

PM. Chaikin, “Organic Superconductivity”, Ed. by V.Z. Kresin and WA. Little,
Plenum Press, New York, 1990, 101

H.J. Goldsmid, J.W. Sharp, J. Electron. Mater., 28, 7, 1999, 869

W.W. Wendlandt, H.G. Hecht, “Reflectance Spectroscopy”, Interscience
Publishers, New York, 1966

TS. Moss, G.J. Burrell, B. Ellis, “Semiconductor Opto-Electronics”, Ed. Wiley &
Sons, New York, 1973, 48-94

D.R. Lovett, “Semimetals & Narrow Band Gap Semiconductors”, Ed. Pion Ltd.
1977, 1

ML. Cohen, J .R. Chelikowsky, “Electronic Structure and Optical Properties of
Semiconductors”, Springer Series in Solid State Science, 75, 1964, 45

AR. West, “Solid State Chemistry and its Applications”, Ed. John Wiley & Sons
Ltd., 1984, 514

See for example H.P. Meyers, “Introduction to Solid State Physics” Sec. Ed.,
1997, 275

H.M. Rosenberg, “The Solid State”, Oxford University Press, Sec. Ed., 1983, 145

43

Chapter 2

Investigation of the Thermoelectric Properties
of the Family of Cubic Semiconducting Quartenary Chalcogenides:

AmBanQ2m+n

2-1. Introduction

In the search for better thermoelectric materials, a new family of quartenary
chalcogenides compounds exhibiting promising tlrennolelectric properties has been
synthesized and characterized. A wide range of values for the different transport
properties have been measured indicating that we might be able to enhanced the by acting
on the composition of the materials.

The first compound discovered belonging to this wide family of compounds of
general formula AmBanern (where A is K or Ag, B is Pb or Sn, M is Bi or Sb, and Q
is Te, Se, or S) was KPbBiTe3 using a flux method by Dr. Chung. These materials
crystallize in the space group Fm 3m and possess the NaCl crystal structure type with
A, B and M disordered on the Na+ cationic sites and Q on the Cl' anionic positions. Such
disorder is particularly attractive for TB materials because mass fluctuation in the crystal
will decrease the mean free path of the phonon and therefore, the thermal conductivity.

In the general formula AmBanQ2m+n, m and n can theoretically have any values

allowing a continuous range of stoichiometry. This is true as long as the elements that are

44

used for A, B, M, or Q have a valence charge of +1, +2, +3 and -2 respectively, verifying

the following charge neutrality equation:

m(charge of A) +n(charge of B) + m(charge of M) + (2m+n)(charge of Q) = 0

Any deviation from this rule will lead to compounds with different structure types and
different properties. The number of parameters present in the general formula of the
compounds, i.e. m, n, A, B, M and Q, should allow us to tailor their physicocherrrical and
transport properties, and hopefully to discover materials with high figure of merit ZT.

The flux method used to discover KPbBiTe3 does not allow the synthesis of
substantial amount of material needed for transport measurements. Therefore, we
explored new synthesis methods in order to obtain large quantities of pure materials
having controlled stoechiometries. Preliminary physicochemical characterization and
measurements were made using our equipment and, depending on the results, promising
samples were sent to other laboratories for additional measurements. The methodology
used during this work is summarized in Figure 2-1.

Several members of the family of compounds studied in this research
(AmBanQZmrn) have already been reported in the literature”. Others can be included in
the general formula if we extend the scope of the elements that can be used for A to Cu
and T1.

Guseinov and al.1 studied and reported transports properties for the systems

AngBiQ3 as well as TleBiQ3. These reported compounds are n-type semiconductors

45

 

 

 

New compound
synthesised

 

 

A

 

 

 

If not promising values

 

l

 

2) solid solutions
3) doping

 

Improvement of the properties by:
1) substitution of elements

 

In our lab:

1) X-Ray diffraction

2) Preliminary measurments:
band gap
Seebeck
RT elect. conductivity

 

 

 

 

 

If promising values

 

Y

 

 

Figure 2-1: Research methodology.

46

 

Samples sent for additional
measurements:
Seebeck coefficient
Elect. conductivity
Therm. conductivity
Number of charge carriers

 

 

indicating that the majority carriers are electrons. A wide range of electrical conductivity
(from 2142 S/cm for TleBiTe3 to 115 S/cm for AngBiSe3) have been measured. This
supports the idea that the transport properties of these materials can be tuned by
changing the stoichiometry and the elements used. Seebeck coefficient of 100 uV/K for
members of the thallium system and a high value of 345 uV/K for AngBiS3 have been

reported. Thallium based compounds were not investigated in this work.

Table 2-1. Known members of the system A’mBanQ2m+n

(With A’= Ag, Cu, Tl; B = Pb, Ge; M = Bi, Sb; and Q = S, Se, Te).

 

 

 

Compound a (A) Reference Compound a (A) Reference
AgGeBiTe; 6. 105 2 AngBiSe3 6
AngBiS3 5.752 3 AngSbTe3 6.260 7
Ag4PbBi4$9 5.874 4 (3113in563 6.046 1
AngBiTe3 6.300 1 TleBiTe3 6.488 1
AngSbs3 5.785 5 TAGS 0’ 8

 

 

0) TAGS: Te/Ag/Ge/Sb system of formula (AngTez)r...(GeTe)x

TAGS are well known for their thermoelectric properties, and can also be seen as
members of the broad family AmBanQ2m+n by writing them as Ag1.,,Gebe,.xTe2(1.x”.x
and replacing l-x by m and x by n. We then obtain the general formula AgmGenSmee2m+n,
which is identical to the one studied in this Thesis. Compounds belonging to this system

were used for power generation. They show a transition from rhombohedral to cubic

47

NaCl structure type at room temperature for a ratio of m/n superior to 3, which was
regarded as an instability problem. For members having a m/n ratio inferior to 3,
measurements show a value of ZT superior to 1 for temperature above 500 K.

The few data available in the literature on the compounds belonging to the system
AmBanQ2m+n support our choice of further investigation. Our goal in this work was to

prepare new members of this large family and study their thermoelectric properties.

2-2. Experimental Section

Reagents

High purity reagents were used as obtained: Potassium metal 99% purity, Aldrich
Chemical Co., Inc., Milwaukee, WI; Silver, Lead metal 99.999%, 200 mesh, cerac,
Milwaukee, WI; Tin metal 99.999%, 200 mesh, Cerac, Milwaukee, WI; Antimony 200
mesh, Cerac, Milwaukee, WI, Bismuth 99.999%, Noranda Advanced Materials, Quebec,
Canada; Tellurium 99.999%, Noranda Advanced Materials, Quebec, Canada; Selenium
>99.5 %, 100 mesh, Aldrish Chemical Co., Milwaukee, WI or 99.999%, Noranda
Advanced Materials, Quebec, Canada and Sulfur (>99.999%) were used in this work.
Binary starting materials were prepared as follow:

KzTe: This material was prepared by mixing 12.7g (0.1 mole) of Te with 7.82g
(0.2 moles) of K into a 250 ml round bottom flask. A ISO-ml volume of NH3 was

condensed into the round bottom flask and cooled down to -78 °C in a bath of dry ice

48

and acetone under nitrogen atmosphere. The solution was stirred overnight and
evaporation of liquid ammonia, afier condensation by slow warrrring to room temperature,
produced the desired materials under the form of yellow fine powder. Great care must be
taken to avoid explosion and exposure of the product to air. K28e and KZS were
prepared under similar conditions.

BizTe3: Mixtures of 24 mole of Bi (5 g) and 36 mole of Te (4.59g) were
loaded into 13 mm Silica tubes, sealed under vacuum (<10‘4 Torr) using a diffusion pump
and heated up to 800 °C in 7 hours. An isotherm at 800 °C for 15 hours followed. The
tubes were then quenched into an ice bath in order to prevent large grain growth and
facilitate the grounding of the materials into fine powders. Bi2$e3 and BiZS3 were
prepared under the same conditions.

PbTe: Mixtures of 48 moles of Pb (10 g) and 48 moles of Te (6.125g) were
loaded into 13 mm Silica tubes, sealed under vacuum (<lO'4 Torr) using a high diffusion
pump and heated up to 680 °C using the following heating profile:

12 72 10 1 hours
50 ——->650 >650 > 100 ——->50 T (°C)

 

PbSe and PbS were prepared using the same experimental conditions.
The materials were then ground into fine powders using a mortar and pestle and checked

for purity by powder X-ray diffraction.

49

Synthesis of AmBanQ2m+n Compounds
Method 1: Binary compounds were prepared according to the reaction below.

nPbQ + (In/2)Bi2Q3 + (In/2)K2Q —> KmenBimQ2m+n EQ- (2-1)
Stoichiometric amounts of KZQ, Bi2Q3 and PbQ were mixed under nitrogen atmosphere in
a vacuum Atmosphere Dry-Lab glovebox. For example, KPbloBiTe 12 was prepared by
mixing 0.026 g of KzTe (0.12 mole) with 0.836 g of PbTe (2.5 mole) and 0.100 g of
BizTe3 (0.125 mole). The mixture was loaded into graphite tubes, which were then
placed into 13-mrn carbon coated Silica tubes. Graphite tubes and carbon coating were
used to lirrrit the extend of glass attack due to the reaction with K2Q (and in particular
KzTe). The tubes were sealed under vacuum (<10'4 Torr) and heated using one of the
following heating profiles and isolated as explained later. In the case of KPbloBiTen, the
heating profile used was H-2. The mixture was heated to 700 °C in 18 hours and let at
this temperature for 120 hours. This was followed by a temperature increase to 750 °C
in two hours and by an isotherm at this temperature for 1 day. A decrease to 50 °C in 24

hours concluded the synthesis.

 

18 96 18 hours

H-1: 50 ————>700 ———>700 ———>50 T (°C)
18 120 2 24 24 hours

H-2: 50————>700—————)700 >750 >750 >50 T (°C)
12 18 140 24 24 24 hours

 

 

H-3: 50———>50(P >700 >700 9750———)750————)50 T(°C)

50

The compounds were then purified by eliminating any alkali polychalcogenides
that had not reacted during the synthesis. Under nitrogen atmosphere, the reaction
products were washed with dimethylformamide (DMF). If traces of polychalcogenides
were present, a brown coloration appeared; DMF was changed until no coloration was
visible. Products were then rinsed with water, methanol, and ether, and left under
nitrogen atmosphere to dry. The compounds obtained were re-melted into 3 or 9 mm
silica tubes in order to be sent for measurements by other laboratories. The use of a 9 mm
tubes instead of a 3 mm silica tubes were found later to constituted a better choice to

minimize glass attack.

Method 11: “Flame Reaction”. The prep was performed according to the reaction:

mA + nB + mM + (2m + n)Q —> AmBanQ2m+n Eq. (2-2)
Stoichiometric amounts of A, B, M, and Q were mixed under nitrogen atmosphere in a
vacuum Atmosphere Dry-Lab glovebox. For example KPbloBiTen was synthesized by
mixing 0.039 g of K (1 mole) with 2.071 g of Pb (10 mole), 0.209 g of Bi (1 mole),
and 1.531 g of Te (12 mole). The mixture was loaded into 13-mrn carbon coated silica
tubes. The tubes were sealed under vacuum (<10“1 Torr) and heated to 150 °C in 1 hour.
This was followed by an isotherm at the same temperature for 1 hour and a decrease to
room temperature in 1 hour. The tubes were then opened and the products loaded into
13-mm Silica tubes, sealed under vacuum and heated using a high temperature torch flame
until melting of content. If the first heating step to 150 ° C was omitted, it was more

difficult to recover the potassium metal and PbQ that were projected on the inner side of

51

the tube during the flame reaction. Therefore, the first heating was intended to ensure

proper reaction of potassium and to keep the entire material at the bottom of the tube.

Method 111: “Flame Reaction”. This method is identical to Method 11 with the exception
that the mixture were mixed under nitrogen atmosphere and loaded into non-carbon coated
tubes. The tubes were sealed heated as previously mentioned, and flamed without being

opened.

Physical and Transport Property Measurements

(a) X-ray powder diffraction: Purity of the products was determined by X-ray

powder diffraction using:

0 a CPS 120 INEL X-ray powder diffractometer using monochromatized radiation, Cu
K-Lm (A = 1.54059A). The standard used for calibration in the position sensitive
detector is silicon powder (Standard Reference Material 640b).

o or/and a Rigaku Rotaflex powder X-ray diffractometer with Ni-filtered Cu K0:
radiation operating at 45 kV and 100 mA.

Accurate d-spacings were determined from the experimental powder pattern data with the

program PROLIX9 using a second-degree polynomial Pearson VII function. The cell

parameters were refined using the program U-Fit'o.

52

(b) Solid State Infrared and UVN is Spectroscopy

Samples were ground and analyzed at room temperature in the near infrared region (6000 -
400 cm") using a Nicolet MAGNA-IR 750 spectrometer equipped with a Collector
Diffuse Reflectance of Spectra-Tech. Inc. The diffuse reflectance spectrum was used to
determine the value of the band gap as explained in Chapter 1 using the Kubelka-Munk
function. Spectra in the 200-2500 nm region were recorded with a Shimadzu UV-3101
PC double beam, double monochromator spectrometer having barium sulfate (BaSO4) as a

reference.

(c) Scanning Electron Microscopy (SEM)

Qualitative microprobe analysis of the products were performed using a Scanning
Electron Microscope JEOL JSM-35C equipped with a Tracor Northern Dispersive
Spectroscopy Detector. Because of overlapping of lines (exited energy levels) between
heavy elements such as Pb and Bi, accurate quantification could not be done. Since
incorrect estimations of Pb and Bi affect the quantification of other elements present, and
because the samples were mainly synthesized as powders, the use of this technique for
quantitative purposes was not possible. Nevertheless, EDS was used to check the

presence of elements in a qualitative way.

(d) Differential Thermal Analysis (DTA)
DTA was done on a Shimadzu DTA-50 thermal analyzer. Samples were loaded into

carbon coated silica arnpoules, sealed under vacuum (with a residual pressure <10“ Torr)

53

and heated to 1000 °C at a rate of 10 °C/min followed by a cooling at the same rate. Equal

amount of alumina sealed in similar silica container was used as reference.

(e) Room temperature four-probe conductivity

Room temperature conductivity was measured using a four-probe home made
measurement system. The system was calibrated using a BizTe3 block as a reference with
its conductivity given by the literature. Because this measurement is strongly dependent
on the shape of the sample, some discrepancies are expected between values measured
with this type of equipment and values measured with different techniques by our

collaborating groups.

(f) Seebeck measurements

Measurements of the Seebeck coefficient as a firnction of the temperature were done using
a programmable Seebeck controller SB100 from MMR Technologies, Inc. The reference
chosen was a 0.002” constantan wire, and all mounting of the sample and the reference on
the stage were made using silver paste. Several runs were performed on each sample in
order to verify the reproducibility, accuracy and variation of each measurement. The

measurements ranged from 80 K to 700 K.

