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The design of a low temperature thermocouple material
THE DESIGN OF A LOW TEMPERATURE THERMOCOUPLE MATERIAL R . S. C R I S P t
and W.
G..HENRY
Division of Applied Chemistry, National Research Council, Otlawa, Canada Received 8 J u n e 1964
A NUMBER of recent publications ~-3 have cited the use of alloys consisting of more or less stable solutions of transition metal solutes in noble metal solvents as elements of sensitive low temperature thermocouples. These thermoelectrically active alloys are all characterized by negative thermopowers in the liquid helium range which vary from 10 or more microvolts per degree for the solutions of iron (0-0050.02 per cent (at.)) in copper and gold to a few microvolts per degree for cobalt (2.1 per cent (at.)) in gold. Little or no attention hos been paid to the other or passive element which must be used in order to form either a useful measuring thermocouple or a differential thermocouple. The passive element may either subtract or add a significant contribution either from or to the overall sensitivity of the couple. The metals commonly used as passive elements are copper and an alloy of silver (0.37 per cent (at.)) in gold, the latter is called variously silver alloy-normal, 'normal' silver, and silver normal. While individually calibrated wires of these metals may be perfectly satisfactory, thermocouples embodying them cannot be used with confidence in the liquid helium region without at least a spot calibration, which is not usually convenient. This behaviour is in contrast to, for example, that of copper/constantan or platinum/platinum-rhodium in the high temperature region above 300 ° K. In addition, copper may show a very large negative thermopower below 25 ° K which can completely cancel the high thermopower of the active element. While the presently available active elements require in general either complete or spot calibrations, a few factors pertinent to the development of a passive element of good reproducibility in the temperature region below 300 ° K, with a positive thermopower in the liquid helium range, are presented here. The material could incidentally be a useful thermoelectric standard. The thermopowers of copper and silver normal Powell, Caywood, and Bunch 4 suggest copper as a suitable reference metal to be used with either goldcobalt or constantan for the measurement of low #Present address: Department of Physics, University of Western Australia, Nedlands, W.A. C R Y O G E N I C S • DECEMBER 1964
temperatures. In general, Copper is not a suitable reference material since the thermopower of copper below about 100 ° K is very sensitive to iron, which is a common impurity in solution, present in parts per million. It is also sensitive to cold work. Gold, MacDonald, Pearson, and Templeton s investigated the effect of iron in copper from several sources. They found thermopowers at 4 ° K ranging from - 2 . 0 to - 6 . 0 I~V/deg.K. In a commercial copper containing 0-002 per cent (at.) iron as oxide, the thermopower was found to be only - 0 . 0 5 pN/ deg.K. While the data of Powell et al. 2 for silver normal/copper show that their instrument grade copper does not exhibit a large negative thermopower at low temperatures, it may perhaps be made from blister copper in which case the iron will be oxidized and out of solution, this will not in general be the case. Clearly, copper mildly contaminated with iron in solution can mask completely the sensitive element. Pearson 6 has discussed the influence of cold work on the thermopower of copper. Below 40 ° K the magnitude of the effect depends on the amount of iron in solution. A change in the positive direction of 2.3 ~V/deg.K has been observed ~ for copper with a purity of 99-999 per cent. Above 40 ° K in the phonon drag region the thermopower of copper becomes negative relative to annealed copper; the maximum difference is about - 0 - 2 5 ~V/deg.K. Borelius, Keesom, Johansson, and Linde 8 chose silver normal as a thermoelectric reference only because it had a smaller Thomson effect than another alloy. This allowed the Thomson effect to be measured with greater absolute accuracy. The alloy consisted of 0-37 per cent (at.) gold in silver and some other impurity) The silver was alloyed with the gold to render the thermal conductivity as little as possible dependent upon the temperature. This feature also minimized the errors in the Thomson effect determination. As a passive element it suffers from several shortcomings. Firstly the concentration dependence of the thermopower is large, about 1.5 laV/deg.K]per cent (at.) gold, 1° which makes reproducibility a problem. Secondly, since it is a low concentration alloy of a metal of the same valency with an overall electrical resistivity differing little from pure silver, the phonon drag peak is not greatly suppressed and the alloy is susceptible to cold work, and further, for 361
the same reason, the thermopower in all regions is susceptible to small amounts of impurity. As a material which has a small Thomson effect, in the light of later work it is not perhaps the best which might be chosen. Measurements on two commercial silver normals The thermopowers from 5° K to 290 ° K of two samples of commercially available silver normal have been measured, in both the as-received and annealed states, in an apparatus described by Henry and Schroeder ~x and Crisp, Henry, and Schroeder. ~2 The 1.40
1.3o
1.20 HO
1.00 0.90
I 0.80 0"70
JohnsonMatthey
J~
o 0.60 o
.~ 0.so
0.40 0-30 Si~mu~dal~eC;f 0.20
/ ~ Sigmund Cohn (Asreceived)
0-10
I 0
5
10
100
Temperoture •
.
