. .2 “flhfir . ‘ sfimw. 3L3? m. u! A! ‘Kf? s. u" .5... WWW :13: (A; u kw}. y. v3.2.5 .nuou‘... . c a :4- iv. 6 :3: VI. :4, v. .. t." ‘J.o"- I .a 1.! A! I}. V r. - .‘ tar?“ 3‘. .§\ .. If: .,. a in“? hm. fl. Ii... :5. .Vanfiwfltfld5tc3. .I. o 312‘ nv w .1. :5an a! x . o a 55‘- Vn I 1..., L . . an. . .5 Lil .« . ‘ . . . it! at ..1....:n.a.:.n 5: a. . 2.: . 7 in.» .Edf..issag.§x I?! ; ' 1‘ i LIBRARY Michigan 5 rate Universi :y r ‘ ' J ‘ . .Y gig}; is to certify that the 1 "9“ '- 3; f t ' thesis entitled H Thenmopowea 06 Metaflb in High Magnetic FLeZdé presented by Chwan-Kang Chiang has been accepted towards fulfillment of the requirements for ph.D. degree in PhybLCb M jot professor Date June 10, 1974 0-7 639 T 1 ' ‘ it" ~~Muuy 800K BINDERY INC. v ‘yfiRARY BINDERS ‘ mam». ‘ ‘ {Ems ABSTRACT THERMOPOWER OF METALS IN HIGH MAGNETIC FIELDS BY Chwan-Kang Chiang The thermopower of polycrystalline Copper, Silver, Gold, Aluminum, Indium and Lead was measured from liquid helium temperature to 100°K in magnetic fields up to 50 kG. Large enhancement of thermopower by the magnetic field was found and a peak in the temperature dependence of AS(H,T) was observed for the first time. The field results in a large enhancement of the phonon-drag thermOpower in contrast to early expectation of MacDonald and Pearson. We have developed two theoretical models to explain the observed effects. The electron-diffusion model relies on the well-known Mott formula for the diffusion-thermopower, and Wiedemann-Franz law. The phonon-drag model is based on the semiclassical electron dynamics in a magnetic field, and also a concept from Pippard. It is found that these two models together can give a good explanation of the experi- mental results. In the course of these studies we have developed a new technique for measuring thermOpower in high magnetic fields. The method measures directly the change of thermopower due to a magnetic field, thereby obviating the problem asso- ciated with measurements of temperature in a field, and also I _. t . , r . _.‘ A" 1"" ‘, 6 ." 1") .'__.J J) Chwan-Kang Chiang b (4 the problem of a proper reference material in a field. By applying this new method to thermocouple wires we have calibrated Chromel-P versus Au-0.07 at.% Fe and Silver Normal versus Au-0.07 at.% Fe thermocouples in magnetic fields. This is of practical importance for studies of thermoelectricity in a magnetic field. THERMOPOWER OF METALS IN HIGH MAGNETIC FIELDS BY Chwan-Kang Chiang A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1974 To My Patents ii ACKNOWLEDGEMENTS I would like to express my sincere appreciation to Professor F. J. Blatt and Professor P. A. Schroeder for their patient guidance, assistance and encouragement throughout this study. I wish to acknowledge Dr. A. D. Caplin for his guidance and assistance in the experiments and many stimulate discussions. Also I wish to thank Dr. L. Smrcka for his assistance in developing the electron- diffusion model. Thanks also goes to Professor J. Bass, Professor C. L. Foiles, Professor T. A. Kaplan, Dr. J. R. Cleveland, Dr. S. D. Mahanti and Dr. J. M. Tracy for their constant interest in the work and many helpful discussions. I wish to thank Mr. R. W. Cochrane, Mr. M. J. Ford, Mr. J. J. Higgins and Mr. J. Passaneau for their assistance in building up the experimental system, and to Dr. Z. M. Ma for allowing me to use his least-square-fit subroutine. The financial support of the National Science Foundation is gratefully acknowledged. iii Chapter I. II. III. IV. 5. 6. l. 2. 3. TABLE OF CONTENTS INTRODUCTION ...... . ....................... DIFFERENCE METHOD FOR MEASURING THERMO- POWER IN A MAGNETIC FIELD ----------------- Introduction ........................... Principle and Design ....... ... ....... .. Cryostat ....... ........................ Experimental Procedure ................ . 4.1 Tests ...... .......................... 4.2 Runs .... .................. ........... Data Analysis ....... ..... ..... . ..... . . 5.1 The Change of Thermopower in a Magnetic Field ... ....... ............. 5.2 Temperature Difference along the Copper Rod ........................... 5.3 Fringing Field ...... ..... ............ 5.4 The Uncertainties .... ........ ........ Application and Improvement ............ TEMPERATURE MEASUREMENTS IN HIGH MAGNETIC FIELDS ..... ............... . ....... ........ Introduction ...... . ............ ........ Experiments ...... .... ........ . ..... .... Results ............. ..... .............. 3.1 Thermocouples Wires .................. 3.2 Thermocouples ........................ THERMOPOWER OF THE NOBLE METALS AND OF ALUMINUM, INDIUM AND LEAD IN MAGNETIC FIELDS ..... iv 13 13 15 19 19 20 24 24 25 27 27 29 29 29 37 43 Chapter Page 10 IntrOduCtion 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 43 2. Copper, Silver and Gold ....... ........... 44 2.1 Sample Preparation ..................... 44 2.2 ThermOpower in Transverse Magnetic Fields ................................. 47 3. Aluminum, Indium and Lead ................ 52 3.1 Sample Preparation ..................... 52 3.2 Thermopower in Transverse Magnetic Fields ................................. 55 4. Summary on Experimental Results ............ 68 V. THERMOELECTRIC THEORY IN A MAGNETIC FIELD ............................................... 71 10 IntrOduction 0000000000000000000.00000000000 71 2. The Electron-Diffusion Model ............... 73 3. The Phonon-Drag MOdel 000 ...... 0000000000000 83 VI. DISCUSSION AND CONCLUSION ......... ..... ........ 93 1. Comparison with Experiments ................ 93 2. Discussion and Conclusion .................. 98 REFEMNCES 00000 000000 0000000000000000 0000000000000... 111 APPENDIX REFERENCE TABLES FOR LOW TEMPERATURE THERMOCOUPLES IN MAGNETIC FIELDS 00000000000000.00000000000000 115 Table LIST OF TABLES The Characteristics of Thermocouple Samples ............................ The Characteristics of Samples ..... The Values of S(H.T)/S(0,T) for the Noble Metals at 48 k6 .............. Therm0power Peak Temperatures of Zero Field and of 48 k6 ................. The Comparison between the Electron- Diffusion Model, the Phonon-Drag Model and the Experimental Results vi 30 48 S3 69 Figure 3.6 LIST OF FIGURES Page The Principle of the Difference Method for Measuring Thermopower in a Magnetic Field ................ . 7 The Relation between the Sample, the Cryostat, the Superconducting Magnet and a Typical Magnetic Field Profile ..................................... 10 The Schematic Representation of the AS(H,T) Cryostat ................. 11 A Typical Result of the Temperature Gradients along the COpper Rod ... 16 The Fringing Field of the Oxford Superconducting Magnet as a Function of the Central Field ............. 17 The Correction of the Temperature Gradient along the COpper Rod .... 23 The AS(H,T) of Au-0.07 at.% Fe ... 31 The Thermopower of Au-0.07 at.% Fe in Magnetic Fields .................. 32 The ThermOpower of Chromel—P in Magnetic Fields. The Inset is the AS(H,T) of Chromel-P. ....... ..... 33 The AS(H,T) of Silver Normal Alloy ........................ ......... .... 34 The Therm0power of Silver Normal in Magnetic Fields .................. 35 The ThermOpower of Type Chromel-P versus Au-0.07 at.% Fe Thermocouples in Magnetic Fields. The Data Point (0) are Taken from a Longitudinal Field 60 kG of von Middendorff ... 38 vii Figure Page 3.7 The Change in the Thermo—emf of Type Chromel-P versus Au-0.07 at.% Fe Thermocouples in Magnetic Fields. The Data Points (V) are Taken from a Longitudinal Field 60 kG of Sample gt a}, .... ........................ 39 3.8 The Thermopower of Silver Normal versus Au-0.07 at.% Fe Thermocouples in Magnetic Fields ................ 41 3.9 The Change in Thermo—emf of Silver Normal versus Au-0.07 at.% Fe Thermocouples in Magnetic Fields .. 42 4.1 The Oxidizing Annealing System .... 45 The AS(H,T) of the Noble Metals. Fields: a=48kG; b=35kG; c=26kG; d=17.4kG; e=8.7kG; f=4.4kG; g=l.7kG 000.000.000.000000000000000000.0000000 49 4.3 The Therm0power of the Noble Metals in Magnetic Fields .......... ......... 51 4.4 The Magnetic Field Dependence of the AS(H,T) of the Noble Metals ....... 54 The AS(H,T) of Aluminum ..... ...... 56 4.6 The Sign Change in the AS(H,T) of Aluminum .......................... 58 4.7 The Magnetic Field Dependence of the AS(H,T) of Aluminum .......... ..... 59 4.8 The Thermopower of Aluminum in Magnetic Fields ............................ 60 4.9 The AS(H,T) of Indium ............. 61 4.10 The Magnetic Field Dependence of the AS(H,T) of Indium ................. 62 4.11 The ThermOpower of Indium in Magnetic Fields ......... ..... .............. 63 viii Figure Page 4.12 The AS(H,T) of Lead .............. . 65 4.13 The Thermopower of Lead in Magnetic Fields ............... ........ ..... 66 4.14 The Magnetic Field Dependence of the AS(H,T) of Lead .. ............. .... 67 5.1 A Typical Magnetoresistance Results (a, b, c) and the Envelope Function (b', which is Calculated from b) for the Electron—Diffusion Model ...... 80 5.2 The Fermi Surface of COpper and the Influence of a Magnetic Field ..... 86 5.3 Contours of Fermi Velocity (Expressed in the Unit of the Fermi Velocity of Free Electron) for COpper ......... 90 6.1 Calculated (Dashed Curves) and Experi- mental (Solid Curves) Results of AS(H,T) of COpper as a Function of Temperature at Three Field Values ...................................... 95 6.2 Calculated (Dashed Curves) and Experi- mental (Solid Curves) Results of AS(H,T) of Aluminum as a Function of Temperature at Three Field Values ............. 99 6.3 The Separation of the T- and T3-Depen- dence of AS(H,T) for COpper ....... 103 6.4 The AA(H) of COpper as a Function of Magnetic Field .................... 104 6.5 The AB(H) of Copper as a Function of Magnetic Field ........ ....... ..... 105 6.6 The Separation of the T- and T3-Depen- dence of AS(H,T) for Aluminum ..... 106 6.7 The AA(H) of Aluminum as a Function of Magnetic Field .................... 107 ix Figure 6.8 The AB(H) of Aluminum as a Function of Magnetic Field ............... CHAPTER I INTRODUCTION Our program was largely stimulated by interest in the electron-magnon interaction in ferromagnetic metals. Previous studiesl’2 indicated that the electron-magnon interaction played an important role in the transport processes of ferromagnetic metals. Since the study of thermopower is a useful method to understand a scattering process and a magnetic field is a powerful instrument for resolving the degeneracy of the electronic system, it is of interest to see how the electron-magnon interaction responds to the applied magnetic field. Therefore, we needed to measure thermopower in strong magnetic fields in a temperature range from liquid helium temperature to room temperature. This immediately presented us with the problem of temperature measurements in strong magnetic field, which is one of the most difficult techniques in low temperature solid state physics. In addition to the problem of measuring temperature in a magnetic field, we also faced the difficulty that no. thermoelectric standard in non-zero fields was in existence. Normally, the absolute thermopower of a material is estab- lished by measuring the thermopower of a couple in which one arm is a metal whose absolute thermopower has been previously determined. However, until now no absolute thermopower at non-zero fields has ever been determined except at tempera- ture below about 18°K when the reference arm of the thermo- couple may be superconducting. Due to the experimental difficulties only few attempts have been made to measure the thermopower of pure metals in a magnetic field. MacDonald and Pearson3 measured the thermopower of copper and COpper alloys in 1957 and con- cluded that the influence of a magnetic field on a pure monovalent cubic metal is very small and the phonon-drag thermopower will be uneffected by the field. Recently, Averback, Stephan and Bass4'5 have produced some evidence that in aluminum and indium not only the electron diffusion thermopower but also the phonon drag thermopower has a field dependence. By means of the development of a new method, which we call the "difference method" we are able to measure the thermopower of polycrystalline metals in strong magnetic fields at wide temperature range. This now opens the whole field of magnetothermoelectric effects to experimental and theoretical studies. We have made extensive studies on this subject, although only limited results will be reported in this thesis. In the thesis the new experimental technique, the difference method for thermopower measurement will be described in detail in Chapter II. An important application of this method is to calibrate thermocouple wires in high fields. These calibration results are contained in a reference table entitled "Reference Tables for Low Tempera- ture Thermocouples in Magnetic Fields"6’7. The calibration will be described in Chapter III and the reference tables are included in the Appendix. Six metals which belong to three types of electronic structure were studied. The full experimental details and the results are included in Chapter IV. In Chapter V, we begin with a very brief review of current theories and then we will present two theoretical models to explain the observed results. Finally, in Chapter VI, the results of the calculation will be compared with the experiments. CHAPTER II DIFFERENCE METHOD FOR MEASURING THERMOPOWER IN A MAGNETIC FIELD 1. Introduction There are two basic methods for measuring absolute thermopower: the integral method and the differential method. Many techniques related to these two methods have been developed. A quite complete description of these techniques is given by Barnard.8 In the integral thermopower measurement, a constant temperature bath is used which holds one junction of the thermocouple at a known temperature, the other junction is raised in temperature and the total emf measured over the temperature range of interest. To obtain thermopower from the data one differentiates the voltage versus temperature curve. In the differential measurement the thermopower is obtained directly by raising both junctions of thermocouple to the required temperature, and then further increasing one junction by a small temperature AT, and measuring the small emf AV created. The thermOpower at T+AT/2 is then simply AV/AT. In both methods the absolute thermopower of the sample is obtained in terms of a standard reference used as the other arm of the couple. The accuracy of the two methods is about the same, and depends on the accuracy of measuring emf, temperature and temperature difference. When a strong magnetic field is present, these con- ventional methods become very difficult to use. The temperature measurements in a strong field are one major problem. We will discuss this subject in the next chapter. However, even with an adequate thermometer, the experiment is still rather difficult. The reason is that both branches of the thermocouple are in the field and contribute to the measured thermopower. The absolute thermopower of the sample can not be deduced without a known reference. A common solution to the reference problem is using an 9’10 it was assumed that the change of alloy. In early work thermopower due to a field could be neglected because of the higher resistivity of the alloy. This reference branch introduces, to the result, an unknown uncertainty which increases with increasing applied field. A superconducting material can be used as the reference, if the temperature range of interest is below its transition temperature. This option works at very low temperatures when the field is not very high. Alternatively, a measurement can be carried out as a function of field at a fixed temperaturell'lz. But, there is a technical difficulty related to the temperature control. A relatively large uncertainty on the thermopower results is, therefore, unavoidable. A major problem in the measurement of thermopower in a magnetic field is that either the thermocouple or the lead wires must pass through a region of inhomogeneous magnetic field and temperature. This is an experimental necessity which one can not avoid if a conventional method is used. Therefore, a new method is desirable. We have developed a third method, the difference method, which is a combination of two conventional methods. MacDonald and Pearson3 had made a similar but complicated system which was not very successful. Our method is an improved version of their technique. We are able to circum- vent both temperature and reference problems and obtain directly the thermopower difference due to the magnetic field. This method is relatively simple and powerful. In this chapter we will describe the difference method in detail. The description is divided into five sections: design, cryostat, experimental procedure, data analysis, and application and improvement. 2. Principle and Design If two different metals A and B are connected as shown in Fig. 2.1a, and if the two junctions are kept at different temperatures T1 and T2, a thermoelectric emf is developed in the circuit. The thermopower is defined as SBA E SE - SA = dV/dT . (2.1) pamwm owumcmmz m CH HmonOEHmne msfiusmmmz How tonne: mocmnmmmwo osu mo mamfiocaum one H.N .mflm 2: E > < + fl >< + .4 . -< m m .7 «F .. Z 1 P {we .....l... 2 F “00000.0000000000000000000000V400000m < mm 4 where SBA is the thermopower of metal B relative to metal A, and SA and SB are the absolute thermopowers of metal A and B, respectively. The Seebeck effect still exists, if A and B are the same metal but in a different state. In this work, we let A be in a magnetic field H, and replace B by the same metal A, but in zero magnetic field (denoted by A' in Fig. 2.1b), then S = AS(H,T) = S(H,T) - S(0,T) (2.2) AA' where T is the temperature of the sample at the limit AT+0. Equation 2.2 forms the basis of the difference method. The magnetic field produced by a magnet has its own pattern and extends over a finite region. Since we are unable to restrict the field, our design must adapt to the field profile. A typical field profile of a superconducting magnet is shown in Fig. 2.2b. (An electromagnet can be used equally well with a different sample arrangement.) The arrangement in this type of field is shown graphically in = 4.2°K and T Fig. 2.2b, where we have T 2 = T. The tempera- 1 tures T and T2 extend over the isothermal range AB and DC, 1 respectively. In other words, the thermoelectric emf gener- ated in the section BC is transmitted to A and D through two isothermal ranges. We recall that no thermoelectric emf can be generated without a temperature gradient. Hence VAB = VCD = VEF = 0 (2.3) and VAF = VAB + VBC + VCD + VDE + VEF = VBC ' VED T T =f S(H,T') dT' -f S(0,T') dT' (2-4) 4.2 4.2 Differentiating Eq. 2.4, one obtains Eq. 2.2. There is a non-vanishing voltage V , if and only if BC and DE are in a different state. In this design we use the sample itself as reference, which is a meaningful way to detect the change. In designing a cryostat, we require a cryostat such that the measured voltages to satisfy Eqs. 2.3 and 2.4. Figure 2.2b shows a schematic of the arrangement for a supercon- ducting magnet. 3. Cryostat Based on the design of Fig. 2.2b, we have constructed the cryostat shown schematically in Fig. 2.3. A typical magnetic field profile in relation to the cryostat configura- tion and to the magnet is shown to scale in Fig. 2.2. Our cryostat is suspended such that point C is in the central field region of the sblenoid used to generate the magnetic field. The distance C-D is made sufficiently great (17 cm in our case) so that point D is located in the weak fringing field of the solenoid. Measurements for our magnets 10 maflmoum oaowm owuocmmz amowmaa m can nomad: mcauosocoonomsm map .umumoauu on» .onEmm on» soo3uon :ofiumamm one m.~ .mHm 3V 2: cc on ON 0. O 3.: I 3m: ..... L B n: .256: I 2526E8kiflw m . 1 .. _ cu m - i ...... medal. - m on t i. l 0' $)\I\’))\1\1111\(I\ zsqdasfi I I 11 ”(I F fl‘r————A D I g- t \( E TCorGT2——// ) Sample COpper Rod t (OFHC) ! Can Heater E * GTI ‘ / CT SOMP'G i / / MR L// / 0 I 2 3 L_.|__L_l SCALE(CM) I B UI—lua Fig. 2.3 The Schematic Representation of the AS(H,T) Cryostat 12 showed that the field at D was between 3 and 4% of the central field HO . For Ho equal to 50 kG the fringing field is 1.7 kG. The sample wire, approximately 2 meters in length, is attached to the measuring leads at points A and F. Both of these junctions are submerged in the liquid helium bath, and they are in close proximity to each other, and hence in the same fringing field. The sample is then brought into the high field region isothermally, in contact with the helium bath (section A-B). At point B the sample wire enters the vacuum can through an epoxy feed-through. At least three turns (longer than 20 cm) of the wire are wound on the can to insure the sample junction is truly at the bath temperature. Inside the can the sample wire is thermally anchored at C and D and along the entire length C-D, to a 0.635 cm diameter, 18 cm long OFHC copper rod attached to the top flange by a thermally insulating support. The temperature of this rod can be controlled by a heater wound near its center. Finally, the wire is brought back to the bath temperature along D-E, passes through another epoxy feed-through into the helium bath and is attached to the measuring lead at F. Point E is a copper binding post which is near the bath temperature. The two sections of the continuous wire which have a temperature gradient are each coiled about the vertical axis on a paper form and are about 20 to 50 cm in length, thus 13 reducing the heat loss by conduction to the helium bath. Though this is not such an important consideration in some measurements, it proved essential in measurements on pure metals. The use of these coils also assures that the magnetic field is normal to the sections of wire with the temperature gradient. The temperature of the COpper rod was measured by means of a Chromel P versus Gold-0.07 at.