54

(g) Measurements performed in other laboratories

Promising samples were sent to different research groups in order to verify the
accuracy of the preliminary measurements and to perform variable measurements not
possible in our facilities. These research groups are those of:
- Professor C. Uher, Department of Physics, University of Michigan, Ann Arbor,
Michigan“. This group performed most of the thermal conductivity studies reported
here.
- Professor C. R. Kannewurtf, Department of Electrical Engineering and Computer
Science, Northwestern University, Evanston, Illinois”.
- Professor T. Hogan, Department of Electrical and Computer Engineering & Material

Science and Mechanics, Michigan State University, Michigan State University,

Michigan”.

2-3. Results and Discussion

Synthesis and Crystallographic Data
(1) K/Pb/Bi/Te system

KmenBimTeZmrn compounds were synthesized using Method 1, and obtained in a
"lava" like form. A brown coloration was observed in the DMF solution during the
isolation process indicating that amount of KzTe had been left unreacted. Lead-rich

members such as KPbgBiTem and KwaBiTelz were obtained using the heating profile

55

H-2, while members having lower Pb content were synthesized using the heating profile
H-3.

X-ray powder diffraction patterns of the compounds KPbgBiTelo and
KPbloBiTelz (See Figure 2-2a and 2-2d) were in excellent agreement with the NaCl
structure type without any detectable impurities. The lattice parameters were calculated
using the program U-Fit and are equal to 6.459 (1) and 6.471 (2) A for KPbgBiTem and
KPmeiTelz respectively (see Table 2-2). In the case of the low lead content members
such as KPbBiTe3, the NaCl cubic phase was present (see Figure 2-2b) but poor
crystallinity of the samples prevented the determination of accurate lattice parameters.

The use of flame reactions (Method 11 and III) was introduced in order to decrease
the time necessary to the synthesis of the compounds allowing faster decisions in the
research orientation, as well as obtaining more crystalline low lead content compounds
that could not be synthesized using Method 1. The crystallinity of those members such
as for example KszBiTe4 improved (see Figure 2-2c), but no relation was observed
between the lattice parameters and the amount of lead and tellurium present in the system
(see Table 2-2). Furthermore, discrepancies appeared between identical compounds made
with identical experimental condlfirrnexample, Method IIa was identical to method
IIb and identical to Method 11 with the exception that no carbon coated was used to
prevent glass attack. Most certainly, vaporization and deposition of some elements
(notably Pb) to the colder parts of the tubes as well as loss of KzTe during glass attack

can account for the differences in the values of the lattice parameters. Re-alignment of the

56

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

§ .. (a) (d)
s 4.. §
5 35. § 7 3 § N
- . Qwr r.--.-:--.-l.-J ...... .4 L. A
(b) (e)
UL] J*
r.- t at l l at '1'
(C) (0
.§‘
8
E
M . l 1. Li I .“J
0 20 40 6O 80 100 120 0 10 20 30 40 50 60
26) (degrees) 29 (degrees)

Figure 2-2: X-ray powder diffraction patterns of (a) KPbgBiTelo, (b) KPbBiTe3,

(c) KszBiTe4 (using flame reaction), (d) KPbloBiTelz (e) impurity phase in KszBiTe4,
and (f) calculated BiTe.

57

X-ray beam that occurred between the measurements can also account for a shift of the
peaks and therefore a difference in the values of the cell parameters.

In addition, as the amount of lead is decreased (i.e. smaller n values), an impurity
phase became dominant (see Figure 2-2e). Comparison between BiTe, BizTe3, szBizTes,
PbBi4Te7, and PbBizTe4 showed that these compounds have similar X-ray powder
patterns as noted by Zhukova and Zaslavskii”. A closer look at the low angle peaks
indicates that the impurity phase formed is most probably BiTe (see Figure 2-2f).
Annealing of the compounds at 750 °C for 1 day removed the impurity phase.

All methods used to synthesized members of this system showed drawbacks.
Method I involving a slow homogenous heating left unreacted small amounts of KzTe,
while the flame Methods 11 and III allow loss of some elements by condensation on colder
parts of the tubes and prevent good homogeneity. In both of these methods, reactivity of
K2Te toward silica caused the loss of some potassium and tellurium. This problem was
minimized in Methodl by using graphite tubes, but not eliminated. The decision to use
flame Method 11 and III for further work has been made because no particular method

appeared to be better. Therefore, we choose the fastest ones.

58

Table 2-2. Cell parameter of KanBiTew members for different experimental conditions.

 

Composition Method I Method 11 Method IIa Method IIb Method 111 a

 

 

 

KszBiTe4 6.475(1) '

KPb4BiTe6 6.455(1) 6.456(3) 6.471(1)
KPbéBiTeg 6.451(1)1 6.466(1)1 6.444(1)

KPbgBiTem 6.459(1) 6.451(1)1 6.527 (9)1 6.441(2) 6.471(1)
1<:1>meiT.=:12 6.471(1) 6.453 (1)1 6.452(1)

 

': Presence of an impurity phase in the powder pattern.

(2) K/Pb/Bi/Se systems

Compounds of the general formula KanBiSen+2 (with n = 1, 2, 3, 4, and 5) were
obtained using the experimental conditions of Method I with the heating profile H-l,
while members with n = 8 and 10 were synthesized using heating profile H-2. No
coloration was observed in the DMF during isolation indicating that all K2Se reacted.

Powder X-ray diffraction showed pure NaCl cubic phases (see Figure 2-3a). The
cell parameters were calculated and are reported in Table 2-3. PbSe is given in reference
(see Figure 2-3b). Contrary to the K/Pb/Bi/Te system, members with low lead content
(n=1) were successfully synthesized.

It is useful to treat the K/Pb/Bi/Se system as solid solutions (KBiSe2)1-x(PbSe)x.
This approach is possible because both KBiSez and PbSe crystallize with the same NaCl
structure type. Any value of x between 0 and 1 should give a compound with a cell
parameter between those of KBiSezls, i.e. 5.92 (1) A and PbSe”, i.e. 6.1213 (8) A.

Surprisingly, the cell parameters of the KanBiSen+2 compounds are higher than these two

59

 

200

(a) \ (c)

220

 

 

 

 

 

 

 

 

 

 

 

 

 

JUUMW l . I ll lll .1 ll 1

-J;..l-..l...l..

0 20 40 60 80 100 1200 10 20 30 40 50 6O 70 80
29 (degrees) 29 (degrees)

 

Figure 2-3: X-ray powder diffraction patterns of (a) KPb3BiSe5, (b) PbSe, (c)
K2PbBi2Se5, and ((1) calculated BiSe. (The peaks corresponding to the correct cubic

phase in (c) are marked by arrows).

60

values. The lattice parameter of PbSe was calculated on powder and showed a slightly
lower value of 6.105 (2) A. We did not synthesize KBiSe2 in order to check the cell
parameter but some doubts are raised toward the value of the cell parameter given in the
literature. The cell parameters of the selenium compounds were plotted as a function of x
(see Figure 2-4) and a value of 6.332 A for KBiSez can be extrapolated. As expected a
linear trend exists as the cell parameter decreases when x increases. Vegard’s Law17 is
well followed by this system indicating that the stoichiometry of the compounds are
close to the expected ones. The possibility of small amount of PbSe formed as impurity

can account for some slight shift in the cell parameters.

Figure 2-4: Cell parameter variation in the system (KBiSe2)1-x(PbSe)x.

 

6.40 ,
6.35
6.30
6.25
6.20
6.15
6.10
6.05
6.00:L1441..1.rrr...1.

 

Cell Parameter (A)

 

 

 

In a similar way than for the tellurium system, impurities are formed when x < 0.5
(see Figure 2-3c). Simulated powder patterns showed that one of them is probably BiSe,
which is isostructural to BiTe (see Figure 2-3d).

Compounds synthesized using flame Method II show inconsistencies in the cell

parameters as it was noticed for the K/Pb/Bi/Te system. (see Table 2-4). In this case, the

61

loss of PbSe by deposition on colder part of the tube is responsible for these

discrepancies.

Table 2-3. Cell parameters for selected members of the family KanBiSen+2 (with n = 1,

2, 3, 4, 5, 8, 10) and KPmeiSn+2 (with n=1, 4, 8).

 

 

 

Composition Cell parameter (A) Composition Cell parameter (A)
KPbBiSe3 6.217 (2) KPbBiS3 5.998 (1)
KszBiSe4 6.188 (4) KPb4BiS6 5.949(1)
KPb3BiSe5 6.165 (3) KPbgBiSm 5.935 (1)
KPb4BiSe6 6.1528 (8)

KPbsBiSe7 6.141 (3)

 

KPbgBiSem 6.1416(8)
K145103134.12 6.136(1)

 

(3) K/Pb/Bi/S system

Comparable results to the ones obtained for the selenium system were observed
for the sulfur compounds. KPbBiS3, KPb4BiS(,, and KPbgBISlo were synthesized using
method I and the heating profile H-2. No coloration was noticed in the DMF solvent
used to wash the products during isolation indicating that all the K28 reacted.

Powder patterns obtained from X-ray diffraction showed pure cubic phases in
perfect accordance with the NaCl cubic structure (see Figure 2-5a). PbS is given as

reference in Figure 2-5b. As for the K/Pb/Bi/Se system, the sulfur system can be seen as

62

a solid solution of (KBiSz)1-x(PbS)x. The calculated cell parameters were plotted as a
function of x with the cell parameter of KBiSz18 taken from the literature and being equal
to 6.040 (1) A, while the cell parameter of PbS was calculated on powder and equal to
5.9286 (4) A. Figure 2-6 shows that the system follows Vegard’s Law, and as a
consequence indicates that the stoichiometry of the compounds synthesized are close to
the expected ones.

As for the previous systems, Method 11 gave inconsistent results (see Table 2-4)

due to the vaporization and deposition of PbS on the inner sides of the silica tubes.

Table 2-4. Cell parameters for members of the KanBiSe2+n and KPmeiSz+n systems

made by “flame” induced reaction.

 

 

 

Composition Cell Parameter (A) Composition Cell Parameter (A)
KPbBiS3 5.971 (1) KPb4BiSe6 6.135 (1)
KszBiS4 5.949(1) KPbgBiSelo 6.141 (1)
KPb4BiS6 5.9354(1) KPmeiSen 6.130(1)

10453131310 5.9382 (6)

KPbloBiSIZ 5.9345 (7)

 

63

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

: .8. (a) (b)
53.
a N : ,b
E a ... E
N 3 3
2 m 2
§ V "m" c
8 o'“ 8
M 3 I“
x 111.1 -1.-.
0 20 40 60 80 100 120 0 20 40 60 80 100 120
29 (degree) 29 (degree)

Figure 2-5: X-ray powder diffraction patterns of (a) KPbgBiSlo and (b) PbS.

 

6.10 _
6.05 '
6.00 '

5.95

 

Cell Parameter (A)

 

 

 

5.90

l
E
tn
0

Figure 2-6: Cell parameter variation in the system (KBiS2)1_x(PbS)x.

64

(4) Ag/Pb/Bi/Te System

Members of the system AgmBanQ2m+n were synthesized using experimental
conditions described in Method III. The products obtained had the form of gray shiny
ingots.

X-ray powder patterns of the compounds listed in Table 2-5 exhibit pure cubic
phases similar to the one shown in Figure 2-7 and are in total agreement with the NaCl
structure type. After rewriting the system Ag/Pb/Bi/T e as the solid solution
(AgBiTe2)1_x(PbTe)x, a plot of the cell parameters as a function of x (Figure 2-8) shows
that the system deviates from Vegard’s Law for high value of x. Additional compounds
need to be made in this region to see a more clear trend. Nevertheless, the stoichiometry

of the compounds should be in relative agreement with the targeted compositions.

Table 2-5. Cell parameters for members of silver based systems.

 

 

7 Compound Cell Parameter (A) Compound Cell Parameter (A)
AngloSbSn 5.905 (1) AgszBizTe5 6.239(2)
AngwaTelz 6.4415 (4) Ang3BiTe5 6.416(2)
AgSntiSu 6.259 (2) Ang6BiTe3 6.429 (2)
AngloBiSelz 6.118 (1) AgSngBiSelo 5.927 (1)

 

In the case of the Ag/Sn/Bi/S system, plate crystals of SnS grow as an impurity

phase when tin rich members such as AgSngBiSm were synthesized with flame reaction.

65

 

 

200

 

o
N
5‘ N
'5
t:
o
H
5 8’1
N
N <1-
Ng 8i N
: v
M ‘1' o ON
3 NN
~o~o

 

 

 

'—
u—
—-
I AJ...IA4L.1--ALAL

0‘20” 40 60 30 100 A120
29(degrees)

 

Figure 2-7: X-ray powder diffraction pattern of AngloBiTelz.

 

Cell Parameter (A)

 

 

 

Figure 2-8: Cell parameter variation in the system (AgBiTe2)1-x(PbTe)x.

66

(5) Other systems
Three more systems were briefly investigated using method 11. They are those of
K/Pb/Sb/T e, K/Sn/Bi/T e, and K/Sn/Sb/T e. Ingots were obtained from the flame reactions.
Members with high Pb content showed pure cubic phases in perfect agreement
with the NaCl structure type. The lattice parameters were determined and reported in

Table 2-6.

Table 2-6. Cell parameters of members of the K/B/M/T e system (where B is Pb or Sn

and M is Bi or Sb).

 

Compound Cell Parameter (A) Compound Cell Parameter (A)

 

 

 

KPbSbTe3 * KSnBiTe3 *
KPbSSbTe7 6.448 (2) KSnsBiTe7 *
KPbIOSbTelz 6.460(4) KSnloBiTen 6.2922 (1)
KSnSbTe3 *

KSnSSbTe7 6.278 (2)
KSnloSbTelz 6.364 (4)

 

* accurate cell parameters could not be calculated due to the presence of an impurity
phase.

Based on the powder pattern of KSnBiTe3 (see Figure 2-9) the impurity phase
was attributed to BiTe but because low angle peaks are difficult to observe due to
background noise, some doubts remain. Similarly, the impurity phase present for

KSnSbTe3 and KPbSbTe; is attributed to SbTe that is isostructural to BiSe.

67

Members of the K/Pb/BiSe and K/Pb/Bi/S systems were successfully synthesized
using Method 1. Due to the higher reactivity toward silica of K2Te compared to KZSe or
K2S, control of the stoichiometry in the K/B/M/T e systems is problematic using either of
the methods presented.

Most of the systems investigated showed the presence of a stable impurity phase
having the BiSe structure type (when values of n/m reach 1). In the case of the
Ag/Sn/Bi/S system, the binary SnS formed along with the desired cubic phase.

The family of compounds AmBanQzm+n can be seen as the solid solution
(AMQ2)1-X(PbQ)X. In the case of the K/Te based systems this approach is not possible
because KBiTe2 and KSbTez apparently do not have a NaCl structure type. Attempts of
making these compounds with the NaCl structure type were unsuccessful. Concerning the
K/Pb/Bi/T e system, the value reported in the literature for KBiSez is questionable, being

too low to be used for the solid solution system (KBiSe2)1-beSex.

 

Intensity

 

 

 

AAAAAAAA

0 20 40 60 80 100 120
29 (degrees)

 

Figure 2-9: X-ray powder diffraction pattern of KSnBiTe3.