300 (°K)
Figure 1. The thermopower of normal silver
first sample was purchased from Messrs. Johnson, Matthey & Mallory in the form of a bare wire, 0-005 in. diameter, and the second from the Sigmund Cohn Corporation in the form of a fibre-glass covered wire of the same diameter. The annealing was performed in Pyrex capsules at 550 ° C for 12 hr in purified argon at 0.3 arm. Two samples of the Sigmund Cohn wire were measured in the as-received state and found to agree within the estimated error of +0.015 laV/ deg.K; most of the deviations are about 0.005 IxV/deg.K. The results of the measurements are shown in Figure 1 along with the silver normal result given by Borelius, Keesom, Johansson, and Linde. 13 It is seen that the Sigmund Cohn wire has a thermopower as much as 0.2 pV/deg.K less than the Johnson Matthey wire and that neither agree with the silver normal, which is believed to have been annealed, measured by Borelius et al. 13 We have no explanation for the behaviour of these two samples on annealing but note that analysis showed that both contained 0.37 per cent (at.) gold and in addition the first sample contained a trace of bismuth. Th,e Sigmund Cohn Corporation have kindly informed us that their sample was hard drawn from an ingot prepared by 362
bottom casting, from a graphite crucible, a melt prepared from silver 99.99 per cent pure, and gold 99-999 per cent pure. Information regarding the other sample was not forthcoming. The results of Figure 1 are presented as evidence of the high degree of irreproducibility of silver normal from batch to batch and its sensitivity to heat treatment. Design of a good passive element The design requirements for a thermocouple material for low temperature use are much the same as those for use at normal temperatures, namely, good mechanical and metallurgical stability under the conditions to be encountered, a high degree of reproducibility from batch to batch, resistance to thermal cycling and, in addition, though not essential, ease of preparation, fabrication, and handling, and a low thermal conductivity. Since all the existing active elements have negative thermopowers which are relatively small in the low temperature region, it is desirable that the passive element have a positive thermopower to provide maximum sensitivity. While an alloy with a large positive thermopower below 20 ° K would be most desirable such is not at the moment forthcoming and the best choice must have a thermopower which is at least positive below 20 ° K. Above this temperature the sensitivity of existing active elements is high enough that this consideration is not of great importance. The considerations in the design of a suitable passive element to fulfill the above requirement, will now be discussed in relation to the existing knowledge of the thermopower of the ~ solid solutions of nontransition metals in noble metals. The properties of the noble metals will be discussed first and then the effects of alloying on them. It is admitted that alloys based other than on the noble metals may eventually prove even more satisfactory. The thermopowers of the noble metals are separable into three general parts, the diffusion thermopower, the phonon drag contribution, and the low temperature iron contribution. The diffusion thermopower dominates at very low temperature, T < 0D/30 and at normal temperatures T/> 0D. This term should be negative according to the simple theory TM but in fact it is positiveA s The positive peak which falls between OD/30 and 0D/3 has been identified as due to phonon drag. The sign implies a preponderance of Umklapp processes. 16 At very low temperatures where both the diffusion and phonon drag terms become small, large negative thermopowers arise which are associated with dissolved transition metal impurities, notably iron. With respect to iron, the three noble metals behave somewhat differently. Iron dissolves in a sensible amount in copper and gold whereas it is virtually insoluble in silverA ~ Pearson and Templeton TM were CRYOGENICS.