% Iron thermo- couple, attached to the rod at point D, in the weak fringing field. At high fields when the effect of the fringing field on the thermocouple could not be ignored, the temperature was corrected by using our results. To determine if the copper rod was, indeed, at uniform temperature, we employed a differential thermocouple attached at points C and D. The various thermocouple voltages were measured with a Keithley Model 180 digital nanovoltmeter and a Keithley Model 147 nanovoltmeter. The thermocouple for measuring the temperature T was read by a digital voltmeter with l micro-volt resolution. Magnetic fields were produced by an Oxford superconducting solenoid for fields below 50 kG and a RCA solenoid for fields up to 100 kG. 4. Experimental Procedure 4.1 Tests Prior to the start of the experiments, we had made various tests to make sure the apparatus did work as we 14 expected. The major test was to determine the temperature dif- ference along the copper rod. Two calibrated germanium resistance thermometers (GT 1 and GT 2 in Fig. 2.3) were mounted on the two ends of the copper rod. The tests were made under various conditions: with and without sample, good vacuum and bad vacuum in the can, heater on and heater off, temperature increasing and decreasing, etc. A small amount of exchange gas (< 10 micron) did help to keep the temperature difference small. Also the heat flow through the sample should be reduced as much as possible. The germanium resistor thermometer, GT 1, does change calibration in a magnetic field. We, therefore, also used a capacitance thermometer, CT, located adjacent to GT 1 to determine the magnitude of the temperature difference along the copper rod in a magnetic field. The result of the above tests indicated that, although there were small temperature gradients along the copper rod, the temperature differences between C and D never exceeded 5% of the temperature of the rod, and was at all times less than 1°K. After these tests, GT 2 was replaced by a Chromel-P VS Au-0.07 at.%Fe thermocouple. This is possible because the thermocouple has small field dependence in low fields. (see Chapter III). We used a differential thermocouple to measure the temperature difference along the rod and removed all germanium thermometers and capacitance thermometer. This 15 arrangement made the measurements more efficient and reduced the thermal leakage. Since the thermOpower of this thermocouple is increasing in a magnetic field, the voltage reading of the differential thermocouple gives a upper limit on the temperature gradient. (If the calibration tables are used, we can obtain a correct result of the temperature gradient). A typical result of the temperature gradients along the copper rod as a function of temperature is shown in Fig. 2.4. The next step was to determine the fringing fields. The fringing field H was measured as a function of the central f field Ho . The result is shown in Fig. 2.5. The distance between the two points C and D of Fig. 2.3 was 16 cm. Since these fringing fields were small compared to the central field, (less than 4% of HO), they can be considered as zero field to the first approximation, although we ultimately did correct for the effect of the fringing field on the measured voltage. 4.2 Runs A typical AS(H,T) experiment started with a zero field run. We performed the measurement outside the magnet. The thermo-emf of the sample, ideally, should be zero. That is not true in the real case. Since the sample is not strictly homogeneous, small variations of thermopower along the sample will cause finite thermal voltages. Our acceptable criterion was that a sample had thermal voltages less than 16 6 1 l f l A D o\° Dragoon 0% k6 v 000 D 3 _ Ch: [3 Cl V7 kG _ 04 ‘:¥§5£“A£§i>cj AL (3 RG 7’; ° ”8 L: m “1.. > A (h n 1329306000 0 o a) 1" 0- AA A A A A- {3 A ‘3 l l J I O 20 4O 60 80 I00 To (°K) Fig. 2.4 A Typical Result of the Temperature Gradients along the COpper Rod l7 2 1 I I T Oxford Magnet 0 A‘ V ' - I9- 0. l 0 IO 20 30 4o 50 Ho ( kG) Fig. 2.5 The Fringing Field of the Oxford Super- conducting Magnet as a Function of the Central Field 18 5 micro-volts at 100°K. During this run, the system is carefully checked for vacuum conditions and other troubles to avoid unnecessary waste of liquid helium in cooling the magnet. In the magnet run the cryostat is arranged as shown in Fig. 2.1. A magnetic flux sensor (MistoR) was used to determine the relative position between the sample and the field. This position was pre~determined in the test period. For each field, we measured the thermo-emf of the sample as a function of temperature. The temperatures are obtained from the reading of Chromel versus Au-0.07 at.%Fe thermocouple. The temperatures were incremented in steps of l°K to 5°K. At the same time, we recorded the temperature difference deve10ped along the heating copper rod. We stopped at about 100°K or at a temperature where the thermo-emf from the sample saturated. The sample was cooled down by allowing small amounts of helium exchange gas into the vacuum can and the process repeated for the next magnetic field value. The following field sequence was normally used: 0.87 kG, 1.7 kG, 4.4 kG, 8.7 kG, 17 kG, 26 kG, 35 kG, 43 kG and 48 kG. Due to time limitation some fields were occasionally skipped. At the end of a run, all connections were checked once more to verify the sign of the measured thermo-emf. l9 5. Data Analysis 5.1 The Change of Thermopower in a Magnetic Field The raw data from a run was in the form of a thermo- electric emf as a function of temperature, arising from the difference in thermopower of sections DE and BC of the sample at a fixed magnetic field. This data was first displayed graphically to obtain a general idea of the behavior of AS(HOT). Next we converted thermocouple voltages into temperatures. A computer generated calibra- tion table with accuracy 10 mK was used for this conversion. The calibration data of Chromel-Au+0.07 at.%Fe thermocouples was taken from Sparks and Powelll3. The change of thermo- power was then computed by a computer prOgram, which made a least squares fit of five neighboring data points to a quadratic function and then differentiated with respect to temperature. AS(HOT) was evaluated at the central data point only. We shall refer to the output of the computer program as the direct result. No smoothing was included in the direct results. In arriving at the final result three corrections must be made to the direct result. The first correction is the correction for inhomogeneity. Inhomogeneity of the sample, if any, was detected by the zero field measurement. We simply subtracted the zero field result from the direct result. The second correction is the correction due to the temperature difference along the copper rod. We shall 20 discuss this correction in detail in the Section 5.2. The third correction is the correction due to the finite fringing field. This correction shall be considered in Section 5.3. The final result after these corrections, is AS(H,T) = S(H,T) - S(0,T) 5.2 Temperature Difference Along the Copper Rod In our measurements, a small temperature difference AT does develop between C and D on the c0pper rod. (see Figs. 2.2 and 2.3.) How much does this contribute to the measured thermo-emf? A simple analysis is provided by the following. As shown in Fig. 2.2b, the temperature at D is T, which was measured in the experiments. At C the temperature will be T + AT in the actual experiment. The measured thermo-emf is T T+AT E = j S(Hf,T') dT' + f S(VH,T') dT' 4.2 T (2.4) 4.2 + f S(HO,T') dT' T+AT where we used S(VH,T') to represent the thermopower along CD, which can not be defined precisely, since we do not know the temperature versus field variation along this length of wire. The thermo-emf along AB is essentially zero, since the temperature difference is extremely small in the helium 21 bath. We can rewrite Eq. 2.4 as 4.2 E = [T [S(HO,T') — S(Hf,T')] dT' + E l (2.5) The first term of the above equation is V the quantity we AF, need. The second term E1 is the correction due to the existence of AT, i.e. T+AT E1 = f [S(VH,T') - S(H ,T')] dT' (2.6) T o In an ideal condition AT = 0 and E = 0. For a small 1 AT, we estimate the correction from the field dependence of AS(H,T) as follows: (a) If AS(H,T) saturates at low fields we obtain an approximation by setting S(VH,T) ~ S(HO,T) (2.7) so E ~ 0 (b) If AS(H,T) is significant only at very high fields then S(VH,T) ~ S(Hf,T) and. (2.8) E ~ [S(Hf,T) - S(HO,T)]° AT 1 22 (c) In general, AS(H,T) is intermediate between cases (a) and (b). As an approximation, we assume 1 E1 ~ 2AT -[S(Hf,T) - S(HO,T)] (2.9) ~ lAT - AS(H T) (2.10) 2 0’ We show this correction graphically in Fig. 2.6. The measured thermo-emf is the area ABC'CD. The result we need is the area ABC'D. The correction is the area C'CD. A triangle probably is a fair approximation to the area C'CD, which is given by Eq. 2.9. In Fig. 2.6 AT = T' - T has been greatly enlarged to clarify the picture. In our experimental work, we found there was very little change in the pattern of AT during one series of runs. Thus we could use one set of AT to make this correction. Differentiating Eq. 2.10 we obtain _ .. l 5.1.. . Sl — d El/dT — 2 dT [AS(HO,T) AT] (2.11) where S1 is the correction term for AS(HO,T). This correction was done by a computer program similar to the one used for calculating thermopower. The correction due to the temperature difference along the copper rod was less than 3% of AS(H,T). 23 com Hammou asp mcoam usowomuo onsumuomfioa may no soauoouuoo one m .N 2: .3 .0; _m_ 24 5.3 Fringing Field The fringing field correction is done graphically. We plotted the change of thermopower as a function of field at a given temperature. When the central field was low the fringing field was negligible and no correction was needed. As the central field was increased there was a finite fringing field. To obtain AS(H,T) = S(H,T) - S(O,T), we added the change at the fringing field to that at the central field, using the measured fringing field as a function of central field and the measured change in S at low central fields. Mathematically we have AS(Hf,T) = S(Hf,T) - S(O,T) (2.12) AS(HO,T) = S(HO,T) — S(Hf,T) (2.13) so AS(H,T) = S(HO,T) - S(O,T) (2.14) AS(HO,T) + AS(Hf,T) The size of this correction depended on the field dependence of the thermopower of the sample, and the temperature range. The largest correction was about 10% of the direct result. For the most cases it was less than 5% of the final result. 5.4 The Uncertainties Errors entered into the final result of AS(H,T) from the non-exact corrections and the uncertainties in the measure- ments. The uncertainty in the temperature of the hot 25 junction was less than 0.05°K. The uncertainty of individual voltage readings was 10"8 volt. The reading was good to three significant figures. The correction for the temperature difference, Eq. 2.10, contained an approxima- tion. We estimate this uncertainty to be less than 3% of AS(H,T). The correction of the fringing field depended on the exact measurements related to the location of the sample and the field at that point, and also on the number of data points at low field values. In our case we estimated the uncertainty was less than 3% of AS(H,T). Therefore, we concluded the uncertainty of the final results, i.e. the -8 curves of AS(H,T) is 5% or less, or i 10 V/°K whichever is greater. 6. Application and Improvement The difference method is the only method at present capable of measuring the absolute thermopower of a con- ductor in magnetic field above the transition temperature of a superconductor. However, the method is only good for a wire sample. For future work on various types of samples: particularly single crystals,two standardizations should be done by this method. First, we should establish a standard reference material, at high fields, comparable to lead which is employed for zero field measurements of therm0power. With the present techniques it is very difficult to perform a measurement of Thomson heat and to construct the absolute 26 thermopower scale in magnetic fields. The difference method provides the solution to this problem. To this end we have measured S(H,T) for lead and for Ag-0.37 at.%Au (silver normal), an alloy frequently used as a secondary standard. The results of these measurements will be discussed in later sections. A very small field dependence alloy Ag+l.5 at.%Au has been studied14. Second, it is necessary to calibrate commercial thermo- couple wires in magnetic fields. The thermo-emf in magnetic fields may be measured by many other methodslz, but the change in thermopower is best obtained using the difference method. Details of this work are described in the next chapter. For more precise studies the system should be built by using two heaters to control the temperature of the copper rod so that the difference of temperature along its length can be eliminated. Careful study at low fields should also result in a better correction for the fringing field effect. The difference method is applicable not only in a transverse magnetic field but also in a longitudinal magnetic field. All the experimental results reported in chapter III and IV are in transverse magnetic field unless otherwise stated. CHAPTER III TEMPERATURE MEASUREMENTS IN HIGH MAGNETIC FIELDS 1. Introduction In the temperature range from 4.2°K to 100°K, germanium resistors are the most commonly used thermometers. Unfor- tunately, they have a very strong magnetic field dependence. Accurate measurement of the temperature in the presence of high magnetic fields is difficult, because there are no convenient cryogenic liquids available for vapor pressure thermometry in this temperature range. The prOperties of germanium resistors in high fields have been studied by 15 and Neuringer and Rubin16. A change by Neuringer g2 31., as much as a factor 10 has been observed in a field of 130 kG at 4.22°K. Moreover, the magneto-resistance of a germanium resistor also has an orientation dependence. Nueringer and Rubinl6 suggest that germanium resistors not be used in a field above 25 kG. Other types of thermometers have also been studiele. Most thermometers are found to have a magnetic field dependence, except gas and capacitance thermometers. Gas thermometers offer an absolute standard of temperature. However, employing gas thermometers in a magnetic field at 27 28 low temperature is extremely tedious and inefficient. Capacitance thermometers are found to be magnetic field independent. This was first reported by Brand 17 and Fiory,18 who used Potassium Chloride (KCl) 19,20 2291-. crystals. Further studies were done by Lawless using SrTiO3 glass ceramic capacitance thermometers. The reports indicate that this type of thermometer may be a secondary standard for the measurement of temperature in high fields. However, the SrTiO capacitance thermometer has poor repro- 3 ducibility, especially at a temperature higher than 30°K. Thermocouples are probably the most convenient tempera- ture sensing transducers. Although various types of ther- mocouples are widely used for the measurement of temperature in the helium range, i.e. from 4.2°K up, a Chromel-P versus Au-0.07 at.%Fe thermocouple appears particularly well suited by virtue of its large thermopower at low temperatures. The thermopower and thermoelectric emf of this couple in zero field have been measured carefully, and calibration tables published by the National Bureau of Standardsl3. As a result of this work this thermocouple has gained wide popularity among cryogenic workers. Unfortunately this thermocouple also suffers from the same disadvantage of field dependence. We thought it worthwhile to study this thermocouple using the newly developed difference method. The aim of this work was to obviate the restriction to zero magnetic field. As a result of this study, we obtained a set of calibra- tion tables6'7. These reference tables for low temperature 29 thermocouples in magnetic fields are contained in the Appendix. In this chapter, we discuss the work related to the calibra- tion of these thermocouple wires in fields up to 100 kG. 2. Experiments We measured three thermocouple wires, Chromel-P (KP), Silver-0.37 at.% Gold (AgN), and Gold-0.07 at.% Iron (AuFe). These three wires are generally used to form two types of thermocouple: Chromel-P versus Gold-0.07 at.% Iron thermo- couple (KP-AuFe TC), and Silver—0.37 at.% Gold versus Gold-0.07 at.% Iron thermocouple (AgN-AuFe TC). The char- acteristics of the wires are listed in Table 1. All samples were purchased from Sigmund Cohn Corporation. The measurements were made on the individual wires by using the difference method. Two samples of AuFe from the same spool were measured to check the variation between the samples. We also extended the magnetic field from 50 kG to 100 kG by using our RCA superconducting magnet. 3. Results 3.1 Thermocouple Wires Figures 3.1 to 3.5 show the thermopower and AS(H,T) of AuFe, KP and AgN wires in zero and two transverse magnetic fields of 48 and 80 kc between 5°K and 100°K. The zero field thermoelectric power of AgN was obtained from Foile521, 3O m.HH moo.on om>Hmomu mm GoupOU mm.o mHHB eeoow.umem.o+nm>aam HmEHoz um>aam H.H no.0“ oo>flooon mm conmB ma.o muflz asaaoagomoa+amxoaz euamaonso maamamm mamsoooauona mo moepmwumuomuano one m.v No.0“ om>woomu mm conmB ma.o oHHB coun.umho.o+eHoo mm m.um no.0Iofi H.m OHQMB Axom.svm\xx.oomvm u mmm Ax.\>nv huflocmmoaom pounce ucoEumauu ummm coauMHSmcH lass mwam mama modaa mEouH 31 Om we Tum 3.0-3. mo 2..me a was CE ._. 9» On ON 0_ _ A _ on. o\o 48.0.0: :4 Tm .mE (l‘H)Sv (Mo/A”) 32 ~‘l0 _. X § 1 .. E- 3 l4 C) 0.. o h- ; Au-0.07at.%Fe '- -Ie- - sons -22 l L l 1 J 1 o 20 4o 60 TEMPERATURE (°K) Fig. 3.2 The Thermopower of Au-0.07 at.% Fe in Magnetic Fields 33 '0 T T T T T— T 8 *- CHROMEL° P 4 I; 3 6 - ZERO FIELD 4 .3 80 k6 Q 1 CD “é 4' ' (I O I I I I I I Lu E g * 3 :2» 2 ... )- 3 -.4 o ‘ .‘o * .3 ‘ :0 O 1 1 i L _L J O 20 4O 60 TEMPERATURE (°K) Fig. 3.3 The ThermOpower of Chromel-P in Magnetic Fields. The Inset is the A S(H,T) of Chromel-P. 34 oo. mofiad HmEHoz nm>HHm mo 35 ... Om Om 3.5m a was 0v In .mE ON _ — 23 0x mv 03 cm (l'H)SV (Mu/W) 35 moaowm oeuonmmz ca Hosuoz Ho>Hem mo HosoGOEhone one 00. A x. v mmbk 3 _ ZERO a E '2 FIELD § § Io - - 8 L- .4 6 l 1 l l 1 l I J J o 20 40 so 80 I00 TEMPERATLRE ( 'K ) Fig. 3.8 The Thermopower of Silver Normal versus Au-0.07 at.% Fe Thermocouples in Magnetic Fields 42 60 I I f r 8C)kG Donoooooaauaoofi 50. -( 0° AgN vs Au-Fe T.C. 40’ : 60kG “I ; o ooo°° o o o o o o 3 . m 0 0°° 5 30% .° - <5 ° 0° 48 k6 U o 0' IE 0 3' 8 a0 a. g 20? o" -l 5 0.. f“ BOkG '0 '— 0' ...”...“‘ c-I In“. T 8.7 kG o W.........! 0 0 0 0 I 0 0 0 0 1 0 0 0 0 ) o 20 40 so 80 mo TEMPERATURE ('K) Fig. 3.9 The Change in Thermo-emf of Silver Normal versus Au-0.07 at.% Fe Thermocouples in Magnetic Fields CHAPTER IV THERMOPOWER OF THE NOBLE METALS AND OF ALUMINUM, INDIUM AND LEAD IN MAGNETIC FIELDS 1. Introduction No measurements seem to have been made on simple metals previous to experiments by Taylor and Coleslo. Extensive work on copper and copper alloys was one by MacDonald and 4’5 have Pearson3. More recently Averback, Stephan and Bass measured aluminum and aluminum alloys at very low tempera- tures. Sirota 33 31.11 measured the field dependence of single crystal aluminum. The result of Averback gt g1. shows that not only the electron-diffusion thermopower, but also the phonon drag thermopower has a magnetic field dependence. As regards the latter their results were only an indication of the pattern that may exist. With the difference method described in Chapter II we are able to measure the thermopower of noble metals in strong magnetic fields at higher temperatures. The measurements, performed in the temperature range where the phonon density is much greater than in previous studies, now clearly demon- strate that the magnetic field has a profound effect on the phonon drag thermOpower. Our measurements have been extended from noble metals to aluminum, indium and lead, so we could compare our results at low temperatures with the work of Averback EE.El'4'5° 43 44 2. Copper, Silver, and Gold 2.1 Sample Preparation The copper sample was made from a piece of 14 AWG Belden copper wire. The heavy polythermaleze coating of the wire was removed by burning in a gas flame. The oxidized material on the surface of burnt wire was washed off in a nitric acid bath. The clean bare copper wire had a diameter 1.47 mm. This wire was then drawn through tungsten carbide dies and diamond dies to 0.18 mm. After each pass through a die the first section of wire (about 5 - 20 cm) was cutt off. Acetone was used if lubricant was needed during the drawing procedure. The fine wire was wound onto a 9 mm Vycor glass tube. The ends were held in place with loops of spare copper wire. The copper wire with tube was washed in dilute NaOH solution to remove finger grease. After a rinse with distilled water the wire was etched in dilute HNO3 solution for a few minutes. Then it was washed again with distilled water and rinsed with methyl alcohol. This cleaned copper wire was annealed in an oxidizing atmosphere to remove magnetic impurities from metallic solution. The oxidizing annealing was done in a system shown in Figure 4.1. We inserted the wired tube into a 15 mm Vchr glass tube A. Tube A was approximately 60 cm long and was seated in a Lindberg Type 54082A furnace. One end of the tube was connected to a pumping system. The other end of 45 Eoummm meanmocnm manuacnxo one A.” .mam 03.5 0682 32.300 a a 2 c. a m 00°C.»:hm N 32. 333m 3:... $20 46 the tube was connected to a 70 cm long capillary. There was a needle valve at the end of the capillary. The valve was used to control the pressure inside tube A. Finally, the valve was connected to a rubber hose with a glass tube B at its end. Prior to annealing the air flow rate was checked with an oil drop in the horizontal glass tube B. The oil drop should move at a speed of the order of 1 mm/min. A scale was set up for fine control of the pressure. When the annealing of the copper started, the system was pumped down to approximately 0.5 microns. The temperature of the furnace was then raised to about 500°K for three hours. The needle valve was carefully opened to admit air while the pump was still running. We set the pressure to approximately 1 micron 700°K. The annealing took about 70 hours. After the annealing the furnace was turned off and the copper allowed to cool inside the furnace. The copper sample was the central section of the annealed copper wire. The residual resistance ratio - RRR = R(300°K)/R(4.2°K) - was 265. The silver sample was made from Cominco 6N silver. The silver was cleaned carefully. They were etched in a mixed solution of NH OH and H202 (approximately 3:1) for 10 minutes, 4 and soaked in HNO3 solution for a half hour to remove any bare metal contaminant. The silver shots were melted in a graphite mold to form a silver rod. The silver rod was 47 rolled down to 1 mm wire with a rolling mill. This wire was then drawn to 0.26 mm diameter through tungsten carbide dies and diamond dies. For the oxidizing annealing we used the same procedure for the copper sample. The pressure was 10 microns and the temperature was 650°C. After 70 hours we found its RRR was 500. Pure gold wire came from Wesgo Company. It was 0.20 mm in diameter and 5N in purity. We annealed the gold wire at atmospheric pressure at 600°K for 48 hours. The RRR was also 500 for the gold sample. A summary of the characteristics of these samples is shown in Table 4.1. 