68

Physical Properties
(1) K/Pb/Bi/Te system

Using diffuse reflectance infrared spectroscopy, band gaps were observed and
values of 0.38 eV for both KPbgBiTelo and KPbloBiTen were determined (see Figure
2-10). This value classified these compounds as narrow band gap semiconductors. No
well-defined bang gap was detected for KPbBiTe3, KszBiTe4, and KPb4BiTe6 although
one is expected. The shape of the absorption spectrum suggests that a self-doping effect
takes place masking the true band gap.

Self-doping in these materials is derived from defects created during the synthesis.
The rapid synthesis and fast crystallization may cause anti-site defects, vacancies and
even non-stoichiometry. These factors create energy levels between the gap which absorb
light thus masking the true band gap. It is possible that these defects may be repaired by
proper annealing of the materials after synthesis.

Differential thermal analysis of these compounds do not show any endothermic
peaks, indicating that the melting point of these compounds lay above 1000 °C (limit of
our DTA analyzer). Remelting the compounds into silica tubes showed that the materials
react with the silica, with accompanying glass attack. The amount of glass attack
increases with increasing the content in potassium. Nevertheless, the compounds melt
congruently. This is an important property since it allows the material to be used at high

temperature without being decomposed.

69

32

 

Ifi' Ti
1

31

IIII
I

30 / Defect States

29

28

ITITITII I

OL/s

27

26

IIIrTITIIII

Eg=0.38 eV

25:-

 

 

 

p
)-
24 111111111111 11111111111

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Energy (eV)

Figure 2-10: Optical absorption spectrum of KPbloBiTelz showing the energy gap.

70

(2) K/Pb/Bi/Se system

Energy gaps for selenium compounds were calculated to vary from 0.46 eV to
0.675 eV for KPbloBiSelz and KPbBiSe3 respectively (see Table 2-7). Contrary to the
previous system, the band gaps here were well defined.

As mentioned above, we can treat the system as a solid solution of KBiSez and
PbSe. The variation of the band gaps as a function of x is not a linear function as a
plateau is reached for values of x inferior to 0.5 (see Figure 2-11). The value used for
PbSe was taken from the literature as 0.26 eV. A typical example of an absorption
spectrum for KPbsBiSe7 is shown in Figure 2-12.

Compounds obtained from flame reactions did not show well defrned absorption
spectra (see Figure 2-13), again probably because of self-doping effects caused by the
rapid synthesis of these materials. Differential thermal analysis did not show any melting

peaks below 1000 °C.

Table 2-7. Energy gap for members of the family of compounds KanBiQn+2.

 

 

 

Composition Energy Gap (eV) Composition Energy Gap (eV)
KPbBiSe3 0.68 KPbgBITelo 0.38
KszBiSe4 0.67 KPbloBiTelz 0.38
KPb3BiSe5 0.66 KPbBiS3 0.87
KPb4BiSe6 0.64 KPb4BiS6 0.7 1
KPbsBiSe7 0.62 KPbgBISm 0.61
KPbgBiSelo 0.50

KPbloBiSelz 0.46

 

71

 

0.8

 

 

 

 

 

A 0.73 r. -
a : T
v 0.6;- O
8* :
0 0.5;.
@042.
=1 :
“J 0.3;.
: D
()2 '....1

0.4 . 0.6 0.7 0.8 0.9 1
x

Figure 2-11: Variation of the energy gap as a function of x for the system

(KBiSez)1-x(PbSo)x-

 

16

15

l4

13

01/5

12

ll

    

10 ‘ Eg=0.62 eV

 

 

9 111111111111Lrlrrrrlrrrr

0.5 0.55 0.6 0.65 0.7 0.75
Energy (eV)

 

Figure 2-12: Optical absorption spectrum of KPbsBiSe7 showing the energy gap.

72

 

 

 

 

 

 

 

 

 

22 22
20 ’ ‘ ,j 5 ‘L
20 ’ll 18 l 7 '38:; ”£55 if
/ ‘ " ‘
l «Irv- .. / ' .51.:
18 / W...“ 16 ' ‘ ':
l '
8” ll g 14
‘6 ,1 12
/ 10
14 ,1
/ 3 '
12 1’ 6 .........r......--1.rr-1r.---.rrmrr-
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Energy (eV) Energy (eV)
(6) (b)

Figure 2-13: (a) Optical absorption spectrum of KPbloBiSelz. The band gap of the
compound is masked by mid gap energy levels. (b) No band gap appears after annealing

of the sample for 24 h at 400 °C.

 

24

22

   

Ot/s

Eg=0.64 eV

 
 

 

11.141

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
Energy (eV)

 

 

igure 2—14: Optical absorption spectrum of KPbgBiSw showing the energy gap.

73

(3) K/Pb/Bi/S system
Higher values of band gaps were observed for the corresponding sulfide members

compared to those of Se and Te analogs. The values of the well-defmed band gaps

reported in Table 2-7 vary from 0.61 for KPbgBiSmto 0.87 eV for KPbBiS3. An example
of an absorption spectrum for KPbgBlSlo is shown in Figure 2-14.

In the products obtained with the “flame reaction”, no band gaps were observed

due to self-doping effects as discussed above.

DTA did not show melting peaks below 1000 °C. Furthermore, experiments of
melting sulfur compounds loaded into silica tubes showed that their melting point is

higher than those of the tellurium and selenium systems, and at least as high as the melting

point of the silica tubes.

(4) Other Systems

The absorption spectra of members of the silver systems did not show any clear
band gap transitions. Their absorption spectrum has similar characteristics to the ones

showing a self-doping effect, nevertheless, in the case of AngloBiTelz the band gap was

observed and estimated at 0.28 eV.

No band gaps were visible for KSnloBiTelz and other members of the K/Sn/Sb/T e
system. The band gaps for the K/Pb/Sb/Te members are not well defined due to a broad

tail as shown in Figure 2-15. They can be roughly estimated to be between 0.26 and 0.33

74

eV for KPb5SbTe7 and between 0.12 and 0.28 eV for KPbIOSbTelz. DTA was not

performed on these systems.

15.5

 

15

14.5

01/8

14

 

Eg=0.26 eV

13.5 / A '
t. 5,. :.u-v“’-7——'

0.25‘ ‘ ' 03' ' l 0.35‘ 0.4 ‘ ' 0.45
Energy(eV)

Eg=0.33 eV

 

 

 

Figure 2-15: Optical absorption spectrum of KPbSSbTe7 showing a broad tail.

As expected the values of the energy gaps for members of the system KanBiQn+2

follow trends. As 11 increases in the K/Pb/Bi/Se and K/Pb/Bi/S systems, the energy gap

decreases approaching the values of PbSe and PbS respectively. If Q is changed fiom Te
to Se and to S the band gap increases because we substitute heavy atoms by lighter ones.

The band gap values for the different systems studied suggested that the

K/Pb/Bi/T e, ~ 0.38 eV, and Ag/Pb/Bi/T e systems, ~ 0.28 eV, are the most promising for

thermoelectric investigations. The values for the K/Pb/Bi/S system appear to be too high

75

(from 0.61 to 0.87 eV) compared to the <0.5 eV that is desired. Such band gap value is
one of the requirements that a material must follow in order to be a viable TE material at
room temperature. If the band gap is too high, the conductivity will be too low;
conversely, if the energy gap is too low, minority carriers can be created that adversely
affect the Seebeck coefficient. All other systems investigated show band gap values that

lie in the desirable range and we classify them as “narrow band gap semiconductors”.

Transport properties
( 1) K/Pb/Bi/T e system

Preliminary Seebeck coefficient measurements on pressed pellets of members of
the KanBiTew system (see Figure 2-16) showed that all the tellurium compounds were
n-type, indicating that the majority carriers are electrons. The materials show narrow
band gap semiconductor behavior as the absolute value of the Seebeck coefficient rises
with temperature (as a metal) but possesses a high value over —100 uV/K (as a
semiconductor). The Seebeck coefficient trends to 0 uV/K at 0K. These compounds
possessed similar values at room temperature and no relationship was noticeable between
the value of the Seebeck coefficient and the variation of the amount of lead in the samples.
This indicates that we might be able to change the amount of lead in the system until an
optimum value of the electrical conductivity is reached, without affecting much the
Seebeck coefficient. Selected values of the Seebeck coefficient at room temperature are

-130 uV/K for KPbBiTe3, -110 uV/K for KPbgBiTem and -140 uV/K for KPbloBiTen.

76

KPbBiTe3, KPbgBiTelo and KPbloBiTelz were sent for further characterization.
The results for KPbBiTe3 (see Figure 2-17) showed a Seebeck coefficient of -47 uV/K at
room temperature. Measurements on KPbsBiTem and KPbloBiTelz showed similar
values (Figure 2-18) of -41 and -47 uV/K at 300 K respectively. In both cases, the
thermopowers obtained were much lower than the ones measured with our system.

Why do these values differ so much from our measurements? The first
hypothesis advanced was the following. As mentioned previously, since the products of
the reactions did not have an ideal morphology for measurements (i.e. homogenous, bulk
samples without physical holes), ingots were made by re-melting the compounds. It was
these ingots that were shipped to Professor Uher Lab for measurements. In theory, no
differences should exist in the measurement of the Seebeck coefficient between cold press
pellet sample and ingot. We attributed the observed differences to the fact that during the
making of the ingots, a change of the electronic composition of the material occurred either
by loosing small amount of some elements or by creating new defects. These processes
change the doping state and can dramatically affect the value of the Seebeck coefficient as

explained in Chapter 1.

77

 

 

0
O KPbBiTe3
-20 _
A KPb BiTe
l- % 2 4
'40 ~ 83 o KPbBiTe
r Ooéé 4 6
2‘ 60 l 908$? >< Kranem
o
> -80 _ Ooéé
5 o 88.1.
_ 000‘»
m . 0° )6
_ 000%)?
-100 . OOSOQA
: 08XAAAAA
420 T °8656 AAAAAA
F ”figoo A
- — a O
_16Oinrrrrrrhrrrmrrrrrrrr 1 1 ET

 

 

50 100 150 200 250 300 350 400
Temperature (K)

Figure 2-16: Seebeck coefficient as a function of temperature for members of the system

KanBiTem synthesized using “flame” reaction (cold pressed pellet measurement).

 

 

 

 

1800 , 10
S 0
1600 g
' 5 -10
A 1400 b 3
_-2 w
E ’ : O E?
to . I <
o 1200 ~. -30 5
. —: -40
1000 l
’ j -50
goo-11.1.. .1111

 

. .1....1....r....1....4_60
0 50 100 150 200 250 300 350
Temperature (K)
Figure 2-17: Seebeck coefficient and electrical conductivity for KPbBiTe3 (ingot).

78

The thermal conductivity values of KPbgBiTe 10 and KPbloBiTelz were measured
to be ~ 2.0 W/m-K and ~ 2.2 W/m-K respectively at room temperature (see Figure 2-19).
No contribution from radiative losses were noticeable in the plots. These values are very
low and encouraging because they are only slightly higher than that of BizTe3. In the
latter, the thermal conductivity can be decreased significantly by solid solutions
experiments of Bi2-bexTe3 or BizTe3-xSex. Therefore we can expect to lower the thermal
conductivity of our compounds by introducing similar disorder on the anionic and/or
cationic sites through substituting for example some Bi atoms by Sb, or some Te atoms
by Se atoms. Electrical conductivity measurements of ingot samples gave values of 600
S/cm and 800 S/cm for KPbgBiTelo and KPbloBiTelz respectively at 300 K (see Figure 2-
20). The value of KPbBiTe; is in the same range and equal to 900 S/cm (see Figure 2-17).
The variation of the conductivity with temperature in both samples shows a metallic
behavior. The conductivity values at room temperature are in the range of what is desired
for thermoelectric applications and close to the value of BizTe3 (2 900 S/cm).

These transport properties are promising despite the low Seebeck values
measured. A ZT at room temperature of 0.015 for KPbgBiTem and 0.027 for
KPmeiTeu, can be computed using the data obtained (see Figure 2-21). The differences
between the measurements on cold press pellets and ingots is at this time attributed to a

change in the electronic structure of the materials when remelted.

79

 

 

 

 

 

 

 

 

0 Kl’bfiBiTeI0
D KPb BiTe
IO 12
O
U o
O
v D O
’ D
I D O
r D 92
l ad
50 100 150 200 250 300
Temperature (K)

Figure 2-18: Seebeck coefficient measurement of KPbgBiTelo and KPbloBiTelz (ingots).

K (W/mK)

 

 

”ido‘mlsldmzoo”

DOD C] m1
000 0 0C

 

 

O Kl’baBiTel0
Cl KPb BiTe
10 12

 

 

A 1 L44 A

A 250 300

Temperature (K)

Figure 2-19: Thermal conductivity of KPbgBiTem and KPmeiTen (ingots).

80

2000

 

 

 

 

 

 

 

NU o KwaBiTen
1300 f a KPb BiTe
. 00 8 10 _
1600 E ‘bo
. 00
A E 00
a 1400 L Q,
Q ' 0o
z; 1200 I 00
1: ~ 0 o
MIL—31:1 O o
1000 _ Q:
t Bamboo O o o
800 . :10 D oc
i U U U
600 *1...1...-_.nn_n.MaghmEm'
0 50 100 150 200 250 300
Temperature (k)

Figure 2-20: Electrical conductivity of KPbgBiTelo and KPbloBiTelz (ingots).

 

  

 

0,03 22¢
' 0 KPb BiTe
0.025 8 1°
U KPb BiTe U
10 12
0.02 D
g 0.015 13
C] O
0.01 0
Cl 0
1:1
0.005 Cl 00
6998 O
O r...i..L.i..,.|...r
O 50 100 150 200 250 300
Temperature (K)

Figure 2-21: ZT versus T for KPbgBiTe 10 and KPbloBiTelz.

81

Hall measurements gave the number of charge carriers (see Figure 2-22). The
values at room temperature are 8.5 x1019 charge carrier per cm3 for KPbgBiTem and about
5 x1019 carriers per cm3 for KPbloBiTelz. These high numbers of carriers tend to confirm
that the compounds are already doped as previously indicated. They are in range of the
values that are considered favorable for TE materials (see chapter I). Mobilities (see
Figure 2-23) were also calculated fiom the number of charge carriers using Eq.2-3.

o = N e p. Eq. 2-3
They are respectively equal to 100 and 50 mz/V-s for KPbgBiTCm and KPbloBiTelz. We
are far from mobilities of 1000 cmzN-s that are usually found for the best TE materials.
For reference”, BizTe3 has a mobility of l200 cmzN-s and PbTe a mobility of 1700
cmzN-s. The importance of having high mobility is evident if we consider the quality

factor of a material as defined by Tuomizoz

3/2
Q1= N,- u,[—’] Eq. 24

where the indices j relate to the electronic band, NJ- is the degeneracy of the band. A
quality factor can be attributed to each band. In turn, QJ- is proportional to the B factor
(See for example Mahan)”, from which ZT is proportional with. High mobility is
therefore needed to increase the quality factor which in turn increases the efficiency of the

material for TE application.