DECEMBER
1964
able to produce, by quenching from 940 ° C, a silveriron alloy which has a negative thermopower. In general, the earlier measurements mentioned by them give positive thermopowers down to at least 2 ° K for annealed silver specimens of high purity. The thermopower of noble metal low concentration alloys in the non-phonon-drag regions appear to follow quite well the Nordheim-Gorter relationship ~6
where S is the observed thermopower; p~ is the resistivity due to the ith scattering mechanism which includes lattice, solute, and defect scattering; p is the total resistivity; and S~ is the characteristic thermopower of the ith scattering mechanism. The usefulness of this relationship has been demonstrated by Gold et al. s in discussing the iron impurity in copper at low temperatures and by Pearson 6 in discussing the influence of cold work on the thermopower of A.S. and R. copper. Crisp et al., 12 in determining the thermopower of iron-free copper, have demonstrated the attenuating effect of other solutes on the iron contribution. Crisp et al. 12 and Crisp and Henry 19 have demonstrated the applicability of this relationship at high temperatures and have determined the characteristic thermopowers of a number of solutes in copper and silver. Blatt and Kropschot 2° made some measurements on copper-based alloys containing 1-0 per cent (at.) of several solutes and concluded that the phonon drag contribution is markedly decreased when the mass difference between the solvent and the solute-is large. Crisp et al. 12 showed that for zinc, gallium, germanium, and arsenic in copper where there is only a small mass difference, but a progressively increasing nuclear charge difference, the phonon drag peak at first decreases rapidly with concentration and then resurges at higher concentrations creating a minimum in the thermopower versus concentration curve. Crisp et al. 12 have also shown that in the coppergallium, copper-germanium, and copper-arsenic systems the thermopower versus concentration curve at 290 ° K, where the diffusion thermopower dominates, has a shallow minimum at approximately the same concentration as in the phonon drag region. These results taken in conjunction with earlier measurements on the noble metal based alloys, copper-aluminium, zl copper-tin, 22 and copper-silicon, 23 suggest that a minimum occurs at a lower concentration, the larger is the resistivity change per atomic per cent of solute. The thermal conductivity of noble metal alloys decreases and rapidly becomes appreciably less temperature dependent with increasing solute concentration. The electronic component, which is the major contribution in alloys with concentrations of the order of a few atomic per cent and greater, and which dominates CRYOGENICS
• DECEMBER
1964
at high and low temperatures, varies inversely with the residual resistivity. The lattice component varies in a more complicated fashion with such parameters as mass difference, volume difference, and dislocation density.24. 2s It follows from the foregoing brief survey that for an improved passive element the following points should be noted: (1) Since a positive thermopower at low temperatures is a prime requirement, silver whose low temperature thermopower is inherently positive and which has a low solubility for iron is to be preferred as a base metal. (2) A fairly high solute concentration is desirable so that unintentional impurity and cold work scattering is attenuated by the dominance of the solute scattering. (3) The solute should have as large as possible a mass and effective nuclear charge difference from the solvent in order to suppress the positive phonon drag peak, which is sensitive to cold work. (4) The solute concentration should be as near as possible to the minimum in the concentration dependence of the thermopower in order to promote reproducibility from batch to batch with slightly varying solute concentration. (5) While the thermopowers of as-drawn wires of either pure metals or low concentration alloys may be much less susceptible to accidental cold work than annealed ones, the same is not true for a high concentration alloy where the impurity resistivity dominates. Experience in this laboratory has shown that the accidental annealing of a high concentration alloy, for example with a soldering iron, is more serious than minor incidental cold work. Neither is nearly as serious as the accidental annealing of a cold-worked either pure or low concentration alloy. Thus for a concentrated alloy, the annealed state is preferred. (6) The combination of (2) and (4) will ensure a low thermal conductivity and effective thermal isolation.
A possible alloy Following the points just outlined, a silver-gallium alloy containing approximately 4.8 per cent (at.) gallium was chosen for some preliminary, measurements. While germanium and arsenic would possibly suppress the phonon drag and other effects more thoroughly, the solid solutions of these alloys are metastable. The concentration was chosen by inference from the measurements in this laboratory on the copper-based alloys and it may, in actual fact, be some distance from a concentration minimum. The alloy was prepared as described by Crisp et al. 12 from electronic grade gallium purchased from the Eagle-Picher Co. and from silver prepared by electrolysis in this laboratory. A similar grade of silver may be purchased from several companies. The 363
purity of the silver is o f the order o f 99.999 per cent; the gallium contains less than 0.0001 per cent (at.) iron. The purity is probably relatively unimportant in view of the high gallium concentration. The annealing was done at 550 ° C for 24 hr in Pyrex in purified argon at 0.3 atm. The measured absolute thermopowers o f the 0.020 in. wires of this alloy in the annealed and as drawn state are shown in Figure 2. 0"401
o-3o~-" ,
~
The properties o f the alloy designed above for use in thermocouples which make it desirable in that application also make it suitable as a thermoelectric standard material. Before such a new standard is put forward, however, it must be confirmed that the o p t i m u m alloy has indeed been chosen especially as regards reproducibility and concentration independence. This would have to be followed by thermoe.m.f, measurements against a superconductor and by careful T h o m s o n effect measurements to establish a new reference scale.