2.2 Thermopowers in Transverse Magnetic Fields A zero applied field measurement, AS(0,T), gives a check on the homogeneity of sample. We found that the thermopower due to inhomogeneity was less than 0.05 uV/°K for all three samples. Measurements of AS(H,T) were then performed in magnetic fields. The results of AS(H,T) are shown as a function of temperature for a sequence of fields in Fig. 4.2. For a given field there is a peak in the AS(H,T) versus temperature curve. The peak temperature is found to be closely related to Debye temperature, 6 , of the noble D metals. For all three metals the peak occurs at T/eD ~ 0.07. 48 .Hn on .un m .Hn we .Hn on .Hn on Imemmn Hoocnn Hen yea am HH< one son one an Esoom> Hoocnd oo>eooou mm do em 0 com com omo con ooom oovm coma com com mom mmm mm.o Hm.o mm.o om.o mm.o mH.o Asa any anew monEmm mo moeumeuouoonono one H.v manoe. ooneaou ESHUEH nnoo ocsEmHm ommoz oocHEou nooaom oouoom he cH am so m< DU oemfimm Fig. 49 l5'—*'—1"'-"1 “I “1‘ . b Cu I ~ A ,e ~ r "/ [f .5 p— ,I/ ‘/g —I / ti “—4 .l__1-___,n_ ..-fl x: _ O \. > a. J U) <1 I l O 20 4O 60 8O IOO TEMP. (°K) 4.2 The A S(H,T) of the Noble Metals. Fields: a=48kG; b=35kG; c=26kG; d=17.4kG; e=8.7kG; f=4.4kG; g=l.7kG 50 The peaks shift slowly to higher temperature with increasing field. The size of the peak increases monotonically with applied field H . In the high field range the peak size is comparable to the phonon drag contribution to the zero field thermopower. To see the behavior of the thermopower in magnetic fields we add AS(H,T) to the zero field thermopower. The results of S(H,T) as a function of temperature are shown in Fig. 4.3. The zero field thermOpower of copper below 20°K is taken from sample #1 of Gold g£_gl.26. Above 30°K, they are taken from the 'special' copper sample of Henry and Schroeder27. The zero field thermopowers of oxidized silver and gold are from Pearsonza. Below 12°K, the thermopower is an extrapolation to the result of Anderson and Nielsenzg. The low temperature thermOpowers of the noble metals are ‘extremely sensitive to iron contamination. The data we used are from experiments where such effects have been minimized. We have also oxidized our sample to remove the magnetic impurities?8 Had iron contamination been important in the samples an additional characteristic field dependence, typical of a Kondo alloy, would have been present at the lowest temperaturezz. The absence of any such anomaly is good evidence for the efficacity of our oxidation pro- cedures. From Fig. 4.3, it is clear that the zero field thermo- power has been enhanced. The new peak is at lower tempera- ture, and moves toward the zero field peak temperature with 51 (uV/°K) S OO 20 4O 60 80 IOO TEMP. (°K) Fig. 4.3 The Thermopower of the Noble Metals in Magnetic Fields 52 increasing field for high fields. The Magnetic Field dependence of AS(H,T) is shown in Fig. 4.4. Each curve represents a typical dependence. At low temperatures, below the peak temperature, the thermo- power tends to saturate as the field is increased. A -1inear behavior is seen in the high field region above the peak temperature. In the temperature range where saturation is approached the thermopowers are enhanced several times in magnitude. Table 4.2 gives the values of S(48 kG)/S(0), the ratio of the thermopowers at 48 kG and at the zero field. 3. Aluminum, Indium and Lead 3.1 Sample Preparation The aluminum sample was obtained from Sigmund Cohn Corporation. It was 0.40 mm in diameter and 5N in purity. We drew it down to .26 mm in diamond dies. The sample was carefully cleaned before annealing. The oxidizing anneal- ing was done on the sample in So vacuum at 500°C for about 3 hours. The RRR was 1300. The indium wire was purchased from the Indium Corporation of America. It was 0.51 mm in diameter and 5N in purity. The RRR of the indium sample was 5400. The total length of the sample was about 2.5 m. The extra length was used for increasing the length in the temperature 53 H.m m.m m.m s.m m.s H.m o.s m.m m.v «.4 e.m o.m meow mmmmmm mmmmmm on we om Anmouw on we nev noom no mo me Mo on no G ousuouomsoe manna: manoz one no“ Ae.ovm\xe.mem mo mosnm> one N.v oanme (pNV°K) AS(H,T) Fig. l5 1* I I I IO*- Cu 20°K ‘ .5 r- - _ IO°K o l i l L _ lEi‘K _ 20 Ag L5 - - LO r - 8°KL .5 ' ‘ o l L 1 1 to - Au |2°K ~ 9°K .5 - 4 O 1 L L l 0 IO 20 3O 40 50 H (k6) 4.4 The Magnetic Field Dependence of the A S(H,T) of the Noble Metals 55 gradient so as to reduce the heat leak through the sample. We let the sample set on the apparatus after mounting for three days. The indium sample was therefore annealed at room temperature for 3 days. The 69 grade polycrystalline lead wire was obtained from Cominco Incorporated. It was 0.25 mm diameter. Its RRR was about 6000. The resistance at 4.2°K was obtained from the extrapolation of magnetoresistance measurements at 4.2°K. Since the lead sample had a high thermal con- ductivity, we increased the length of the sample to reduce the heat flow through the sample. The portion of the sample in the temperature gradient was about 80 cm long 3.2 Thermopowers in Transverse Magnetic Fields The aluminum sample had very good homogeneity; itS' thermopower in zero field was less than 0.01 uV/°K. The results of AS(H,T) are very interesting. Figure 4.5 shows AS(H,T) as a function of temperature in three measured fields. Two points on this figure are particularly notable. First, the peak of AS(H,T) versus temperature curve is negative in contrast to the positive peak of the noble metals. As in the noble metals, the peak temperature is also approxi- mately at T/eD = 0.07, and moves to higher temperature with increasing magnetic field. Below the peak temperature the magnetic field dependence of AS(H,T) tends to saturate. Second, AS(H,T) changes sign at approximately 12°K for all 56 3‘ ‘2'0’ 47.8 kG ‘ > 5} Al "-5* . . 26.IkG * 4 » I ’. <1 -I.O~ / I ~05» < 0.0. 1 . ..r/ o to 26 3‘0 40 5‘0 60 TEMP. (°K) Fig. 4.5 The A S(H,T) of Aluminum BI xhw i: 57 measured fields. This portion is enlarged in Fig. 4.6. The AS(H,T) as a function of field is shown in Fig. 4.7. Below 12°K, AS(H,T) has a strong tendency to saturation. The zero field thermOpower of aluminum is taken from Huebener30 and added to the change due to the field. The results are shown in Fig. 4.8. A sign change, at low temperatures, due to the magnetic field is clearly demon- strated. This behavior is in good agreement with results of Averback gt al.4'5. At higher temperature, it seems that the phonon drag thermopower is also enhanced in magnitude by applied magnetic fields. The enhancement seems to create a new peak in the AS(H,T) temperature curve. Indium has an electronic structure similar to that of aluminum, but their zero field thermOpowers are quite different. Our measurement shows that AS(H,T) of indium is negative and no sign change is seen down to 4.2°K. The result of AS(H,T) is shown in Fig. 4.9. Again, a peak is shown in this AS(H,T) versus temperature curve. Its behavior is also similar to that of aluminum and the noble metals. The peak temperature is again about at 0.07 0 . The magnetic field dependence of AS(H,T) for indium is shown in Fig. 4.10. The zero field thermopower of indium is shown in Fig. 4.11. Our result has a slightly smaller peak than that reported by Bosacchi and Huebener3l. Never- theless, the strong negative AS(H,T) reduces the peak as much as 30% at 48 kG, and turns the thermopower below l9°K 58 .2 I I I 1 48kG f I 26 k6 2 ,I L 8.7 kG ._ O 3 L7 kG 1 {i C) ...; ’13.. I ‘2 _| Al ...2 l I l l 4 6 8 IO l2 l4 T (°K) Fig. 4.6 The Sign Change in the A S(H,T) of Aluminum S9 Sufigam mo 3..me q 0:» mo mocmocmmwo cam“; canon—mm: one 56 .mfim 8.: I on ov on ow o. o~.o fowl. . 0.0 i . .. r Xom_u._v 00 D [AV 0 _< v 404' XoNNuF SV (>1./N’) 6O I 1 I I I I T T .5” ‘ o > 3 -l r- u m + . -2» .1 -3. ZGIG - 48kG 1 L l l L I l L O 20 4O 60 80 IOO TEMP. (°K) Fig. 4.8 The ThermOpower of Aluminum in Magnetic Fields 61 EdwocH mo A9.mvm < 0:9 m4. .3... 62 .5505” no 3..me < m3» m0 mocmvcmmmo pamwm owumcmmz one 6.: I on 0... pa? ow o. XoON oaé omflh . 63 0% b 40 so so T (°K) A-Orfl' ‘ ‘ i In > .3- -|.O¥‘ ‘ m D -|.5r * -———I7 k6 The.Therm0power of Indium in Fig. 4.11 Magnetic Fields 64 negative. A negative peak is formed in the AS(H,T) versus temperature curve at approximately 8°K. This peak tempera- ture moves toward lower temperature with decreasing field. Pure lead goes superconducting at 7.2°K. The critical temperature moves to lower temperature when a magnetic field is present. In most of our AS(H,T) measurements there is a finite fringing field in the top section of the sample. At high fields, the fringing field is sufficiently large so that the entire sample is normal. However, as the field decreases the portion of the sample in the fringing field will become superconducting and its thermo- power will drop to zero discontinuously. In the computer analysis of the data these two regions must be handled separately. The result of AS(H,T) versus temperature is shown in Fig. 4.12. The discontinuity of the curves is due to the superconducting transition at 7.2°K. If we plot S(H,T), using the zero-field thermOpower as deter- mined by Christian 32 al.32, we obtain a well-defined peak which again occurs at about T ~ 0.07 0D . This peak also has similar properties to those of aluminum and indium. The magnetic field dependence of AS(H,T) is shown in Fig. 4.14. 65 wmmn Ho AB.mvm< man. ~H.¢ .mnm l m..- 0.... V S (mm’) 66 oaumcmmz CH pmmq mo moamflm Hmsomoaumna one ma.v omnflh l N._.. ov 67 puma mo Aa.mvm < on» no monopcmmmo pamflm oaumcmmz one ¢H.¢ .mflm on O? on ON 0. S 68 4, Summary on Experimental Results The thermopowers of polycrystalline copper, silver, gold, aluminum, indium and lead have been measured from 4.2°K to 100°K in transverse magnetic fields up to 48 kG. For a given field there is a peak in the change of thermo- power versus temperature curve. The peak has the following characteristics: (1) The peak occurs at a temperature between eD/ls and eD/12, where 0D is the Debye temperature of the metal. (2) The peak temperature shifts to higher temperature when the applied field is increased. The shift is about 2 to 5°K as the field increases from 0.87 kG to 48 kG. (3) The peak appears approximately where wt ~ 1 , where w is the cyclotron frequency and T is the relaxation time. (4) The size of the peak increases monotonically with increasing field. The increment is greatest on the high temperature side of the peak, but the half widths of the peak has only a small variation. (5) The peak can apparently be significantly depressed by alloying with a small amount of non-magnetic impurities, for example, Au in Ag. (See Fig. 3.4) (6) The sign of the peak can be either positive or negative. For these six metals the peak has the same sign as the phonon-drag thermOpower except in indium. 69 Ha om ma ha mm 0x mvum Ae.mvm< mo xmma om mm mm om mm Nb 0" xmmm Clog: moa moa mmv mod mmm mvm no .mEmB chemo am 2H ad :4 m4 90 mamumz ox we mo pom pamflm oumN mo mousumquEmB xwmm Hm3OQOEHm£B m.v magma 70 The experimental AS(H,T) values have the following properties: (1) At low temperatures, below the peak, AS(H,T) always tends to saturate at high fields. (2) At low temperatures the temperature dependence of AS(H,T) is not linear but between quadratic and cubic. (3) In the region where AS(H,T) saturates, the values of AS(H,T) are several times the zero field thermopower. (4) In a given field AS(H,T) decreases approximately exponentially at high temperatures. (5) The AS(H,T) of aluminum shows a sign change at 12°K. The cross-over points of AS(H,T) versus temperature curves appears independent of the magnetic field. CHAPTER V THERMOELECTRIC THEORY IN A MAGNETIC FIELD 1. Introduction Early in the 1940's, thermoelectric effects in magnetic fields were studied by Sondheimer and Wilson33’34. They proposed a quasi-free electron model, and extended the model from one conduction band to two conduction bands. In experiments on sodium MacDonald and Pearson3 found that the one band quasi-free electron model did not predict the correct change of thermopower in a magnetic field. The two-band model is more sophisticated and has more flexi- bility to account for the observed data, but one must realize that Sondheimer's expression was derived for two spherical energy bands, and was valid only if the field was transverse to the temperature gradient. In a longitudinal field this calculation yielded no field dependence of transport properties. Nevertheless, the two-band concept is very useful if the two-band parameters can be properly defined and if one avoids longitudinal effects. Later in 1956 Lifshitz, Azbel and Kaganov35'36 suggested a semiclassical theory to explain the magnetoresistance in metals. Bychkov, Gurevich and Nedlin37 applied the theory to calculate the electron-diffusion thermopower. Gurevich and 38 Nedlin and Lang and Pavlov39 calculated the phonon-drag 71 72 thermopower. This semiclassical theory required the solution of the Boltzmann equations for electrons and for phonons, and is applicable only in the high field limit. Gurevich and 38 Nedlin predicted a linear magnetic field dependence of AS(H,T), which disagrees with our observation. Averback and Wagner40 extending the work of Bychkov, Gurevich and Nedlin37 obtained an analytic form of the electron-diffusion thermo- power. A review of the electron-diffusion thermopower based on the semiclassical theory is given by Abrikosov41. Since the existing theories have limited ability to explain the experimental results, we shall try to develop a theory which is able to cover the observations. In this chapter we will present two theoretical models: (1) the electron-diffusion model and (2) the phonon-drag model. Both models are able to account for most experimental features and also are very simple. We shall discuss these models in detail. We shall not discuss the zero field thermopower except where it is necessary for understanding our theory. There are excellent surveys on this subject given by MacDonald42, Huebener43, and Barnards. The general transport theory can be found in many solid state theory books. Quantum oscillation effects are ignored here, since we are dealing with polycrystalline samples at high tempera- 44,45 tures. Those quantum theories are able to give a successful prediction of the frequency of oscillation of thermopower in magnetic field, but not of the amplitude. 73 2. The Electron-Diffusion Model We assume that the experimental conditions are such that the measurements yield the adiabatic thermoelectric power, i.e. we take field fi = (0,0,H), heat current 6 = (Q,0,0) and electrical current 3 = 0. We also consider only isotropic conductors. The thermopower is then given by33 (VT) S = S + S d xx xy (VT)X (5'1) where Sij are the components of the isothermal thermo- electric power tensor, (VT)i are the components of the tempera- ture gradient. From the thermal conductivity tensor we also obtain m, Exes (VT = "' K (5‘2) x W where Kij are the components of thermal conductivity. We now assume that S is given by the Mott relation46. _ Bing 61“ Here e is the electron charge, a is the electrical con- ductivity, e is Fermi energy and L0 is Lorentz number. F If we further assume the validity of the Wiedemann-Franz law, then with the aid of Eqs. 5.1 and 5.2 we arrive at the 74 result of Averbach gt al.5 Sd = o eLOT [(gg')XX - (gg')xy (315)] xx 8 F (5.4) where the primes denote differentiation with respect to energy 8. We now rewrite Eq. 5.4 in terms of the resistivity tensor. We make use of the following relations "‘0 II 0 II II Q "'0 ll ‘ lro IIQ l I "D II Q In our case (isotrOpic conductors) we have 0‘1 2 = '02 o where ‘31 = 2 C’1 O .15 = - 0' 0 p1 O ' g = —pz 03 0 D — -02 ' 2 _ 2 2 01 02 .. 325 pxx (5.5) (5.6) (5.7) Hence 75 O . _ . x eLoTIxx <22 >xy (af;>1€ F . . 325 -eLOT[(g g)xx + (2 g)xy (pxx)]€ F —eL OT{(-;;)[(2 2’xxp xx (p g)xyp yxl}E 8F -eL THl—Hm'og) 1} O pxx _ =_ XX 8 F -eLOT( XX) XX EZF 82.anx -eLOT( Be ) (5.8) 8F Thus we regain an expression analogous to the Mott formula, where p xx in the transverse magnetic field. power due to the magnetic field, AS (H,T) is the diagonal component of the resistivity tensor The change in the thermo- = Sd(H,T) - Sd(0,T) can now be expressed in terms of the magnetoresistance ratio as o (H) - o (0) xx (07x as follows 0 X o' (H) p' (0) AS (H,T) = eLo T [——35-’3——-— - L] x(H) xx(0) 3}? o'xx(H) oxx(H) [WWW] 8F = eL T[(ADLD 4' 1).] Ap/p + 1 SF 76 Finally, we have (A ) 1+ Ap p 8 Ap 8F AS(H,T) = -eLOT [ The above equation is derived for the transverse field but it is also valid in longitudinal fields. Equation 5.9 is valid provided the Wiedemann-Franz law and the Mott relation hold. To proceed further it is necessary to employ some model from which the logarithmic derivative of the magnetoresistance ratio can be derived. However, even without the use of such a specific model, some fairly interesting general conclusions can be obtained from Eq. 5.9 provided Kohler's rule46, namely 9% = f(H/p,e) is applicable. We then have .. _1 _ 3f a a__ a: AS(H,T) - eLoT {1+f [ m D as lnp + 38]: (5.10) F Since S(O,T) = -eLoT (2%22) , it follows that Eq. 519 and 6F Kohler's rule lead to a Kohler-like relation for AS(H,T), namely [S(H,T) = g(S(0,T), H/p) (5-11) Without invoking a specific model from which the Kohler function f(H/p) could be evaluated, we can still make further progress in establishing certain general behavior patterns for AS(H,T). We consider three commonly encountered 77 situations; an uncompensated metal without open orbits, for which the magnetoresistance saturates; a compensated metal, for which the magnetoresistance does not saturate; and an uncompensated metal with open orbits, for which the magnetoresistance also fails to saturate. Since, for our purposes the cause for non-saturation and the functional relationship between Ap/p and H is not critical, we divide our discussion into consideration of two cases. Case (a). Metals whose magnetoresistance saturates at high fields. Case (b). Metals whose magnetoresistance fails to saturate at high fields; we assume that in the high field limit Ap/p = A(H/p)8. Let us, for convenience, assume that the magneto- resistance is given by an expression of the form47, B a = M (5.12) where A and B are constants which are independent of tempera- ture and magnetic field, but they are energy dependent. B is a numerical constant. Cases (a) and (b) are distinguished formally by the condition B # 0 for case (a) and B = 0 for case (b). In the high field limit, Eq. (5.12) shows the saturation. a = A/B (5.13) CD 78 In the low field limit, we have do = A(H/p)B (5.14) It is easy to show the following relations Bindo = aznA _ Baznp 38 as 38 (5.15) 32nda>u 3£n(A/B) 36 36 Thus, at high fields, Eq. 5.9 becomes 32nd co AS(H,T) = -eLO T {— [(1- ——)(3§nA - Bagnp) + §"(“§E“)]} l+d e F (5.16) At very low temperatures where electron scattering is elastic this equation is equivalent to the formula derived by Averback and Wagner40. For a metal whose magnetoresistance fails to saturate the Eq. 5.16 should be written as BQnA 3£n0)} l+a ( Be -8 38 (5'17) AS(H,T) = -eLO T { 6F For both cases (a) and (b) the temperature and magnetic field dependence of AS(H,T) will be determined in large measure by the "enve10pe function" F. F = T (—2— (5.18) 79 A typical F is shown in Fig. 5.1. At a sufficiently high magnetic field and in a pure metal, a > 1 at low temperature and decreases toward zero with increasing temperature. Consequently, the envelope function for a pure metal will increase approximately linearly with temperature at low temperatures and high fields, and it will diminish to zero as the resistivity increases with temperature. It forms a peak whose shape is determined by the form of the temperature dependence of the resistivity and the form of the Kohler function. We note that regardless of the behavior of the magneto- resistance, saturation or failure to saturate, the thermopower always saturates at high magnetic fields. This general result from Eq. 5.16 of the model appears to be obeyed in those metals which have been investigated experimentally. The saturation value of AS(H,T) is, however, different for the cases (a) and (b), which we shall now examine separately. The two terms inside the square bracket of Eq. 5.16 are dominant at opposite extremes. At a fixed high field (1 - a/am) increases from zero to unity with increasing tem- perature while a/a0° decreases from unity to zero. Hence, 32nd . 3£nA _ 3£np w . . 1f ( as B_§E_)e and ( Be gFare of OppOSlte Sign, as may F well be the case, Eq. 5.16 predicts a change in sign of the magnetothermopower as the temperature is changed. At an "infinite" field, i.e. in the high field limit and fixed 80 4 I T r r /"\ / \ ' d / \b ./ / \ / l \ /- 3.. / . __ / \\ ./ j , \ ./ / a ‘ -/ b X / ' \ g; 2 — / \ ..J 5 I c / \ . I . \ ‘3. I ./ \ < / / \ V l ' \ I .// \ " I ./ \ " I ./ \\ I I / \\ , _/ \\ I/ ‘~~i__ 0! l 1 _ ....___.__ _ o 20 40 so so IOO T (°K) Fig. 5.1 A Typical Magnetoresistance Results (a, b, c) and the Envelope Function ( b', which is Calculated from b) for the Electron-Diffusion Model 81 temperature, the saturation value is given by Binam 35 ) (5.19) 8F AS(w,T) = -eLOT ( Since we assume that the constants A and B in Eq. 5.12 are independent of temperature, it follows from Eq. 5.19 that the saturation value of AS(H,T)/T is also temperature inde- 8£na pendent. Indeed this parameter ( as ) can be determined 6F experimentally from the high field limit of AS(H,T). More- over, since Eq. 5.19 does not involve the derivative of the zero-field resistivity explicitly, the saturation value of AS(H,T)/T is not only independent of temperature but also independent of composition for alloys for which Kohler's rule remains valid. Turning now to the low field and low temperature region we have remarked on the possibility that AS(H,T) may reverse sign with increasing temperature for a fixed value of field. In Eq. 5.16 the parameter (aggA -8 3%23) can be determined 5 F experimentally, for example, the value of magnetoresistance at that temperature and field for which AS(H,T) = 0, where (1 - a/am)(8 aggp — 3§§A) = <§—)(3%§ (5.20) EF EF Qualitatively, we would then expect that the temperatures at which AS(H,T) = 0 will shift to higher values with increasing 82 field. Of course, Eq. 5.20 is a consequence of assuming Eq. 5.12 for Kohler's rule. In contrast with the situation that pertains when the magnetoresistance saturates, the behavior of AS(H,T) in case (b) is significantly different. In this case the saturation value is given by m _ _ 8£nA _ 3£np ) (5.21) SF We find that the saturation value of magnetothermopower should depend on (§%%2) , i.e. on the zero field diffusion thermopower. This means? first, that even in a pure metal AS(®,T)/T may now depend on temperature eSpecially in the temperature range in which the electron relaxation time changes from being dominated by impurity-electron to phonon-electron scattering. The value of (§%%E) changes from-l/ZeF to -3/2aF in the free electron model?F Second, since the diffusion thermopower at zero field depends sensitively on alloying, AS(w,T)/T should also depend on alloying provided Kohler's rule remains valid. However, the temperature dependence of AS(H,T) becomes simpler. There is only one constant to be determined, and presumably no change of sign in AS(H,T) occurs. 