82

 

o KPb BiTe Cl KPb BiTe
19 8 10 10 12

 

 

 

 

 

 

910 "l'j'fi""I""I'—'"l'"'Ifi"—"
81019 I-o O o O -
: O O o O :
111/K710”: .‘
E E I
:6IO'9} .3
19 .
510 EC] U E] Cl C] D Cl 1
41019 :rr.ii....i...L1....1....|.urrr...:

O 50 100 150 200 250 300 350

Temperature (K)

Figure 2-22: Charge carrier concentration for KPbgBiTelo and KPbloBiTelz as a function

of the temperature.

 

 

 

 

3001' 0--
+ . 1
» O KwaBlTen‘
b O . d
250 o a KPbsBlTelo ‘

r 0 .
A200” —4
“.- » o .
(I) 1
— . 1
O .
”>150: .
t O 1
E 1 O ,
=- > 1
100_ o -
ID 0 D ‘
> D D D 1
> J
0hra--n. A--ir.--1.. Anni

 

 

 

0 50H100‘ 150 200 350 300350

Temperature (K)

Figure 2-23: Temperature dependence of the mobility of samples of KPbgBiTelo and

KPb loBiTe 12.

83

(2) K/Pb/Bi/Se and K/Pb/Bi/S system

It was not possible to obtain reproducible Seebeck values for members of selenium
system. Contacts problems at the level of the sample could be the cause of the problem.
Another possibility is the set up of our to device that is set to measure compounds with
medium to high electrical conductivity.

Measurements on pressed pellets of KPbloBiSIZ (360 tiV/K at 310 K) show high
reproducible positive values for the Seebeck coefficient (see Figure 2-24). This impressive
value has nevertheless to be taken with care because of the uncertainty on the accuracy of
the measurements. Because both p-type and n-type materials are needed for their
integration in thermoelectric modules, one needs to have both n- and p-type materials.
Low values of electrical conductivity ranging from 1 to 3 S/cm were measured for both
Selenium and Sulfur systems.

The samples were not studied further. Instead, efforts were focussed on the

tellurium systems that showed more promising results.

(3) Ag/Pb/Bi/T e System

Seebeck coefficient and electrical conductivity values for the sample
AngloBiTelzwere measured (see Figure 2-25). The samples morphology was that of as-
made ingots, and gave values of about —100 uV/K and 700 S/cm respectively at room

temperature.

84

 

600
500 ’—

400

IITW’YY

S (NV/K)

300 3 O
200 :—

100 '-

 

 

4 J l L *4 l A L

O h 1 1 . 1 . 1 .
300 320 340 360 380 400
Temperature (K)

 

Figure 2-24: Seebeck coefficient for KPmeiSlz (cold pressed pellet).

 

Y I Y Y Y T Y Y T Y Y

-50

S (uV/K)
O
O

-100 :- f

O
O

C o
_] 50 r L 1 A l n A 1_1 l A L L 4 l J 1 1 A l 1 4 4 A l A A A A l A r A A
50 100 150 200 250 300 350 400

Temperature (K)

 

 

 

Figure 2-25: Seebeck coefficient for AngloBiTelz (cold pressed pellet).

85

The sample was re-melted and sent for further measurements and the results show
a conductivity at room temperature of 750 S/cm that agreed well with our in-house
measurement (Figure 2-26). The material exhibits metallic behavior as the electrical
conductivity decreases with the temperature. The Seebeck coefficient at room
temperature is extrapolated to give a value of ~ -80 uV/K which also agree well with our
measurements (Figure 2-27).

Lower values of Seebeck coefficient were expected for the ingot samples compared
to the cold pressed ones in view of the previous differences that were noted between
pressed pellet and ingots in the K/Pb/Bi/T e system. To the contrary, measurements on
the Ag/Pb/Bi/T e system, seem less sensitive to the morphology of the sample.
Preliminary transport properties at room temperature of other silver based systems are

reported in Table 2-8.

Table 2-8. Seebeck coefficient (pressed pellets) and electrical conductivity (on ingots)

for silver containing members at room temperature.

 

 

 

Compound 0 (S/cm) s (uV/K) Compound o (S/cm) S(p.V/K) I
Angmes12 0.14 -2902 AgZPbBizTes 90 -50'
AngloSbTelz 760 -80' Ang33iTe5 630 -50

Ang6BiTe8 1080 -85‘
1: Values measured at 310 K

2: Strong fluctuation of S after 360 K

86

 

3000 _

'.
I
-.’1,‘
’4
I
2500 1,
I
’I
.
D

 

 

 

 

2000'
E :
a 1500_
b I
1000.
500:

0.11441111111L41111.1114411111111111

0 50 100 150 200 25 300 350

Temperature (K)

Figure 2-26: Electrical conductivity of AngloBiTelz (measured on ingot).

 

 

 

 

 

: O gampieg
0 am e

'20 l- A SamgleB ‘

l .

£§~40 i l

3. 1 o ‘

o .

v . Q% 4

”’-601_ -

-80 L _

-100 L 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 L L 1 1 1 1 1 1 1 1 ‘
0 50 100 150 200 250 300

Temperature (K)

Figure 2-27: Seebeck Coefficient for AnglOBiTelz (measured on ingot).

87

As a general trend, the electrical conductivity of members of the Ag/Pb/Bi/Te
system increased with the lead content. Additional work on this system is done by Dr.
Sportouch that tend to confirm that this system is promising for thermoelectric
application. The Ag system seems easier to work with because the stoichiometry is more
easily controllable than the K/Pb/Bi/T e system due to the lack of glass attack and the

good agreements between pressed pellets and ingots-made measurements.

(4) Other Related Systems

Preliminary measurements were made on systems involving Sn and/or Sb along
with K and Te. Table 2-9 gives the room temperature conductivity of compounds
synthesized using flame reactions. Within a system, the conductivity increases as the
amount of lead or tin increases, as previously observed above in other systems. Members
of the system K/Pb/Sb/T e have the lowest conductivities while the highest are found in
the K/Sn/Sb/T e system.

Problems during the measurements of the Seebeck coefficient on pressed pellets
appeared. High fluctuation of the measurements and high differences between the voltage
at the reference and at the sample suggest that the values reported have to been taken with
care. Despite these problems, the introduction of Sn in the system seems to make a
p-type material. This is observed for KSnIOSbTelz, and KSnloBiTen. In these systems,

the majority carriers are holes.

88

Table 2-9. Room temperature electrical conductivity and Seebeck coefficient for members

of the K/B/M/Te system (where B is Pb or Sn and M is Bi or Sb).

 

 

 

 

 

Compound 0 (S/cm) S (uV/K) S (uV/K)
(ingots) (pressed pellets) (ingots)

KPbSSbTe7 13 -70 -3 8
KPbmeTelz 215 -25 -5
KSnSbTe3 210
KSnSSbTe7 2630 +44 +32
KSnmeTelz 4250 +35 ' +28
KSnBiTe3 150
KSnsBiTe7 230 +38 +10
KSnloBiTelz 990 3002 +32

1: Strong fluctuation of S

2: High value of the voltage measured at the sample making this measurement inaccurate.

89

2-4. Concluding Remarks

Several systems of the general formula AmBanQzm+n have been obtained from
two types of synthesis methods: one favoring a thermodynamic synthesis (method 11 and
III) and one favoring a kinetic approach (method I). Table 2-10 summarizes the transport
and physicochemical properties of the different compounds synthesized. In view of the
results discussed, it appears that the silver-based systems prepared with the flame
method behave well while no method proved to be superior for the potassium/tellurimn
compounds. Differences in the absorption spectrum show that the flame methods tend to
produce self-doping effects. The implication of this effect on the transport properties is
important as the properties of pure semiconductors are dramatically changed by defects
or doping impurities.

The use of the flame to prepare ingots changes the electronic structure of the
compounds resulting in changes in the number of charge carriers and decrease the value of
the Seebeck coefficient. Another hypothesis that can account for the differences between
the samples measured at our facility and at other laboratories will be developed in the next
chapter.

The bang gaps of members of the KmenBimTezn+m system (below 0.40 eV) and their
number of charge carriers are in the desirable range for TE applications. The transport
properties are promising and members with high Pb content such as KPbIOBiTelz
constitute good starting materials for further work. This compound possesses promising
transport properties at room temperature: S ~ -47p.V/K, 0’ ~ 8OOS/cm, K ~ 2.4 W/m-K,

which give a ZT of 0.027 with some samples showing a high Seebeck coefficient of —140

90

uV/K. Taking the latter value into account, a respectable ZT of 0.2 is projected at room
temperature.

From all the systems investigated, the K/Pb/Bi/T e and Ag/Pb/Bi/T e systems gave
the best results in terms of transport properties for n-type materials. The substitution of
Pb by Sn creates p-type materials with holes being the majority carriers. Both types of
materials are necessary for the development of TE modules and investigation on the
A/Sn/M/Q systems should be vigorously pursued.

The next step in the investigation of these cubic phases involves the decrease of
the thermal conductivity by creating more disorder in the lattice using appropriate solid
solutions. Such disorder can be created, as already mentioned, by substitution of
appropriate elements on the anionic or cationic positions by other elements belonging to
the same group of the periodic table. An increase of the thermopower is also necessary

and could be achieved by such doping experiments as well.

91

Table 2-10. Physical and Transport properties for members of different systems.

 

 

 

 

 

 

 

 

o3 S 7 mg Sago Seize—3.
8m 3.3 So 2% \ M33 image—M
8.3 was 33 \ 2% 2.885%.
Red 2 com S- mac 5% 3952.5.
mad 2 o8 :1 was on}. sotmafiz
2o 2.. £5.5—
Qesé 3.39 SE:
SE ea. :6 Em Sam.— 3 55 =8 meaaoaaou

 

 

 

 

 

 

 

 

92

References

10.

ll.
12.

l3.

14.
15.
16.
17.
18.
19.
20.

G.D. Guseinov, E.M. Godzhaev, Kh.Ya. Khalilov, F .M. Seidov, A.M. Pashaev,
Inorg. Mater., 8, 9, 1972, 1377-1381

S.K. Plachkova, I.V. Odin, A.A. Sher, A.V. Novoselova, Inorg. Mater., 16, 7,
1980, 823-825

J.H. Wemick, Am. Mineral., 45, 1960, 591-598

L.H. Brixner, Am. Mineral., 50, 1965, 259-260

S.N. Hoda, L.L.Y. Chang, Am. Mineral., 60, 1975, 621-633

S. Sportouch, M. Bastea, P. Brazis, J. Ireland, C.R. Kannewurf, C. Uher, M.G.
Kanatzidis, Mat. Res. Soc. Symp. Proc., 545, MRS, 1999, 123

l. Borissova, St. Decheva, St. Dimitrova, P. Moraliisky, Godishnik Na Sofuskiya
Universitet, Fizicheski Fakultet, 65, 1972, 167-176

E.A. Shrabek, D.S. Drimmer, “Properties of the General TAGS System”, in CRC

Handbook of Thermoelectricity, Ed. by D.M. Rowe, 1994, 267

M. Evain, J .M. Barbet, P. Deniard, R. Brec, Powder Diffraction Meeting,
Toulouse, France, 1990

M. Evain, U-Fit:”A Cell Parameter Refinement Program”, Institut des Materiaux
de Nantes, France, 1992

C. Uher, J. Yang, S. Hu, Phys. Rev. B, 59, 13, 1999, 8615-8621

T.J. McCarthy, S.-P. Ngeyi, J .-H. Liao, D.C. DeGroot, T. Hogan, C.R.
Kannewurf, M.G. Kanatzidis, Chem. Mater., 5, 3, 1993, 331-340

T. Hogan, N. Ghelani, S. Loo, S. Sportouch, S.-J. Kim, D.-Y. Chung, M.G.
Kanatzidis, ICT Meeting, Baltimore, 1999, In Press.

T.B. Zhukova, A.I. Zaslavskii, Krystallografiya, 16, 5, 1971, 918-922

G. Gattow, J. Zemann, Z. Anorg. Allg. Chem, 279, 1955, 324-327

Y. Noda, S. Ohba, S. Sota, Y. Saito, Acta Crystallogr. B, 393, 1983, 312-317
L. Vegard, Z. Phys, 5, 1921, 17

O. Glemser, M. Filcek, Z. Anorg. Allg. Chem., 279, 1955, 321-323

G.D. Mahan, Solid State Phys. , 51, 1998, 81

D. Tuomi, J. Elechtrochem. Soc., 131, 1984, 2319

93

Chapter 3

Decreasing the Thermal Conductivity of KPbloBiTen

by Mass Fluctuation via Solid Solution Experiments

3-1. Introduction

Optimization of the transport properties of TE materials involves the decrease of
the thermal conductivity to a value close to 1 W/m-K'. Reduction of the lattice thermal
conductivity can be obtained by different scattering mechanism due to electron-phonon in
heavily doped compounds, electron charge transfer in mixed valence systems, or mass
fluctuation. The latter can be achieved via solid solution experiments (also referred to as
alloying). For example, the thermal conductivity of BizTe32 can be successfully reduced
from 1.7-1 .9 to 1.5-1.6 W/m-K (depending on the number of charge carriers) when alloyed
with szTe3.

Results from exploratory synthesis and preliminary measurements showed that
high-lead content members of the KanBiTen+2 system possess one of the most
promising transport properties among all systems investigated in this Thesis. These
compounds are members of the general family of quartenary chalcogenides AmBanQ2m+n
(where A is Ag or K, B is Pb or Sn, M is Bi or Sb and Q is Te, Se, or S), and crytallize

with the NaCl cubic structure type.

94

Among all the compositions investigated, KPmeiTelz appears to be the most
appropriate candidate for further work. This choice was driven by the conclusion that
the Seebeck coefficient was relatively high and not (or little) a sensitive function of the
value of n, in contrast of the electrical conductivity that increases with 11. From a
practical point of view, members with high values of n proved to be more easily
synthesized using the “flame reaction” (Method 11 and III in Chapter 2) because of their
low content in potassium, and less glass attack.

Promising transport properties were observed for KPbloBiTelz and reported in
Chapter 2. The Seebeck coefficient at room temperature is equal to -47 uV/K on ingot
and -l40 uV/K on cold pressed pellet; the electrical conductivity is close to 800 S/cm, and
the thermal conductivity reaches ~2.2 W/m-K.

Statistical disorder is already present in the K/Pb/Bi/Te system. Atoms of K, Pb,
and Bi occupy the same positions in the cationic sub-lattice of the crystal (the Na+
position in the NaCl'structure), while the tellurium atoms seat on the anionic sub-lattice
(Cl' positions). Additional disorder is possible on these sites by replacing some Pb atoms
by Sn or Bi atoms by Sb. Furthermore, the anionic positions occupied by Te can also be
disordered by introduction of selenium and/or sulfur atoms. The systems K/Pb/Bi/T e,
K/Sn/Bi/T e, and K/Pb/Sb/T e, as well as the selenium analogues, are members of the same
general family studied in this Thesis. Having the same chemical bonding (ionic-covalent)
and being isomorphous to the cubic NaCl type lattice, solid solutions between them
should be possible. Substitution of potassium atoms by Cs, Rb or Ag should also be

feasible but this was not investigated in this work. By carrying out such substitutions,

95

the thermal conductivity of KPbloBiTelz is expected to drop to a value closer to the one

of optimized BizTeMSex alloys or perhaps even lower.