Annealed
0"20I--
REFERENCES I
0"00 ~ -0"I0
o -0.20 E -0.30 ~-- -0.40
As_drown/
r 5
i I0
I moo Temperature ---a,,-
I. MACDONALD,D. K. C., and PEARSON,W. B. Proc. roy. Sac. A241, 257 (1957) 2. POWELL, R. L., BUNCH, M. O., and CORRUCON~, R. J. Cryogenics 1, 139 (1961) '~ 3. BERMAN,R., and HurCrLEY,D. J. Cryogenics 3, 70 (1963) 4. POWELL,R. L., CAYWOOD,L. P. Jr., and BUNCH, M. D. 300 (°K)
Figure 2. The thermopower of an alloy containing approximately 4"8 per cent (at.) gallium in silver
The predictions on which the design o f this alloy was based are borne out in that: (1) The thermopower is positive at low temperatures. It is also incidentally small. (2) The p h o n o n drag peak is effectively suppressed. That it is not absent is surprising in view of the considerations of Blatt and Kropschot. 20 (3) The difference between the as-drawn and annealed thermopowers is small. The m a x i m u m difference between the as-received and annealed Sigmund C o h n silver normal in the low temperature region is about 0-25 ~tV/deg.K whereas for the silvergallium alloy it is only 0.05 I~V/deg.K; in the high temperature region the improvement is not as striking but the silver-gallium alloy is still appreciably better. A t h e r m o e l e c t r i c referdnce standard
Since thermopowers m a y be measured with a precision o f + 0.01 IxV/deg.K, there is a need, at least for research purposes, for an absolute thermopower standard which is k n o w n with a similar accuracy. U p to 18 ° K the absolute thermopower o f lead is k n o w n with an accuracy o f +0.015 IxV/deg.K; 26 above this temperature the accuracy drops and at r o o m temperature is about + 0 . 1 5 ~tV/deg.K. 19 It is at present the most accurate existing absolute thermopower scale. The pure metal lead, however, suffers f r o m two major disadvantages, namely, its low mechanical strength ~ d its high thermal conductivity at low temperatures.
364
Temperature, Its Measurement and Control in Science and Industry, Vol. 3, p. 65 (Reinhold, New York, 1962)"
5. GOLD,A. V., MACDONALO,D. K. C., PEARSON,.W.B., and TEMPLETON,I. M. Phil. Mag. 5, 765 (1960) 6. PEARSON,W. B. Phys. Rev. 119, 549 (1960) 7. POWELL,R. L., RODER,H. M., and HALL,W. J. Phys. Rev. 115, 314 (1959) 8. BOREUUS,G., KEF.SOM,W. H., JOHANSSON,C. H., and LINDE, J. O. Proc. Acad. Sci. Amst. 33, 17 (1930) 9. BOREUUS,G., KEESOM,W. H., and JOHANSSON,C: H. Proc. Acad. ScL Amst. 31, 1046 (1928) 10. BORELIUS,G., KE~OM, W. H., JOHANSSON,C. H., and LINDE,J. O. Proc. Acad. Sci. Amst. 35, 15 (1932) 11. HENRY, W. G., and SCHROEDER,P. A. Can. J. Phys. 41, 1076 (1963) 12. CRlSP, R. S., HENRY, W. G., and SCHROEDER,P. A. Phil. Mag. 10, 553 (1964) 13. BOREUUS, G., ~ M , W. H., JOHANSSON,C. H., and LINDE, J. O. Proc. Acad. Sci. Amst. 35, 10 (1932) 14. WILSON,A. H. The Theory of Metals, p. 202 (Cambridge University Press, 1953) 15. ZWL~N,J. M. Advanc. Phys. 10, 1 (1961) 16. MACDONALD,D. K. C. Thermoelectricity; An Introduction to the Principles, pp. 47, 109 (Wiley, New York, 1962) 17. HANSEN, M., and ANDERKO, K. Constitution of Binary Alloys, pp. 20, 203, 580 (McGraw-Hill, New York, 1958) 18. PEARSON,W. B., and TEt~n'LETON,I. M. Can. J. Phys. 39, 1084 (1961) 19. CRISP, R. S., and HENRY,W. G. Phil. Mag. Submitted 20. BLAX'r,F. J., and KROPSCHOT,R. H. Phys. Rev. 118, 480 (1960) 21. NORBURY,A. L. Phil. Mag. 2, 1188 (1926) 22. ANDREWARTHA,G. G., and EVANS,E. J. Phil. Mag. 31,265 (1941) 23. DOMENICALI,C. A., and OTTER,F. A. J. appl. Phys. 26, 377 (1955) 24. KEMP,W. R. G., KLE~NS, P. G., and TAINSH,R. J. Aust. J. Phys. 10, 454 (1957) 25. KEMP, W. R. G., KLE~mNS, P. G., TAINSH, R. J., and WnrrE, G. K. Acta Metall. 5, 303 (1957) 26. CnmS~AN, J. W., JAN, J. P., PEARSON,W. B., and TEMPLETON, I. M. Proc. roy. Sac. A245, 213 (1958)
CRYOGENICS-
DECEMBER 1964
and W.
