The Measurement of Low TemperaturesTHE PROPERTIES AND APPLICATIONS OFTHE GOLD-IRON ALLOY THERMOCOUPLE

Robert BermanClarendon Laboratory, Oxford

In the rapidly advancing field of cryogenic engineering and researchthe accurate measurement of very low temperatures has becomeincreasingly important. Alloys of gold with small amounts of iron

have very large and reproducible thermoelectric powers in this rangeand are successfully used as the active limbs of sensitive and stable

low temperature thermocouples.

The applications of low temperature technologyare increasing rapidly. Liquid air and liquid oxygenhave been used for some time, liquid air for rapidfreezing of food and liquid oxygen as a compact andlight source of the gas not requiring heavy steelcylinders for its transport. Liquid hydrogen is nowa rocket fuel and represents an almost infinitelyplentiful non-pollutant fuel for the future.

Liquid helium is the extreme coolant for purposessuch as the reduction of "noise" in telecommunicationsystems, for example in the Goonhilly receiver, andmore particularly, for maintaining superconductorsin the non-resistive state. Many metals and alloyslose all electrical resistance at very low temperatures,and certain alloys can carry large currents in highmagnetic fields without reverting to the normal,resistive, state. Electromagnets for fields up to —150

kG with zero resistance and no power consumptioncan be constructed. Such magnets are used ex-tensively in research laboratories all over the worldand are beginning to have wider application. Iffusion reactions become possible for power genera-tion, it is likely that the magnets to contain theplasma will be superconducting. Small, light, iron-free electric motors and generators with super-conducting windings can be built for many purposes,especially where the rate of rotation is not too high.A prototype motor for ship propulsion has beenbuilt and other applications can quite readily beenvisaged (1).

A problem common to all research and develop-ment on these lines is accurate determination of thetemperatures involved. If we wish to interpret themeasured properties of matter, we must relate tern-

In the development of super-conductors for powerengineering applications oneof the most important para-meters is the transition tem-perature at which they revertto the normal state. In thisapparatus at the CentralElectricity Research Labora-tories at Leatherhead thesample is contained in avariable temperature capsuleheld just above the surfaceof liquid helium in the dewarin the foreground. Thecapsule temperature is moni-tored in the range 4.5 to20K by a gold-iron/Chromeithermocouple

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Parametric amplifiers, hand-ling very weak signals atmicrowave frequencies as insatellite communications andin long distance telephony andtelevision, need to be main-tained at the lowest possibletemperature to minimise in-terference by random noise.This helium refrigerator, oneof a range specially designedby British Oxygen for thispurpose, operates in the range12 to 20K using gold-ironthermocouples to monitor thetemperature

peratures to the thermodynamic scale, implicit inall theoretical expressions involving temperature.

Thermometry at Low Temperatures

The Kelvin temperature scale, as defined from theSecond Law of Thermodynamics, has a singlereference temperature which is the triple point(t.p.) of water, taken as 273.16 K. The standard wayof realising this scale experimentally is by gasthermometry, based on the fact that in the limit ofvanishingly low pressures the product of pressure,P, and volume, V. for a fixed mass of gas is pro-portional to the thermodynamic temperature, T. Thenumerical value of T on the Kelvin scale is given by

T (PV)T

273.16 (PV)t p

Accurate gas thermometry is a difficult art and isused to determine the Kelvin temperature of certainfixed points, such as the freezing and boiling pointsof pure materials, and to calibrate other, more easilyused, thermometers. Down to the triple point ofhydrogen (13.81 K), the International PracticalTemperature Scale (IPTS-68), agreed in 1968, isbased on the temperature variation of the electricalresistance of very pure platinum wire. Below thisthere are agreements as to the temperatures to beascribed to the boiling points of the pure heliumisotopes, 3He and 4He, as functions of pressure. Thelatest were in 1958 for 4He and in 1962 for 3He.