3-2. Experimental Section

Reagents
All reagents were elements. As mentioned in the previous chapter, high purity K,

Pb, Bi, Te, Se, S, Sn and Sb were used.

Synthesis

Method 11 described in Chapter 2 was used for the synthesis of all compounds
described in this chapter. For example, KPbloBiTe6Se6 was prepared by mixing under
nitrogen atmosphere, 0.052 g (1.33 mole) of K, 2.762 g (13.3 mole) of Pb, 0.2786 g
(1.33 mole) of Bi, with 0.6316 g (8 mole) of Se and 1.021 g (8 mole) of Te. The
mixture was loaded into a 13-mm carbon coated silica tube. The tube was sealed under
vacuum (< 10“1 Torr ) and heated for 1 hour at 500 °C (pre-reaction). The tube was
opened and the material was transferred into a new l3-mm silica tube (without carbon
coating in order to be able to see the melt during the next step). The tube was then sealed
under vacuum at the same residual atmosphere and heated with a high temperature torch
flame. Members of solid solutions other than KwaBiTeIMSex were heated to 150 °C for

1 hour instead of the 500 °C used in the pre-reaction step.

96

Physical and Transport Measurements.

See previous chapter.

3-3. Result and Discussion

Synthesis and Crystallographic Data
(1) The solid solutions KwaBiTeIMS,

Unfortunately, solid solutions in this system could not de prepared due to phase
separation. Stoichiometries having values of x equal to 1, 3, 6, 9 corresponding
respectively to the formulae KPmeiTeHS, KPbloBiTeoS3, KPbloBiTe686, and
KPblOBiTe3Sg were tried. In each case, the X-ray diffraction powder pattern of the
products show a mixing of two phases (see Figure 3-la) corresponding to members of the
KanBiTen+2 and KanBiSn+2 systems. As the amount of tellurium was increased in the
system, the intensity of the peaks corresponding to the tellurium phase increased as the
phase became dominant. Annealing of the samples for 1 day at 750 C did not result in a
single phase (see Figure 3-1b). Phase separation is a consequence of the large ionic size
difference between telluritun and sulfur atoms that do not favor good stacking in the NaCl
structure type. Such effects are well known for solid solutions of ZnTe-ZnS3, where the
solid solutions exists only up to 8 mole percents of ZnTe in ZnS and up to 5 mole

percents of ZnS in ZnTe. In our case, we only investigated solid solutions having from 9

97

 

 

S: Sulfur Phase

(8!) ' (b)

 

 

 

 

 

 

 

 

0 20 40 A 60 ‘ 80‘ 100 120 0 20 40 A 60 ‘ 30‘ ‘100 120

(C) L (d)

 

 

 

 

 

 

 

 

 

 

 

A A A A A A A A A A A AAAAAAAAAAAA

0 20 4O 60 80 100 120 0 20 40

 

1
60 80

100 120

 

 

(e) ' (0

Intensity

 

 

 

 

 

 

 

E
1
f

A A A A A J A A A A A A A A A A A A A A A A A

 

 

 

0 20 40 60 80 ‘100 A120 0 20 4O 60 80 100 120
29 (degrees) 29 (degrees)

 

Figure 3-1: X-ray diffraction powder patterns of (a) KPbloBiTe389, (b) KPbloBiTe389
after annealing, (c) KPbloBiTe98e3, (d) KPbloBiSe389, (e) KPbloBio5Sbo5Te6Se6, and (f)

KPbloBiTelz (shown for comparison).

98

 

to 91 mole percents of KPbloBiTelz in KPmeiSlz, therefore solid solution outside this

range might be possible.

(2) The solid solutions KPmeiTeIHSex

In contrast to the previous system, the Te/Se one formed solid solutions readily.
The compounds KPmeiTenSe, KPbloBiTe98e3, KPmeiTe6Se6, KPbloBiTe3Se9, and
KPmeiTeISe“ corresponding respectively to values of x equal to 1, 3, 6, 9, and 11 were
synthesized in two identical batches (a) and (b). Small quantities of products in batch (a)
were made (between 1 and 1.2 g), while the objective of batch (b) was to obtain enough
sample (between 2.5 and 5 g) for measurements. Every sample of each batch shows pure
powder pattern corresponding to a single NaCl type phase (see Figure 3-1c).

The cell parameters were calculated and follow, as expected, a linear dependence
on composition, i.e. Vegard's Law4 (see Table 3-1 and Figure 3-2). Surprisingly, when
selenium and tellurium are mixed in solid solution, the system behaved well under the
conditions of Method 11, while the end-members show inconsistency in the values of the
cell parameters under the same experimental conditions. The differences in the values of
the cell parameters that appeared between the compounds of batch (a) and (b) is

attributed to a lack of homogeneity in batch (b) due to the larger quantity synthesized.

99

6.550

 

A 1
1‘5 6.450
a z
«E, r
g 6.350 E.
On I
d) L
.2 1
E 6.250 ;
..1 E

6.150 :

 

 

8 1321211131

b

A AJLJAAAALJAAAA

 

 

1.
N—
1.

‘8”‘1'0“‘fi2

Value of x

Figure 3-2: Cell parameter variation for the solid solutions KPblOBiTe|2-xSex.

Table 3-1. Cell parameters for solid solutions of KPbloBiTe12-xSex.

 

 

 

Compound Cell Parameter (A) Cell Parameter (A)
batch (a) batch (b)
PbloBiTeSen 6.203 (2) 6.219(1)
KPmeiTe3Se9 6.262 (3) 6.257 (2)
KPbloBiTe6Se6 6.346(2) 6.365 (2)
KPbloBiTegse3 6.431 (2) 6.444 (2)
KPbloBiTenSe 6.478(1) 6.493 (2)

 

100

 

 

(3) The solid solutions KwaBiSeIMSx

In accordance with the reasonable size differences between sulfur and selenium
atoms, solid solutions of these two systems gave a pure single phase. Values of x equal to
l, 3, 6, 9, and 11 corresponding respectively to the compounds KPmeiSeHS,
KPmeiSeoS3, KPbloBiSe6S6, KPbloBiSe389, and KPbloBiSeS“ were prepared. All
samples show pure cubic phases in perfect agreement with the NaCl structure type (see
Figure 3-ld). The cell parameters were calculated and reported in Table 3-2. The lattice
parameter decreases with x, as small atoms (S) substitute larger ones (Se). The system
deviates from Vegard's law as shown on Figure 3-2. Instead, the observed lattice
parameters follow a parabolic dependence on compositions of type:

a= xla. + xzaz +Aa.

Urusov5 studied different deviations from Vegard’s law using geometric models.

In the case of the NaCl structure, he concluded that secondary and higher shift orders are

responsible for parabolic deviations. These shifts are created by atomic displacements

that can be expressed as 6,. = {7%) where 1' is the order of the shift, A is a constant

depending of i, u = éAR, and R is the interatomic distance. We can expect such effect to

be present in the system studied because of the high disorder on both anionic and cationic
sites. Such distortions in the structure due to atomic displacements seem to be

responsible for the deviation from Vegard’s law observed.

101

 

 

Table 3-2: Cell parameters for solid solutions of KPbloBiSe12-xSx.

 

 

 

Compound Cell Parameter (A) Compound Cell Parameter (A)
KPbloBiSeS” 5.931 (2) K1>16111Bis69s1 6.079 (2)
KPbloBISC389 5.977 (2) KPmelSCHS 6.097 (2)

KPbIOBiSe6S6 6.029 (2)

 

 

6.150 _

6.107
‘/

6.100 :
6.050 :

6.000 :

Cell parameter (A)

5.950 :

 

 

 

 

E
5900 L41111111111111111,1,,l
0 2 4 6 8 10 12
Valueofx

Figure 3-3: Cell parameter variation for the solid solutions KPbloBiSe12-xSx.

(4) Solid solutions of the type KPmeil-,beTe6Se6
Members of the solid solutions KPbloBi1-bexTe6Se6 (where x = 0.25, 0.5, and
0.75) were synthesized. X-ray powder patterns show pure cubic NaCl phase for all

samples (see Figure 3-11). The cell parameters were calculated as previously mentioned

102

and are reported in Table 3-3. From these data, we can see that the cell parameters
deviate slightly from Vegard’s law similarly to the KPbloBiSe12_xSx solid solutions (see
Figure 3-4). The value calculated for KPbloBiTe68e6 in the previous chapter has been
used for the case x = 0, which corresponds to the same stoichiometry. By extrapolation,

the cell parameter of KPbmeTe6Se6 can be estimated to be close to 6.258 (2) A.

6.35

 

6.30 '

 

 

.2'1..1.-.1...1-..1-..
650 0.2 0.4 0.6 0.8 1
Valueofx

 

 

Figure 3-4: Cell parameter variation for the solid solutions KPb 10Bi1-beTe6Se6.

Physical Properties

Thermal Analysis

Differential thermal analysis of solid solutions KPmeiTeIMSex did not show any

melting peaks in accordance with the lack of similar peaks for the two end-member

103

systems KanBiTen+2 and KanBiSen+2. Similarly, the compounds KPbloBi1-bexTe(,Se6

did not show any clear endothermic peaks either (see Figure 3-5).

10

 

880 °C

878 °C

Exo.

 

935 °C

Endo.

 

 

 

 

 

-50

 

300 400 500 600 700 800 900 1000
Temperature (C)

Figure 3-5: DTA of KijoBiogssbojsse6S6 showing the recrystallisation and melting

temperatures.

Nevertheless, sharp exothermic peaks corresponding to recrystallisation
temperatures (Tcryst) were observed and reported in Table 3-3. This suggests that melting
indeed occurs below 1000 °C but the corresponding endothermic peak is masked by the
broad background which begins to increase endothermically above 880 °C. Such increase
could be due to the initiation of reactive glass attack by the material. Such glass attack was

observed on the DTA tubes indicating that these differences are most certainly due to a

104

loss of K and Se that reacted with silica. Small exothermic peaks can be seen around 940
°C and can be attributed to the melt of the material. This does not constitute the melting
point of the material but instead it must be seen as the melting point of a Te-rich
composition due to the change in the stoichiometry that occurred during glass attack.
These values are nevertheless indicative of the range of melting temperatures for the solid
solutions investigated. The lattice parameters calculated from X-ray powder diffraction
after the DTA experiment show an increase in their values to a value close to the one of

PbTe 6.462 A, supporting the above discussion.

Energy Gap

Due to self-doping effects created by the rapid cooling of the material during
synthesis (“flame” reaction), no band gaps were observed on diffuse reflectance spectra
for members of the solid solutions KPbloBiTe12_xSex as well as for KPbloBiSeS”,
KPbloBiSe3S9, and KPmeiSe6S6. Energy gaps were nevertheless observed for
KPmeiSe983 and KPbloBiSenS and calculated to be 0.51 and 0.45 eV respectively.
These values have to be considered as upper limits and do not constitute the true band
gaps that must lie below. Therefore it is difficult to compare them and to conclude that
KPb10B186953 possesses a higher band gap than KPbloBiSeHS. In fact, we expect the
opposite since the system KanBiSn+2 was observed to have higher energy gaps than

KanBiSen+2.

105

 

Table 3-3. Cell parameters, energy gaps, recrystallization and melting temperatures

(Tcryst and Tm), for members of the system KPb 10Bi1-bexTe6Se6.

 

Value of x Cell Parameter (A) Eg (eV) Tcrys, (°C) Tm (°C) Cell Parameter (A)

(before DTA) (after DTA)

 

 

0.25 6.329(3) 0.35 890 939 6.476(4)
0.5 6.308(2) 0.34 898 935 6.454(2)

0.75 6.285(2) 0.32 878 935 6.452(1)

 

27

 

26.5 .

26.

25.5 .

25.

01/8

24.5 .

E,=0.33 eV
24 1

23.5 v/

0.3 0.35 0.4 0.45

Energy (eV)

 

 

 

Figure 3-6: Optical absorption spectrum of KPmeiO.SSb0.SSe6S6 showing a band gap.

106

Energy gaps were observed for solid solutions KPbloBi1-bexTe6Se6 (see Table 3-3
and Figure 3-6). Substitution of Bi by Sb decreases the band gap as expected, because
lighter atoms replace heavier ones. Although no band gap was observed for
KPbloBiTe6Se6, we can estimate it to be slightly above 0.35 eV considering the values

obtained for the solid solutions KPbloBi1_bexTe6Se6.

Transport Properties

(1) The solid solutions KPmeiTeIHSex

Transport properties for different members of this system are summarized in
Table 3-4. Room temperature electrical conductivity show an increase with increasing Te
content in the samples of batch (a), but no trend was observed in batch (b). By
substituting selenium for tellurium atoms, we increase the band gap and therefore should
decrease the electrical conductivity. This explains the trend observed as more Se atoms
are introduced in the system. Surface effects and non-homogeneity might be responsible
for the constant values of the electrical conductivity measured for samples of batch (b).

Seebeck coefficient measurements on the samples of batch (a) show strong
fluctuation in the values of S at temperature between 450 K and 500 K. This
reproducible feature is shown in Figure 3-7 that represents the third Seebeck measurement
cycle of the compound. Such fluctuation is believed to be due to a dilatation of the

pressed pellet with increase in temperature that could produce cracks. As the

107

temperature decreases, the pellet contracts, restoring the original contacts. This
hypothesis is supported by the observation of a transversal line (possibly the crack line)

on the some sample surface afler measurements.

-80

 

-100 . D

-120 . D

-l40 - U D

SON/K)
C]
D

'160 '- C1
-180. a D

-200 .

 

 

 

-220 1 1 . 1 1
250 300 350 400 450 500 550

Temperature (K)

Figure 3-7: Seebeck coefficient for KPbloBiTel ISe (batch a) measured on cold pressed

pellet.

Because of the good values obtained from the sample KPbloBiTel ISe of batch (b),
i.e. S = -l62 uV/K and o = 570 S/cm, the material was sent for additional measurement.
The thermal conductivity, after correction due to the radiative losses (see Figure 3-8), is

about 1.78 W/m-K at room temperature. The linear variation of the radiative part as a

108

function of T3 validates the correction made (see Figure 3-9) as explained in Chapter 1.
As expected, by mixing Te and Se atoms in the Cl' site we decreased the long range
ordering and we were able to decrease the thermal conductivity by about 15 % in the case

Of KPbloBITel 1 SC.

Table 3-4. Room temperature Seebeck coefficient (on pressed pellet) and electrical

conductivity (on ingot) for solid solutions KPblOBiTe12-xSex.