G..HENRY
Division of Applied Chemistry, National Research Council, Otlawa, Canada Received 8 J u n e 1964
A NUMBER of recent publications ~-3 have cited the use of alloys consisting of more or less stable solutions of transition metal solutes in noble metal solvents as elements of sensitive low temperature thermocouples. These thermoelectrically active alloys are all characterized by negative thermopowers in the liquid helium range which vary from 10 or more microvolts per degree for the solutions of iron (0-0050.02 per cent (at.)) in copper and gold to a few microvolts per degree for cobalt (2.1 per cent (at.)) in gold. Little or no attention hos been paid to the other or passive element which must be used in order to form either a useful measuring thermocouple or a differential thermocouple. The passive element may either subtract or add a significant contribution either from or to the overall sensitivity of the couple. The metals commonly used as passive elements are copper and an alloy of silver (0.37 per cent (at.)) in gold, the latter is called variously silver alloy-normal, 'normal' silver, and silver normal. While individually calibrated wires of these metals may be perfectly satisfactory, thermocouples embodying them cannot be used with confidence in the liquid helium region without at least a spot calibration, which is not usually convenient. This behaviour is in contrast to, for example, that of copper/constantan or platinum/platinum-rhodium in the high temperature region above 300 ° K. In addition, copper may show a very large negative thermopower below 25 ° K which can completely cancel the high thermopower of the active element. While the presently available active elements require in general either complete or spot calibrations, a few factors pertinent to the development of a passive element of good reproducibility in the temperature region below 300 ° K, with a positive thermopower in the liquid helium range, are presented here. The material could incidentally be a useful thermoelectric standard. The thermopowers of copper and silver normal Powell, Caywood, and Bunch 4 suggest copper as a suitable reference metal to be used with either goldcobalt or constantan for the measurement of low #Present address: Department of Physics, University of Western Australia, Nedlands, W.A. C R Y O G E N I C S • DECEMBER 1964
temperatures. In general, Copper is not a suitable reference material since the thermopower of copper below about 100 ° K is very sensitive to iron, which is a common impurity in solution, present in parts per million. It is also sensitive to cold work. Gold, MacDonald, Pearson, and Templeton s investigated the effect of iron in copper from several sources. They found thermopowers at 4 ° K ranging from - 2 . 0 to - 6 . 0 I~V/deg.K. In a commercial copper containing 0-002 per cent (at.) iron as oxide, the thermopower was found to be only - 0 . 0 5 pN/ deg.K. While the data of Powell et al. 2 for silver normal/copper show that their instrument grade copper does not exhibit a large negative thermopower at low temperatures, it may perhaps be made from blister copper in which case the iron will be oxidized and out of solution, this will not in general be the case. Clearly, copper mildly contaminated with iron in solution can mask completely the sensitive element. Pearson 6 has discussed the influence of cold work on the thermopower of copper. Below 40 ° K the magnitude of the effect depends on the amount of iron in solution. A change in the positive direction of 2.3 ~V/deg.K has been observed ~ for copper with a purity of 99-999 per cent. Above 40 ° K in the phonon drag region the thermopower of copper becomes negative relative to annealed copper; the maximum difference is about - 0 - 2 5 ~V/deg.K. Borelius, Keesom, Johansson, and Linde 8 chose silver normal as a thermoelectric reference only because it had a smaller Thomson effect than another alloy. This allowed the Thomson effect to be measured with greater absolute accuracy. The alloy consisted of 0-37 per cent (at.) gold in silver and some other impurity) The silver was alloyed with the gold to render the thermal conductivity as little as possible dependent upon the temperature. This feature also minimized the errors in the Thomson effect determination. As a passive element it suffers from several shortcomings. Firstly the concentration dependence of the thermopower is large, about 1.5 laV/deg.K]per cent (at.) gold, 1° which makes reproducibility a problem. Secondly, since it is a low concentration alloy of a metal of the same valency with an overall electrical resistivity differing little from pure silver, the phonon drag peak is not greatly suppressed and the alloy is susceptible to cold work, and further, for 361
the same reason, the thermopower in all regions is susceptible to small amounts of impurity. As a material which has a small Thomson effect, in the light of later work it is not perhaps the best which might be chosen. Measurements on two commercial silver normals The thermopowers from 5° K to 290 ° K of two samples of commercially available silver normal have been measured, in both the as-received and annealed states, in an apparatus described by Henry and Schroeder ~x and Crisp, Henry, and Schroeder. ~2 The 1.40
1.3o
1.20 HO
1.00 0.90
I 0.80 0"70
JohnsonMatthey
J~
o 0.60 o
.~ 0.so
0.40 0-30 Si~mu~dal~eC;f 0.20
/ ~ Sigmund Cohn (Asreceived)
0-10
I 0
5
10
100
Temperoture •
.