In an actual experiment, a thermometer may berequired with certain characteristics not obtainable

with either a platinum resistance or with a liquid-vapour system. For example, high sensitivity may berequired over a particular temperature range, or alow heat capacity for rapid response. Many practicalthermometers depend on changes of electrical resis-tivity with temperature, since resistance changes canbe measured with great accuracy by standard methods.To obtain large changes of resistivity at low tem-peratures impure materials are generally required,and the calibration depends on the exact amount ofimpurity added. Such thermometers must, therefore,be calibrated individually, or at least a few calibrationpoints must be checked to derive the whole cali-bration from the known form of its variation fromone sample to another.

Thermometers of suitably "doped" germaniumare very stable over long periods of time and re-peated temperature cycles, although errors of afew mK (10-3K) can be introduced if they are notrecalibrated during prolonged use. Carbon thermo-meters are usually in the form of commercial radioresistors consisting of small graphite particles em-bedded in a bonding material. Most have poorlyreproducible calibrations, because the contacts amongthe graphite crystallites and between them and theelectrical leads are altered on cycling the temperature.

It is sometimes more important to determine asmall temperature difference accurately rather thanan absolute temperature. It may then be moreconvenient to use a thermocouple, which is an in-strument producing a voltage dependent on thedifference in temperature of two junctions between

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A2

A 1

12 A 3

T i

Fig. 1 The principles of thermocouple ther-mometry. A,, A Z and A3 are wires joined attemperatures T, and T 2. A, and A, are connectedto the voltmeter

dissimilar conductors. Thermocouples also have theadvantage of very low heat capacity as they consistessentially of two "points" at the junctions ofthin wires. Thermocouples have not until recentlybeen used much at low temperatures because thethermoelectric power (the e.m.f. produced for unittemperature difference) of most combinations obeysthe Third Law of Thermodynamics in a docile way,decreasing gently to zero at absolute zero.

Thermocouples

If a temperature gradient is established along anelectrical conductor there will, in general, be an e.m.f.set up between its ends. We might envisage makingconnections to a voltmeter as in Fig. 1 to determinethis e.m.f., where Al represents the conductor with itsends at temperatures Ti and T2. Purely to shortenthe discussion without affecting the principle to beillustrated, let us assume that the voltmeter is alsoat T 2. Because of the temperature difference alongAl an e.m.f. is set up in it, but the same e.m.f. wouldbe set up in the opposite direction in A 2 if this is madeof the same material as A l . As there is no temperaturedifference along A3 and no e.m.f. between its ends, thenet effect is that no voltage will be measured by thevoltmeter. No matter how the temperatures arejuggled, no voltage will be recorded if all three armsare made of the same material.

If, however, arms A 2 and A, are made of a con-ductor in which the e.m.f. produced is different fromthat in Al for the same end temperatures, the volt-meter will measure the difference between these twoe.m.fs. If one junction is held at a fixed temperatureand the voltage E (T) is measured while the tem-perature of the other junction is varied, the thermo-

electric power, S, of the thermocouple is defined as

S= atat temperature T. At absolute zero S must

be zero, and for many commonly used thermocouplecombinations S decreases monotonically with de-creasing temperature and is so small below liquidhydrogen temperatures that the thermocouplebecomes difficult to use. However, thermopowerdepends so delicately on details of the electronicstructure, that no "anomalous" behaviour shouldcome as a surprise! For example, even the sign of thee.m.f. for different conductors for fixed T i and TZ

is not always the same and for a given conductormay vary with temperature.

The anomalous behaviour of thermopower whichis relevant here was discovered by Borelius and hisco-workers in 1932 (2). The addition of smallquantities of transition metals to a noble metal canenhance the thermopower enormously, and may evenlead at low temperatures to a thermopower whichincreases with decreasing temperature and finallyonly tends rather slowly to zero.

For a number of years thermocouples, in which theactive arm was made of gold plus two atomic percent cobalt, were used quite extensively. However,the exact amount of cobalt which is in solid solutionis sensitive to the thermal and mechanical treatmentof the wire and the calibration was too irreproduciblefor many purposes. In addition, the sensitivitybecomes rather small at liquid helium temperatures.