 

 

 

 

Compound SRT (uV/K) SRT (uV/K) o “(S/cm) CRT (S/cm)
batch (a) batch (b) ' batch (a) batch (b)
KPbloBiTeSe” -97 -97 270 640
KPbloBiTe3Seo -95 -1 15 340 570
KPbloBiTe68e6 -150 -156 407 780
KPbloBiTeoSe3 -102 --- 646 470
KwaBiTel 18c -94 -162 782 570

 

The Seebeck coefficient was measured to be equal to -60 uV/K at room
temperature (see Figure 3-10) and is in the range of other previous samples measured
outside our lab. Its negative sign indicates that the charge carriers responsible for
electrical conductivity are electrons. This value is lower than what we recorded on
pressed pellet (-l62 uV/K). In Chapter 2, we attributed the differences in the Seebeck

measurements between cold pressed pellets and ingots, to a change in the electronic

109

structure of the materials taking place perhaps near the grain boundaries. Nevertheless,
KPbloBiTeHSe was sent as obtained from synthesis, thus the previous explanation does
not hold anymore.

Electrical conductivity at room temperature was measured to be about 460 S/cm
(see Figure 3-10), which is close to what we measured (570 S/cm) but lower than the
value recorded for KPbloBiTelz for the reason mentioned previously. In accordance with
all the samples studied so far, the temperature dependence is typical of a metallic
behavior.

As mentioned, no band gaps were observed in the diffuse reflectance IR.
spectrum, but the plot of the Seebeck measurement showed a minimum that can be used
to calculate it as explained in Chapter 1 (see Figure 3-11). Using Eq. 1-14, the band gap at
415 K can be estimated to be equal to 0.11 eV. During the study of the K/Pb/Bifl" e
system, we estimated the energy gap of KPmeiTeu to be around 0.38 eV. Due to self-
doping this value is an upper limit and the calculated band gap from Seebeck
measurements on KPbloBiTeHSe indicates that the real band gap of KPbloBiTen should

lie between 0.11 and 0.38 eV.

110

1.95

 

 

1.9

Q 1.85
E

E 1.8
)4

1.75

1.7

Figure 3-8: Thermal conductivity of KPbloBiTeuSe before and after correction.

0.14

0.12

0.1

0.08

0.06

Rad. Losses (W/m-K)

0.04

0.02

O K corrected
X K non-corrected

A L A 1 l l l A 1 I A 1 1 1 1 1 1 L A A A A J L A L J_L J

 

 

Temperature (K)

 

 

 

C]

A liLAJLAj—LALLAJAAlllllllALALJ

 

 

1107 1.5107 2107
T3 (K3)

Figure 3-9: Radiative losses as a function of T3.

111

2.5 107

o (S/cm)

Figure 3-10: Seebeck coefficient and electrical conductivity for KPbloBiTeHSe.

S (“V/K)

 

 

 

 

1000 0
:52, 1
900 ImbAAA 1 -10
: Cb A41 .
: DUE] we. 1
800 - 3% o 1 -20
. A 4
I ‘ C] A A ‘
700 C D D AA —0 -30
1 4— a D 1
1- [:1 A
u [:1 <
600 : :1 :1 A 21 3 -40
I 00 I
500 : 51 E [:1 I -50
' E1:12
.- A 4
400 E A81 -50
0 50 100 150 200 250 300

-105

-110.

-115 r-

-120 -

-125 -

-130 1

-l35 »

-l40

250

Temperature (K)

 

 

 

 

300 350 400 450 500

Tempererature (K)

550

Figure 3-11: Seebeck coefficient showing a minimum for KPbloBiTenSe.

112

(317/01) s

0.030

 

0.025 1

0.020 -

0.015 .

ZT
[:1

0.010 . C]

0.005 . 13

 

 

 

0,0000 1 mum-1151;111:111? ...................

Temperature (K)

Figure 3-12: Figure of merit ZT for a sample of KPbloBiTel lSe.

113

The measured transport properties on KPbloBiTeHSe gave a figure of merit ZT
equal to 0.026 at room temperature (see Figure 3-12), which is similar to ZT calculated
for KPbloBiTelz at the same temperature. Even though, we succeeded in decreasing the
thermal conductivity of KPmeiTelz by introduction of disorder in the anionic sites,
lower value of the electrical conductivity compensated the gain obtained in the figure of

merit. Introduction of appropriate doping agents should raise this value to a higher level.

(2) The solid solutions KPmeiSeIHSx

Surprisingly, no problems were encountered during measurements of the Seebeck
coefficient on cold pressed pellets for solid solutions KwaBiSem‘Sx (see Figure 3-13) in
contrast of measurements on the individual KmenBimSe2m+n and KmenBimSZmrn systems.

The variations of the Seebeck coefficients and the electrical conductivities as a
function of the temperature agree: an increase of S results in a decrease of 0
(see Table 3-5). This is observed for all the TB materials. Electrical conductivity values
are lower than for the ones measured for solid solutions of KPbloBiTe12.xSex. Generally,
alloying of a system such as K/Pb/Bi/Te with one having higher band gaps such as
K/Pb/Bi/Se, raised the transition energy and therefore decreases the electrical
conductivity. In contrast, when more Se substituted S atoms in the solid solutions
KPbloBiSe12-xSx, 0' increased. No samples were sent for additional measurement because
of the low electrical conductivities (below 500 S/cm) compared to members obtained in

other families.

114

Table 3-5.

Room temperature Seebeck coefficient (on pressed pellet) and electrical

conductivity (on ingot) for solid solutions KPblOBiSe12-xSx.

s (11V/K)

Figure 3-13:

pellets).

 

Compound O'RT (S/cm) SRT (uV/K)

 

* KPbloBiSeS” 765 -98
10610131812389 370 - 42 (at 310 K)
1061013181168, 210 -107
KPbloBiSe983 115 -214 (at 310 K)
KPbloBiSeHS 135 -198

 

C1 x=11 0 x=8 + X=1

 

 

 

 

Ox=9 Ax=3
0
-50. 00000000000
13
-100- 1:1
0
oggggggggg
-150~
-200- ++111
A Z++++
250 A AZ++
-1 A A
A A
A
-300 ‘

280 300 320 340 360 380 400 420
Temperature (K)

Seebeck coefficient of the solid solution KPblOBiSe12-xSx (cold pressed

115

(3) Other solid solutions of KPbloBi1-be,Te6Se6
In addition to solid solutions on the anionic positions, further disorder is possible
in KPmeiTe6Se6 by replacing some bismuth atoms by antimony. Promising results

emerged from preliminary measurements (see Table 3-6).

Table 3-6. Room temperature Seebeck coefficient (on pressed pellet) and electrical

conductivity (on ingot) for solid solutions KPbloBi1-bexTe1;Se6.

 

7 Value of x 0m (S/cm) SRT (uV/K)

 

0.25 990 -152
0.5 595 -200
0.75 380 -280

 

The values of the Seebeck coefficient are negative and increased significantly with
x, to reach a maximum for x=0.75. Surprisingly, the electrical conductivity of
KPmeio_7SSb0,25Te68e6 is in the same range than for KPmeiTelz contrary to what was
observed for the solid solutions of KPbloBiTe1.xSex. Nevertheless, this is in accordance
with the decrease of the energy gap observed (from 0.38 eV for KPmeiTe1.,1Sex to 0.35
eV for KPmeio_7SSbo,25Te6Se6). Energy band calculations would be useful to show the
effect of substituting Sb for Bi on the energy band diagram. Transport properties results

obtained from samples sent were encouraging, disappointing, and intriguing.

116

Encouraging, because the thermal conductivities show a decrease as the amount
of antimony increases in the system to a value approximately equal to 1.1 W/m'K at room
temperature for the sample KPmeio,258bo.75Te6Se6 (see Figure 3-14). This value is lower
than the thermal conductivity of BizTe3 (1 .5 W/m-K) at room temperature. The family of
compounds investigated in this work, proved to have a thermal conductivity that can be
decreased easily by introduction of additional disorder in the lattice. Due to the freedom
in the composition and stoichiometry, several solid solutions were made and more can be
prepared until a low limit in K is reached.

Nevertheless the results were also disappointing and intriguing because the
electrical conductivities at room temperature were measured to be about half of our
measurements (see Figure 3-15). Electrical conductivities were re-measured on our
equipment after received back the samples, and agreed measurements made outside our
laboratory. The difference between the two sets of measurements that we made in our
laboratory resides in the fact that the first set (that gave the best values) was made on
ingots from synthesis, uncut, while the second set of measurements were made on ingots
cut from the center of the bulk materials. Because of the technique employed for
conductivity measurement (four-probe touching technique), the samples measured must
have a flat surface as well as being physically homogenous.

Differences in the measurements are most certainly due to surface homogeneity
problems of the uncut ingots, the smaller ingots cut with a diamond saw having a more
homogenous and “clean’ surface. Another plausible explanation is the possibility of

having a gradient of concentrations in the material created during the synthesis. It is

117

known than during single crystal growth of BizTe3, different part (top, middle, and

bottom) of the crystal show different transport properties. In our case, it is suspected

that the flame reaction employed creates a gradient of concentration not only following
the transversal axes (as commonly seen in single crystal growth) but also from the center
of the ingot to the outer part.

Finally, the most interesting measurements were those of the Seebeck coefficient.

The values are equals to —100, -95, and ~120 uV/K for the compounds with x = 0.25, 0.5

and 0.75 respectively (see Figure 3-16). These values are much lower (of about 50%)

from what we measured on pressed pellet samples taken from the top part of the uncut

ingot (see Figure 3-17). Two possibilities were considered to explain these differences:

1- The carrier concentration is not the same in all parts of the ingot as advanced
previously. Therefore, the samples that we use to make the measurement (top part of
the ingot) and those sent for further measurements (core of the ingot) do not contain
the same charge carrier concentrations.

2- In theory, the Seebeck coefficient should not be different if measured on powder or on
ingot. Nevertheless, is it possible that in the case of these compounds, the physical
state (press pellet or ingot) of the sample can affect the value of the measurements?
Additional investigations are needed to better understand and perhaps take advantage

of this effect.

118

In order to check these hypotheses, pieces of ingots measured outside our
laboratory were cut and re-measured. The ingots were then ground, cold pressed into
pellets, and measured a third time. Figure 2-18 shows the results. The pressed pellet
samples show an increase of the Seebeck coefficient of about 50 to 65 % compared to the
ingots. We do not have any explanation for this differences but it is interesting to note
that p-type BizTe3 used in industry is under the form of a pellet while the n-type is under
the form of an ingot.

From Seebeck measurements, we conclude that differences of charge carrier
concentration exist in different parts of the sample. Nevertheless, this can not account by
itself for the change in the values when measurements are made on ingot and pressed
pellet of the same sample. Further work needs to be done to explain this effect.

Compared to KPbloBiTelz, the figure of merit for the best of these materials
KwaBi0_sSbo_5Te6Se6 (see Figure 2-19) tripled due to a low value of the thermal
conductivity and an increase in the Seebeck coefficient. If we can double the Seebeck
coefficient by making sintered press pellet without loosing too much conductivity, the

ZT could increase significantly. Such experiment were carried on in Chapter 4.

119

Cl x=0.5 O x=0.75 <> x=0.25

 

 

1.6
1:1
1.5 . §1
o
o
l 4 - o <>01> oQ>°oQ>OQI><9<>°oQ>qud>Q>WOW
g: 1.3.
E
E 1.2 .
8:
1.1 1
1 .
0.9

 

 

 

50 100 150 200 250 300 350 400
Temperature (K)

Figure 3-l4a: Thermal conductivity for the solid solutions KPbloBil-bexTe6Se6 (on

ingots and before correction).

120

 

 

 

 

 

1.5
1: Wm?
1:1 1111;5ij
1.4 1- C1 [113%5313
[IUD
E]
1.3. DUB
A :13
5%
\ 1.2.
5.
¥
1.1.
1 1
0.9

50 100 150 200 250 300 350 400
Temperature (K)

Figure 3-14b: Thermal conductivity for the solid solutions KPbloBi1-bexTe6Se6 (on

ingots and after correction).

121

1000

 

 

00% D x=0.5
(2% O x=0.75
8001 <><>ooo <> x=0.25
A 600.
a
O
a
b 400.
200.

 

 

 

O 1 1 1 1 1
50 100 150 200 250 300 350 400
Temperature (K)

Figure 3-15: Electrical conductivity for the solid solutions KPbloBi1_bexTe6Se6 (ingots).

122

 

 

 

 

-40 1
1
E? -80 _
> 1
3
m
-120 _
1
-160 _
1 1: We

 

50 10011150112001 12501130011350 400M450

Temperature (K) A

Figure 3-16: Seebeck coefficient for the solid solutions KPbloBi1-bexTe(,Se6 (ingots).

123

 

-100 1
1 O x=0.5(top)
_150 ~ A x=0.75 (top)
: o
-200 — OOooo
_ 000
g; A 0150
" A
. o
E -250 __ .1 1
m f AAAAA A o
-300; 1 A 891
“ AA 069A 1
1 0883 1
-350 L o
1 o
-400» 11A11 1111111

 

 

 

250 300 350 400 450 500 550
Temperature (K)

Figure 3-17: Seebeck coefficient for the solid solutions KPbloBil-bexTe6Se6 (pellets).

124

 

 

 

 

6O 0 x=0.50 ingot
' r O x=0.50 pellet
E o A x=0.75 ingot
'80 _— . A x=0.75 pellet
o
[ o
-100 — A . O
_ A o
: ‘ A . O
-120 _ ‘ A ' .
g; : “ A
- A
: -l4O __ A ‘
5? l
-160 _ O o
l A O O O
-180 _ A A o o
- A A O
_ A o
-200 l— A A A
-220 "

 

 

 

 

£30011 1320LJ'340‘1 ‘3601‘ 13801 114001
Temperature (K)

Figure 3-18: Seebeck coefficient for the solid solutions KPbloBi1-bexTe6Seé (ingots and

pressed pellets).

125

 

0.20

0.15 .

0.10 -

ZT

0.05 .

 

0.00 ,
50

Figure 3-19: Figure of merit ZT for the solid solutions KPbloBi1-bexTe68e6.

  

 

 

D x=0.25
O x=0.75
<> x=0.50
0
00
<30
<9
0
(exams?
0()0 D
0° 00
000 .0 O [:1
O0 . O
O
106 150 200 250 300 350 400

Temperature (K)

126

3-4. Concluding Remarks

It has been shown in this chapter that reducing the thermal conductivity of
members of the family of compounds A,,,B.,MmQ2m+n is possible by introducing further
disorder in the structure on the anionic and on the cationic positions. A reduction of 50%
of the thermal conductivity was obtained for the compound of formula KPbloBiTelz by
alloying with KPbloBiSelz and by substitution of some atoms of Bi by atoms of Sb. It
has also been discovered that the physical state of the material, i.e. ingot or cold pressed
pellet, affects the value of the Seebeck coefficient. In addition to this effect, a gradient of
temperature during synthesis is most certainly responsible for a change in the charge
carrier concentration along the ingots synthesized during flame reactions. It is important
to note that if we succeed in having an electrical conductivity of about 400 S/cm on
pressed pellet, the ZT at room temperature would be extremely promising (0.50) due to
the high values of Seebeck coefficient and to the low thermal conductivity. In this case,
we would expect to have even lower thermal conductivity on pressed pellets (not
measured) than on ingots due to an increase in the grain boundary, increasing further the
figure of merit.