300 (°K)
Figure 1. The thermopower of normal silver
first sample was purchased from Messrs. Johnson, Matthey & Mallory in the form of a bare wire, 0-005 in. diameter, and the second from the Sigmund Cohn Corporation in the form of a fibre-glass covered wire of the same diameter. The annealing was performed in Pyrex capsules at 550 ° C for 12 hr in purified argon at 0.3 arm. Two samples of the Sigmund Cohn wire were measured in the as-received state and found to agree within the estimated error of +0.015 laV/ deg.K; most of the deviations are about 0.005 IxV/deg.K. The results of the measurements are shown in Figure 1 along with the silver normal result given by Borelius, Keesom, Johansson, and Linde. 13 It is seen that the Sigmund Cohn wire has a thermopower as much as 0.2 pV/deg.K less than the Johnson Matthey wire and that neither agree with the silver normal, which is believed to have been annealed, measured by Borelius et al. 13 We have no explanation for the behaviour of these two samples on annealing but note that analysis showed that both contained 0.37 per cent (at.) gold and in addition the first sample contained a trace of bismuth. Th,e Sigmund Cohn Corporation have kindly informed us that their sample was hard drawn from an ingot prepared by 362
bottom casting, from a graphite crucible, a melt prepared from silver 99.99 per cent pure, and gold 99-999 per cent pure. Information regarding the other sample was not forthcoming. The results of Figure 1 are presented as evidence of the high degree of irreproducibility of silver normal from batch to batch and its sensitivity to heat treatment. Design of a good passive element The design requirements for a thermocouple material for low temperature use are much the same as those for use at normal temperatures, namely, good mechanical and metallurgical stability under the conditions to be encountered, a high degree of reproducibility from batch to batch, resistance to thermal cycling and, in addition, though not essential, ease of preparation, fabrication, and handling, and a low thermal conductivity. Since all the existing active elements have negative thermopowers which are relatively small in the low temperature region, it is desirable that the passive element have a positive thermopower to provide maximum sensitivity. While an alloy with a large positive thermopower below 20 ° K would be most desirable such is not at the moment forthcoming and the best choice must have a thermopower which is at least positive below 20 ° K. Above this temperature the sensitivity of existing active elements is high enough that this consideration is not of great importance. The considerations in the design of a suitable passive element to fulfill the above requirement, will now be discussed in relation to the existing knowledge of the thermopower of the ~ solid solutions of nontransition metals in noble metals. The properties of the noble metals will be discussed first and then the effects of alloying on them. It is admitted that alloys based other than on the noble metals may eventually prove even more satisfactory. The thermopowers of the noble metals are separable into three general parts, the diffusion thermopower, the phonon drag contribution, and the low temperature iron contribution. The diffusion thermopower dominates at very low temperature, T < 0D/30 and at normal temperatures T/> 0D. This term should be negative according to the simple theory TM but in fact it is positiveA s The positive peak which falls between OD/30 and 0D/3 has been identified as due to phonon drag. The sign implies a preponderance of Umklapp processes. 16 At very low temperatures where both the diffusion and phonon drag terms become small, large negative thermopowers arise which are associated with dissolved transition metal impurities, notably iron. With respect to iron, the three noble metals behave somewhat differently. Iron dissolves in a sensible amount in copper and gold whereas it is virtually insoluble in silverA ~ Pearson and Templeton TM were CRYOGENICS.