83 3. Phonon-Drag Model Consider a conductor with a temperature gradient along the x-direction. The non-equilibrium phonon system will create a phonon flux flowing from the high temperature and to the low temperature end of the conductor. These phonons will interact with all other particles, such as electrons, impurities, defects and also other phonons. At high temperatures the phonon-phonon interactions are strong so that the phonon system maintains itself near equilibrium. When the temperature is reduced the phonon-phonon interaction become less important. The phonons now start to transfer their momentum into the electron system via the electron-phonon interaction. In other words, the phonon flux drags the electrons to the cold end of the conductor. This extra force produces the phonon drag thermOpower. The theory of phonon-drag thermopower in the absence of a magnetic field has been developed by Bailyn48. The phonon-drag thermOpower Sg(0,T) is given by K% e22 Tv-w[-8fo/Be] e geZZTvzl-BfO/Be] Sg(O,T) = - (5.22) D) where K is the thermal conductivity, e is the charge of electron, T is the electron relaxation time. v(k£) is the velocity of electron in wave vector k and band 2, f0 is the Fermi function of the electrons, and 84 w(k£) = (afO/ae)’l Z [p(jq;k£,k'2')+p(jq;k'2',kfi)] k'IL' (5.23) x [3N0(jq)/3kT]v(jq) in which No(jq) is the equilibrium distribution of phonons of wave vector q and polarization j. p(jq;k£,k'£') is the relative probability that the jq phonon will engage in the interaction that sends the electron state from k2 to k'fi'. For low temperatures, using a free electron model the above equation gives a simple result for temperature dependence of Sg(O,T), namely 3 Sg(0,T) « T (5.24) The contribution of the phonon-drag thermopower, therefore, can be identified from the temperature dependence. In the real metals the phonon drag thermOpower can be either positive or negative. This is due to the existence of Umklapp processes. In normal processes we have while in Umklapp processes we have k + q = k' + g (5.26) where k and k' are the wave vector of the electron before and after scattering, and g is a reciprocal lattice vector. 85 Umklapp scattering generally reverses the velocity of the electron and therefore gives a positive contribution to the phonon drag thermopower49. Based on the above picture, the probability P(q) contains two parts, i.e. P(q) = PN(q) + PU(q) (5.27) where the subscripts N and U refer to the normal processes and the Umklapp processes, respectively. In the case of a nobel metal, we may assume a finite probability PU(q) which gives the positive component of the thermopower. This positive component is so large that it exceeds the negative component and gives a positive phonon-drag thermopower. The major part of the PU(q) comes from the neck region of the Fermi surface. If we assume that electron-phonon scattering processes are not affected by a magnetic field, the redistribution of electron states on the Fermi surface due to the field may play an important role in the observed effects. In the following we shall examine the distribution of electrons on the Fermi surface before and after the field is present. Let us consider the Fermi sphere shown in Fig. 5.250'51. In the absence of the field the electrons are distributed around the Sphere, statically. An electron remains in its position until it is scattered by phonons or other quasi-particles. After the scattering the electron occupies Fig. 5.2 The Fermi Surface of COpper and the Influence of a Magnetic Field 87 a new position on the Fermi sphere and stays there until the next scattering occurs. The scattering processes involve both normal processes and Umklapp processes whose ratio depends on g, k, and temperature. Now we turn on the magnetic field. The field results in a Lorentz force acting on the electrons, and also on the ions. It is easy to show that the Lorentz force on the ions is small compared to the nearest neighbor interaction between ions. For the field we used, the ratio is of the order of 10-4. Therefore, the phonon system is not affected by the magnetic field. However, the electron is affected by the field. Its wave vector k is changed according to Mk = (e/c). v x H (5.28) Since the Lorentz force is always perpendicular to the velo- ‘city‘vector v, this motion is limited to the constant energy surface normal to H. The magnetic field sweeps an electron on the Fermi surface around the Fermi sphere about an axis parallel to the field. In other words, the picture of the model will be: the electron on the Fermi sphere will travel in an orbit around the Fermi sphere, driven by the Lorentz force, until it is scattered. After the scattering the electron changes to another point on the Fermi sphere, start its journey again until it is scattered again. As we have seen in the Fig. 5.2 the Fermi surface of COpper is not a perfect sphere. The electron will travel 88 through the area where the scattering probability and the relaxation time is different. The fact that some electrons must pass through both the neck region where the Umklapp scattering dominates and the belly region where the normal scattering dominates must be taken into consideration. To proceed further, we divide the orbits on the Fermi surface into two classes: (a) orbits that intersect a neck, and (b) orbits that do not intersect a neck. As shown in Fig. 5.2 the cases (a) and (b) are not a single orbit but a wide band. We shall call them the neck band and belly band, respectively. The properties of a neck region (for copper a neck region including a neck of about 20° angular radius and the shoulder area) are: the relaxation time for the electron-phonon scattering is short52 with a large probability for Umklapp scattering, which is responsible for the positive component, 83, of the phonon drag thermopower in zero field49. Contrariwise, the properties of the belly region are: the relaxation time for the electron-phonon scattering is longer with a large probability for normal scattering which is the source of negative component, 5:, of the phonon drag thermopower. For electrons in the belly bands the magnetic field does not have significant influence in the electron-phonon scattering. The contrary is true in the neck bands. The magnetic field sweeps electrons from the belly region to the neck region and vice versa. This concept was first 89 suggested by Pippard51. We now examine the motion of the electrons on the Fermi sphere. Halse53 reviewed the Fermi velocity of COpper. The contours of Fermi velocity for COpper is shown in Fig. 5.3. We see that the Fermi velocity is smaller near the neak region than the bellies. For a given magnetic field, the sweeping rate is smaller in the neck region than in the belly region. In other words, the electrons will tend to stay in the neck region longer than in the belly region. Thus, the electrons will be easy to be scattered when they are traversing the neck region, due to a short relaxation time associated with the neck region. The contrary is true for the electrons traversing the belly region. We then expect that the chance of an electron to be scattered in the neck region is higher than in the belly region during its journey. As we remark before, there is a large probability for Umklapp scattering in the neck region. Because of the large probability of scattering at the neck region the electron distribution will be comparatively close to the equilibrium distribution fO even in the absence of a magnetic field. On the other hand the distri- bution of electrons on the bellies will be considerably different from fo , since there few interactions tending to restore equilibrium on the belly. Now if we apply a magnetic filed, because of the above mechanisms, electrons entering the neck region from bellies will tend to rapidly come to Fig. 5.3 (16 9O 3 “:TM mm am am mm mm mm mm m1 1’ an :éégb om // [111] am [110] Contours of Fermi Velocity (Expressed in the Unit of the Fermi Velocity of Free Electron) for COpper 91 the local neck equilibrium. Meanwhile, electrons moving from neck to belly will tend to carry with them the neck distribution, since the scattering necessary to restore local equilibrium is small on the bellies. Thus the simultaneous application of both temperature gradient and magnetic field produces a different distribution of electrons from that where the temperature gradient acts alone. Returning now to our hypothesis on page 85 that electron-phonon scattering processes are not affect by the magnetic field, and that the redistribution of electron states in the Fermi surface may play an important role, we see now how such a redistribution can take place. The redistribution will affect both the electron diffusion thermOpower and phonon drag thermOpower, and it is not obvious how these would be separated. Another picture is as follows. Again we assume that the phonon electron interaction is indepedent of magnetic field, but the phonon drag thermopower does depend on what happens to the electrons before and after the inter- action. This is the idea behind the theory of Bailyn and Dugdale48 whereby Sg can be split into i components Si , corresponding with groups of similar carriers. If 0. is 1 the corresponding electrical conductivity, then _ i s — Z 3— s. (5.29) 1 T 92 where CT is the total conductivity. Where Si are con- sidered independent of field, Oi are field dependent. Hence the contribution to 89 from the ith region can be profoundly modified by the magnetic field. In the case of COpper, the relevant regions would seem to be those belly regions containing no orbits intercepting the necks (OBSB), the belly band, and those regions of the Fermi surface containing orbits which do intercept the necks (oNSN), the neck band. It is reasonably certain that OB and ON will vary differently on applying a field and thus affecting the contributions from the two regions. In the case of aluminum, the relevant regions would be the second and the third band of the Fermi surface. We meight expect the effect of the magnetic field 51 has should saturate when wt ~ 1 although as Pippard shown, true saturation does not set in until wt >> 1 (about wT ~ 10) When wT ~ 1 , an electron is able to make a complete trip around the Fermi surface. For still higher fields, the effect of the sweeping the elec- trons reaches its limit. Therefore, we expect that the magnetothermOpower will saturate in high fields. Since the orbit of the electrons is determined by the direction of the magnetic field we meight also expect the field effect on the thermOpower to be anisotrOpic. Other factors such as alloying which change zero-field phonon-drag ther- mOpower could also affect the magnetothermOpower. CHAPTER VI DISCUSSION AND CONCLUSION 1. Comparison with Experiments The two theoretical models presented in the last chapter will now be compared with the experimental results. We shall determine the parameters of the electron-diffusion model and make a quantitative comparison with the observed values. No quantitative comparison is made on the phonon- drag model. A qualitative comparison between the experi- mental results and the phonon-drag model is given in Table 6.1. The comparison shall center on the two repre- sentative metals: COpper and aluminum. The results for the rest of metals follows a pattern similar to that which we will see in the copper and aluminum. Since the transverse magnetoresistance of COpper does not saturate, the electron-diffusion model gives the following formula for computing the AS(H,T). — — —G-—— AS(H,T) — eLOT (1+a) D (6.1) where _ 3£nA _ 3£np 6F We assume that the phonon-drag thermOpower is uninfluenced by the magnetic field. This assumption was also adapted by 93 94 MacDonald3. In obtaining a "theoretical curve" the para- meter D was normalized to the magnitude of the peak of the measured AS(H,T) for H = 48 kG. From AS(H,T) at H = 48 kG and T = 30°K we obtained D = 21.4/5F . Using this D value and the measured data of a we calculated AS(H,T) as a function of temperature at different fields. The results of the calculation (dashed curves) are shown in Fig. (6.1) tOgether with experimental results (solid curves). The agreement between the experimental and calculated curves is remarkably good in view of the crudeness of the model and the many assumptions we have made. In particular the following qualitative features of the experimental data are reproduced by the calculated curves. (a) AS(H,T) for a given H increases with increasing temperature at low temperatures, reaches a peak and there- after falls off. The temperature of the peak is in the neighborhood of 30°K. (b) At any temperature AS(H,T) is a monotonically increasing function of magnetic field. (c) At sufficiently low temperatures and high magnetic fields the thermopower exhibits a well defined saturation even though the magnetoresistance fails to saturation. (d) The temperature at which the peak in AS(H,T) appears shifts toward high values with increasing field. The close agreement between the experimental and calculated curves suggests that, within the limits of our model, the (IdV/l() AS(H,T) Fig. |.5 I!) 95 1 I T T 48 k6 I ‘\ I \ \ 35kg“, \\ \\ COPPER I \ \ I \ \ I \ \ II \ \ -4 II \ \ ll \ \ I, \\ \\ I, ‘ \\ [I \ \ 6.1 Calculated (Dashed Curves) and Experimental (Solid Curves) Results of A S(H,T) of COpper as a Function of Temperature at Three Field Values 96 parameter D is not a sensitive function of magnetic field. However, the value of D is unphysically large, i.e. implies an energy dependence of a more than one order of magnitude greater than (éégfl) . Also, the parameter D is tempera- ture dependent. 54’55 considered the Recently, Nielsen and Taylor Sd(0,T) term by taking into account the second order effect of intrinsic two phonon processes in the electron-phonon interaction. They found that the Sd(0,T) should contain a non-linear contribution. Rosler56 performed a variational calculation and gave a similar prediction for alkali metals. In other words, a term which is similar to the phonon drag term may be included in the electron-diffusion thermOpower- If we denote the linear term of Sd(0,T) as de(0,T), then where Sdg(0,T) is the contribution to the electron-diffusion thermopower from the Nielsen-Taylor calculation. Although GuenaultS7 argued that the Sdg(0,T) is negligible at very low temperatures we shall not ignore the possible contribu- tion from this effect, especially when the temperature is higher. Sdg(0,T) has a T3-temperature dependence at low temperatures, which is similar to the zero-field phonon drag thermOpower. If we include the Nielsen-Taylor term into our electron-diffusion model, the temperature dependence and the 97 magnitude of the parameter D may be justified. Moreover, the non-linear temperature dependence of AS(H,T) at low temperatures can also be understood. To calculate AS(H,T) for aluminum, an uncompensated metal, the electron-diffusion model provided the formula _ _ a E_ AS(H,T) — eLOT (1+a) (c1+c2 am)€ (6.4) F = BRnA _ alnp where Cl ( Be 8 36 )e (6.5) F Bindm and C2 = ( Be )6F - Cl (6.6) The magnetoresistance of aluminum saturates at moderate high fields, but Kohler's rule fails to be obeyed at very high fieldssa. We find that a of aluminum exhibits a large anomaly near 20-30°K59. In order to proceed with the calcula- tions we assumed Kohler's rule is obeyed by the magneto- resistance of aluminum. We made a crude extrapolation of the low field magnetoresistance to obtain the high field limit a0° . There are two parameters to be determined. First, the ratio Cl/CZ is obtained from the temperature where the AS(H,T) changes sign. The magnitude of parameters Cl and C2 are normalized to the peak value of AS(H,T) at 26 kG. We find C1 = +49.6/eF and C2 together with the a from Kohler's plot were used to calcu- = -66.2/€F. This set of parameters late the AS(H,T). The results of the calculation (dashed curves) and observed data (solid surves) are shown in Fig. 6.2. 98 It is apparent that there are many differences between the calculated and the experimental curves, although some qualitative features are retained. (a) The cross-over point of AS(H,T) is shifted to higher temperature with increasing field, while the experi- mental data shows that it is nearly constant. (b) At the temperature below the peak of AS(H,T), the calculated values decrease rather than increase with increasing field. (c) The calculated peaks of AS(H,T) appear at tempera- tures substantially above those observed. Figure 6.2 also suggests that, the parameters C1 and C2 will depend strongly on the field and temperature. Also, we are aware that this set of parameters is unrealistically large. These discrepancies may be related to the failure of Kohler's rule and the assumption we have made on the para- meters. Despite the obvious inadequacy of the model in this case, some qualitative features are again reproduced. 2. Discussion and Conclusion We have presented two different models to explain the experimental results. The predictions of the models and the ' experimental facts are summarized in Table 6.1. A glance at table 6.1 shows that both theories are able to explain the general picture of the experimental results. However, some weaknesses do exist in the models. 99 .5 r l I l , \ ‘~\ 0 b '7 \ I x 1 r ’1...»- \\ \\ \ l’z’ \ \ \ II ’I \\ \‘\ / I,/ \ ./ \ ".5 b \ \ \ // III '4 \ \ / // ’1 Q \ ‘ I / l’ x a G ‘ ’ ’ / :’ 57k \ \ I I / ‘ \ \ \ I I ” ... _' _ \\ \ \’/ ,’ ll .4 \\_\ \ X, ”I A ‘ \ l/ I” (— 26kG ‘ \ ,1 x c- - Y I d (D \x ’/ q \ -2 _ 48H; '1 ALUMINUM -2.5 l:— ‘ l L ‘ O 20 4O 60 80 '00 T (K) Fig. 6.2 Calculated (Dashed Curves) and Experimental (Solid Curves) Results of I)S(H,T) of Aluminum as a Function of Temperature at Three Field Values 100 mooomma 02 wow wow I\+ wow wow wow wow muoomma manwmmom manflmmom mow I\+ manwmmom manfimmom mm» mow Hopoz monolcococm Hopoz comeMMHolcouuomHm mnasoaaa H< ca omcmao swam .mEoB 30a um AB.me< moonwalcoz madman roam um mopmusu6m AB.mvm< xmom mo swam xmmm mo onwm Hzes um xmmm .QETB god: 0» mumwam xwom xmom muHSmom Hmucoswummwm muHSmmm amucofiflnmmxm map can H0602 mmnolaocozm any .Hmpoz coflmSMMHoacoupomHm map cmmzuon somHummEoo one H.w OHOMB 101 First, we shall point out that the parameter D which gives Fig. 6.1 is too large (~ 20 times) compared to the free electron expectation. We shall now try to determine the parameter D in the free electron theory region. Con- sider the zero field thermopower, which contains two components, i.e. S(O,T) = Sd(0,T) + Sg(0,T) (6.7) At low temperatures we expect the following simple relation to hold S(O,T) = A(0)T + B(0)T3 (6.8) ‘where A(0) and 8(0) are constants. Equation (6.8) should be ‘valid in the temperature range where impurity scattering dominates. If we assume it holds also for the change of thermopower in a magnetic field, then S(H,T) = A(H) T + 3(a) T3 (6.9) and AS(H,T) = AA(H)T + AB(H) T3 (6.10) lBased on our resistivity data we assume Eq. (6.10) is good 11p to ll°K for both COpper and aluminum. Therefore, we may £3eparate low temperature AS(H,T) into the electron-diffusion 102 component and phonon-drag component according to Eq. 6.10. The analysis and the results of AA(H) and AB(H) are shown in Figs. 6.3 to 6.5 for COpper, and in Figs. 6.6 to 6.8 for aluminum. Now, if we require that the parameter D satisfies only the AA(H) term, the value of D will be 0.8/eF for copper. With the new value of D, the peak of AS(H,T) at 48 k6 is only 0.05 uV/°K. This is too small to account for the experimental results, and favors the phonon-drag model. In the case of aluminum, the electron diffusion term is positive, the same sign as in COpper, and there is no sign change. From Eq. 6.1, we can determine C at the high 1 field limit, and C2 from one other point. At H = 26 kG, we obtained C = 15.4/5F and C2 = 4.8/eF . The positive 1 diffusion component implies that there is a negative phonon-drag component in AS(H,T) for aluminum, even larger than the total observed change. Next, let us consider the phonon drag model based on the above discussion of the electron-diffusion model. The former model does not preclude the existence of the latter model. In fact, the co-existence of these two models explains the experimental result in aluminum much better than either one alone. For example, in the case of aluminum, the electronfdiffusion thermOpower gives a positive change and the phonon-drag thermopower gives a negative change in the field. At low temperature ASd(H,T) has T-dependence and ASg(H,T) has T3-dependence, so that ASd(H,T) is larger than 103 133 l l l 48 k0 35 no (7 to C U ‘ o .02 r- - A 0 e7 no N x a O \ > =L a o i. F- >1 1', 4.4 k6 55.0) ; 0) <1 (.7 k6 0 .87k6 I I C) l l L_ 0 I00 200 T2 (°K2) Fig. 6.3 The Separation of the T— and T3-Dependence of A S(H,T) for COpper 104 3 l l l I ;:‘ %fi—"”""—4>fl X °\ > ‘r 2" " 9 A Cu I I- - 2 I LO" ‘ 9 Cu 5 .5 F- ...( CD <1 0V 1 l 1 1 0 IO 20 30 4O 50 H (kG) Fig. 6.5 The A B(H) of COpper as a Function of Magnetic Field 106 04 1 1 I j‘ .03 '4 {.02 4 > f} *— >~ .0) .. "2 33 (I) <3 0 C Field: kG ° ".0! l l l _ O 5O (00 (50 200 T” (°K2) Fig. 6.6 The Separation of the T- and T3-Dependence of A S(H,T) for Aluminum 107 (Io'°VI°K‘) 01 I 1\ AI 0 Present Data l A Averback Al, - AA(H) O 1 1 1 1 0 IO 20 3O 4O 50 H ((16) Fig. 6.7 The A A(H) of Aluminum as a Function of Magnetic Field 108 O I r '2‘ ; OPresent 0010 o -| AAverback Ala " “e i _2 1 _ I 55 7 4 -25 1 l 1 l f 0 IO 20 30 4O 50 H (kG) Fig. 6.8 The A B(H) of Aluminum as a Function of Magnetic Field 109 ASg(H,T) and AS(H,T) is positive. With increasing temperature, Sg(H,T) increases faster than Sd(H,T) thus causing the sign S(H,T) to reverse at sufficiently high temperatures. Therefore, the sign change of the thermopower of aluminum in a magnetic field is a natural consequence of the competition between the positive change of electron-diffusion thermOpower and the negative change of phonon-drag thermopower in the presence of a magnetic field. This argument holds also for copper, except that here the change of phonon-drag thermOpower is now positive. In conclusion, we believe that the observed effect of the magnetic field on the thermOpower is due to the changes in electron-diffusion thermopower and in phonon-drag thermOpower. REFERENCES 10. 