Having successfully decreased the thermal conductivity, we will examine in the
next chapter the effect of introduction of doping agents on the best materials obtained so
far, i.e. KPbloBiTe68e6 and KPblOBi05Sb05Te6Se6. We expect to be able to raise the

Seebeck coefficient without affecting to a great extend the electrical conductivity.

127

References

Nv—s

9‘2“.“

GD. Mahan, Solid State Phys, 51, 1998, 81

H. Sherrer, S. Sherrer, “Bismuth Telluride, Antimony Telluride, and Their Solid
Solution”, in CRC Handbook of Thermoelectrics, Ed. by D.M. Rowe, 1994, 211-
237

S. Larach, R.E. Shrader, C.F. Stocker, Phys. Rev., 108, 3, 1957, 587

L. Vegard, Z. Phys., 5, 1921, 17

VS. Urusov, Zhurnal Strukturnoi Khimz'i, 33, 1, 1992, 80

128

Chapter 4

Effect of Doping Agents on the Transport Properties of

KPbloBiTe6866 and KPbloBio,5Sbo,5Tegse6

4-1. Introduction

In the previous chapter, the thermal conductivity K of KPbloBiTen was decreased

significantly by introduction of additional disorder in the structure via different solid
solutions on both anionic and cationic sites. Atomic substitutions of half of the Te atoms

by Se and half of the atoms of Bi by Sb lowered the value of K of about 50%. The

observed value, close to 1 W/m-K, satisfies one of the criteria that a good TE material
should follow‘. Unfortunately, the electrical conductivity decreased also by a factor of
two, compensating the gain obtained from mass fluctuation. The alloying of K/Pb/Bi/Te
system with the system K/Pb/Bi/ Se increased the energy gap to a value lying between the
energy gaps of the two end-members; this, in turn, had for consequence to decrease the
electrical conductivity.

To enhance the Seebeck coefficient and/or the electrical conductivity of
thermoelectric materials, small amounts (usually <1 atomic %) of impurities are
introduced into the compounds. In order for this addition to be fully efficient, the starting
materials must be as pure as possible. As we mentioned in the previous chapter, in view
of the diffuse reflectance spectra, most of the compounds we are investigating seem to be

already self-doped during flame reactions. Consequently, it is expected that doping

129

experiments might not be totally efficient, but we hope to see a trend in the transport
properties as a function of the amount and type of dopant added. The thermal
conductivity measured for KPbloBio,5Sbo,5Te(,Se6, being mainly dominated by the lattice

contribution (K|=0.93 W/m-K and Ke=0.24 W/m-K at room temperature), introduction of

additional carriers should not affect it greatly.

The choice of a doping agent is theoretically straightforward as described in
Chapter 1, nevertheless in practice it is more difficult to have the desired atomic sites
substituted. This implies that several agents must be tried. In this work, we chose two
different approaches to dope the compounds. In the first one, no specific sites were
chosen to be doped and instead, chemical dopants were added to the system in excess. In
the second approach, substitutions on selected atom were made.

The Seebeck coefficient can be written as a function of the Fermi level § asZ:

kB

3:—
e

(5/2+s—.§) Eq.4-1

With k3 being the Boltzmann’s constant and s the scattering parameter. In turn, the

charge carrier concentration is related to the Fermi level 1'; as shown in Eq. 4-2.

n: 2(27zm'kBT/ hz)”2 expf = Aexpé Eq. 4-2
Where m* is the effective mass. Introducing the natural logarithm, the Fermi level is
proportional to 1n (n) and therefore S is proportional to -1n (n), i.e. 1/1n (n). n is the

charge carrier concentration. Since the electrical conductivity can be written as o = neu
(u is the mobility and e is the charge of the majority carriers), S is therefore proportional

to Mn (6). Because of this, if the electrical conductivity increases, the Seebeck

130

coefficient should decrease. Therefore, an optimum range of carrier concentration has to

be found that will Optimize simultaneously S and o.

4-2. Experimental Section

Reagents
All the reagents were taken under their elemental forms. As mentioned in

Chapter 1, high purity K, Pb, Bi, Sb, Sn, Te, and Se were used

Synthesis

The same procedure as the one described in Chapter 3 was followed for the
synthesis of all the doped samples. All elements were mixed in 13-mm carbon coated
quartz tubes. For example, KPbloBiTe6Se6 was doped with 0.05% Sn by mixing under
nitrogen atmosphere 0.052 g (1.3 mole) of K, 2.762 g (13.3 mole) of Pb, 0.277 g (1.3
mole) of Bi with 1.020 g (8 mole) of Te, 0.630 g (8 mole) of Se and 0.0024 g (0.02
mole) of Sn. The mixture was loaded into a 13-mm carbon coated quartz tube, sealed
under nitrogen atmosphere at a residual pressure inferior of 10'4 Torr. The tube was then
heated in a furnace at 150 C for one hour. After opening the tube, the materials were
loaded into a new 13-mm non-carbon coated quartz tube (in order to see the melt during
the next step) and melted using a high torch flame.

An alternative preparation would be to synthesize large amount of material (e.g.
KPbloBiTeéSeé) and to use it at starting material. Unfortunately, it is not possible to

synthesize very large amount of material using the flame reaction because of the

131

exothermic process that occurs. About 4 to 5 grams constitute the charge limit of the
tubes that we tried in order to avoid explosion. Therefore, the material to dope was
synthesized with the dopant already introduced in the mixture.

KPmeiTe6Se6 was doped by Ag, Sb, and Sn by adding weight percentage of
each element as excess to the system. On the other hand, KPbloBiQSSbQSTC6SCG was

doped by both excess and substitution of atomic percentage of Bi by Sn.

4-3. Results and Discussion

Synthesis and X-ray Powder Diffraction Data

X-ray powder diffraction patterns of doped KPbloBiTe6Se6 show pure cubic
single phase in accordance with a NaCl structure type (see Figure 4-1a). The cell
parameters were calculated from these experimental data and are reported in Table 4-1.

Weight percentages of doping agents were added to KPb10BiTeésefi. The choice
of using weight percentages has been found to be inappropriate because, as shown in
Table 4-2, the corresponding mole percentages exceed for values superior to 0.05 %the
limit of what is considered as doping. The addition of impurities (Ag, Sb, or Sn) can then
be more accurately seen as solid solutions experiments. For such cases, it is impossible
to know the composition of the compounds formed. For example, in the case of 1.0
weight % of Ag mixed with KPbloBiTeGSe6, Ag can substitute potassium atoms giving
compounds with stoichiometries ranging from KPmeiTe6Se6 (if no Ag substitute K) to

KmAgongloBiTe‘gSeé, In view of these data, large differences in the values of the cell

132

 

 

(a) g (b)

Intensity

 

 

 

 

 

 

 

 

 

 

 

28 (degrees) 29 (degrees)

Figure 4-1: X-ray diffraction powder patterns of (a) KwaBiTeéseé doped with 0.1 weight

% of Sn and (b) KPb10Bi058b05Te68e.5 doped with 0.23 atomic % of Sn substituted for Bi.

133

parameters were observed between to the cell parameter of KPbloBiTe6Se6 (6.340 A)

calculated in chapter 2 and those of the doped compounds.

Table 4-1. Cell parameters for doped KPbloBiTe6Se6 with different agents.

 

 

 

 

Mole % dopant Cell Parameter (A) Mole % dopant Cell Parameter (A)
0.62 % Ag 6.276(2) 0.57 % Sn 6.292 (1)

1.67 % Ag 6.281 (2) 1.52 % Sn 6.296(3)

16.52 % Ag 6.280 (2) 2.97 % Sn 6.302 (2)

33.04 % Ag 6.281 (1) 15.01 % Sn 6.303 (2)

0.57 % Sb 6.305 (2) 30.03 % Sn 6.302(2)

1.52 % Sb 6.399 (4)'

14.97 % Sb 6.398 (4)'

29.95 % Sb 6.304(5)

 

 

1 Very high values suggesting evaporative loss of materials during flame reaction

Progressive substitution of Ag for K cannot account for those differences, because
no trends are noted in the variation of the cell parameter with the amount of Ag
introduced. Instead, silver atoms seem to substitute potassium until a level is reached and

then be incorporated in interstitial sites keeping the cell parameter constant (1)

 

m A realignment of the X-ray beam of our CPS 120 INEL diffractometer that occurred

between record of the powder pattern of KPbloBiTeGSe6 and those of doped samples
could be responsible for a shift in the calculation of cell parameters. In order to check
this hypothesis, the X-ray diffraction powder pattern of KPbloBiTe6Se6 was re-taken and
the cell parameter re-calculate. A new value of 6.302 (2) A showed that the re-alignment

of the beam is responsible for the considerable shifi noted.

134

 

Table 4-2. Correspondence between weight and atomic percentages of concentration for

different doping agents of KPbloBiTe6Se6.

 

 

 

 

 

 

 

 

 

 

 

Dopant Weight % Atomic % Dopant Weight % Atomic %
Ag 0.02 0.62 Sn 0.02 0.6
0.05 1.67 0.05 1.55
0.5 16.52 0.1 3
1.0 33.04 0.5 15
Sb 0.02 0.57 1.0 30
0.05 1.52
0.5 14.97
1.0 29.95
Table 4-3. Cell parameters for Sn doped KPbloBio5Sb05Te6Seg.
% Sn in excess Cell Parameter (A) % Sn substitution Cell Parameter (A)
0.05 6.297 (2) 0.05 6.300(2)
0.15 6.288 (2) 0.15 6.296 (2)
0.23 6.289 (2) 0.23 6.309 (1)
0.53 6.287 (2) 0.47 6.302 (1)

 

 

 

135

The lattice parameters of Table 4-3 were calculated from X-ray powder
diffraction patterns showing pure cubic phases for all doped samples of
KPbloBi05Sb05Te6Se6 (see Figure 4-1b). The cell parameter of KPbloBio_5Sbo,5Te6Se6
was calculated in Chapter 3 to be 6.308 A. The difference noted from the data of Table

4-3 is not significant enough to be conclusive on the substitution effect of Sn.

Energy gap

The values of the band gaps for doped KPbloBiTe6Se6 samples calculated from
diffuse reflectance spectroscopy are reported in Table 4-4. All the spectra observed show
similar features (see Figure 4-2a) characteristic of self-doped materials. As mentioned
previously, this is probably due to many defects due to the “flame” reaction. No band
gaps were observed for the compounds doped by Sn.

To the contrary of the previous case, compounds of KPbloBinSb05TC6sefi doped
with Sn, show clear band gaps. In view of the diffuse reflectance spectrum, the energy
gaps are most certainly indirect and show a broad tail the real value of 138 (see Table 4.5
and Figure 4-2b). Those features are due to the energy levels created by the impurities
added. The shape of the spectrum indicates that they are probably shallow donor levels
close to the conduction edge. This indicates that the compounds are effectively doped as

expected.

136

 

25

 

 

 

 

  

 

 

 

 

a .
( ) L
g 20 1
15 b....1...il....1..L.1..441....11.r.1..11
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Energy (eV)
b
( ) 42.00 l
40.00 L
38.00 i
m 36.00 -
B 34.00 P
32.00 F
3000 EEg=o.35 eV
E E = 0.38 eV
28.00 / 8
0.3' ' '0335" . 'oi4r . ' 6.215 ' ' 1015' ”(1'55 ' . 0.6
Energy (eV)

Figure 4-2: Optical absorption spectra of (a) KPbloBiTe6Se6 doped with 0.1 weight % Sn

and (b) KPmeio.5Sbo,5Te6Se6 doped with 0.05 % Sn and showing a broad tail.

137

Table 4-4. Energy gaps for KPbloBiTe6Se6 doped with Ag and Sb.

 

 

 

 

% Ag Eg (eV) % Sb Eg (eV)
0.02 no band gap 0.02 0.37

0.05 no band gap 0.05 0.36

0.10 0.33 0.10 0.33

0.50 0.35 0.50 no band gap

 

 

Table 4-5. Energy gaps for KPbloBio,5Sbo_5Te6Se6 doped with Sn.

 

 

 

 

 

 

% Sn in excess Eg (eV) % Sn substitution E8 (eV)

0.05 0.35-0.38 0.05 0.35-0.41

0.15 0.35-0.40 0.15 0.35-0.39

0.23 0.40-0.42 0.23 0.40

0.53 0.36 0.47 0.35-0.41
Transport Properties

(a) Doped KwaBiTeaseg

Among the three different doping agents tried on KPbloBiTe6Se6, Sn presented
the most promising results (see Table 4-6). The electrical conductivity at room
temperature was slightly lower than for the Sb and Ag doped compounds but the Seebeck
coefficient measured on cold pressed pellets show much higher values (see Figure 4-3).
No trend was visible in the variation of the Seebeck coefficient as a function of the

amount of dopant. This was expected due to the uncertainty on the compounds formed.

138

Because of the probable increase of the disorder in the lattice, we expect low thermal
conductivity caused by the formation of solid solutions. An ingot of KPbloBiTeeSeé
doped with 0.1 weight percentage (corresponding to a doping level of 3 atomic % of Sn)
was sent for additional measurements.

The results show a negative Seebeck coefficient of -120 uV/K (see Figure 4-4) at

room temperature, indicating that the majority charge carriers responsible for the
electrical conductivity are electrons. This value is lower than the -160 measured in our
system as expected. In accordance with the observation made in Chapter 3, the
morphology of the samples affects the measurement of the Seebeck coefficient.

A large radiative loss contribution can be seen on the thermal conductivity plot
starting at a low temperature of 100 K. After correction, the thermal conductivity due
only to the electrical and lattice contribution was calculated to be equal to about 0.79
W/m°K (see Figure 4-5). The plot of the residual part versus T3 (Figure 4-6) shows a
linear relationship, which validates the correction made according to the T3 dependence
of the radiative losses, mentioned in Chapter 1. The thermal conductivity obtained after
correction is extremely low (below the required value for TB materials). Because we
added large amount of Sn (3 atomic %), it is reasonable to think that some atoms of Sn

substituted lead atoms making an additional solid solution KPb10-ySnyBiTe(,Se6 that

decreased K.

Unfortunately, the electrical conductivity 0 has a value at room temperature of

150 S/cm, which is much lower than what we measured on our instrument (880 S/cm).
Differences between measurement techniques used in our lab and by our collaborators

cannot account for such differences. Acceptable differences between such techniques lay

139

 

 

 

 

 

 

 

 

 

 

 

 

t O 0.02%Sb
-80'- AAA 0 0.05% Sb
I AA A 0.1%Sb
A400? 000 “AAA 0 1.0%Sb
. 0 AAA
§-120; 00 00 AA
3 : DDOOO 000 AA
m r E] o 00 A
-140_# Dogfifi OoO AAA
» m o
-160 '_ ODDDDDDBDO
-180...rn.1..1.l.ri..l.i....1.11.
250 300 350 400 450 500 550
Temperature (K)
-120_
’ 0 0.02%Sn
440? 99 o 0.05% Sn
-160 -_ 8 999 v 0.1% Sn
A 5 A800 99 a 0.5% Sn
g -130 .- AA 8 99 A 1.0% Sn
> 200: AA8°°0990
3: - f AA Nagggg
”3 -220 1 AA 00
-240A AAA
l‘ A
~260} AAA
-280’..4L1...11111.1m4..1....
25 300 350 400 450 500
Temperature(K)
-90,
400; 00 O 0.02%Ag
°o ° 0.05%Ag
410% 8v 0% v 0.1%Ag
A _ :_ 0V 0 U 0.5%Ag
é 120E D00: V 00000000000
3' -1303 DUO V 0°00
VJ '140 L [3800 V 00
450: D” ogVSB vve
-160§_ Do 0 080 8
17 E . DD V. O .
- (250 300 350 400 450 500 550
Temperature (K)

Figure 4-3: Seebeck coefficient (on cold pressed pellets) for KPbloBiTe6Se6 doped with

different doping agents. (The percentages shown are weight percents).