DECEMBER
1964
able to produce, by quenching from 940 ° C, a silveriron alloy which has a negative thermopower. In general, the earlier measurements mentioned by them give positive thermopowers down to at least 2 ° K for annealed silver specimens of high purity. The thermopower of noble metal low concentration alloys in the non-phonon-drag regions appear to follow quite well the Nordheim-Gorter relationship ~6
where S is the observed thermopower; p~ is the resistivity due to the ith scattering mechanism which includes lattice, solute, and defect scattering; p is the total resistivity; and S~ is the characteristic thermopower of the ith scattering mechanism. The usefulness of this relationship has been demonstrated by Gold et al. s in discussing the iron impurity in copper at low temperatures and by Pearson 6 in discussing the influence of cold work on the thermopower of A.S. and R. copper. Crisp et al., 12 in determining the thermopower of iron-free copper, have demonstrated the attenuating effect of other solutes on the iron contribution. Crisp et al. 12 and Crisp and Henry 19 have demonstrated the applicability of this relationship at high temperatures and have determined the characteristic thermopowers of a number of solutes in copper and silver. Blatt and Kropschot 2° made some measurements on copper-based alloys containing 1-0 per cent (at.) of several solutes and concluded that the phonon drag contribution is markedly decreased when the mass difference between the solvent and the solute-is large. Crisp et al. 12 showed that for zinc, gallium, germanium, and arsenic in copper where there is only a small mass difference, but a progressively increasing nuclear charge difference, the phonon drag peak at first decreases rapidly with concentration and then resurges at higher concentrations creating a minimum in the thermopower versus concentration curve. Crisp et al. 12 have also shown that in the coppergallium, copper-germanium, and copper-arsenic systems the thermopower versus concentration curve at 290 ° K, where the diffusion thermopower dominates, has a shallow minimum at approximately the same concentration as in the phonon drag region. These results taken in conjunction with earlier measurements on the noble metal based alloys, copper-aluminium, zl copper-tin, 22 and copper-silicon, 23 suggest that a minimum occurs at a lower concentration, the larger is the resistivity change per atomic per cent of solute. The thermal conductivity of noble metal alloys decreases and rapidly becomes appreciably less temperature dependent with increasing solute concentration. The electronic component, which is the major contribution in alloys with concentrations of the order of a few atomic per cent and greater, and which dominates CRYOGENICS
• DECEMBER
1964
at high and low temperatures, varies inversely with the residual resistivity. The lattice component varies in a more complicated fashion with such parameters as mass difference, volume difference, and dislocation density.24. 2s It follows from the foregoing brief survey that for an improved passive element the following points should be noted: (1) Since a positive thermopower at low temperatures is a prime requirement, silver whose low temperature thermopower is inherently positive and which has a low solubility for iron is to be preferred as a base metal. (2) A fairly high solute concentration is desirable so that unintentional impurity and cold work scattering is attenuated by the dominance of the solute scattering. (3) The solute should have as large as possible a mass and effective nuclear charge difference from the solvent in order to suppress the positive phonon drag peak, which is sensitive to cold work. (4) The solute concentration should be as near as possible to the minimum in the concentration dependence of the thermopower in order to promote reproducibility from batch to batch with slightly varying solute concentration. (5) While the thermopowers of as-drawn wires of either pure metals or low concentration alloys may be much less susceptible to accidental cold work than annealed ones, the same is not true for a high concentration alloy where the impurity resistivity dominates. Experience in this laboratory has shown that the accidental annealing of a high concentration alloy, for example with a soldering iron, is more serious than minor incidental cold work. Neither is nearly as serious as the accidental annealing of a cold-worked either pure or low concentration alloy. Thus for a concentrated alloy, the annealed state is preferred. (6) The combination of (2) and (4) will ensure a low thermal conductivity and effective thermal isolation.
A possible alloy Following the points just outlined, a silver-gallium alloy containing approximately 4.8 per cent (at.) gallium was chosen for some preliminary, measurements. While germanium and arsenic would possibly suppress the phonon drag and other effects more thoroughly, the solid solutions of these alloys are metastable. The concentration was chosen by inference from the measurements in this laboratory on the copper-based alloys and it may, in actual fact, be some distance from a concentration minimum. The alloy was prepared as described by Crisp et al. 12 from electronic grade gallium purchased from the Eagle-Picher Co. and from silver prepared by electrolysis in this laboratory. A similar grade of silver may be purchased from several companies. The 363
purity of the silver is o f the order o f 99.999 per cent; the gallium contains less than 0.0001 per cent (at.) iron. The purity is probably relatively unimportant in view of the high gallium concentration. The annealing was done at 550 ° C for 24 hr in Pyrex in purified argon at 0.3 atm. The measured absolute thermopowers o f the 0.020 in. wires of this alloy in the annealed and as drawn state are shown in Figure 2. 0"401
o-3o~-" ,
~
The properties o f the alloy designed above for use in thermocouples which make it desirable in that application also make it suitable as a thermoelectric standard material. Before such a new standard is put forward, however, it must be confirmed that the o p t i m u m alloy has indeed been chosen especially as regards reproducibility and concentration independence. This would have to be followed by thermoe.m.f, measurements against a superconductor and by careful T h o m s o n effect measurements to establish a new reference scale.