11. 12. REFERENCES F. J. Blatt, D. J. Flood, V. Rowe, P. A. Schroeder, and J. E. Cox, Phys. Rev. Lett., 18, 395 (1967). M. Bailyn, Phys. Rev., 126, 2040 (1962). D. K. C. MacDonald and W. B. Pearson, Proc. Roy. Soc., London, 5341, 257 (1957). R. S. Averback and J. Bass, Phys. Rev. Lett., 26, 882 (1971). R. S. Averback, C. H. Stephan and J. Bass, J. Low Temp. Phys., 13, 319 (1973). C. K. Chiang, Rev. Sci. Instru., Aug. 1974, (to be published). C. K. Chiang, "Reference Tables for Low-Temperature Thermocouples in Magnetic Fields", Department of Physics, Michigan State University (1974), (unpublished). R. D. Barnard, "Thermoelectricity in Metals and Alloys", Taylor & Francis Ltd., London (1972). J-P Jan, Solid State Phys., 5, 1 (1957). J. C. Taylor and B. R. Coles, Bull. Amer. Phys. Soc., 1, 300 (1956). N. N. Sirta, V. I. Gosishehev, and A. A. Drozd, Soveit Phys., JETP Lett., 16, 409 (1972). H. H. Sample, L. J. Neuringer and L. G. Rubin, Rev. 110 13. 14 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 111 Sci. Instru., 45, 64 (1974). L. L. Sparks and R. L. Powell, J. Research, N. B. 8., A16, 263 (1972). C. K. Chiang, unpublished. L. J. Neuringer, A. J. Perlman, L. G. Rubin and Y. Shapira, Rev. Sci. Instru., 42, 9 (1971). L. J. Neuringer and L. G. Rubin, Temperature, Its Measurement and Control in Science and Industry, Vol. IV, 1085. (Instrument Society of Ammerica, Pittsburgh, Pa., 1972). R..A. Brand, S. A. Letzring, H. S. Sach and W. W. Webb, Rev. Sci. Instru., 42, 927 (1971). A. T. Fiory, Rev. Sci. Instru., 42, 930 (1971). L. G. Rubin and W. N. Lawless, Rev. Sci. Instru., 42, 57l,(l97l). W. N. Lawless and E. A. Panchyk, Cryogenic, 5, 196 (1972). (1972). C. L. Foiles, Private Communication. R. Berman and J. Kopp, J. Phys., Fl, 457 (1971). A. von Middendorff, Cryogenics, 4, 318 (1971). F. J. Blatt, A. D. Caplin, C. K. Chiang and P. A. Schroeder, Solid State Commun. (to be published). T. Knittel, Cryogenics, 6, 370 (1973). A. V. Gold, D. K. C. MacDonald, W. B. Pearson and I. M. Templeton, Phil. Mag., 5, 765 (1960). W. G. Henry and P. A. Schroeder, Can. J. Phys., 41, 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41” 112 1076 (1963). W. B. Pearson, Can. J. Phys., 55, 1048 (1960). H. H. Anderson and M. Nielsen, Phys. Lett., 5, 17 (1963). R. P. Huebener, Phys. Rev., A155, 1281 (1964). B. Bosacchi and R. P. Huebener, J. Phys., {1, L29 (1971). J. W. Christian, J-P Jan, W. B. Pearson and I. M. Templeton., Proc. Roy. Soc., London, A115, 213 (1958). A. H. Wilson, "Theory of Metals", Combridge Univ. Press, (1936). E. H. Sondheimer, Proc. Roy. Soc., A152, 484 (1948). I. M. Lifshitz, Y. M. Azbel and M. I. Kaganov, Soviet Phys., JETP, A, 41 (1957). I. M. Lifshitz and V. G. Poschanakii, Soviet Phys., JETP, 5, 875 (1959). Yu. A. Bychkov, L. E. Gurvich and G. M. Nedlin, Soviet Phys., JETP, 19, 377 (1960). L. E. Gurevich and G. M. Nedlin, Soviet Phys., JETP, 19, 546 (1960). I. G. Lang and S. T. Pavlov, Soviet Phys., JETP, 55, 793 (1973). R. S. Averback and D. K. Wagner, Solid State Commun., 11, 1109 (1972). A. A. Abrikosov, Solid State Physics, 11, 1 (1972). 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. .57. 113 D. K. C. MacDonald, "Thermoelectricity: An Introduc- tion to the Principles", John Wiley, New York (1962). R. P. Huebener, Solid State Physics, 11, 64 (1972). Y. Ono, J. Phys. Soc., Japan, 15, 1280 (1973). J. A. Woolam, Ph. D. Thesis, Department of Physics, Michigan State Univ. (1967). F. J. Blatt, "Physics of Electronic Conduction in Solids", McGraw-Hill, New York (1968). G. T. Meaden, "Electrical Resistance of Metals", Plenum Press, New York (1965). M. Bailyn, Phys. Rev., 151, 480 (1967). J. S. Dugdale and M. Bailyn, Phys. Rev., _51, 485 (1967). E. Fawcett, Adv. in Phys., 11, 139 (1964). A. B. Pippard, Proc. Roy. Soc. , London, A212, 464 (1964). F. J. Koch and R. F. Doezema, Phys. Rev. Lett., 11, 507 (1970). M. R. Halse, Phil. Trans., Roy. Soc., London, A255, 507 (1969). P. E. Nielsen and P. L. Taylor, Phys. Rev. Lett., 21, 893 (1968). P. E. Nielsen and P. L. Taylor, Phys. Rev. Lett., 25, 371 (1970). M. Rosler, Phys. Stat. Sol., 37, 391 (1970). A. M. Guenult, J. Phys., 11, L1 (1971). 114 58. R. J. Balcombe and R. A. Parker, Phil. Mag., 21, 533 (1970). 59. c. K. Chiang, unpublished. APPENDIX APPENDIX REFERENCE TABLES FOR LOW-TEMPERATURE THERMOCOUPLES IN MAGNETIC FIELDS I. Chromel-P versus Gold-0.07 at.% Iron Thermocouples Magnetic Field Page Zero Magnetic Field ....... ........ ....... 117 5 kG .................. ..... ............. 119 10 RG .................................... 121 15 k6 .................................... 123 20 kG .......................... ..... ..... 125 25 kG ............................. ...... . 127 30 kG .................................... 129 35 kG .................................... 131 40 kG .................................... 133 45 kG .................................... 135 50 kG ........... ..... .................... 137 60 kG .................................... 139 70 kG ...... ..... ......................... 141 80 kG ......... ..... . ...... ............... 143 90 kG ...... ........ . ...... ............... 145 100 kG . .............. ............... ...... 147 II. Silver Normal versus Gold-0.07 at.% Iron Thermocouples Magnetic Field Page Zero Magnetic Field ..... ........ ..... .... 150 5 kG .................................... 152 10 kG .................................... 154 15 kG ............................ ..... ... 156 20 kG .................................... 158 25 kG .................................... 160 30 kG ......................... ...... ..... 162 35 kG .................................... 164 40 kG .......... ..... .... ..... ............ 166 45 k6 .................................... 168 50 kG ........ ....... ..................... 170 60 kG .................................... 172 70 RG .................................... 174 80 kG .................................... 176 90 kG .................................... 178 100 kG .................................... 180 115 Chromel-P versus Gold-0.07 at.% Iron Thermocouples 116 117 PtPCENT IRON CHROMEL P VERSUS GOLD‘0.07 AT. KG AT S(UV/K) INCREMENT S (UV/K) E 1 EMF(HV) CHAN( EMF (UV) TEMP. (DEG. K) .704 12.638 13,342 00 o. 00 20 45 39575 03694 17260 44556 11111 00000 00000 c o o o 0 00000 47A¥$3 93387 00.0. 38384 23568 00000 00000 0 o o o 0 67890 1 87414 71628 82110 O O O. 0 30459 24020 35789 .0000 66666 11111 00000 00000 0 o o o 0 00000 47074 93076 O O 66 0 07407 01356 11111 00000 00000 c o o o o 12345 11111 37892 52002 00000 0000 0 29786 68986 99999 on... 66666 11111 00000 00000 c o o o 0 00000 75542 55555 0.... 41852 80135 12222 00000 00000 000. 0 67890 1110-52 17255 33444 00000 O. O O I SRZYlb 30516 98887 000.. 66666 11111 00000 00000 0 o o o o 00 000 79609 43218 O O O O 0 06306 68023 22333 00000 00000 a o o o o 12345 22222 3174 4433 000 .045 -.0 18706 27306 76665 06... 66666 11111 00000 00000 0 o o o 0 00000 33909 63961.. .6 6. 6 30630 57802 33344 00000 00000 0 o co 0 67890 22223 05161 32211 00000 O O O. 0 61043 13.11976 55444 O O I O 0 66666 11111 00000 00000 00000 00000 O O O O O 12345 33333 73260 00001 00000 a o o o 0 63511 55567 44444 .0... 66666 11111 00000 00000 O O O O 6 00000 73840 16050 O. O. C 95285 1.3568 55555 00000 00000 0 o o o c 67890 33334 37035 11222 00000 O. O. 0 41149 80246 45555 no... 66666 11111 00000 00000 0 o o o 0 00000 87817 49405 06.00 174117 01356 66666 00000 00000 O O O O I 12345 44444 81246 23333 00000 0.... 78040 92693 56667 66666 11111 00000 00000 a o o o 0 00000 57190 17408 O O O O C 40740 80.135 67777 00000 00000 a o o o 0 67890 44445 118 PEQCENT IRON CHROMEL P VERSUS 60LD-0.07 AT. KG AT S(UV/K) INCREMENT (UV/K) EMFHN) tHAh ()1: (wn EM? K) TEMP, ”m6. 79901 33344 00000 O O O O C 76556 78889 00 no 0 66666 11111 00 000 00000 on... 00000 5.3623 5.3109 0 O O O 6 74184 68013 77888 00000 00000 O. O O O 12345 55555 22333 44444 00000 0 o o o 0 80369 61593 90001 O O O. D 67717 11111 00000 0.0000 0 o o o o 00 000 87079 88990 O O O O 0 56802 88899 00000 00000 0 o o o a 67890 55556 36048 82715 12233 O O 0 O I 77777 11111 00000 00.000 0 0 O O 0 00000 56093 24793 0 o o o 0 74186 3,5738.0 99990 00000 00000 0.0.. 12345 66666 .043 .044 .044 .043 .043 .044 .043 .043 .043 .042 15985 04837 44455 O 6 O O 6 77777 11111 00000 00000 0 o o o c 00000 13016 71616 0 o o o 0 31863 24579 00000 11111 00000 00000 0 o o o 0 67890 66667 92580 16049 66777 O O O O 0 77777 11111 00000 00000 o o o o 0 00000 60918 20.9530 0 o o o c 18642 12468 11111 11111 00000 00000 .0... 12345 77777 32322 44444 00000 0 o o o 0 35802 37160 88990 c o o o c 77778 11111 00000 00000 O O O O 0 00000 95486 8765.5 0 o o o 0 97531 91357 12222 11111 00000 00000 O O O O 0 67890 77778 46891 48261 00112 O O O O 0 88888 11111 00000 00000 0 o o o 0 00000 95610 56791 000.. 97532 80246 23333 11111 00000 00000 O O O O I 12345 88888 11110 44444 00000 0 o o o c 23455 59371 22.334 0 o o o 0 88888 11111 00000 00000 0 o o o 0 00000 30176 36926 O. O O 6 08653 89135 33444 11111 00000 00000 0 o o o 0 67890 88889 10009 44443 00000 O O O O 0 66665 59371 44556 no on 0 88888 11111 00000 00000 0 o o o 0 00000 07054 15962 O. O. 0 20976 79024 44555 11111 00000 00000 O O O O O 12345 99999 09998 43333 00000 00 oo 9 54320 59371 66778 .0 O. 0 88888 1111 00000 00000 0 o o o 0 00000 85621 85208 0.... 43219 68023 55666 1111 00000 00000 O O O O C 67890 99990 1 S(UV/K) INCREMENT PiRCENT IRON (UV/K) KG 119 CHANGE AT EMF(HV) (UV) CHROMEL P VERSUS GOLD-0.07 AT. EMF K) TEMP. (DEG. .702 12.658 13.360 08 01 o o 00 22 5.00 45537 14693 17260 44556 11111 01014 00000 0 o o o 0 480.60 93387. c o o o 0 38384 23568 00000 00000 67890 1 43081 716.18 22110 O O O O O 14 47.3 12808 35 668 66666 11111 83738 01122 65345 82853 C O O I C 07307 01356 111111 00000 00000 12345 11111 16613 52012 000.00 0 O 0 O 0 40652 36653 99999 66666 111111 “034 -040 -045 -051 -056 -062 -067 -072 -076 -081 35935 21000, O I O O O 4185.... 80135 1.2222 00000 00000 67890 11112 17255 334 a 4 00000 O O I O O 14272 06273 98877 66666 11111 52538 87530 O C O O C 85296 680.13 22333 00000 00000 12345 22222 -0044 -0042 -0037 -0034 00000 00000 67890 22223 .5161 2221.1 00000 O 0 O O 0 61043 08643 54444 66666 11111 25.802 0001]. 0 I O O 0 1.1111 2.1940,. 726.15 C O O C . 52851 35680 44445 00000 00000 12345 33333 73260 00001 00000 c o o o o 63511 22234 44 4 4 4 66666 111111 57913 0 o o o o 1111.1 26937 04837 0 o o o 0 84073 13568 55.555 0080 00000 67890 33334 8000 00000 1.2345 44 444 91347 23333 00000 O O O O O 01485 70360 56667 66666 11111 00000 00000 0 o o o 0 67890 44445 120 PEHCENT IRON CHROMEL P VERSUS GOLD‘0.07 AT. KG 5 AT S S(UV/K) (UV/K) INCREMENT EMF(UV) CHANGE UN) EMF K) TEMP. (DEG. 71012 3h£744 00000 0.... 003200 00000 O O .0 C IsfiJQRJ RE535CJ 3?:2J4 44£794 00000 0000.. 91:3899 .491§Ld 990K?! .0... 0675;! ll;{ll '1oa8 -1049 R0 “1051 -1052 -10 0RX907 417745 0.... 071718 c3080]. 882643 Ofixxuo 00000 0.00 0 651990 S§E336 .044 .044 .044 .045 .044 .044 .045 .045 .044 .044 Aonxguo onxguo 0000. 173945 662906 OAXUOOV onxguo o 0000 675990 6A29°7 .045 .044 .044 .043 .043 OQQVLQ lqz748 bbhgil O O I O C 77777 11111 -1055 71.55 -1054 -105“ -1054 .ISCil4 71xgls 00.000 97éi60 07r308 17:51] ‘i:£ll “fixuonv .UOfiXUO 0.... I52J4R. 77777 31:£J7k 44£744 OAXUOHV .000.- 705308 270339 8RX299 I O O O C 77777 11111 33333 SHSSS O O O O 0 11111 697:33 39?:00 coo... n6649kU 914937 .12?3&C 11;:11 00000 005200 .0... 67890 77778 .042 .042 .04? .04 .043 097338 4RX§OO onyélz noon 0 BHXQUU 11:01] 00000 00000 00000 12345 REfiQUB 11111 46£794 onxxuo 0000.- 907£C3 .991#Il 2?:QJ4 0.... 883308 11111 -1054 -1055 -1056 -105? ‘1058 -1059 “1060 “1061 ‘lobz “1062 95508 70370 .0... 87532 79135 31:744 11111 003200 onxguo 0000 0 655290 885309 .042 .040 .040 .040 .040 SRE£DS 5033’] “QRCJO coo... BHzgda 11111 I§l91id .bgoku6 .0... AKUBAYQ 783:6“ Qaéibs 101111- 00000 00000 .000. 12345 99999 09998 43333 onxguo 0.... 54320 _591§!l .Ob7%l8 O. .0 O BuidflAu 11111 “5:200 nXUOfiXU 00 to. £51990 908290 1 121 PEPCENT IRON CHROMEL P VERSUS GOLD-0.07 AT. 10. KG AT S(UV/K) INCREMENT S (Uv/K) EMF- (UV) CHANGE ((JV) EMF K) TEMP. (DEG. .371 852 523 14 13 01 O. .50 «(0 4R. 9?Tél8 1519045 752333 0000. nCQb?KU 4df047 ZHaglo on... “QREgO 11111 SR5112 3adf66 96Efi67 BRX?Q3 on... QREKVS 215308 nxguonv ODXYUO 0000. 676270 1 8?EXXU 407317 22110 . . . . . 803966 1379/5 3RZ¥IB .000. .66A?06 11111 Isidbg 65:681.» «J SA$£62 SQéflCO 0000. 17:?18 013956 11111 onxguo onxyuo ..... 1?:?QS 11111 753995 QDXXUZ onfifixu on... «J6?3:O 09§9C9 90A298 0.... 65:?00 1111 \iJQb?» 39%100 ..... n§8900v nglébqu on... hiégbz QXYLJS lzggdz Ohxxuo onngo on... 6§A990 1111ic 1;LCSTV 1:?444 OHXYUO one no 5RZ318 6?3949 8H¥LI6 65:306 1111 7l5fi60 3?K:IS .0... 953:96 695313 29§iJ3 OnXYUO 005300 .000. 173745 2?5:£d 313yb3 .4413J3 OORXUO ...... FD4GX76 P317430 bbREfb 6hZPOb 11111 -045 -051 -058 -064 -069 “075 -080 “086 -091 -097 8?T£I9 1264024 000.. .J9AXC9 "bfinfiul 313944 003200 AUOHXUO coo... Aglaqu .C?3%C3 0R7569 37:410 OHXEUO 0.... 613945 7R3?IO 44444 OOAZYO 11111 435.99 452.46 468.90 405.33 501.75 .onxxuo .onxxuo ...-co 1?;9QS 4J31§2J p?117:1 0005:! .UOAXUO ...... 095390 OQARUZ 43AZWQ 0... o GhXYOO 11111 “(81304 .UOliid 000... 110511 p255 .159 O... n940 IWEJ Qéfib 567 35 583.76 .005200 .008x00 one. 0 676270 .J31gd4 3REXJS 111629; 003200 00.... 31?}49 1Eil9l. 441945 0.0.. 66666 11111 '1029 ‘1035 “1040 ‘1046 “1051 9?:906 IEOOQKU oo 00. A061X76 .011746 662906 .003200 005x00 o. oo- IBEJQRJ 44£794 973537 731J313 OOEXUO ...-co 805%!4 481548 SQIYOb o... . 66h:Yb 11111 6?;LC7 5685;! 0000. 11:11] .- ..a 9Gf2liy 515LJ0 .0... 29éic9 891574 .6674I7 .OORXUO 005x00 00.0 o 676X70 “AXTQS 122 PERCENT IRON CHROMEL P VERSUS GOLD-0.07 AT. IO.KG AT 8 S(UV/K) CHANGE (UV/K) INCREMENT EMF(UV) EMF (UV) TEMP. (DEG. K) 27150 88990 a o o o 0 111.12 37éil3 74209 .0000 52962 68913 774188 00000 00000 0 o o o 0 12345 55555 23344 44444 00000 00 o o c 81482 27150 99001 c o o o 0 66777 1.1111 47.147 00111 o o o o 0 22222 ..... 49932 87789 c o o o 0 96307 46801 88899 00000 00000 0 o o o c 67890 55556 .04 .042 .046 .045 .045 72838 49382 11223 O. 0.. 77777 11.5111 0.5580 22223 on o o a 22222 ..... 53523 02470 as... 52964 35680 99990 00000 00000 .0 .0. 12345 66666 35544 44444 00000 c o o o c 24578 13.3333 0 o o o 0 22222 ..... 99548 37272 0.... 18631 212579 00000 11111 00000 00000 0 o o o 0 67890 66667 50480 94827 56677 O O 6 O C 77777 11111 01235 44444 no... 22222 ..... 69783 84186 O I O O 0 86419 02467 11111 1111.1 00000 00000 0.... 12345 77777 00000 00000 O O O O 0 67890 77778 33322 44444 00000 no... 14791 37150 00112 0.00. 88888 11111 12334 55555 no... 22222 ..... 83386 01235 .0... 75319 80245 23333 11111 00000 00000 00.90 12345 88888 12211 44444 00000 on... 00000 0 0000 00000 67890 88889 41498 50306 00000 98753 68024 44555 11111 00000 00000 0.... 12345 99999 21008 59370 66778 O O O O 0 88888 11111 67891 55556 0000. 22222 ..... 28830 39642 0.... 20987 68913 55566 11111 00000 00000 0000. 67890 99990 123 PEPCENT IRON CHROMEL p VERSUS GULD'0.07 AT. 15. KG AT 9 S(UV/K) (UV/K) INCREMENT EMF(HV) CHANGE EMF (UV) TEMP. (DEG. K) .589 0.00 .46 .32 .00 45 75173 1£Ef48 65432 no... 49070 84043 4n¥5811 0.... 45556 11111 00000 00000 on... 67890 1 82419 18406 21110 O O O O 0 80454 43774 35678 00000 66666 11111 05690 82854 0.... 29529 01356 11111 00000 00000 at... 12345 11111 32232 42012 00000 .0... 79186 80197 89988 .0... 66666 11111 11111 76786 21098 00.00 63063 80235 12222 00000 00000 on... 67890 1112 17255 33444 00000 ..... 5RZ316 40627 88776 .0... 66666 11111 56789 21098 ..... 111 25377 75307 0.... 07417 78023 22333 00000 00000 000.0 12345 22222 52073 44433 0000 -00 19929 38417 65554 66666 11111 01234 87654 .0... 34033 40616 .0... 41740 57802 33344 00000 00000 00000 67890 22223 04060 32211 00000 0000. v 95599 42087 44433 00000 66666 11111 56781 32100 00000 92431 05937 0.... 73962 35680 44445 OnKXUO OnXYUO CO... 12345 33333 62370 00001 00000 00000 31411 77789 33333 0.... 66666 11111 09876 11234 ..... 84075 nu481R. 0.0.0 95184 13568 55555 00000 00000 000.0 67890 33334 47146 11222 00000 .0... 52373 02469 44444 66666 11111 53219 O O O O 0 34618 93726 no... 07306 01356 66666 00000 00000 on... 12345 44444 00000 00000 on... 67890 44445 124 PEPCENT IRON CHROMEL P VERSUS GOLD-0.07 AT. KG 15. AT § S(UV/K) (UV/K) INCREMEKT EMF(UV) CHANGE EMF (UV) K) TEMP. (DEG. Sgliic 34344 OORXUO .000. 767th 947416 675168 000.. bbbbb 11111 00000 00000 O O O O O I5fi395 55REiD ‘;A;OO OQQixb QQQAXU 00.00 06677- 11111 00000 00 000 no... 67R§RU SSREfO r20628 271,00 Iii£d3 O O O O 0 77777 11111 161£Y1 001§AC coco. . 75:5(2 “90:25 nQJSRia ooooo KSfiVbh 333080 QQQéKU 1 00000 00000 0.0.. \AEJQS ,9p666 «gbssq. .94444 000 o .0 .0 .1619]. 5914.83 33445 .0... 77777 .1111]. .5937]. 273%?“ on... “(2275; ..... 69745 48272 O O O C 0 18631 23579 00000 11111 00000 00000 00000 .b7895v 196b67. .046 .045 .044 .044 .043 716003 widblq, beb75. 0.0.. 775LI7 ‘11111 cg?147 hQRfiEJ on... 75§£d2 ....- .128711 n6407é4 00000 861419 ngd467 .11111: 111:11 00000 00000 00000 IAQJQS 77777 .044 .044 .045 .044 .042 115902 9483;: «[5899 .0... 7775;! 11:111 0?E£lg 6666ZV no... 22?5§C ....- 9391;! «€199Rv 0.0.. 7§5%08 glizfo laggdz 1111.1. 00000 00000 O O O O 0 67890 77778 .044 .043 .043 .043 .044 605%39 IGKVQB n9011l. 0.... n3¢688 11111 113467. 779LI7 .0... 73§£62 ..... Q‘Edb3 .Ugolau 0.... bhifAV ABOBARJ .533334 11111 00000 00000 at... IaéJQS nBBBBRV 221371 L79444 00000 as... .1347Hv 17:!39 221513 .000. ”95868 11111 9073:? wanaflu on... 22?§3¢ ....- 40941. FQBOQRV on... 754§ku s1913R3 .gJ444 11111 00000 00000 on... 67866v BBREXV 013325 487qu “adfbb 0.... akzgdfl 11111 OnXYUO nXYUOO .0... Ii£345 032999 OQAXVB 43hiiJ 00000 00.00 00000 00000 00000 67890 ggqégv l PERCENT IRON 125 20. KG AT CHROMEL P VERSUS GOLD-0.07 AT. TEMP. (DEG. K) .364 48 72 .0 34 ll 03 08 04_ 00, ..A 01 20 45 10128 10036 56432 99020 99030 72703 0.0.. 45566 1.11111 00000 00000 ...O. ,67890 1 37419 5.8287 11100 . o o o . 68465 56777 ..... 33333 05439 50753 0.... 41741 02357 11111 00000 00000 0.... 12345 11111 73263 0.0112 00000 O O I O C 74263 11086 99988 0... 0 66666 11111 16912 76554 33333 91353 22109 85295 80235 _12222 00000 00000 ...00 67890 111.12 -0036 -0039 -0044 -0049 -0048 78457 28494 87766 ..... 66666 11111 22211 32109 .0000 33332 91810 76318 29639 78023 22333 00000 00000 .0... 12345 22222 6317 4 44433 00000 ..... 18706 05184 65544 66666 11111 09987 86543 22222 32786 40505 63962 57802 33344 _ 00000 00000 ..... ,67890 22223 05161.63371 32211 00001 00000300000 0.... .0... ..... .— 61043 74745 19754 33345 43333 33333 .0... 0.... 66666 66666 1111111111 65421,98642 21098,65432 .6... ....o 22211,11111 01072360483 04815282582 .....fl..... 95184 07396 35780 23568 55555 00000 _00000 .....A..... 12345.67890 33333333334 L 2 _ 59236 11222 00000 0.0.. 09140 78136 33444 66666 11111 19754 19876 ..... 86571 59372 .0... 28518 01356 66666 00000 00000 0.... 12345 44444 93467 23333 00000 . o. o . 92629 82592 45556 66666 11111 21098 54310 ..... 88188 61728 0.... 41740 80135 67777 ,00000 300000 .0... 67890 44445 S(UV/K) INCREMENT PERCENT IRON (UV/K) 126 20. KG EMF‘UV) CHANGE AT (UV) CHROMEL P VERSUS GOLD-0.07 AT. EMF TEMP. (DEG. K) RURXC3 1:?Q94 00000 on... 77792 60483 67778 0.... 66666 11111 2?3%§l 0.123“ 31412 (159743 7453!“ 6RKYI3 751688 n20005v .UOnXYU 0.... 193725 SREi25 605835 7?:315 BQéXUO coo... 66h;;l 11111 _88326 373fi42 .18R1C9 FDGRXYI .88899 00000 00000 00000 675x90 S§E536 .046 .045 .045 .047 .047 .161395 AUQQIJB 11:152 000 no 7751,? 11‘511 .U7fi318 QXVOI{1 ..I:!l 970.66 987 88 15 936.35 953.48 1005 003390 003300 0.0.. 193945 66666 .045 .045 .045 .045 .046 .046 .045 .045 .045 .044 AUSOQ;L «31261. 159945 .0... 775517 1:011]; nxguonv OOKXUO 00000 ,67890 6A2907 7?;Ldb CXUQQiu RZ30b7 0.... 77%Ll7 ll:§ll IQQEXHU C3367;l O O O I 0 11111 9?|41%J 71:?61. 9722C0 0):?08 1‘;:£1 I:l]i:l ooaxxu .OOXYUO IBEJQR. 77777 .045 .044 .045 .044 .044 0044 .044 .044 .042 .043 IRKYQB 8??!15 7REXV9 .0... 775LI7 110511 -1080 -1085 -1089 4-1.94 ’1098 ,QOEfQB 004105 8R3319 915336 l?5§£d 11111 00000 00000 0.... 67890 77778 9&009EJ 0482J7 005911 0.0... BHXOUB 11111 37;!“8 Ofl:§11 000.00 P32C2?. ... .. 6Q¥379~ Sfizglg 7:3319 BanéS 9fi531ia 11111 AXUOhfiv_ .00000 onxguo 00.... 12345H BRXQUB 812257 ..lfifiYQB 2232J3 BHfigba 11111 1:38124 273233 2?5§£d .25362 169091u abbkfikl .7Q{iJS 1;?Q4h. 11111 onxxuo 0.000. 67§XYO aflsgbg Q§£JSS 27(159 4a£ibS 0.000 BHKYUB 11111 1;AU0U, 44£7Q3 OHRXUO IO... 6754I6 37ii39 6&5LI7 0.0.. BHKHUB 11111 1547lfib SREfob coo... 275fiC2 ... .. 716116 302991 .00.. 77A287 ,OBQIQJ SREfDG I}!!! 003200 005200 00.... 675290 AVQQOKV .1 S(UV/K) INCHFMENT PERCENT IRON (UV/K) 127 25. KG EMF(UV) CHANGE AT MN) CHROMEL p VERSUS GOLD-0.07 AT. EMF K) TEMP. (DEG. .450 44 37 44 ll 06 02 no 01 20 20 45 32128 49092 431.. 2?. 708220 215514 26924 .0... 55566 11111 85228 44282 23445 22093 48660 61730 24579 00000 00000 00000 67890 .1 37964 R4953 11000 o o o o 0 30959 27625 67899 66666 11111 26215 68011 0.... 55666 53288 52087 000006 63063 02457 111‘] 00000 00000 00.0. 12345 11111 78717 18122 00000 0.... 40455 ,11098 _66655 25896 76543 07418 90245 ”12222 A 00000 A 00000 67890 , 11112 32703 17283 87766 0 o. .0 66666 11111 00000 00000 .193945 22222 -0047 -0046 “.042 ’00y0 -0035 16.586 {6.540 6.498 16.460 16.425 00000 000'. 67890 .22223 16261 32211 00000 O O. I. 74035 04814 0.000 17306 45790 44445 00000 00000 ,67890 12345 33333 73270 ,00001 00000 on... 29188 A 10112 33333 66666 11111 95050 54310 33333 67890 70360 .0000. .29518 _23S78 _55555 _00000 _00000 33334 38136 11222 00000 on... 19039. 45802 33344 66666 11111 51617 87542 22222 38434 36048 40739 02356 00000 00000 06000 85596 27273 62952 ,80135 66666. 67777 _00000 ,00000 1123aé3 44444. .0... 67890 44445 S(UV/K) INCREMENT PERCENT IRON (UV/K) KG 128 25. EMF(UV) CHANGE AT (UV) CHROMEL P VERSUS GOLD-0.07 AT. EMF TEMP. (DEG. K) .039 .042 .040 04 0.2: 35568 37159 6672! 0.... 66666 11111 AXUOAKV nxyuoo 0'... .1?5?45 55555 .044 .044 .045 .044 .044 .046 .045 .046 .046 .046 407176 65433 00.... 29630 56802 88899 nxguoo. onxyuo 000.. 67890 55556 .50ZXC8 A7£504 011id2 O O. O. 775LI7 11111 65678 10012 10425 .456RHv. 7:?!86 35780“ 99990_ Auonxgu nXUOHXV 0.6000 12345 66666 3Q£315 93837 23344 0000. 77777 1:411]. 005200 OOKXUO 00000 67890 66667 .046 .045 .046 .046 .044 .045 .044 .045 .044 .044 .044 .046 .044 .042 .044 .044 .043 .043 .042 .042 -085 A-ogg -1002 10 17 ‘10 ’10 .167;}1 4Qéid9 00.... fixi530 lic4fifiu 1511111 111111. .UOOXXU nXUOan 0.00. .19234R. 77777 17.747 17.791 7.836 17.880 17.924 -1025 {:35 ‘1045 ’1051 412335 64210 c 006. 8AXZd0 915557 12222 1111 onxxuo .0nKXUO 0.... 67890 77778 84804 £75504 90:911 .6000. 7u8688 117:!l AXUODXV 00000. .193945 88888, 812768 .819115 1955J3 8H§H88 11111 PE3791. 04827 44455 .0..- 885398 11111 519159 145633 00.0. 293§£d ..... p96325 037958 0000. 