140

 

S(ufififl<)
O
O

-100 '

I
O

-120 '

CI)

 

 

 

140Cr
0 50 100 150 200 250 300

Temperature (K)

Figure 4-4: Seebeck coefficient of KPmeiTe6Seé doped with 0.1 weight % of Sn

 

 

 

 

(ingot).
1.00 _
O K (total) 0
0'95 E” A K (after correction) O
A 0.90 :- O O
E r .0
E 0.85 _— O 9
K . g O O O
L Q A A A A A A A A A A A
0.75 :— @%
010:..,.r.,........,....,....,....
O 50 100 150 200 250 300

Temperature (K)

Figure 4-5: Thermal conductivity of KPbloBiTeéSeé doped with 0.1 weight % of Sn
(ingot).

141

0.15

 

 

 

 

T

I O

3 i

330.10:

.3 i O

Q)

.2

'3 f

60.05~

a .

“4 E

0.00:..9...6...,.7f.,,.7,..fi5..., 7

0 510 110 13.510 210 2.510

Figure 4-6: Radiative losses versus T3 for thermal conductivity of KPbloBiTe6Se6 d0ped
with 0.1 weight % Sn (ingot).

400

 

350 g

300 g

0' (S/cm)

250 3
200

150 ~
f
0

 

 

100

 

1 fr

Tj T Y

50 ' 500

”100"'150"'200"'250'
Temperature (K)

Figure 4-7: Electrical conductivity of KPbloBiTeGSe6 doped with 0.1 weight % of Sn
(ingot).

142

around 100%, instead of the 400% noted for this measurement. It has been observed that
oxidation of the surface of the materials appeared for the potassium members of the
family studied in this Thesis. Etching with diluted HCl restores the integrity of the
surface. This degradation effect along with is probably responsible for the differences
noted. A decrease of the number of charge carrier could be the cause of the metallic

dependence of 0 shown in Figure 4-7. Such decrease could be attributed to bounding of

the charge carriers (electron) with holes, and defects.

From the data obtained, we calculate a room temperature value of ZT of 0.081.
This is an improvement from the previous measurements due to a decrease of the thermal
conductivity and an increase of the Seebeck coefficient. The low electrical conductivity
is responsible for keeping the figure of merit from further increase. By proper treatment

of the surface of the material before measurement, we should obtain higher value of o. If

the conductivity were keep at 880 S/cm, we would obtain a ZT at room temperature of

0.47.

(b) Doping of KPmeio,5Sbo,5Te58e6

From the previous discussion on doped samples of KPbloBiTC6SC6, introduction
of Sn in KPbloBio5Sbo5Te6Se6 was realized. Atomic percents lower than 1% were used
in order to avoid solid solutions.

Sn was added in excess with the hope that the Seebeck coefficient will increase as
observed for KPbloBiTe6Se6. Atoms of Sn were also substituted for Bi in order to

introduce additional charge carriers and increase the electrical conductivity.

143

Table 4-6. Transport properties for KPbloBiTe6Se6 doped with Ag, Sb, Sn measured at

our lab (0 measured on ingots and S on cold pressed pellets).

 

 

 

 

 

 

Dopant % Gar (S/Cm) Sm (uV/K) SMAX (RV/K) TMAx (K)
Ag 0.02 800 -110 -l47 390
0.05 1 190 -95 -140 520
0.1 875 -110 -147 410
0.5 930 -120 -162 470
Sb 0.02 792 -100 -160 480
0.05 1120 -110 -162 400
0.1 1240 -85 -145 490
0.5 1025 -125 -157 440
Sn 0.02 700 -140 -220 460
0.05 740 -160 -210 450
0.1 880 -160 -220 430
0.5 600 -140 -210 440
1.0 600 -180 -270 460

 

144

Excess of Sn

As expected, a tremendous increase in the Seebeck coefficient was observed on
preliminary measurements of cold pressed pellets of doped compounds. Unfortunately,
measurements on ingots show a decrease by a factor to 3 to 4 from the previous values
(see Figure 4-8). A trend is visible as the Seebeck coefficient increases slightly with the
amount of Sn introduced. It is difficult to account for a trend in the values of the
electrical conductivity.

The room temperature electrical conductivity measurements do not show any
clear trend. Similar measurements on cold pressed pellets show low values as expected

due to grain boundary effects (see Table 4-7).

Table 4-7. Electrical conductivity of KPbloBio5Sb05Te6Se6 doped with various amount

of Sn (measured on cold pressed pellets and on ingots).

 

Concentration dopant o (S/cm) on ingot o (S/cm) on pressed pellets

 

 

 

0.05 % 500 3.5
0.15 % 480 10
0.53 % 310 2.5

 

After annealing under nitrogen atmosphere of the material doped with 0.15% Sn,
for 5 days at 500 °C, the electrical conductivity increased to 64 S/cm. The corresponding

Seebeck coefficient was measured to be —263 uV/K. Further annealing for 1 day at 650

°C, raised 0 to 350 S/cm but decrease S to —80 ptV/K (see Table 4-8).

145

 

-280 .

 

 

 

 

 

(a) . a 0.05%
* A 0.15%
'300 T U D D o 0.23%
t D D D o 0.53%
-320 _— 13 1:1
A : Cl E]
g -340. U
> l“ O
3 360 A
: g Q A A A
-380 ? ° 8 O A A
. O o
-400 l g
-4202..,...,f..,...,...,...,-..
280 300 320 340 360 380 400 420
Temperature (K)
(b) -80; D 0.05%
t D A 0.15%
. A 0 0.23%
" O O 0.53%
-]00 ~ ‘2
A ’ O C]
"S . A
1 12 O 0 g
‘m" ' 0 “ o o E]
O o 13
. E a 1:1
- _ e
140 . O 2 (a) [:1
O 8
~160.. ...f-f,_9nfl

 

 

 

280 300 320 340 360 380 400 420
Temperature (K)

Figure 4-8: Seebeck coefficient of KPb 10Bi0,58bo_5Te65e6 doped by excess of various

amount of Sn on Bi sites (a) measured on cold pressed pellets and (b) on ingots.

146

Table 4-8. Effect of annealing on the transport properties of pressed pellets of

KPbloBio_5Sbo_5Te6Se6 doped with 0.15 % Sn.

 

 

 

Conditions (I RT(s/cm) sRT (uV/K) Szo (mW/m-K) ZT (predictionfa)
Initial 10 -367 0.13 0.039

After first annealing 64 -263 0.44 0.13

After second annealing 350 -80 0.22 0.068

 

(a): ZT predictions were made using K of ~1 W/m-K
The power factor 826, reach a maximum of 0.44 mW/m-K after the first

annealing. If we use a value of l W/m'K for the thermal conductivity, a predicted ZT at
room temperature is equal to 0.13. These experiments are in agreement with the
observation made by F ano3 on sintered pressed pellets of PbTe. He concluded that donor
levels are introduced in lead telluride pressed pellets during the powdering process. This
created a cross over of inverse carrier sign since PbTe was p-doped. Similar explanation
can be adopted to explain the differences that we observed between Seebeck
measurements on cold pressed and ingot samples. Our materials being n-type, powdering
introduces acceptor levels (defects) that recombine the charge carriers and increase the
Seebeck coefficient. Annealing of the pellet restore the initial properties observed on

ingot by eliminating the donor levels.

147

 

Substitution of Sn for Bi

The measured values for 0' and S are similar to the one obtained in the previous

case (see Table 4-9). The materials are n-type as expected indicating that the charge
carriers are electrons. No increase in the electrical conductivity is observed suggesting

Sn did not substitute the Bi atoms.

Table 4-9. Seebeck coefficient and electrical conductivity at room temperature for

KPmeio,5Sbo.5Te6Se6 doped with various amount of Sn.

 

 

Concentration Sn SRT (uV/K) pellet SR1 (uV/K) ingot Om (ingot)

 

 

0.05 % excess -300 -80 500
0.15 % excess -367 -90 480
0.23 % excess -365 -96 500
0.53 % excess -370 -103 310
0.05 % substitution -175 -93 370
0.15 % substitution -300 -106 300
0.23 % substitution -345 (at 320 K) -90 500
0.47 % substitution -342 (at 320 K) -70 297

 

4-4. Concluding Remarks

Doping experiments on KPbloBiTe6Se6 and KPbloBio_SSbo_5Te6Se6 show that
excess of Sn increased considerably the Seebeck coefficient measured on cold pressed
pellets. Nevertheless, these values are much lower when measured on ingots. In view of
the conclusion made by Fano and considering the annealing experiments, the difference

noted between pressed pellet and ingot Seebeck measurements is most certainly due to

148

 

the introduction of acceptor levels during the grinding process. These levels are
attributed to defects created by the pulverizing the materials. Such defects could be
surface traps and may be eliminated by annealing the pressed pellets, restoring the
original Seebeck coefficient measured on ingots and increasing the electrical
conductivity.

It was not possible to raise o for the solid solutions KPmei0_5Sbo,5Te6Se6 by

substitution of Sn for atoms of Bi. Such substitution did not seem to take place and the
results of Seebeck and electrical conductivity measurements are similar to those obtained
when excess of Sn was introduced in the system.

As excess amount of Sn is increased in the system, the values of the Seebeck
coefficient increase. No maximum in the Seebeck coefficient was reached suggesting
that even larger amount of tin should be introduced until a maximum is reached. The

increase in the Seebeck coefficient does not correspond with a pronounced decrease of o.

This is encouraging for further increase of the power factor 826.

Annealing for 5 days at 500 °C of pressed pellets of KPbloBio,5Sbo_5Te68e6 doped
with 0.15 % Sn gave a predicted ZT of 0.13 (if we assume a thermal conductivity of
1 W/m-K). Further studies are necessary to take full advantages of the powdering effect.

Finally, it is important to point that the materials should be synthesized first and
then doping agents should be added. This probably would result in more clear trends and
more accurate data. Unfortunately, this was not possible using the flame method. Ingot

growth using the Bridgeman method could resolve this problem.

149

References

H

G.D. Mahan, Solid State Physics, 51, 81, 1998, 111

2 CM. Bhandari, D.M. Rowe, “Optimization of Carrier Concentration”, in CRC
Handbook of Thermoelectrics, Ed. by D.M. Rowe, 1994, 43

3 V. Fano, “Lead Telluride and Its Alloys”, in CRC Handbook of Thermoelectrics,

Ed. by D.M. Rowe, 1994, 257

150

 

Conclusion

The investigation of the family of cubic chalcogenides compounds of general
formula AmBanQm+n show that the system K/Pb/Bi/Te possess the most promising
transport properties among all the other systems studied. In this system, no clear
dependence of the Seebeck coefficient (S) on the value of n was observed, to the contrary

of the electrical conductivity (0) that increased with n. This observation lead to a further

study of the member KPbloBiTelz.
It has been observed that the thermal conductivity of this compound (2.2 W/m~K)
can be successfully decreased by introduction of disorder in both anionic and cationic

sublattices. The lowest value of K was measured for KPbloBio,5Sbo.5Te6Se6 doped with

0.1 weight % of Sn. This very good value of about ~0.78 W/m-K is most probably due to

substitution of some Pb atoms by Sn (0.1 weight % correspond to 3 atomic % of dopant).
Tin seems to play a decisive role in the enhancement of the Seebeck coefficient.

The values were observed to be extremely high for cold pressed pellets of doped samples:

from -140 to —180 uV/K for addition of Sn in excess to KPbloBiTe6$e6 and from —300 to
—380 uV/K for addition to KPbloBio5Sb05Te6Se6. Measurements on ingots gave
unfortunately lower values: from —80 to —105 uV/K for KPbloBio.5Sbo.5Te6Se6 and about
—120 uV/K for KPmeiTe6$e6 doped with 0.1% Sn. Nevertheless, these values are the

highest measured in this work. In contrast, of Sn, addition of Sb and Ag do not seem to

affect the values of the Seebeck coefficients.

151

Addition of antimony increased the electrical conductivities to values slightly

above 1000 S/cm without affecting largely the Seebeck coefficients. Further work should

investigate the role of Sb as a chemical agent to increase a. The effect on the power
factor 820 of introduction of both Sb and Sn in the system must also be study in more

details.
A synthetic method must be found in order to synthesis large amount of material

that can be used for doping experiments. This would suppress the uncertainty on the
composition of the materials obtained because of the mixing of the dopants to the
elements before synthesis.

The differences noted between measurements of the Seebeck coefficient on cold
pressed pellets and ingots are attributed to the introduction of defects in the structure
during the powdering process. The defects create acceptor levels that “kill” the electrons
which are the main charge carriers as shown by the negative sign of the Seebeck
coefficients. This had for consequence to decrease the charge carrier concentration n.
As it has been demonstrate in Chapter 4, because the Seebeck coefficient is proportional
to 1/Ln (n), S is therefore increased. Annealing experiments proved that these defects
can be eliminated. The Seebeck coefficients were then restored, after several annealing
processes, to values close to the ones observed on ingots. Accordingly, the electrical
conductivity values increased as the grain boundary effects are decreased.

An optimum power factor was reached after annealing for 5 days at 500 °C.

Using a conservative value of l W/m-K for the thermal conductivity K, a ZT of 0.13 at

room temperature was calculated for KPbloBio5Sbo5Te6Se6 doped with 0.15 atomic % of

Sn and annealed as described above. Additional experiments need to be done using

152

 

shorter annealing time (24 h instead of 5 days). A higher power factor could be obtained

which would be accompaigned by a lower value of K due to the shorter annealing time.

The differences in electrical conductivity between measurements made at our
laboratory and by our collaborators can be attributed to three factors:
1. A difference of charge carrier concentrations exists in different part of the
ingots due to the use of the “flame” reaction.
2. A surface effect takes place for most of the samples investigated. Such
degradation of the surface can nevertheless be repaired by etching in
diluted HCl.

3. An error due to the difference between the techniques employed for

measurement of o with our collaborators can account for values decreased

by a factor of 2.

The narrow band gap compounds studied in this Thesis constitute promising
thermoelectric materials. Further improvement of the materials pass by the resolution of
the problems evoked above. Investigation of the silver system Ag/Pb/Bi/T e might be an
alternative to the use of potassium that is responsible to glass attack and that limit the
amount of material that we were able to synthesis.

It is obvious that a lot of work need to be done to improvement the n-type
material KPbloBiTeu and to develop a p-type analogue, necessary to the creation of

industrial modules.

153