Annealed
0"20I--
REFERENCES I
0"00 ~ -0"I0
o -0.20 E -0.30 ~-- -0.40
As_drown/
r 5
i I0
I moo Temperature ---a,,-
I. MACDONALD,D. K. C., and PEARSON,W. B. Proc. roy. Sac. A241, 257 (1957) 2. POWELL, R. L., BUNCH, M. O., and CORRUCON~, R. J. Cryogenics 1, 139 (1961) '~ 3. BERMAN,R., and HurCrLEY,D. J. Cryogenics 3, 70 (1963) 4. POWELL,R. L., CAYWOOD,L. P. Jr., and BUNCH, M. D. 300 (°K)
Figure 2. The thermopower of an alloy containing approximately 4"8 per cent (at.) gallium in silver
The predictions on which the design o f this alloy was based are borne out in that: (1) The thermopower is positive at low temperatures. It is also incidentally small. (2) The p h o n o n drag peak is effectively suppressed. That it is not absent is surprising in view of the considerations of Blatt and Kropschot. 20 (3) The difference between the as-drawn and annealed thermopowers is small. The m a x i m u m difference between the as-received and annealed Sigmund C o h n silver normal in the low temperature region is about 0-25 ~tV/deg.K whereas for the silvergallium alloy it is only 0.05 I~V/deg.K; in the high temperature region the improvement is not as striking but the silver-gallium alloy is still appreciably better. A t h e r m o e l e c t r i c referdnce standard
Since thermopowers m a y be measured with a precision o f + 0.01 IxV/deg.K, there is a need, at least for research purposes, for an absolute thermopower standard which is k n o w n with a similar accuracy. U p to 18 ° K the absolute thermopower o f lead is k n o w n with an accuracy o f +0.015 IxV/deg.K; 26 above this temperature the accuracy drops and at r o o m temperature is about + 0 . 1 5 ~tV/deg.K. 19 It is at present the most accurate existing absolute thermopower scale. The pure metal lead, however, suffers f r o m two major disadvantages, namely, its low mechanical strength ~ d its high thermal conductivity at low temperatures.
364
Temperature, Its Measurement and Control in Science and Industry, Vol. 3, p. 65 (Reinhold, New York, 1962)"
5. GOLD,A. V., MACDONALO,D. K. C., PEARSON,.W.B., and TEMPLETON,I. M. Phil. Mag. 5, 765 (1960) 6. PEARSON,W. B. Phys. Rev. 119, 549 (1960) 7. POWELL,R. L., RODER,H. M., and HALL,W. J. Phys. Rev. 115, 314 (1959) 8. BOREUUS,G., KEF.SOM,W. H., JOHANSSON,C. H., and LINDE, J. O. Proc. Acad. Sci. Amst. 33, 17 (1930) 9. BOREUUS,G., KEESOM,W. H., and JOHANSSON,C: H. Proc. Acad. ScL Amst. 31, 1046 (1928) 10. BORELIUS,G., KE~OM, W. H., JOHANSSON,C. H., and LINDE,J. O. Proc. Acad. Sci. Amst. 35, 15 (1932) 11. HENRY, W. G., and SCHROEDER,P. A. Can. J. Phys. 41, 1076 (1963) 12. CRlSP, R. S., HENRY, W. G., and SCHROEDER,P. A. Phil. Mag. 10, 553 (1964) 13. BOREUUS, G., ~ M , W. H., JOHANSSON,C. H., and LINDE, J. O. Proc. Acad. Sci. Amst. 35, 10 (1932) 14. WILSON,A. H. The Theory of Metals, p. 202 (Cambridge University Press, 1953) 15. ZWL~N,J. M. Advanc. Phys. 10, 1 (1961) 16. MACDONALD,D. K. C. Thermoelectricity; An Introduction to the Principles, pp. 47, 109 (Wiley, New York, 1962) 17. HANSEN, M., and ANDERKO, K. Constitution of Binary Alloys, pp. 20, 203, 580 (McGraw-Hill, New York, 1958) 18. PEARSON,W. B., and TEt~n'LETON,I. M. Can. J. Phys. 39, 1084 (1961) 19. CRISP, R. S., and HENRY,W. G. Phil. Mag. Submitted 20. BLAX'r,F. J., and KROPSCHOT,R. H. Phys. Rev. 118, 480 (1960) 21. NORBURY,A. L. Phil. Mag. 2, 1188 (1926) 22. ANDREWARTHA,G. G., and EVANS,E. J. Phil. Mag. 31,265 (1941) 23. DOMENICALI,C. A., and OTTER,F. A. J. appl. Phys. 26, 377 (1955) 24. KEMP,W. R. G., KLE~NS, P. G., and TAINSH,R. J. Aust. J. Phys. 10, 454 (1957) 25. KEMP, W. R. G., KLE~mNS, P. G., TAINSH, R. J., and WnrrE, G. K. Acta Metall. 5, 303 (1957) 26. CnmS~AN, J. W., JAN, J. P., PEARSON,W. B., and TEMPLETON, I. M. Proc. roy. Sac. A245, 213 (1958)
CRYOGENICS-
DECEMBER 1964