9R§lb3 .98024 .94555 11111 nXVOOKv AUOOKXU 0'... 152J4R. 99999 311111 44444 008x00 .00.. 4RZ¥£8 .159197 ,666771 ...... 8HZRO8 11111 S(LHI/K) INCREMENT PERCENT IRON (UV/K) 129 30. KG EMF(UV) CHANGE AT ([JV) CHROMEL p VERSUS GOLD-0.07 AT. EMF TEMP. (DEG. K) .354 03 07 o. 01 04 09 01 20 20 45 53423 28812 32222 00000 36025 42124 69246 on... 55666 11111 93162 37863 34567 31937 31150 73952 24579 00000 00000 00000 67890 37469 22015.1 11100 O O O O C 85954 69913 78900 .0... 66677 111-Ii 31989 82467 78888 79943w 75444 to... 85296 02457 11111. 00000 00000 00000 12345 11111 .5193.42 23292 43224 00000 00000 29786 95306 99998 66666 1111 56379 88876 88888 11 32 41 38 41 22 5g; .OnKXUO nXYUOO. 0.... 67é2?0 1112 67230 44555 00000 0000. 03188 27261 87766 00... 66666 11111 87394 54310 00000 88888 55093 08629 0.... 84184 79124 22333 .OnXYUO nXUOnXu 0.00. 12345 22222 88307 44443 00000 no... 02992 72730 55444 no... 66666 11111 93704 87542 77777 26613 50504 1184l41 67912 33344 00000 00000 000.0 67890 22223 27161 32211 00000 03265 74209 33332 66666 11111 70370 09754 76666 00000 72371 ,00001 ,00000 00003 86967 88890 22223 00000 66666 11111 .00000 00000500000 00..., 12345 67890 33333 33334 48146 11222 00000 0.... 19040 23681 33334 0.00. 66666 11111 81471 32087 55544 68298 81582 63952 02357 66666 00000 00000 OI... 12345 44444 92368 233371.} 00000 91408 37047 44555 66666 11111 47037 53208 44443 93127 61616 .00.. 85184 80235 67777 00000 00000 000.0 67890 44445 S(UV/K) INCPFMEKT PERCENT IRON (UV/K) 130 30. KG EMFtUV) CHANGE AT (lIV) CHROMEL p VERSUS GULD-0.07 AT. EMF K) TEMP. (0E0. .038 .040 .040 .041 .042 66679 15937 66677 0.... 66666 11111 04715 75320 33333 57348 28529 17417 78023 77888 .003200 003300 0.0.. 1?§?45 55555 .043 .044 .045 .045 .044 .045 .045 .046 .046 .046 267560 26150 88990 0.00. 66667 11111 94838 87542 22222 70807 76443 41852 57802 88899 00000 00000 no... 67890 55556 50628 49382 007512 0 O O O 0 77777 11111 39528 19875 on... 21111 85511 34579 96307 5790 9990 93 00000 00000 on... 12345 66666 58405 711614. 23344 0.... 77777 11111 ,66104 14826 52974 24579 00000 11.11] 00000 00000 00000 67890 66667 0046 .045 .045 .045 0044 .045 .044 .046 .044 .043 .044 .044 .046 .043 .044 IAY§60 04938 55566 O O O 0. 774117 11111 36463 IfOZREJ 29742 12468 11111 31111 00000 00000 00000 12345 77777 59592 26150 77889 C .0 C C 77777 11111 60693 49372 99001 .0... 77888 11111 00000 00000 12345 88888. .33332 .44444 ,00000 69257 60593 l?5fic3 0.... 88888 11111 09875 66789 31301 70(547 97642 79135 33444 11181 $003290 ,032000. 00002 00060 67890 88889 .043 .042 .043 .04‘ .oaf 02578 82604 34455 no... 88888 11111 30841 01123 0000. 11111 77213 04749 .0... 1:2864 78024 44555 1111 n3000Kv OnXYOO .0000 .laga4fi. 99999 22100 44444 00000 00.00 02333 93715 56677 88888 11111 00000 00000 00.60 67890 99990 1 S(UV/K) INCREMEKT PERCENT IRON (UV/K) KG 131 35. EMF(UV) CHANGE AT (UV) CHROMEL P VERSUS GOLD-0.07 AT. EMF K) TEMP. (DEG. .?70 15.58 15.85 05 01 o o 06 03 20 20 45 01128 23008 3.8/.221 o o o o c 34575 70009 03578 c o o o 0 66666 11111 82388 20454 46789 20.253 23842 84074 24679 00000 00000 0 o o o 0 67890 .1 30409 66800 90011 0 o o o 0 67777 11111 05778 27146 c o o o 0 00111 11111 42742 11123 0 o 0 o 0 18529 12467 11111 00000 00000 O O O O O 12345 11111 74780 74728 00998 O O O O 0 77606 11111 00000 00000 0 o o o 0 67890 11112 19616 75431 O O O O 0 11111 11111 88324 19740 O I O I 0 17418 89134 22333 00000 00000 0 o o o 0 12345 22222 00000 00000 0 o o o 0 67890 27223 49262 00000 O O 6 O C 23153 52087 33322 O O O O 0 6666.0 11111 89013 08753 090.99 1 764 470 .16 952 791 445 446.82 463 00000 00000 O O O O O 12345 33333 74250 000001 0000 0 62499 66667 22222 66666 11111 45,078 19753 ,98888 17408 35813 84079 2 4673 5555.5 5 _ “ 00000 00000 0 o o I 0 67890 33334 27046 11222 00000 c o c o 0 18828 90257 23333 66666 11111 90123 10864 O O O O 0 88777 77940 69260 95285 02457 66666 00000 00000 0.... 12345 44444 912.58. 23333 00000 O O O C C 78053 0370“ 44455 0 o o o 0 ,66666 11111 45678 20864 77666 02768 48272 .0... 17407 90245 67777 00000 00000 0 o o o 0 67890 44445 S(UV/K) INCREMENT PERCENT IRON (UV/K) KG 132 35. EMF(UV) CHANGE AT (UV) CHROMEL p VERSUS GOLD-0.07 AT. EMF TEMP. (DEG. K) 24579 82604 56677 66666 11111 90134 21975 66555 44757 84074 30730 79024 77888 00000 00000 .0000 12345 55555 15284 93827 78899 66666 11111 57913 31986 O O. C. 55444 34982 20877 00000 74074 57902 88899 00000 00000 00000 67890 55556 .047 .045 .046 .046 .047 16285 26150 00112 00000 77777 11111 69260 42198 44433 15253 77891 .0... 18520 45791 99990 00000 00000 0.... 12345 66666 06183 59483 22334 00.00 77777 11111 49517 64320 33333 52523 36937 00.0. 74196 24679 00000 1111 00000 00000 0.0.. 67890 66667 .046 .045 .045 .046 .045 94950 72616 45566 .0... 77777 11111 41864 98654 22222 01772 27285 O O O O 0 41964 13468 11111 11111 00000 00000 .0... 12345 77777 .045 .044 .045 .045 0044 59493 04938 77788 O O O O C 77777 11111 21986 32098 22211 16362 29754 .0... 29753 01357 22222 11111 00000 00000 00000 ;91806. 77778 72692 27150 99001 0.00. 77888 11111 00000 00000 .044 .044 .044 .042 .041 60467 49371 11223 no... 88888 11111 87655 10987 0.060 11 U11721 .56814 to... 19764 89135 ,33444 #11111 ,00000 ”00000 0'... .0... 12345,67890 88888. 88889 2 52321 44444 00000 00000 52634 71305 .0... 21086 79124 44555 11111 00000, 00000 00000 12345 n29996/ .042 .041 .042 .042 .041 23578 71593 56667 0.0.. 88888 11111 133 PtRCENT IRON CHROMEL D VERSUS 60LD'0.U7 AT. 40. KG A1 K) TEMP. (DEG. .501 A90 90 14 11 “20 A20 45 387178 32445 11111 O. O. O «39n375 35040 56891 66667 11111 246:52 P37157 57901 11 61R59l 171744 ,95296 24679 003200 005x00 on... 67Ragv 1 .089 .077 .024 -.054 -0056 -0062 -0053 -.047 -0058 '0062 “30404 nZI948 12221 0.000 77777 1111111 71923 64947 0.000 21:344 11111 19997 67913 00... 305$22 149468 11111 nxuonxv onxyuo 0.3000 19:945 11111 «29242 «26260 lnxy99 no... 774166 111111 “54527 9n7§10 ..ooo ,455REJ 11111 22769 56665 .0... 9A5£U7 91356 .122?5; 005200 OnXXUO on... ,67890v 111112 171293 666223 003900 .0... 98670. 151149 877453 .0... .96666 11111 87370 98754 44444 11111 r25978 429452 0000. 415141 80152J 2153J3 003200 00000 0.... 12345 222?5. -0057 -0055 -0049 -0044 -0043 7?5:96 385384 .54433 000.. 66666 11111 12221 20864 .0... 44333 11111 451930 83892u 0.... 740733 680113 33444. 008200 005x00 on... 678°6v 222954 .21384 .33211 008200 0.... .p... .23028 18605. «22222 0.... ,66666 11111 008200 008200 12345 333133 0Q5L60 1100011 OnXYUO .0... “83511 Q:§222 .0... 66666 11111 107141 1:?042 000.00 211111 111111 ,92471 952792 .9000 175396 «39679 .55555 .00x200 onxguo 000). .67890 .33334 1:9U47 171222 onxuon on. on 422693 746803 9:5233 .66666 11111 .84173 Q§l520 coco. AUOOXHU 111111 51980 4797Zu 0.000 «28417 129467 .66666 005x20 nuoonfiv 00000 12345 2 2 .H _ 5 0345/ 35333 00000 .0... .36052 69360 3344R3 ,66666 11111 997473 .7530H. 99998 41253 93716 .0... 30639 9124K. 67777 OOKXUO ODXXUO coo-o .6789nv .44444_4444 fSUJV/K) INCHEMENT (UV/K) 16.541 10.584 16.625 16.667 16.710 16.755 16.799 16.844 PLRCENT [RON thQU 16.936 KG 134 40. EMF(UV) CHANbE AT (LIV) CHROMEL P VERSUS GOLD-0.07 AT. EMF K) TEMP. (0E6. .030 .043 0041 .04; 0043 95296 53186 00 o o 0 88877 49819 16295 6295.2 79024 77888 00000 003300 0 O O O 0 193945 55555 .045 o 09‘! o 048 .046 .046 42099 42075 77766 18067 30976 96296 57902 0 8.9.80 Q 00000 00000 0 o o o 0 67890 55556 0 047 .045 .048 .047 .046 .045 .049 .046 .045 .047 .047 0044 .046 01.148 0049 .045 .046 .046 0044 JMb .046 0045 0095 .045 0044 .043 0096 .044 .044 .044 .044 .043 MM4 .042 .042 38639 82726 90011 O O O O 0 679177 11111 99024 31086 0.... 66655 45017 66789 30741 46791 0.9900 1 00000 00000 0 o o o o 12345 66666 43941 16050 22334 00000 7754I7 11111 69371 42198 on... 55544 72387 14704 696318 24689 00000 111)] 00000 00000 000.0 67890 66667 61728 6.6320 44444 21636 94951 . . . . . 53086 13568 1111.... 11.111 00000 00000 12345 77777 51716 72615 67788 O 0 O O 0 77777 11111 41730 98654 33333 36116 85319 31974 02357 22222 11111 00000 00000 ..... 67890 77778 27271 04938 99900 . . . O 0 77788 11111 63962 21987 33222 58572 87778 ..... 20864 91246 23333 11111 00000 00000 7 .....V 12345 88888, 40482 27150 11223 . . . .. 88888 11111 96308 54320 22222 26474 90247 21975 80135 34444 11111 00000 00000 0 o o o 0 67890 88889 69357 48371 33445 ..... 88888 11111 64211 98765 0 o o no 11111 61265 04627 0.... 42197 79124 44555 11111 00000 00000 ...... 196945 99999 H£32224}... 44444 00000 . . . . . 18.562 18.604 18.646 18.689 18.730 00000 43210 . .0 . 0 11111 85621 28418 ..... 64320 68024 55666 ‘1101 00000 00000 0 o o o 0 67890 99990 135 PERCENT IRON CHROMEL P VERSUS GOLD-0.07 AT. KG 45. AT S(UV/K) INCRFMENT (UV/K) EMF(UV) CHANGE (lJV) EM? K) TEMP. (DEbo .Yaa 16.661 16.849 05 01 o. 03 05 03 o. 03 20 20 45 78123 16929 10010 .0... 64570 63249 9nY£C3 .0... 675%!7 11111 405114 05537 0.0.. 68023 111 97689 9R5{x4 .0... 96318 24689 00000 00000 no... 67890 1 3714/0 52045 00000 C 6 C O . 30959 92171 34433 on... 77777 11111 28436 98626 45677 1111] 65402 82603 53085 13568 11111 00000 00000 00000 12345 11 111 .ladUQS ,02344 00000 88888 11111 99286 57999 .29630 01357 22222 00000 00000 00000 67890 III-112 i 00000 00000 0.... I§EJ45 22222 -.060 -0060 -Jb4 ’JM? .5044 11706 48233 54433 66666 11111 87641 64208 .0... 77776 11111 10549 38269 00000 17406 78023 33444 00000 00000 00000 ,67890 22223 Qi5905 33221 00000 0.... 76005 96420 28222 no... 66666 11111 73940 53066 66655 11111 lQéXYI 35803 no... 39528 56801 44455 00000 00000 192945 33333 93260 00001 00000 coco. 63511 99901 11122 on... 66666 11111 50493 31853 .000. 55444 11111 22233 57913 0.0.. 40639 35689 55555 00000 00000 00000 67890 33334 37046 11222 00000 no... 41151 24681 22223 on... 66666 11111 82603 06530 0000. 43333 11111 59410 57036 000.0 51840 13468 66666 .UOnKXU .OnXYUO 0.... 192945 44444 OPEfig 47Au97 33444 66666 11111 715i62 75297 0.... 22211 11111 38672 92605 .0... 63962 91246 67777 00000 00000 00060 67890 44445 S(UV/K) INCPEMENT IRON PERCENT (UV/K) KG 136 45; EMF(UV) CHANGE AT (UV) CHPOMEL p VERSUS GOLD-0.07 AT. EMF K) TEMP. (0E6. .038 .040 .041 .042 .044 77804 15948 55566 .0... 66666 11111 60 483 42964 00.00 11000 118111.. 13016 05173 no... 95285 79124 77888 00000 00000 00.00 12345 55555 82749 27160 77889 .000. 66666 11111 72840 19642 09999 1 59819 07542 0.... 28529 67912 388899 00000 00000 00000 67890 55556 77767 44444 00000 0.... 63063 50594 90001 O O O O D 67777 11111 63187 97520 0000: 88888 19180 21224 63074 46891 99990 00000 00000 O C O C. 193945 66666 06305 93837 12233 00... 77777 11111 65445 86420 #77777 .7845! 57037 00.... _l8630 “34680 00001 11.51111 00000 00000 00000 .67890 66667 30630 27161 44556 0.00. 77777 11111 67913 86431 66666 27821 15062 O O O O 0 85308 13578 1181!] 11111 00000 00000 00000 12345 77777 .045 0044 0047 .045 .045 .046 .044 .044 .046 .044 59616 59493 66778 .0... 77777 11111 68258 97642 55555 53634 85208 0.0.. 53196 02457 22222 11111 00000 00000 .0... 67890 77778 26060 82716 89900 0.0.. 77788 11111 11558 42086W 80235 91346 23333 11111 00000 00000 00000 12345 88888 36157 04937 11122 .0000 88888 11111 27272 31087 CO... 44433 ,57348 765558 67913 42097 34444 11111 00000 00000 00.00 67890 88889 53233 44444 00000 000.0 25703 26059 33444 00... 88888 11111 84074 54310 0.... 33333 81028 60282 00000 54309 79134 44555” 11111 00000 00000 .0000 12345 99999 21420 44444 0.0000 0000. 56022 37260 55667 coco. 88888 11111 29865 97654 22222 04486 83952 00.00 76432 68024 55666 11111 00000 00000 00.00 67890 99990 137 PLHCENT IRON CHROMEL P VERSUS GOLD‘0.07 AT. S(UV/K) EMEKT EMF(UV) S CHANGE (UV/K) INCH EMF (UV) TEMP. (DEG. K) .098 08 10 34 o. 77 11 OS 05 03 2o 20 45 54673 02356 00000 0000. 39525 18284 43445 0.... 77777 11111 89376 98330 00000 69246 111 26141 92728 000.0 08530 34680 00000 00000 000.0 67890 1 331/411 40258 00000 O ,6 O O 0 85409 88612 55554 O O O O C 77777 11111 00000 00000 00.00 12345 11111 78242 8109’ 01100 00000 24286 42225 32109 0000. 77776 1111 00000 00000 00000 67890 1 112 62773 67658 00000 at... 08141 91591 88766 on... 66666 11111 70959 66431 0.000 11111 22222 48558 19740 17418 90245 23333 00000 00000 12345 22222 30926 66854 00000 on... 88971 48273 54433 0.... 66666 11111 11196 08631 so... 10000 22222 44995 61593 0.... 41730 79024 33444 00000 00000 000.0 67890 22223 35598 43211 00000 on... 83891 85209 22221 0.000 66666 11111 39404 96429 99998 11111 75146 69246 00000 62951 57802 44455 00000 00000 00000 12345, 33333 17282 10001 00000 .00.. 03191 ,87779 11111 0.... 66666 11111 37036 11222 00000 0.000 41140 02469 22222 66666 11111 69134 30852 77666 11111 46941 80258. 85173. 13568 66666 00000" 00000, 00..., 123452 444442 92357 23333 00000 on... 91496 15815 33344 66666 11111 67901 96318 55554 11111 14081 14816 00000 06295 .01346 77777 00000 00000 000.0 67890 44445 138 PERCENT IRON 50.7KB CHROMEL P VERSUS GOLD‘0.07 AT. AT £MF(UV) 5 S(UV/K) CHANGE (UV/K) INCPFMENT EMF (UV) TEMP. (DEG. K) 79036 33444 00.000 0 I o o 0 23566 52963 00000 44333 11111 77191 0:7563 00000 28516 69134 77888. OnXYUO OnXYUO OI... 1%EJ4R. 55555 .040 .044 .045 .045 .044 .049 .046 .047 37271 04936 77788 00000 66666 11111 03693 16520 on... 32222 11111 60662 97421 00.00 41RE§C 68913 66699 00000 00000 000.0 ,67690 55556 8 .047 06316 37271 99001 000.0 66777 11111 72729 75207 00000 11110 11111 27722 008201 77670 44445 00000 00000 52086 53166 00099 111 _65092 .41653 95207 46801 908200 _OnXYUO OnXYUO 0.000 192945 66666 _ 24793 35680 0001 11111 .00000 00000 00000 67890 66667 .046 .046 .047 0046 .046 .047 .044 .047 .046 .046 .045 0045 .044 .043 .046 .043 .049 .045 .044 .043 171306 04948 44455 O O I CO 77777 11111 55444 42066 99988 15352 71617 O 6 6 C 6 08530 23579 11111 11111 00000 00000 .6... 12345 77777 37406 37271 66778 0.... 77777 11111 16039 60593 69990 6 O O 6 6 77778 11111 26158 62715 01122 .0... 66666 11111 03604 64219 ,66665 33770 90136 6§5fl9 80245 .34444 _ 11111 00000 00000 67690 66669 00000 OOOOOH ...... IéEJ4R. 99999. .045 .040 .043 .044 .041 11489 26046 55666 66666 11111 47460 594063 000.0 98754 66024 55666 00000 00000 00060 67690 99990 139 PERCENT IRON OflmMU.P‘WR3wSGOU%fio07ATo 60. KG AT 5 SUN/K) INCRFMEKT (UV/K) EMF(UV) CHANbE EMF (UV) TEMP. (DEG. K) -JRB 18.430 “m2 8 .22 .00 45 58487 57941 11000 .090. 79570 46721 20999 00.00 88777 11111 00380 84491 82570 1112 47255 77888 .20864 35680 00000 00000 00000 67890 73641 14680 00001 30409 95809 88775 0.... 77777 11111 60715 83441 0.... 13456 22222 07789 86417 .0... 20863 24579 11111 00000 00000 .0... 12345 11111 73774 95998 01000 0.0.. W..... 29251 04557 53210 0.... 77777 11111 37916 71478 .0... 67777 22222 “02458 .37023 ,18630 .12468 22222 00000 00000 00000 67890 11112 71938 80146 99876 0.... 66666 11111 46480 99988 0.... 77777 22222 15088 43296 0.... 74174 91346 23333 00000 00000 no... 12345 22222 44123 76655 00000 0.... ..... 40974 93616 55443 .0... 66666 11111 82042 18520 32222 66666 11111 67912 240315 11000 00000 00.00 88561 87778 11111 .0... 66666 . 11111 05058 85307 no... 55554 22222 78888 91357 0.000 _4l739 46790 44455255556 2 2 00000 00000 00000,00000 0.... 12345367890 33333 33334 93803 01122 00000 no... 03114 90246 12222 0.0.0 66666 11111 02344 52963 0000. 44333 22222 89251 91469 .000. 52840 24579 66666 00000 00000 no... 12345 44444 50246 23333 00000 000.0 99151 81582 23334 000.. 66666 11111 32096 07407 no... 32221 22222 89176 14815 673962 02357 77777 00000 00000 000.0 67890 44445 0'7 I171" Ill-0'11: ..... 41101111 -111 I 111111 ..... JENT S(UV/K) Ncpgk 1 PERCENT IRON (UV/K) KG 140 60. EMF(UV) CHANGE AT (UV) CHROMEL p VERSUS GOLD-0.07 AT. EMF TEMP. (DEG. K) 42975 41741 00000 11000 22222 95598 94940 ..... 85185 80235 78888 00000 00000 0.... 1123424 55555 23565 44444 00000 coco. 81627 50493 67778 0.... 66666 11111 31098 85285 .99988 11111 18067 73186 ..... 18518 78023 88999 00000 00000 00000 67890 55556 .046 .044 .046 .048 .046 37317 82726 89900 ..... 66677 11111 00000 00000 ..... 12345 66666 57046 44544 00000 on... 29939 15059 11222 .0... 77777 11111 58148 85307 ..... 66665 11111 61154 57914 00000 07429 45790 00001 11111 00000 00000 00.00 67890 66667 .048 .046 .046 .047 .044 73960 49383 33445 . . . .. 77777 11111 26160 52075 no... 55544 11111 86078 71605 0.000 64196 24679 11111 111161 00000 00000 ..... 12345 77777 .047 .045 .046 .044 .045 .046 .044 .045 .045 .044 72827 72615 56677 .0... 77777 11111 50516 20752 0.0.. 44333 11111 45992 17308 ..... 41974 13468 22222 11111 00000 00000 ..... 67890 77778 37271 04938 88899 ..... 77777 11111 16273 07520 no... 32222 11111 01883 64211 as... 20864 02357 33333 11111 00000, 00000 at... 12345, 88888 .044 .045 0044 .043 .044 .043 .042 .043 .044 .042 50471 27150 00112 ..... 88888 11111 00000 00000 .0060 67890 88889 46935 48271 22334 ..... 88888 11111 01258 75319 ..... 00009 1111 08202 80282 210767 80235 45555 1111 00000 00000 03000 12345 99999 22310 44444 00000 on... 79233 59482 44556 00.00 88888 11111 38418 86542 99999 13039 72840 ..... 43109 79134 55666 11111 00000 00000 00060 67890 99990 S(UV/K) INCHEMENT PtRCENT IRON (UV/K) KG 141 70. EMF(UV) CHANGE AT (UV) CHROMEL D VERSUS GOLD-0.07 AT. EMF TEMP. (DEG. K) .293 30 85 .. ll 08 07 00 05 08 09 05h 20 20 45 74482 89119 43210 ..... 39575 44312 06432 ..... 98888 11111 22755 79449 to... 04813 11122 34.66 5329 71.85 -90.32 108.70 00000 00000 00000 67890 .1 23696 79891 00001 .0000 30459 56775 10987 . . .. . 88777 11111 35613 07132 00000 67901 22233 72687 91108 ..... 65318 24689 11111 00000 00000 00000 12345 11111 78205 91510 01111 00000 24227 64987 65321 . .... 77777 1111 31.97 33 35: 33.33 33.57 %2 216.55 523‘ 268.87 286.08 00000 00000 on... 67890 11112 05496 09988 10000 ..... 72893 78891 09877 0.000 76666 11 111 32662 78888 ..... 33333 33333 01360 22197 ..... 30730 02357 33333 00000 00000 on... 12345 22222 93659 88765 00000 no... 41501 24604 65443 ..... 66666 11111 44169 76531 ..... 33333 33333 77967 39493 ..... 73063 80235 34444 00000 00000 00000 67890 22223 40444 95086 22211 no... 66666 11111 09749 07530 as... 32222 33333 380 358 284 013 469.74 -486.05 00000 00000 ..... 12345 33333 555 342417 311000 00000 0.000 08430 53334 11111 as... 66666 11111 35776 85296 .0000 11100 33333 08516 01356 ..... 17395 56891 55556 ,00000 00000 no... 67890 33334 93812 00000 .0000 00000 00000 on... 12345 44444_ 70145 23333 00000 ..... 00150 58148 22333 ..... 66666 11111 48259 62951 ..... 88777 22222 94349 ,70369 00000 29517 12467 77777 00000 00000 ..... 67890 44445 S(UV/K) INCREMENT PERCENT IRON (UV/K) KG 142 70. EMF(UV) CHANGE AT (UV) CHROMEL P VERSUS GOLD-0.07 A1. EMF TEMP. (0E6. K) 799.11 33344 005300 0.0 .0 76567 .1504J7 44455 0.00. 66666 11111 «260748 84173 66655 22222 4705;?! 395273 .....A 40730 91246 78888 00000, 00000 0.00. 12345 55555 16050 2A7550 66778 .0... 66666 11111 38406 06306 on... 54443 22222 15375 95297 63063 79124 88999 Aonxxuo .005200 00000 67890 55556 .047 004 .042 .048 .046 95195 72716 Oltsgc 00... 77777 11111 43221 74185 0.... .1110“. 22222 56237 45791 .52964 46791 00001. .1111 00000 00000 00000 67890 66667 18494 15049 33444 O O O O C 77777 11111 11009 29639 09998 21111 71917 48160 18631 34680 11112 11111 00000 00000 0.000 12345 77777 .047 .044 0046 .046 .045 .044 .045 .045 .043 .044 15172 48372 55667 00... 77777 11111 99888 63074 coo-o 88877 11111 84264 51730 ,86319 13578 22222 11111 00000 00000 .0... 67890 77778 61693 61594 78889 0.... 77777 11111 00000 00000 0'... 12345 88888 63334 44444 00000 to... 92582 ,83716 90011 .0... 78888 11111 82842 75208 0.000 55554 11111 12918 11134 64208 91356 634444 11111 ,00000 00000 00000 67890 88889 32242 44444 00000 0000. 57935 04837 22233 no... 88888 11111 00000 64208 44443 11111 07054 79160 .0... 64410 80246 45555 11111 8 00000 00000 0.0... 12345 99999 22219 844443 .00000 79121 15048 44555 0.... 88556 11111 07237 63184 no... 33322 1111'. 82858 49382 00000 86532 79135 55666 11111 00000 00000 00000 67890 99990 1 IIIII lllll 143 PERCENT IRON CHQOMEL P VERSUS GOLD-0.07 AT. KG 90. AT S(UV/K) INCREMENT (UV/K) EMF(UV) CHANGE (tJV) EMF TEMP. (DEG. K) 522. 51 16 o a 10 22 07 06 O. 06 08 00 07 20 20 45 79575 69219 81864 0.... 99686 11111 15683 75586 .0... 27147 11222 52558 69973 0.... 65432 35791 00000 00000 0 o o o 0 67890 1 23691 10119 11110 O 0 O I 0 30454 88645 32109 O O O O O 88667 11111 08329 97366 0.... 91345 23333 45392 81333 0 o o o 0 09753 34680 11112 00000 00000 0 o o o o 12345 11111 2:792 40202 ll‘lll o 0000 00000 00000 0 o o o 0 67890 1112 0876?. 21111 11111 O I O I O 13608 31986 21987 0.... 77666 11111 04139 13566 on... 99999 33333 73837 57775 .0... 85296 02457 33333 00000 00000 0 o o o o 12345 22222 53644 09R76 10000 6 6 6 . C 30406 67814 65443 00... 66666 11111 39.69 39.65 39.57 39.44 39.28 28556 39504 00000 39639 90245 34444 00000 00000 0 o. o 0 67890 22223 96116 54432 00000 O. O I 0 71093 84064 22211 0.... 66666 11111 39.08 38d“ 38.58 38.30 37.99 21540 81357 52840 79024 44555, 00000” 00000 0 O o o o 12345, 33333 74701 11000 00000 0 o o o 0 62556 21000 11111 0 o o o 0 66666 11111 62602 63962 0 o o o 0 77666 33333 35432 89012 000.0 62951 57802 55566 00000 00000 0 o o o 0 67890 33334 62672 01112 00000 O 6 6 O C 24079 12457 11111 no... 66666 11111 46802 84073 .0... 55544 33333 23619 34578 O O O O O 73951 35680 66667 00000 00000 6 6 O I C 12345 44444 .026 .029 .028 .033 .035 54250 03693 22223 66666 11111 00000 00000 000'. 67890 44445 S(UV/K) INCREMEKT PERCENT IRON (UV/K) KG 144 80. EMF(UV) CHANUE AT (UV) CHROMEL D VERSUS GOLD-0.07 AT. EMF TEMP- (DEG. K) 79901 33349 00000 000.0 76556 60482 34445 no... 66666 11111 27261 17907 6.... 21110 33333 70794 61506 .6... 96295 91346 79898 00000 00000 0.... 12345 55555 33346 44444 0000 0 no... 92595 6IéXv4 56667 0.... 66666 11111 59368 39626 .0... 09998 32222 ,36337 28529 28528 89134 88999 00000 00000 .0... 67890 55556 .046 .045 .044 .046 .046 16062 93827 78899 .0000 66666 11111 00000 00000 0.000 12345 66666 73949 16059 00111 on... 77777 11111 74285 40617 no... 66554 22222 87291 11224 07418 56801 00011 11111 00000 00000 000.0 67890 66667 .047 .045 .045 .346 .46 61628 49382 22334 0.000 77777 11111 .046 .045 0049 .044 QWM .046 0044 0043 .043 .046 49826 71615 45566 O O. .0 77777 11111 00000 00000 .6... 67890 77778 26928 04837 77788 O O O 6. 77777 11111 97890 41853 to... 00999 22111 82400 08654 on... 07531 12468 33333 1‘10 .044 0043 .043 0095 .u42 25946 26059 99000 on... 77888 11111 35676 07418 .0... 98887 11111 ,65742 333345 97531 ”91357 ,34444 11111 00000_00000 00000 0.... 12345 88888 ,00000 00060 67890 88889 03703 48271 11223 no... 86868 11111 51580 52641 no... 77666 11111 58534 67713 97642 80246 45555 111113 00000, 00000 0.0... 12345 99999 69347 59482 33445 .000. 86886 11111 25259 73075 00000 55544 11111 00870 69274 00000 08754 89135 55666 11111 3 00000 00000 no... 67890 99990 S(UV/K) INCREMENT PERCENT IRON S (UV/K) KG 145 00. EMFHN) CHANGE AT (UV) CHROMEL P VERSUS GOLD-0.07 AT. EMF TEMP. (DEG. K) -0851 01 02 08 20 20 45 00000 00000 00000 67890 _ 1 78696 74130 01170 .6... 80459 84281 54311 no... 86558 11111 37786 55268 00000 35789 33333 74759 49244 0.... 42197 35780 11112 00000 00000 00000 12345 11111 73297 14122 21111 C O. . C 29781 05419 97653 I O. O 0 .I777?. 11111 40.84 ‘”067 42.36 “594 (L42 22183 .42949 .0000 53085 24679 22222 00000 00000 00000 67890 11112 83815 22232 11111 .0... 30216 64185 21087 0.00. 774766 11111 01411 81356 .0. 444 444 43. 44. 70119 25664 00000 30741 13468 33333 00000 00000 0.... 12345 22222 05500 209H7 17000 0.... LY}666 33358 65432 .0... 66666 11111 00000 00000 000.. 67890 22223 -JBI 'JMS “OWN -JBE ’de --0.29 EMS -JWQ .004 50082 39519. 21110 0.... 66666 11111 OnfiXYU 00000 .0... 114345 33333 16.072 16.860 6. 48 IOJMQ 16.048 17134 27383 on... 21100 44444 _89974 33333 .0... ‘7395 67902 55566 .00000 00000 000.0 67890 .33334 59399 001‘] 00000 C. . C. 00000 00000 0.... .45345 44444 58725 22233 00000 0.000 86350 36926 11122 on... 66666 11111 .68149 38494 00000 76655 33333 15239 .56802 0.000 17306 23578 77777 00000 00000 00.00 67890 ,44445 |&-_ 146 PERCENT IRON CHROMEL P VERSUS GOLD’0.07 AT. 90. K6 AT S(UV/K) INCREMEKT (UV/K) EMFIUV) CHANGE (UV) .EMF TEMP. (DEG. K) 57701 33344 00000 6 . O O 0 52990 93605 23344 0.... 66666 11111 51653 06173 no... 54433 33333 94486 59372 28518 01356 88888 00000 003200 000.. 12345 55555 24927 93726 ,45566 66666 11111 19752 94062 000.0 22211 33333 96721 73963 ,41741 80135 89999 00000 00000 00000 67890 55556 53555 44444 00000 00000 25050 15049 77886 66666 11111 00000 00000 ,67890 12345 66666 0 045 .047 .047 .045 .045 .046 .0 52949 38271 99001 0.... 66777 11111 28.47 51:28 26.98 26.47 81893 1001 00000 29630 56802 00011 1111 00000 00000 on... 66667 5576 4444 000 000 50528 61504 12233 O O O O 0 77777 11111 00000 00000 0.000 12345 77777 55755 44444 00000 no... 38505 93837 34455 0.... 77$Ll7 11111 46941 49406 on... 32221 22222 31327 37161 00000 30853 24579 22222 11111 00000 00000 6.... 67890 77778 16161 26150 66778 0.0.. 77777 11111 00250 28407 on... 10009 22221 95860 74198 0000. 08631 12468 33333 11111 .OnXYUO OnXYUO 0'00. 1:234é3 88888 .044 .045 .044 .043 .044 50471 49372 88990 .0... 77778 11111 62951 30630 00000 99888 11111 92027 66666 no... 97531 91357 34444 11111 00000 00000 000.0 67890 88889 58984 62840 00000 77666 11111 55938 78712. 00000 97642 80246 45555 11111 H OnfiX!U_ 00000 192945 99999. 23221 44444 .000 on. .0 on 81356 72604 23344 00... 88888 11111 94083 51729 0.... 55443 11111 79604 46937 00.00 08653 89135 55666 11111 00000 00000 coal. 67890 99990 1 147 PtRCENT IRON CHROMEL P VERSUS GULD“U.07 AT. KG AT 100. S (UV/K) INCPEMENT (UV/K) EMF(UV) K) TEMP. (DEG. CHANGE M (UV) -1025“ 24.335 23.081 .00 .67 09 .00 19.88 0 20 20 452 75482 827081 63622 0 o .0 o 11... 49575 91121 30419 .000. 10998 2??!11 101357 74213 6.... 627174 12233 "56322 W68601 m00009 m46801 11 00000 00000 .0000 67890 1 23696 43646 111111 0 I O O 6 30459 74725 76431 0.... 88888 11111 33697 02058 0.... 79123 33444 60661 96035 .0000 76531 35791 11112 00000 00000 0000. 145545 78248 44944 11011 0.... 24280 16728 06764 0.... 87777 11111 56371 96628 45677 h44444 21713 54183 .97520 24680 22223 _00000 ,00000 , M67890 11111 11112 57255 53443 11111 O I. .0 58616 28406 31097 0.00. 775766 11111 .OnXEUO .005200 0.06. 193735 22222 54259 33197 11100 on... 17501 39891 64322 no... 66666 11111 07832 21097 0.... 99988 44444 30741 85059 .0... 29628 01356 44444 00000 00000 00000 67890 22223 61328 51741 11000 66666 11 111 45555 00000 00000 0.000 12345 33333 85701 11000 00000 WOO... ,...0 00000 00000 00000 .67890 33334 n, _ 73491 01112 00000 000.0 645.47 v661.44r 637.24 903:53 .026 .029 .030 .032 .034 98804 70370 01112 no... 66666 11111 00000 00000 .67890 44445 148 PERCENT IRON CHROMEL P VERSUS GOLD’0.07 AT. KG AT 100. b 9(UV/K) (UV/K) INCRFMENT EMFIUV) CHANGE EMF (UV) K) TEMP. (DEG. 69901 33344 010000 I I O O 0 09889 47159 22333 66666 11111 17306 16283 no... 98877 33333 60929 60382 63952, 02357 88888 00000 00000 0.... 155J45 55555 24059 48371 44556 0.... 66666 1111 l 39481 940E?! 000.0 66655 33333 05350 83952 0.0.. 851535 80235 89999 00000 00000 000.0 67890 55556 .044 .045 .095 .048 .046 38317 60504 67788 0.0.. 66666 111 111 33206 61615 0.000 44332 33333 89399 85308 on... 18528 78023 99000 111 OOXYUO OOOXXU 0.... 12345 66666 .044 .046 .046 .047 .045 .045 .046 .047 .046 .045 17305 93837 89900 0.... 66677 11111 15701 04837 00000 21009 33332 28717 75443 on... 52963 57802 00011 11111 00000 00000 00.00 67890 66667 06394 26150 1:1d23 0.... 77777 11111 00000 00000 .0... 12345 77777 0096 .045 .046 .045 .046 .044 .044 0046 .045 0096 .044 .043 0096 .044 .042 05162 59483 33445 .0... 7%LI77 11111 27748 25949 00000 63085 24679 22222 11111 00000 00000 0.... 67890 77778 60617 72615 56677 .0... 77777 11111 11494 06285 0000. 43322 22222 06004 62086 .0... 31964 13468 33333 11111 , OnXXUO 00000 0.... 1:5545 88888 14046 04937 88899 as... 7754!? 11111 00000 00000 000'. 67890 88889 26835 26059 00111 00.00 88888 11111 28218 49504 00.0. 09998 21111 25262 55467 00... 20964 91246 45555 1111] 00000 00000, 00000 1?§945 99999 .043 0043 .043 .044 .042 81480 38261 22334 0.0.. 88888 1111 1 37584 93830 no... 77666 11111 12105 89148 00.0. 20975 80135 56666 11111 00000 00000 .0... 67890 99990 1 II. Silver Normal versus Gold-0.07 at.% Iron Thermocouples 149 150 PtHCENT IRON NUPMAL VERSUS GOLD-0.07 AT. bILVER KG 0. A1 tMF(UV) CHANGL (Uv1 Eur K1 TEMP. (DEb. .acn 1109133 15.360 UB 00 20 20 7R#LSO 20902 6631?. 0.... 1J.187 1J.o92 19.059 14.396 14.616 14.761 1QOUI¢7 14.680 14.868 14.811) 14.732 14.620 14.4Hb 14.433 14.1bo 000....UxU ”.0000 o o o o o «UOOOU 22.91 35.96 h4.13 76.61 00000 00000 0 o o o o 67AKYU l .169 .086 .0 3 -00?2 “0052 00.000 UOUUO o o o o 0 00000 .nUIthO 311987 0 o o o 0 «JR 272 9.083% 00000 00000 c o o o o 17:?“5 1111!]. 42411.7 8.1356. 01.1111 0 o o o o U00.U.\U O O O O O OOOOHU RAYAC? 4171afl~ o o o O o 7%ch1RJ IOHQIAE 11122 00000 00000 0 o o o o _ 67890 11112 R7369 78999 111.1111 0 O O O 0 81823 REXUll 93048 O O O O 0 {ijJJ 11111 0413.000 00 U00 0 O O O O 00.UCO 5.13.13 .07 41:358 0 U . O . 0.11.703 3SOHU. 00000 00000 123/45 22222 0Q,751 090.90, 211.1111 0 o o o o 34721 11.18.19 .0864). o o o o o “JR—22.2.. 1111 1A 00000 0.0000 0 o o o 0 00000 90?.35 0.0.6.14 . . . . . 59./.57 0131417. 3.1.333 00000 00000 0 o o o c 67890 22223 8119/40; 88776 11111 O O O O O 3n7§Ib 4be3 06053 0 o o o 0 81.111. 111.11 00000 .U..1UAUHU.U o I o 0 0 00000 213 V “393 . O . 34.0 901 .. .fi‘~44 09.60 #1.R§ 3 3 00000 OnXYUO O O O O 0 192945 311953 48404 (055414 111111 0 O O O 0 46239 7.1016 liubfb O O O O O 1.1000 1111... 0.0000 0.0.0 .U.U o o o o 0 00000 427.59 438.68 449.68 460.91 411.05 00000 00000 0 o o o 0 67890 33334 0413062 33322 11111111.... 0 o o o 0 05597 3QAw31 48109 O O O O O UOXYU9 11.1.11 0.00 0.00 0.00 0.00 0.00 rfi14 Q31. .59122 0 o o o 0 113.22 R 9012 4.6.5.55 00000 OnXYOO O O O O O lafiJQS 44444 941RJ5 1110.U III-111.1) o o o 0 o 9.798 9.68" 9.573 9.465 9.360 000.00 0.UUOU o o o o 0 00000 825.08 CPU/49...). O O O O 0 2110.0 3456.7 SSRQS 00000 00000 a o o o o 67890 4144/45 S(UV/K) INCHFMEKT IRON PERCENT (LPJ/K) 151 5 KC ,1 ( tMFuW) CHANGE AT (NV) EMF 979.69 SILVFR NOPMAL VEHSUb K) TEMP. (OED. 29742 09999 10000 .0... 89286 5H1wh7 81095 0.... 99956 00000 00000 00000 00000 444.49 su~.oo 607.02 00000 OnXYUC 0.... 193745 55555 615.04 .089 .098 .086 .084 .082 7939, 89124 76054 0.... 56558 00000 UUUUU 00000 00000 OnfiXUO OnXXUO 00000 .b7AKv0 SKEflbb 09864 R7777 00000 ..... 78040 h813b 38210 0.... 66655 00000 00000 00.00 00000 hb7.64 679,08 6&4.21 00000 00000 .000. 192945 66L?06 692.38 700.45 00000 00000 no... 00000 05348 54318 ..... 9h429 01233 77777 00000 00000 no... 67890 66667 .057 .066 -JM6 .064 .0b3 82089 37047 65543 ..... 77777 00000 00000 on... 00000 50078 51715 00000 75207 45677 77777 00000 OnXYUO 0.0.0 Iid34dJ 77777 22099 66685 00000 on... 75567 15937 38110 00.00 77777 00000 00000 ..... 67890 77778 77654 SSSSS 00000 .00.. 7.020 0.963 0.907 0.552 (”798 b.745 OJMZ b.040 00.000 .U..UHUOO . . . . . 00000 65979 77653 00000 07418 28344 RRRRR 003200 00000 0.... 1?3945 88888 33210 55555 00000 ..... Ddflg b.b39 00000 OOOUU on... 00000 .bdghid 1R517 ..... S1831 9hb7H 89989 700000 00000 00000 .67890 88889 OQRR7 54444 00000 .0... ..._. 90847 84949 44338 0.... 00000 00000 00000 ...O. 00000 40241 27148 0.... 84173 89001 88099 00000 00000 ..... 12345 99999 00000 OOOUU 0000. 00000 51933 03467 ..... 36284 28334 gggqq 00000 00000 0000. b7fiXvO ,99990 S(UV/K) INCREMENT IRON PtHCEN] (UV/K) KG 152 5. EMF(UV) tHANGE VtHbUb 60LD°0.07 AT. AT (UV) EMF R NORMAL JILVE K) C TEMP, (DEU. 120053 ”‘— 16.640 0.00 .0Q .65 09 20 20 00 45 .987 .03 20752 IQ. RUG, ll IUQ3P5L 22946 545263 ‘d7i140 O O O O O 3J449 1111 1 3.9.58.0 OI;5ld 37:18|A 50025 9700 “um 23507 onxyuo OHXYUO 107890 1 2 4216 511.210, «fifldfld? 90235 l‘i:l 0000.0 0.0000 on 000 123/45 11111 62437 R1356 011-111 0 O O O 0 20.0310 332,836 7104471 0 o o o . QQMHQ 11111 .?b .20 27 .(7 .67 4 «(H9 9 ~14938U 0000. 7261.5 envoyl). 1‘{AC2 onfixgo ,Onfixgu .0... 67890 1:!!I2 87369 789.99 11111 O O O O 0 51883 unnunull .95 h, 4?. o o o o 0 35.3.3.5 III-1111 23Q.72 253.62 267.33 OOXYUO OXXUOO O O O .0 17:345 2222?. 2H0.59 29Q.lb OQ;L51 0999;“? 21:}!1 O O O C O 3 97 >91 11:}d3 0504?. Jaddd ‘II 1“ 11 .89 .29 .29 .J0 .30 79136 21947 7nflc97. 08345 1.33.4,‘3 00000 onxyuo o o o I 0 67890 22223 83940., 88176 111111 0 O I O 0 30.178 46.803 UHKEbj O O O O O altfll ll;fll 113Ed3 3.41:3 33 000 00 00000 00000_ O O O O. 19§JQS 33333 .418379 9418548494 .1110 06554 4 lllll‘llll O I O I O O I 0 O 0 0000000000 muonfixuonxxuo o o o I o c o o o 0 6789067890 444.953.5334 95062 ‘1‘}11 O O O O 0 0.5597 ”5.9631 4)Tku9 . O O O I OOBXU9 1111 0.0008 0,2565 0 O O O O 12222 89012 “AISCJCJ 00000 00000 0 o o o o 12345 414/444 153 SILVER NORMAL VLHSUS GOLD-0.07 AT. PERCFN] IRON TEMP. (DEU. m 5... O 0 ca... 00000 01000 on... 00000 000.. on... .000 00000 00060 00000 00000 00000 00000 00000 OOOOO 00000 0006) 00000 00000 ommmm mmmmm mflflflfl NNNQN 40003 03019 ommmm mmmw oomwo'mrumw O0$NO mwafi O0GN© mtumw O0®NO W¢WNW O0®N0 mcwm H 00600 00060 OOOOO 000°C OQOOO 06000 09000 00000 OCJOOO 0000C) DUI) 131313331) 13' EMF (UV) 530.05 SRQ.25 999.30 607.3% 616.30 629.13 653.87 642.52 651.09 659.98 667.98 676.31 6H4.56 692.73 700.82 70R.85 7|6.RO 724.54 732.4H 740.22 747.90 755.93 743.04 770.92 777.93 775%.28 792.57 799.79 I) f.) 7 . D J. ¢$wNN fl 0N0“ \0Ov-‘H 0 1mm IF'JT’D" b o o o o o C‘CN U‘INCWN N‘ 33‘5" D \J J7 O U" .... p. a: N 0 CL 889.59 , a r I» C I o O J 901.46 097.83 914.15 020.42 026.65 932.8} 958.94 045,07 Ar 5. LMF(UV CHANGE .36 .Jb .35 ..5h .36 .35 .35 .35 .55 .J5 .35 .33 03“ 034 03", .34 .34 .59 KG ) S (UV/K) 9.256 9.159 9.062 6.906 dob7h b.7H7 (30099 5.013 “.589 50"?“7 H.367 6.¢Rd d.dla 5.134 b.0hU 7.9Hb 7.914 1.543 7917‘. 7.705 COCONQ wawwx N O I O O O ~1CI~C~CO Char—NU (A cmcxrm -«»0UW— CDNNQJO 'N'O’U’U‘IN wC S(UV/K) INCREMEKT O'COOO 03000 CO .102 .099 .097 .094 .09g .089 .OHH .086 .084 o O '3“ N .060 UVU‘JVJ'VJ" UTUWLHUTJ‘ Ji'fi OWNJQJ L‘LflO‘xx 00 S(UV/K) INCREMENI .G44 IRON PLRCENI (UV/K) 12.280 12.630 KG 154 10. tMF1UV) CHANU1‘ AT (UV) EMF SILVER NORMAL VERSU: GOLD-0.07 AT. TEMP. (DEb. K) 4.22 5.00 02730 7.6570 C). 411?? 0296).. (”v0.1.9.9 9.5.2.40 o o o o o 3JHHQ 11.1111 .45 .67 .81 .93 1.01 92732 (966.06. 0 O O U 0 7.60250; 23.56? 00000 00000 0 o o o 0 67890 I 00000 00000 0 o o o o .IP3745 11111 1.7860 91.357 011.111... 0 O O O O 5.50““ .53047 70531. O O O O O 4 “94.9 111. Ill 1222?. 2222?. 0.... 11.111 973.40 6.1935 . 9.17930 (0 89 12 1.1.1122 00000 .0800 6780.0 111112 2.01.479 .H 8.990. 11.11.111.11. 23961.3 07001.1. 9804/. o o o o o 333J3 11111. 22233 22222 O .0 .0 11111111.. 77791... AC12271 . O O . 049.11g 14%qu 22922 00000 00.000 . . . . C 1.2345 22222 00,751.. 090.99 2111.111 0 C O O 0 39721.. 11123 ..Udhuqa . O . O 0 3.82302 lllkl Qibhila 22./.7155 o o o o 0 1111.1... 38./04 21847 ._813AR 023,95 _ 31.3.1. 3 00000 00000 0 o o o 0 678.90 22223 H3949 8977.0 11111.11. 0 I O O 0 30178 46803 06.053 0 o o o . 21.1.1.1. 11.111111 070236 ..53J33 O C O O 0 111.1111. 370.89 142.85 394.64 ‘ 00000 00000 12345m 33334 33333 417.64 428.95 14.8494 6.5544 1.1.1111. O I O C O 46./.39 7.1.01.6. 1.0-07.5 0 0 O O 0 1.1000 1111.1 67.801 33d 44 O O O O 0 11111 440.05 451.01 4h1.80 472.4h .00000 .00000 67890 9.13052 1.1193915!— 11111.11... 0 O . O 0 111.431) 10.205 10.165 10.039 9.917 1.42 1.42 1.43 1.44 1.44 57 493.34 482.96 503. 00000 . 00000 .0...“ 12345“ 44444. 013.64 623.46 58556 44444 O O O .0 11111 378323 520, 48 o o o o 0 31.221 314557 ._H_Sr3qr3 00000 00000 0 o o o 0 67890 44/445 SILVFR NORMAL VERSUS GOLD-0.07 AT. 155 PtRCEN1 IRON AT 10. KG TEMP. EMF EMF(UV1 5 S(UV/K) (0E0. (UV) CHANUE (UV/K) INCHEMLNI 51000 58101“ 10“h 90258 -0102 52.00 550.35 1.46 9.159 -.OQQ 53.00 599.46 1.45 9.062 ‘.097 SQOOU 609.47 1095 5.968 -0094 55.00 617.39 1.45 6.676 “.092 56.00 626.22 1.45 6.787 -.oa9 57.00 634.06 1.45 6.699 -.0HH 58.00 643.68 1.95 50Q13 -0086 59.00 65?.19 1.45 6.589 -.094 60000 660.67 10““ doq47 “.082 61000 th.QH 1.9“ 60367 -0080 62.00 677.41 1.44 6.208 “.079 63.00 665.65 1.44 5.210 ’.O7R 64.08 693.83 1.44 6.134 ’.076 6500 701.Q2 .6.“ £30000 -0074 66.00 709.95 1.44 7.986 -.074 67.00 717.90 1.45 (.914 -.o72 68000 725.7% 1.45 [0843 -0071 69.00 733.59 1.45 7.774 -.069 70000 741.33 1.95 (0705 -0069 71.00 749.01 1.45 7.038 ‘.067 72000 706.62 1046 70572 “.066 73.00 764.16 1.46 7.506 “.066 74000 771.63 1.96 70942 -0064 75.00 779.05 1.47 7.379 ‘.063 76.00 786.40 1.47 7.317 -.062 77000 793.69 1097 70258 -0062 78-00 900.92 1948 [0195 -.ObU 79.00 R08.09 1.4H 7.136 '.059 80.00 915.20 1.48 7.077 “.059 81000 RZBIZH 1.49 (0020 '0087 82000 889.24 1.99 0.903 -0057 83.00 936.18 1.49 6.907 '.056 84.00 843.06 1.49 6.852 -.055 85.00 849.89 1.50 6.798 .054 86000 Rsbo6fi 1050 0.745 -0053 87000 Rh3938 1.50 60002 -00L).1 88.00 970.08 1.50 6.640 -.092 89.00 876.66 1.50 6.589 -.051 90.00 983.23 1.50 0.539 -.050 91-00 889.74 1.50 6.439 “.050 92.00 996.21 1.50 6.440 “.049 93000 002.62 1050 bngd -0048 94.00 904.99 1.50 0.344 -.048 95.00 915.31 1.50 6.d97 '.047 96.00 021.53 1.50 0.850 '.O47 97.00 927.81 1.50 6.205 “.045 98.00 933.99 1.50 6.159 ‘.046 99.00 940.13 1.50 6.114 *.O45 100.00 946.68 1.50 0.070 ‘.O44 156 IRUN #tRLFNT NORMAL VERSUb BOLD-0.07 AF. SILVER 15. KG Al S(UV/K) (UV/K) I’JCREMENT E EMF(UV) (HAND (UV) EMF K) TEMP. ([)ELJo .472 0.00 .00 20 20 45 00285 72227 44321 0.... 77972 57920 bOJha 0.... JQuqq 11111 1.09 lo‘*9 1.88 2.08 2.29 0.5730 646.19 0 . O . . 13.7160 81a£h8 00,000 00000 c o o o 0 6.7890 1 4h325 Ofifigb ‘NHHHJJWIJ o o o o o 5 14.906 1%.962 1a.91 14.943 14.576 SH3149 Qthi7. 00.00 22222 QR.76 lln.AQ l~7.60 129.65 155.50 00000 00000 192345 11111 ‘92957 0111].. O C O C . 20.6.07 86168 70.3191 0 O I O 0 “494.4 11111 1&180h. 1.0.502 O O O O 0 05048 7H918 AUOOOO 00000 0 o o o 0 67890 11112 7713)) Ola/.23.; OHIOHC O O O O . QJJJJ 11111 89 .n9 H9 H9 90 O O 0 22,822 2Q2.39 256.23 2h9.99 $33.46 q(3.77 00000 00000 0 0 o o o 123/#5 22222 8.19wa 00999 O O O O O ... 1n¥353 Dgncedc} Ouxu42 O 0 O O O 5?.de 1.1111 959999 0 o o o a 22222 9147!] 8850.“. . . . . . 0.2.380 02346 1‘33143 00000 00000 0 o o o 0 67890 22223 00000 00000 0 o o o 9 12345 33333 4849/9 6.5594 0.... 4,0259 7161.10 108.]..3 o o o o 0 1.1000 11111 56802 .0001}. o o o o 0 333103 (+5017 6775].. o o o o 0 01234 314567 4144414, 00000 00000 0 o o o 0 67890 333319 356H9 11111 33333 8,603.... 603,9/4 . O O O . 45...“..rfirfi R..9.U.IZ hhrfiévrfi. 0000.0 00000 0 O o o c 12345 4441.4“ 9418.5 111100 111,1 o o o O o 9.79M 9.h8‘+ 9.573 90‘46‘; 9.360 015%J3 2.2.222 O O O O O 3331¢3 85691 7.06.1.6 O 0 O O O .554 41) 345h7. 95:19.5 00000 00000 0 o o O 0 67890 “44“5 SUN/K) INCHEMLKI IRON HLRCFMT b (UV/K) godqd 9.159 k'70 05/32 5 .908 5.576 KG 157 15. FMFHW) AT LHANHL (UV) FMF SILVER NORMAL VERSUB GOLD-0.07 AT. K) TEMP. (DEG. .102 OW) 097 .094 .092 3.89 JOC‘J 304,5 3oéb 3.60 34680 911/352 0 O O O O PHSCIAU...7 HQ. U11. 95666 OOJXYL OOXEUO O O O O O 12345 55555 .0H9 OHH .OH6 OUHQ 00732 79397 89124 70654 0.... SHUHH 773(68 226d). 0.... 33333 628.04 6%S.44 654.08 00000 00000 0 o o o 0 67890 55556 662.51 09864 H7_(__/.’ 00000 0 o o o 0 78040 huh/13.0 3221.10 0 o o o 0 58.855 3.28 3.89 3.69 3.69 3.30 670.92 679,25 637.50 695.68 703.73 00000 000.00 0 o o o 0 123145 66666 QBIQQ 77700 00000 .0... 0011!... 33333 0 0 O O 0 «1.15.333 15748.0 876/42 197.51). 116/......“ 77777 00000 00000 0 o o c 0 67.890 6.6667 .067 .Ofib .050 Q ”ht. .063 .062 .0.2 HUN/7089 1.7..UQ7 40.313 914 o o o o 0 77777 33333 0 o o o 0 33.333 7.5801 940.59 0Rh30 65h78 77777 00000 OGRXUO O 0 O O O 15§345 77777 050 059 00")" 75557 18937 .J..Cll\U O O O O 0 7777.7 33333 33333 .0... 3311.33 647,44 2R§LVO RS297 9.9001 77RAHR. 00000 00000 0.... 67890 77778 7.020 6.963 6.907 o.d%d US? .057 .056 055 .054 0.795 6.745 0.602 (3.590 6.599 6.539 33334 33333 0.... 3331.31,. 8.03 ..097 O O. 841 345 RRR 9.24.09 $221.39 00000 0008 0....7 IiéJhS 88888 33./....an 00.00.10 0 o o o o 3.34 3.3% 3.34 3.34 3.35 02907. 57.850 8.8.1..an 567.778 RRRRAH 00000 00000 0 o o I 0 67890 88889 098.87 94““4 00.01110: 0 O. O. _ . . .— 90897 8.4949 44.5%.). o o o o 0 6.0006 SShbb 33.4333 0 o. 00 33333 Qhag7 SAXTHI O C C O. RRQ9Q 00000 00000 0 o o o o 13§945 99999 75654 44/44“ 00000 0 o o o o _ . . _. UQKVQO 50.517 3,611.10 0 o o o o bbbbb 77664 33.5.33 0 o o o 0 33333 “58,536. 46890 0 o o o 0 39518 22344 09909 00000 00000 0 o o o 0 67890 99990 1 .‘7 {. .tvll,|tl..1 . 'lll-J; 158 SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENT IRON 20. KG AT S(UV/K) INCREMENT S (UV/K) EMFCUV) CHANGE (UV) EMF TEMP. (DEG. K) :332 .08 “£6 11 01 00 o. 01 03 05V .0 00 “do .60 oo 45 1L691AC nOQIPZu QQJ089 00... 1494:99 11111 goéilS 17fi965 0 0.00 4R5512 Zisza 00000 00000 0 000. A:£Ugo 1 00000 00000 0 0000 lagJQS 11111.5 .488QZV .02465u 1:111]. 0000. .46813v “J0§a{l 87¢§ic 0.... “74444 11111 “ILXYJ 0|f§£d 000.0 SRE#?5 ,la¥LcU 575390 .0000 ?§1160. 7HH;:J l‘5ggd 00000 00000 to... 67§XZU 1112 1901.0 1:944“ ORZYQC . O O C O “iiiéJ 11111 6RKXCQ 2?3:£J £59355 1:358] 7:9J82 000.90 402659 “Eglag figgdzz nxguoo AUOOXXU 0.0.. 1§EJ45 275fi£c -0202 ' £00 -0 99 ’0196 -0192 13.033 {2:238 12.443 12.251 5.36 3:28 5.42~ 5.44 312.34 353:6? 350.55. 362.90 88 26.00 55: 29.00 .OnXYUO OnXYOO 0.0.. 192945 .J3119J w2.35.19 00551 915Ld8 liU87éJ O O O O O 11000 11111 ODEilg bfizybb u55555 444.3% 455.2 466.08 476.74 onfixuo 00000 000... 675290 31§XJ4 OAXEIZ “14:42 11::!l .0... .IREibb 4n¥y42 417109 .000. 0nXXU9 1:!11 045%56 21?:00 11111 O O O I O 6932d6 OQéglb 865743 996329 0I5fi34 ABBBREU CO... SCEibS 83702 86282 0.... 77766 34567 55555 Sonxguo OOXYUO 0000. 67hXZU ALTQQS 7L“. KG 159 20. tMF(UV) CHANGE AT EMF (UV) SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENT IRON K) TEMP. (0E6. “.HB -0099 "338 3093 34629 66677 21098 99988 56778 88888 55555 45792 57888 0.000 54321 89012 55666 00000 00000 0.0.. 12345 55555 99653 88888 00000 01507 90134 77654 88888 90012 89999 55555 00000 00000 00000 67890 55556 09864 87777 00000 .0... 78040 68136 32210 0.0.. 88888 23455 99999 55555 695347 58134 31086 78990 66667 00000 00000 .0000 1234.5 66666 67890 99990 55556 73138 44318 42085 12334 .77777 0 00 00 00000 00000 67890 66667 ‘5067 ‘N066 '5066 '5064 '5063 -0062 82629 37047 65543 0.... 77777 01233 00000 O .0 .0 66666 201 726 CO. 863 678 777 17 753.56 761. 00000 00000 .0... 12345 77777 .06 '5060 “d59- '5059 75567 15937 32110 .6... 77777 00000 00000 6.... 67890 77778 77654 55555 00000 to... 03728 26059 09987 0.000 76666 77889 00000 00.00 66666 32658 88764 63074 23445 00000 00000 12345 88888 ”33210 _55555 A 00000 2099 9483 76655 66666 45 90123 , 01111 .66666 68686 29628 17417 .66788 88888m 88888 ”00000 00000 00000 67890 88889 90247 84949 44332 66666 45678 l 1111 66666 86869 38269 40739 9 0011 , 899996 00000 00000 1 0.... 12345 99999 '5047 3 822 -JMS 'N044 6.250 8:?83 8:373 99863 11111 00.00 66666 926.27 235:2? 944.79 950.85 00000 00000 00000 67890 99990 160 SILVER NORMAL VERSUS GOLD‘0.07 AT. PERCENT IRON 25. KG AT S(UV/K) INCREMENT (UV/K) EMF(UV) CHANbE UN) EMF TEMP. (DEU. K) .337 71 71 O I ll 04 00 01" 20 20 45 37285 05870 32111 O O O C 0 52427 17533 46801 c o o o 0 44455 111151 00000 00000 0 o o o 0 67890 “1 96272 32359 00000 0 c o o c 62031 70712 12110 O O O O 0 55555 11111 00593]. 47035 66777 10781 79012 94050 91346 1111 00000 00000 0 o o o 0 12345 11111 90301 14578 11111 6 6 6 6 6 22998 06035 97642 a o o o 0 44444 11111 56515 67899 “77777 A 32632 _ 19503 .59493 7.8013 11222 00000 00000 0 o o o 0 67890 11112 0:7518 99000 11222 O U I O 0 815?13 67776 08642 O O O I 0 43333 111} "315.08 193 “.203 3§§ 13.060 :82; 1% 13:32? 9357 01111 O O O O 0 8888 358:9: '32%:§%' 26.00 55:88 53:88“ 05050 98877 11111 0 o o o 0 61166 79136 08753 a o o o c 21111 11111 00000 00000 H 60605 66554 11111 0 o o o c 00449 04838 20,875 I O O O 0 11000 11111 25702 333 .44 88888 13017 90084 57889 X34SA¥7 44444 00000 ,00000 12345 33333 67890 33334 06284 4332 1111 o o o o 0 93139 41852 43109 O O O O 0 00009 1111 00000 00000 c o o o o 12345 44444 345 67 55555 88888 1,6035 6 3059 0.000 00098 _ 4 56 67 55555 00000 00000 O O. 0. 67890 44445 S(UV/K) INCREMENT 161 PERCENT IRON (UV/K) EMF(UV) CHANGE UN) EMF SILVER NORMAL VERSUS GOLD-0.07 AT. K) TEMP. (DEU. 305:2J 0an99 111000 00. so 77941 6AZEIB 213u98 OI... QXZVBB 633.37 89 87 8 -0085 -0083 -0090 .17ti07 gnYiJQ 7;!054 o 0... BRHQEB 00111 bkzybb 893368 $5 648 65 659.35 667.34 00000 00000 000 00 61A090v .bqéibé 005964 87777 00000 0.... 7RXV40 6R7156 3?5?§U BHEHUB 293EJ3 éfiZyOb 9:9588 50X711 ?EX§01 O O O 0. 645?19 78900 66Z¥LI 00000 000 00 13§345 66KYPO fkaTA99 77766 00000 O O... Lu43AéJ 8122I0 n79875- o 0... 77%LI7 8.63 8.64 8.64 8.64 8.64 49782 11097éJ o 0000 _7C%EUB ,1OQJ44 H774LI7 00000 0 0000 0 0000 61:690v 6AYOb7 -0067 -0066 -0066 -0064 -0063 -0062 -0062 -0060 -0059 “ -0059 8?:3C9 37047 65543 0.... 77777 L44413a 66:306 BRXPBB 903311 ‘IBQKQd 00.00 617156 Sagila 77§LI7 00000 00000 0.... 12345 77777 7c§367. 1RXZJ7 114110 000'. 77777 397510 652906 BRSRHB 54é311 . 5RXXC3 .0... 303:2d 905Y12 .IRQXUB 00000 00000 0.0... 673990 77778 Oiglda ZAXng 09987 7:9066 0:9776 ngbss Rxgflas Q:QDSQ. R:255R. o 00.0 RXQUBB w?:§917 7'4075g "30730 A:L789 BQSSHB -0047 -0045 -0046 ‘0045 -0044 0:3740 SnE317 Ad7T510 OAZYOO gnKXUB 55:905 BRHRUB 05:00 800 00 90 90v 96.00 97 98 S(UV/K) INCREMENT (UV/K) KG 162 30. EMF(UV) CHANbE AT (UV) SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENT IRON EMF TEMP. (OED. K) .563 .09 .JG 4“ ll 07 08. o. 0.... 0Q, 04. 01 20 20 .45 .1971J0 .164iA9 210510 00000 0?54£d Sléilb 8n7£d3 00.0. “REiDS 11111 .UQQ‘EJ 605%40 3GZ¥IB .U991Zu .IQfiXJ6 .0... GnZYlb ZadiIB 000 00 00000 on... A;A590 I. -0006 '0014 ‘.037 -0097 -0097 69%38]. §Z2901 31iJ21. 0.... 5REXDb 11111 1CX742 7%?003 ...... nbgoXYU 11 16702 013090 0.0000 27.273 015346 1:!III. .005200 OHXUOO o 0000 .193745 11111 497415; SCCIIB 1177:] 0.... 14.952 12:32? 14.468 14.280 ,QICfgb 0:31690 .OnflXYI _ 11111 “27693 ”08504 AQua/71.5.6 7Qfing AxfldP5L onxxgo .0000 LOTBQfiv 1112 2Q7:£J OOKXUg 295:?1 0 out. onxxuo 005300 ,0.9000 675390 AC?5:C3 91:266 SAYQI7 ...... 11:511 11:511 QRXZJg Itlgfifiv .0... 117308 AflQnYIZ 317944 00:200. OnXYUO CO... 192945 311253 60Z916 665354 17:11]. 0.000 8H5fiib n37949 “(Onglb O 0 O O O .1IKYUO 11111 003200 onxyoo 00000 675290 313:5“ thb98 SQ‘i‘C .0... 1:9444 9n¥123 4:55QQ; 00x300 0nx000 IzéJQS 44444. .1fixzds 21100 1:1111. . .... 26350 19877 86543 .0... 906329 800716 007011 c 000. .d95fid2 1111 R71379 .IQ(:UQ 0.... “15:32 QRz3IB .bfifiibs onxxuo .onxxuo o 0000 .675390 .HQQQéJ S(UV/K) INCREMENT (UV/K) 163 30. KG EMF(UV) CHANGE AT (UV) SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENT IRON EMF TEMP. (DEU. K) AdWZYIB 9n¥iJ4 7;!054 Rxgbba .444GEJ 117111 0.0... 9:£d22 11111 1AV198 0:9J83 .0... build1 179367 AY9b66 19864 87777 00000 .0... 7QXV40 6RY156 1<£d10 co... uggfida (39667 117111 on... 9:£d22 11111 9?;i55 7:1J56 0.... 909042 «(8907. 6665;: onxguo 00000 00.00 1:£J4S £39666 -0067 ‘0066 -0066 -0064 -0003 9:4029 1:104? £39543 0.... 77777 QA2999 11111 0.... ?:£622 1111.1 967 837 .0. 429 788 777 759.74 767.35 00000 00000 O O O O O 19§J4S 77%117 7:£099 £39055 00000 ...... 7;?bb7 1;?937 3)T§10 000.0 77777 $5876E4 11111 O 0.00 9:£d22 11111 10;:I6 1:9078 00... 7:?185 039112 78898 00000 00000 0.... 67890 77778 -.057 -0057 -0056 -0055 -0054 01%158 fiTQUS9 0:2957 7:00bb 415:10 11111 00.00 9:£622 111111 nxg180 Qggdbs coco. 9k7030 1:9456 QXEUBB 00000 00000 O O O O O 1i§J45 Rxgbaa 0:2988 1.0.000 00000 273§£C 11111 ’073QT1 9:?028 00000 73073 fi$A689 RXQHBB OnXHUO OnXXUO 00... 5:1690 Q:9589 -0050 “0049 -0048 4 089§ -0047 -0045 -0046 -0045 -0044 6.489 b.440 b.392 8:33? 0c3740 G:2317 924110 AYOObb 164 SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENT IRON 35. KG AI S(UV/K) INCREMENT (UV/K) EMF(UV) CHANGE EMF (UV) K) TEMP. (DEU. 3'54 03 03 02 0 - 1.95 0 20 20 195 1728.0 1.0885 1.1000 0 o o o 0 07977 88650 23456 O O O O 0 555.55 11111 15096 53912 46790 1 10597 03728 0 o o o 0 727138 24578 00000 00000 0 o. I. 67890 1 17581 83430 55432 0 o o o o 55.3.5.3 11111 58877 181493 0 O O O O 1.1223 11111 50637 40/480 0 o o o 0 140.506 02356 1 1111 00000 00000 0 o o o o 12345 l 1111 9887 38788 115111.. 0 O O O 0 201.36 68012 08753 0 o o o 0 5140.44 11111 95637 69134 33444 11111 w71759 11848 .1059 801.123 h11222 _ 00000 00000 0 on o 0 67890 1112 82686 , 99100 1.1272 as... 86026 23210 19753 O O O 0 0 43335 1.1.1.1]. 73840 0.00.12 0 on o a 45355 lill :38 372.66 321.95 33% 360.27 26.00 :88 55 29.0 30.0 27561. 98877 11111 O O O O 0 58376 0.1358 1.9753 0 o o o 0 211.11 11111 00000 00000 0 o o o o 123/45 33333 00000 00000 0 o o o 0 67890 33334 1.8283 43322 11111... c a o 0 c 68685 62964 43.109 0 O O O C 00009 1111 00000 00000 O O O O O 12345 44444 05208 21110 11111 O O O O 0 50880 21985 87543 c a o o 0 99999 00000 00000 0 o o o 0 67890 “41445 S(UV/K) INCREMENT PERCENT IRON S (UV/K) 165 EMF (UV) CHANGE (UV) EMF SILVER NORMAL VERSUS GOLD’0.07 AT. K) TEMP. (DEG. 4|AV64 00999 11000 o_.... A:?606 77788 971098 0.0.. 99988 089123 059000 0.00. 56666 1111 80248 ,69005, ..... Q77431 98Y123 £79666 005300 OnXUOO 0600. 11EJ45 5RE123 10864 082888 00000 00.00 a??? 8.631 8.447 8.795 8 8 .4567éu 00000 00000 Ay9666 1111 275711 85283 00.00 09865 44567 66666 00000 00000 00000 £31890 SCE§56 42199 77766 00000 ..... LYQJQS 81470 n29877 0.... 77777 00000 00000 00.00 ,67890 ,66667 '.067 '5066 .5066 .306“ .5063 '5062 'H062 .5060 ‘0059 -009; .3057 .3057 .5056 -.055 ’.054 82629 370/47 65543 O O. .0 77777 66777 11111 on... .66666 11111 12695 73837 171863 67789 77777 00000 nXYUOO 0.0.0 IiéJQS 7%LI77 75567 15937 32110 00.00 77777 77665 11111 00000 66666 11111 08066 ,13678 ...... .0... .18529 OnYidz 88888 00000 00000 00000 67890 77778 7.020 6.963 6.907 6.852 6.798 00000, 00000 12345 88888 21112 11111 0.000 66666 11111 89684 29628 00000 17417 77899 88888 00000 00000 00000 67890 88889 'N047 -0045 '3046 'HOQS .3044 05940 50517 22110 66666 88762 11111 . O. . . 66666 1111 936.26 942.49 998.66 954.78 960.84 00000 00000 0.000 67890 99990 l— i i in VS .115 KG 166 40. EMF(UV) CHANGE AT (UV) SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENY IRON EMF TEMP. (DEG. K) 0977 458.13 77788 O O O I 0 55555 1111 49904 46525 O O O O 0 57912 11 45505 96431 O O O O O .I39cf; 24579 00000 0800 o o. 00 678 90 1 64777 25877 00011 O O O .0 17036 1579.1 87643 O O O O 0 55555 11111 69692 65395 34556 11111 60452 97382 0 o o o 0 62839 02356 11111 .00XEUO OnXYUO 0.... I§£JQ§3 11111 25156 54555 105:53 O O O 0 0 54444 11111 50044 93680 .0... 67778 11111 3616.1 44394 49483 89124 11222 00000 00000 0 o o o 0 67890 11112 87600 900111 127.22 0 o o o c 81555 55432 19753 O O O I. 43333 11111 183(87. 23456 O I O O 0 88888 11111 69244 66515 O O O O O 7159?. 57891 22223 00000 nXUOan O I O O O 12345 2222?. 9721.6 00009 22221.. 0 o o o 0 69760 110001 19753 O O O O 0 322.22 11111 53073 78990 0 o o I 0 88889 11111 43209 77514 58146 23567 33333 00000 00000 0 o o I 0 67890 22223 57484 98877 111} O O O O O 5846?. 12469 .1973 111} 00000 00000 000.00 67890 33334 18283 43372 1‘11} 0 O O O O 088 00000 0 6 o o 0 44444 05298 21100 1111‘ O O O O 0 6.1902 21998 87543 0 O O I 0 99999 66677 55555 a o o o 0 99999 11111 38134 63059 0 o o o 0 11109 56788 55555 00000 00000 0 o o O 0 67890 44445 S(UV/K) INCREMERT (UV/K) KG 167 40. EMFHJV) CHANGE AT (UV) SILVER NORMAL VERSUS GOLD-0.07 AT. PtRCENT IRON EMF TEMP. (DEG. K) 42974 00999 11000 86706 77788 21098 99988 77777 55555 99999 11111 C7979] 24555 98765 9n¥id3 56666 00000 00000 0 o o o 0 12345 55555 10963 90,888 00000 I O O O 0 55607 90134 7765 4 88888 77899 55555 99999 11111 49532 30738 417208 4 5.677 66666 00000 00000 0 o o o 0 67890 55556 09864 87777 00000 0.... 780 40 68136 32210 88888 023 46 66666 99999 11111 48434 25801 6.6... 75320 89012 6A5Ll7 00000 00000 O O O O 0 193945 66666 42199 77766 00000 0.... 64345 81470 “99875. CO... 77777 7in44 .66775. 9999 llll 85472 1.1086 86419 23455 77777 00000 00000 c o o o 0 67890 66667 76643 .6 666.6 00000 c o o o 0 82629 370 47 65543 O O O O 0 77777 57890 77778 .6... 99999 11111 12768 39493 0.... 74297 67889 77777 00000 00000 0.000 IiEJ4S 77777 -.062 “.062 ‘.060 ‘.059 -0059 ‘.057 -0057 -0056 -0055 ’.054 75567 15937 32110 O O O I 0 77777 00100 888 88 999 99 111-all 324.11 70245 .0... 42963 88888 00000 00000 .0... 67890 77778 03728 26059 09987 76666 00000, 00000 O O. O. 12345 88888 000905 00000 O 00 00 ILEJQS 99999 -0047 -.Oufi -0046 “”0045 -0044 05940 50517 22110 O O O O 0 66666 01196 88877 99999 11111 82028 RVAJ44 O O. O 0 96284 . 95 95 96 93 94 00000 00000 0 o o o 0 67890 99990 .1 S(UV/K) INCREMEKT (UV/K) KG 168 45. EMF(UV) CHANGE AT (UV) SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENT IRON EMF TEMP. (OED. K) :752 2 ,4 01 o. 66 ll 014 02 o o 03 20 20 45 96880 04996 00100 0 o o o 0 37977 72228 11900 0 o o O o 666 66 111 11 65879 28095 0 o o o c 68124. 111 713 80 789 02 84073 24679 00000 00000 0 o o o o 678 90 1 772 997 21 .049 .001 6701.71 33481 1:1865 O O O O 0 6655.3 1111 73144 91196 O O O O I 57889 1111 74904 22083 0 o o o o 9512 0247 1111 00000 00000 O O O O 0 12345 1111 4 7437 13211 22222 70636 96320 20.864 0 o o o 0 55444 11111 21276 27147 0 o o o 0 00111 ,22222 n07393 793951 .6... .72727 080134 12222 00000 00000 O o o O 0 67890 11112 36756 10009 22221 6 6 6 . . 04726 32111 19753 0 o o I 0 32222 11111 00000 00000 0 o o l 0 67890 22223 38494 98877 11111 O 6 O 6 O 3RTi§8 23579 19753 O O O O 0 21111 11111 8 .90 50 04838 76554 .1111 O O O O O _..... 84635 ItbOch 20976 O O O I 0 111000 ,11111 00000 00000 0 o o O 0 67890 33334 39394 4332 1111 O O O O 0 23017 62963 427509 0 O O O 0 00009 1111 03568 66666 0 o o o o 3333 2222 549.10 1:4129 O O O O 0 55555 01234 55555 00000 00000 66.... 11£J45 44444 ,17396 2100 1111 O O O 6 O 69671 19877 89543 .6... 99999 169 SILVER NORMAL VERSUS GOLD—0.07 AT. PERCENT IRON 45. KG AT 5(UV/K) INCREMEKT (UV/K) EMF(UV) CHANGE EMF (UV) TEMP. (DEG. K) 89040 66778 PT£U98 99988 333.91%. 77777 0 O o a o 3.4.333 22222 12468 46776 32109 01233 _ 66666 00000 00000 0 I O 00 12345 55555 18741) 98.888 00000 O I O O 0 911907 80134 77654 88888 00000 00000 a o o O 0 67890 55556 78040 68136 322.10 6 O O O 0 88888 147.199 7766 00000 0 o o o 0 64345 81470 99577 .0... 77777 01223 8888 o o o o 0 31.1333 282?. 16561 3?.197 0 o o o 0 20853 34456 77777 00000 00000 0 o o o 0 67890 66667 82629 37047 6.35.43 6 O I O 0 77777 33333 88888 I o o o 0 33333 22222 89301 39504 O I O O O 18641 77890 77778 00000 00000 O O O O O 12345 77777 -0062 -0062 -0060 ".059 -0059 -0057 “.057 -0056 -.OQS -0054 75567 15937 32110 O O 0 O O 77777 00000 00000 6.... 67890 77778 03728 26059 . 09987 0 oo no 76666 844.54 00000 00000 0 o o o 0 12345 88888 3310 5.5555 0800 00000 . C O 0 . 67890 8889 00000 00000 . O C O . 12345 99999 -0047 8“5 46 -QOQ‘O 05940 50517 22110 O O O . C 66666 79 79 23.78 ‘53: 23.79 23.76 988.86 9 . 956.18 962.41 968.48 0800 00000 O O O O 0 67890 99990 1 170 SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENT IRON 50. KG AT S(UV/K) INCREMEKT (UV/K) EMFlUV) CHANGE EMF (UV) TEMP. (DEG. K) .013 14 77 6. 11 03 06 02 20 20 45 48875 01656 11000 0 o o o 0 02472 20371 65433 66666 11111 16686 22809 CO... 70256 1111 11287 72715 .0... 96295 24679 00000 00000 0 o o o 0 67890 1 14777 71.480 0111?; o o o o 0 17036 42898 21975 O O I 0. 66555 11111 59399 58097 .0... 89112 11222 51149 80084 0.... 18495 12457 111} 00000 00000 c o o o 0 12345 11111 42985 13211 22222 20138 74197 31964 0.... 55444 11111 75340 40593 on... 34445 22222 50477 92206 on... 06160 90235 12222 00000 00000 0 o o o 0 67890 11112 07159 21211 22222 00000 81056 54208 20863 no... 44333 11111 06998 68024 .0000 55666 22222 51465 02183 00000 59360 67902 22233 00000 00000 on... 12345 22222 91974 11000 22222 00.00 76706 65443 19753 so... 32222 11111 00000 00000 00000 67890 22223 31614 99887 11111 .0... 396.85 408.90 420.76 433. 44 . 3 33 28079 47161 20976 to... 1000 11111 00000 00000 no... ,67890 33334 39295 43322 11111 O O O O 0 65143 00000 99000 01345 55555 00000 00000 00000 12345 44444 18417 21110 11111 00.0. 00000 00000 0000. 67890 44445 PERCENT IRON S(UV/K) INCREMEKT (UV/K) KG 171 50. EMF(UV) CHANGE AT (UV) EMF SILVER NORMAL VERSUS GOLD-0.07 AT. K) TEMP. (DEG. 315764 00909 11000 no... 1:9717 779188 QT£U98 0.0.. 0‘7985 00000 00000 0 o o o o 19:945 qaflgbs 119664 OAZUBH 00000 0.... 665:46 901134 74’654 939668 1f3378 1111 00000 Bflfigfla 2?§:£C OfifiTAC 953394 21087 56778 _66666 00000 00000 00000 Aglbgo SCE356 .199394 87777 00000 no... 78040 6H7136 119410 O .0 O. ngbaa 07:?69 9:5(22 0.60., 9:9688 2?;figd 4Q£357 812367 54208 90122 67777 00000 00000 O O O O O 1:534R. 68:966 4?TA¥9 775166 00000 on... .6434éa 81470 “99677. 0.... 77777 115178 31%233 8R5268 5(22?5g :18817. :676R5g 645%08 «3456Av .77777 00000 00000 00000 .67896v .666A;l 7:9643 Ay9666 00000 0.... .-... RX§629 1:1U47 8:2643 0.... 77777 OIL/:6... 144444 0.... “688886 .42295. ”37201. 0;?160 .0... ::9186 7L§990 744778 00000 00000 0.... 1:4344. 744777 “.062 “.060 ‘0059 -0059 7é3367 .15917. 397510 .0... 775177 28.43 28.42 28.42 ‘28046 .64611; a368n¥1 «307:5; Ii£d34 RXQUBB 00000 00000 0.... £31690 77778 28.4 13 31 849.14 856. 863. 869. 876. 883.49 00000 00000 00.00 1:4345 EXQUBB 28.32 28.32 28.32 28.32 28.33 .685 n640 20 .630 .901 .899 890 00000 00000 to... AZlUgo nxguag OnXXYU nXYUOO CO... 19%945 99999 -.047 -0045 -0046 -0045 -0044 n:?940 50517 9fi€l10 O O. .0 536666 00000 00000 O O O O O £31690 A99906v 1 172 SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENT IRON 60. KG AT S(UV/K) INCREMENT (UV/K) EMFCUV) EMF (UV) TEMP. (DEG. K) CHANGE -0108 57 87 .I7 1.... 04 06 02 20 20 45 82825 588 62 22111 97972 68931 4.1987 0 o o o 0 7706.0 1.11111 0800 00000 0 o o O o 678 90 1 11472 95892 0111/.“ o o o o 0 00000 00000 O 0 O O 0 12345 11‘! 00000 00000 o oo o 0 67890 1112 8 4696 22.122 22222 84893 3.1964 42975 O O O O C 44333 1111‘... 32.61 33.05 33.44 33.80 34.13 69961, 03430, 260.48 780.12 22333 00000, 00000 a o o o 0 12345 22222 81751 22111 22222 O o o I o F347?T. 197.05 308.04 0 O O O 0 33222 11111 00000 00000 0 o o o o 123 45 3333 148/471 76.055 1111 O O O O 0 46254 14827 3198b 0 O O O O 1.000 11111 ,080 00000 o co 6 0 67890 33334 52426 1111 C C. C. 0800 0800 o oo on 12345 44444_ 2 569.55 79 9 8 8 ,OnfiXEU 00000 0.000 67890 441445 PERCENT IRON S(UV/K) INCREMEKI (UV/K) KG 173 60. EMF(UV) CHANGE VERSUS GOLD-0.07 AT. ' Ar EMF (UV) SILVER NORMAL TEMP. (DEG. K) 52085 00099 11100 O O. I. 00000 OnXYUO O I O 0. .1?3?45 55555 5R4116 23467 87L354 0.... 88888 00000 00000 00000 .67806v 5:6556 nXUOan OnXYOO OI... .1?§J4S 682966 54310 77777 00000 0.00. 40766 03587. 09877 0.... 87777 82692 23334 no... 88888 33333 87930 “77653 ,64208 45677 77777 00000 00000 00000 .67806v ,66667 00000 OnXUOO 0.... 1?3f35 77777 “.064 -0083 -0061 -009; '5060 “.0 96566 15937 39?§10 .00.. 77777 38.48 38.47 38.45 38.40 19931 30752 23345 88888 00000 00000 0.... 67890 77778 87754 55555 0000 00.0 81495 16049 09987 76666 00000 OnXYUO 0.... 195945 88888 19878 21111 00000 88888 33333 _77230 _30739 .0... .30639 90011 .89999 00000 ,00000 00000 67890 88889 '3050 'H048 .3048 -0047 45792 83839 44332 66666 92605 12233 00000 88888 33333 926.43 932.92 939.38 995.79 952.16 00000. 00000 1i§345 99999 45 46 3 - 'H045 -.049 -0047 6.245 {82 6.109 6.065 6. 6. 38.40 8045 8.48 38.48 38.45 5’ 958.48 3:3? .11 983. 7 39 “977 00000 00000 00000 67890 99990 ....Il: a“ i. . .l‘ t.ll..‘anf r. J. S(UV/K) INCREMEKI PERCENT IRON KG S (UV/K) 174 70. EMF(UV) CHANGE AT (UV) SILVER NORMAL VERSUS GOLD-0.07 AT. EMF TEMP. (DEG. K) -:335 94 28 ll 06 08 o o 05 20 2o 45 BCXYIS 917130 0 O O O 0 05925 1.1122 816.16 43946 31863 35680 00000 00000 0 o o o 0 67890 1 14722 15903 21.122 0 o o o c 17086 04¢??1 976191 66666 111111 11§LIB 44.169 79.123 22333 14538 75.156 07406 23578 11111 00000 00000 c o o o 0 135345. 11111 25695 9§£581. 96308 O O O O 0 55554 11111 217::2 11085 O O O O O 569L78 33333 08239 62798 28383 015946 22222 00000 00000 0 o o o I 67890 11112 -0227 -0230 -.245 ’o226 -0244 '.235 88373 8:?584 53.186 0 O O O 0 44433 1 1111 65884 17272 0 o o o 0 9900.1 33444 19341 6033.... O O O O 0 815115 79023 22333 00000 00000 0 o o o 0 12345 22222 -0218 00000 00000 0 o o o 0 67890 2223 72714 00998 2211.1 0 O o o 0 75873 000.13 3.1975 0 o o o 0 2211.1 11111 615100 36813 .0000 33344 44444 6QX?13 9 1106 25790 12346 44444 00000 00000 O O O O O 12345 33333 89976 766.55 1111.1 0 o o o 0 00000 00000 0 o o o 0 67890 33334 72846 44332 111.11 0 0 o o 0 75737 517 41 54210 00000. 1111‘]. 00000 00000 0 o o o a 67890 44445 PERCENT IRON S(UV/K) INCREMENT (UV/K) KG 175 GOLD-0.07 AT. 70. SILVER NORMAL VERSUS AT EMF EMF(UV) (UV) CHANGE TEMP. (0E6. K) SEORFJ 00090; 11100 O O 6 O D 00000 00000 O O O O O Ii£345 55555 8.844 8.752 8.663 8.577 8.492 53087 .012?33 ,6666Zu .94444 24720 86306 09875 77890 66667 00000 00000 0 o o o o .67808v (#2356 31097 98877 00000 c o o o a “28892 n22469 437730 88888 00000 00000 0 o o o 0 .12345 .96666 64321 77777 00000 .0... 62976 14692 09877 O O. .0 87777 00000 00000 c o o o o $31890 .6666? .085?Eu 21110 77777 44444 39929 13577 .29615v «23456 888R§u 00000 00000 0.... 67890 77778 881.64 0 867.79 874.74 888 895 00000 00000 O O O 0. 12345 88888 48 28 3321 85555 00000 0 o o o 0 .52976 49393. .16655 66666 00000 00000 0 o o o 0 191890 88895. 00000 00000 000.0 I§£J4S n99999 -004? -0045 “.046 -0045 -0044 F50495 4050zv 964110 .0... 166666 47.30 3% 47012 46.87 47 47 993.39 .6 379.7% 985.75 991.59 00000 0:9000 no... £31890 .99990 S(UV/K) INCREMENT (UV/K) KG 176 80. EMF(UV) CHANGE AT (UV) SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENT IRON EMF TEMP. (DEG. K) -0166 03 09 06 05 06 20 20 45 00000 00000 no... #67890 _ . l 19227 790,03 . 11‘22 1208.1 66763 19753 o o o o a 76666 11111 $8.182 36740 O O O O 0 13579 33333 50932 68637 41.851 24579 11111 00000 00000 0 o o o o 12345 11111 97970 33756 222?.2 0 o o o 0 25699 957.15 08530 O O O O 0 65555 11111 89731 35665 ,01234 44444. 65868 387378 0 o o o o 739/49 02356 27.7.22 0800 00000 500000 5 67890 A, 1.1.1.12 17864 66656 22222 O 0 O O 0 00000 00000 000.0 IS§J4S 2222?. 01.1903 ...-.09 89 2211.11, 0.0... . 6 6 432.58 420.28 444 456 468 §’ 85929 44332 11111... O O . Q C 27867 05185 643.10 0 O O O 0 00000 11111 70121 02345 0 o c o 0 33333 55555 21663 612367 728,32 2211!] 111111 0 O O O 0 08075 3097.6 98654 99999 97417 56788 .0... 33333 55555 78875 64.172 ....._O..O. 4.5555 5554“ 34567 3 890112 55555 5 000005 00000 o 6 o o 0 123453 44444. E 55666 __ 00000 00000 000'. 67890 44445 PERCENT IRON S(UV/K) INCREMERT (UV/K) KG 177 80. EMF(UV) CHANGE AT EMF (UV) SILVER NORMAL VERSUS GOLD-0.07 AT. K) TEMP. (DEG. 76318 91009 01110 O I O O 0 00000 00000 A 12345 55555 679.07 55556 “0091 '.086 -0093 3 833 8.857 8.764 8.672 8.581 8.495 54.30 54.38 54.46 497 628 90 653 677 687 9 0 1 00000 00000 on... 67890 54.55 54.64 43220 8H8R8 00000 0.000 18644 12468 43210 0.0.. 88888 31086 78990 .000. 44445 55555 68174 37135 20975 23345 77777 00000 00000 00000 12345 66666 86514 77777 00000 .0... 60540 03581 09877 .0... 87777 40615 ,12233 55555 55555 346953 66542 31975 567789 ,77777 ,00000 100000 00000 67890 66667 71175 67.7. 66 00000 000.0 32149 47036 65543 0.... 77777 00000 00000 6.... 12345 77777 'eao.25 38532 03715 32110 0.... 77777 2% “~86}.75m~ 847 854 00000 00000 000'. 67890 77778 868.79 09887n55442 65555 55555 00000 00000 0000.,00000 .....m..... 23570 50620 93716305949 99887 76554 O O O O O O O O O 0 66666 66666 03693A84101 09877 66666 O O I O O. O O I O 0 54444 44444 55555.55555 68452_42663 76531385173 0 O O O O” O O O O 0 52963596396 78890.01223 88889099999 . _ A 5 00000 00000 00000 00000 occooflooooo 12345 67890 88888 88889 'dfil -JM9 -0048 -.04 -JM? 6.439 6.390 6.342 52? 6. 6. 00000 00000 O 6 O O O 12345 99999 00000 00000 on... 67890 99990 “1 178 SILVER NORMAL VERSUS GOLD-0.07 AT. PERCENT IRON 90. KG AT S(UV/K) INCREMENT (UV/K) EMF(UV) EMF (UV) CHANGE TEMP. (DEG. K) -0940 ll 39 11 O 6 ,d1 22 03 03 o o 08 05 O. 07 20 20 45 54325 90956 2195342 62972 99948 87185 0 o o o 0 98877 11111 6383 09203 5592 1223 77884 550.19 7530 83791 00000 00000 00000 67890 , .1 69722 65214 17.222 0 o o o o ..... 67086 15317 41974 c o o o c 77666 11111 003276 15641 42437 45555 22222 0 o o o 0 57913 33344 01836 46538 0 a o o 0 85295 24679 11111 00000 .UOnXYO O O O O 0 .1?3745 11111 20636 38271 29742 a o o o c 65555 111.11 12 14 O. 67 44 44.69 4 6 o 8 4 49.78 76365 1:171 . 6 O . . _28495 1:4457. A 2222 00000 00000 0 o o o o , 67890 8.11112 81825 53772 97418 0.... 44443 11111 32373 88753 0 o o o 0 01234 55555 97831 2.1712 0 O o o 0 05948 90134 23333 00000 00000 0 o o o o 12345 22222 23126 65431 22222 c o o 0 a 30971 61632 53086 c o o o a 33322 11111 24989 06160 6.... 55667 55555 141.15 05885 0 o o 0 0 25814 67801 33344 00000 00000 0 o o I 0 67890 22223 88246 10098. 22211 O O I C C 35393 09991 41976 0 o o o c 22111 11111 00000, 00000 a 6 o o 0 12345 33333 16836 87665 11111 O O 6 O 6 26859 35826 42097 0 o o o 0 11100 111.11 0800 00000 0 o o o 0 67890 33334 09062 54433 11111 O O O o 0 00000 00000 0 o o o o IAEJ4G. 44444 A 28071 3.1211 1111‘! o o o o a 02254 31976 98654 99999 00000 00000 6 O O C 6 67890 44445 S(UV/K) INCREMEhT PERCENT IRON (UV/K) 179 90. KG EMF(UV) CHANGE AT (UV) SILVER NORMAL VERSUS GOLD-0.07 AT. EMF TEMP. (DEG. K) 87197 00099 111100 0 o o o o 605§Jb £77444 3??!09 guézya 91§LCO 6QX?12 coo... QOAZOO SREfbb 892540. 37A712 .0... 98;LI6 173367 66ZY9O 00000 00000 0 O O O 0 192945 ciDSGEJ -0096 '0094 -0093 ‘.089 -0087 0&3947 qugls 87L¥DQ 883368 OWEfOS “gigla 000... 00000 66zy06 7fi3fiua .105350 ...... ShfiTiu BQKle 68%LI7 00000 00000 000... 67890 SCEflDb r34017v Ragga! OHXUOO 0.0.0 285310 015:?5 415?10 883395 275141 99000 O O O O O 0011 bfizypb 645710 505735 00000 BBEiQI 9&9456 7LI77+c 0008 0008 .....v 1?;f33 £39066 “.071 -0072 -0079 2:85? .14373u ODfiZIO nu9875. .0... 87777 4815. 98R;- 0.900. 00000 99 GAXybb 905fi?! .4420éu .0... 97éido 675390 77778 0800 00000 0 a... 61A690v 6AXYO7 0889.7: 5521.1 7th6iw 652906 AUOOAXU OnKXUO 0.... ..... ... .. . .... 095460,.497233 afbgaEJ 9?ZYUQ 6:?441vad?7510 0.... ..... 77777 77777 1:3368VA050;!O ,OSAiic ZIQQUO 0.... 0.... 00000 00000 6523b6 A39666v " _ , _ nv041zu.J64R;u 175158 1:3567. ..... ..... R¥250¥u 59%703 n:ld154 4:5307 BQXQEB _ ~ . w 00000 00000 00000 00000 .....,..... 12345 67890 77777 77778 880.82 IzéJQS RZQBBB -.055 ’EPS -0053 161,342 n94815u bhaibfl OAZYOO 41XXJ3 117109 OXRUOQ. [066AEJ _0|2?06 _302366 Rigbqfl Ohxzoo ,0800 000... 6:1596v AURKEUQ “.052 -0052 ‘005‘ -0050 -0050 “.048 nXZVgl 1:Lc73 “iiiéd 579066 59.79 59065 59.3 59.13 58.86 000 00 060... 193723 906299 95;:b6 442744 OOO0,0 . . . . . ... .. «(691:1 815949 IIRYUQ . . . . . 65:905 1:2960, 6a5fid6 ...... BREXUB SREibS Q§Ad9i. 61519“ . . . . . “6405;; 7QX290 908290 w l “ 00000 00000 ...... 675:?0 906:?0 18 180 SILVER NORMAL VERSUS GOLD'0.07 AT. PERCENT IRON KG AT 100. S(UV/K) INCREMERT (UV/K) EMF(UV) CHANGE EMF (UV) TEMP. (DEG. K) "1.343 23.795 22.452 07 00 09 00 04 09 20 20 45 00000 100000 67890 19777 00133 22222 0 0 o o 0 00000 00000 0 O o o o .195f45 1111 9741.9 7773.8 0 o o o 0 25101 35801 41863 . . . O . 66555 1111 7.57.98 281369 90234 . 4555.5 55131.5 _7AY081. H . . . . . . 639 40 513468 527222 00000 AOnKXUO 67890 1112 '367.88 18747 75432 22222 . O . . . . .. .. 02514 04963 63086 O O O O 0 33322 1111 58 19 $0.89 61: 62.72 63.18 381.48 9 .81 —h407.es—— 420.64 00000 00000 0 o o o 0 67890 2523 95446 10098 227.11 50626 11012 42086 22211 00000 00000 .....V 123 45 33333 05261 54433 11111 0.... 61932 39418 64320 O . . I . 00000 11111 32124 12345 O O O O 0 55555 66666 83566 614 67 ...... ,0774LI 45678 55555 00000 00000 O O O O . 12345 44444 30050 53198 98754 99999 73088 68013 c o o I o 556 66 66666 55546 76417 . O O r. 0 77776 90123 56666 00000 00000 0 o o o 0 67890 444 45 181 PERCENT IRON SILVER NORMAL VERSUS GOLD“0.07 AT. AT 100. KG EMF(UV) S S(uv/K) (UV/K) INCREMENT CHANGE EMF (UV) TEMP. (DEG. K) #0.. _ T .d’..g:.[‘ H 01019 11009 11110 c 0 o I 0 09989 75555 32109 99998 AYUOOKu nXUOan ..... 193945 55555 “0096 ‘.094 -0093 ‘0090 -0089 8.863 8.769 8.676 8.586 8.497 67.62 67.79 67.95 68.09 68.20 90533 33984 0.000 21087 9n¥§12 67777 00000 00000 0 o o o 0 67890 55556 28322 12468 41i€10 ..... 88888 00000 00000 0 o o o o 12345 66666 88644 77777 00000 . .. .. 46062 02570 09877 ..... 87777 03331 397109 . . . . . 88887 66666 08879 8641;: ..... 64207 78000 779188 00000 00000 0 o 0 o 0 67890 66667 11177 77766 00000 . . . . . ‘22925 36825 65443 ..... 77777 97546 76543 ..... 77777 66666 43514 38269 0.... 52074 1?5iJ4 88888 nXEUOO nXYUOO ..... 185345 77777 -0066 -0066 -0066 -0062 -0062 00000 00000 ..... 67890 77778 11136 71593 99877 66666 00000 00000 . . . . . 12345 88888 922.82 9 9 956 942 949 67.66 67.69 67.69 567.64 67.54 .57 .24 .80 .27 00000 00000 00000 67890 _88889 21200 55555 00000 0 o. I. 76444 05050 43322 no... 66666 75638 31851 ..... 77666 66666 15829 68909 ..... 51749 56677 99999. 00000 00000 00000 12345 99999 17878 54444 00000. . . . . . 36813 50516 11009 ..... 66665 00000 00000 00.00 67890 99990 1 "'1 1611111 WM IUIWNVIHIWIIITIWW 118 . 3 1293 03046 3131