Gold-Iron Thermocouples

MacDonald and his collaborators (3) studied thethermopower of many dilute alloys at low temperature,and the material which has been developed for use

3 10 30 1UU '+^

TEMPERATURE K

Fig. 2 Thermoelectric power of thermocouples:

1—Au+0.03at %Fe vs. Ag+0.37at.%Au2—Au+0.03at.%Fe vs. Chromel3—Copper vs. Constantan

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The lower end of a cryostat, designed and built by OxfordInstruments, for X-ray diffraction studies of powdersamples at all temperatures down to 4.2 K. The maininner components of the cryostat, sample holder andradiation shield are made of copper plated with gold toprovide the minimum absorptivity for radiated heat fromthe outer walls. The temperature is measured with a gold/iron vs. Chromel thermocouple, seen in the centre of thepicture

in thermocouples is very pure gold with smallquantities of iron (4). Figure 2 shows the thermo-electric power of two thermocouples with gold-ironarms and, for comparison, a copper-constantanthermocouple. The latter combination is commonlyused at normal temperatures but its sensitivity fallsgradually with decreasing temperature. For bothcurves 1 and 2 the gold contains 0.03 atomic percent iron, but the second arm is different in the twothermocouples. For thermocouple 1 this arm is astandard alloy of silver plus 0.37 atomic per centgold (known as silver "normal"), which is relatively"inert", so that the thermopower shown representsalmost entirely the thermopower of the Au—Fe alloy.The second arm for thermocouple 2 is Chromel, analloy of 90 per cent nickel, 10 per cent chromiumused in high temperature thermocouples. Thethermopower of Chromel is of opposite sign to thatof the gold-iron and starts to become appreciableabove —20 K, where the thermopower of gold-ironbegins to fall off. The thermopower of the combina-tion is, therefore, the sum of the individual thermo-powers, with the gold-iron being the dominantpartner at low temperatures and Chromel at hightemperatures. This results in a thermocouple withsensitivity not less than 10 uV/K at all temperaturesabove 1 K.

If measurements are confined to temperaturesbelow about 15 K, the thermopower cannot be en-hanced appreciably, and it is sometimes advantageousto use a superconductor as the second arm. Super-conductors have no thermoelectric power, so thatspurious e.m.f.s, which give rise to experimentaldifficulties when using thermocouples, do not arisein them.

The large thermopower of gold-iron is due to thescattering of the conduction electrons in gold by themagnetic moments of the iron. If the iron con-centration is "high", interactions between themagnetic moments reduce the thermopower at thelower temperatures. If the concentration is "low",then at the higher temperatures the magnetic scat-tering is dominated by the normal scattering ofelectrons by lattice vibrations, and the anomalousthermopower is suppressed (5). The starting goldmust be very pure so that electron scattering by

ordinary impurities should be small. For generalpurposes one wants high sensitivity from below 1 Kto about 20 K (above this temperature the secondarm can be chosen to enhance the thermopower),with the sensitivity being not too dependent on ironconcentration. This aim is achieved by an alloycontaining of the order of 0.05 atomic per cent iron.The wire produced by Johnson Matthey is madefrom spectroscopically pure gold with 0.03 atomicper cent iron, while in the U.S.. the standard materialcontains 0.07 atomic per cent iron.

Practical Considerations

Apart from having adequate sensitivity, a thermo-meter must have sufficient reproducibility for thepurpose to which it is being put. Because of its rolein IPTS-68, a great amount is known about thevariability of platinum resistance thermometers, butthere is no comparable corpus of experience withlow temperature thermocouples. However, from thesystematic experiments of Sparks and Powell (6),together with some work of Rosenbaum (7) and ofourselves, we can derive some picture of the rangeof reproducibility of calibration likely to be en-countered when using gold-iron thermocouples.A summary of these experiments is given here.

(a) A gold—iron vs. superconducting niobiumthermocouple was calibrated between 1 and 4 Kbefore and after a series of about forty experiments,

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Calibration of four Gold-0.03 atomic per centIron vs. Chromel Thermocouples with one

Junction at the Helium Boiling Point

Temperature e.m.f. (microvolts) Earlierof variable single batch of alloy batch ofjunction r - -m alloy

(K) Reel 1 Reel9 Reel 17

4.21 0.0 0.0 0.0 0.0

10.11 82.0 81.4 82.2 88.8

20.15 231.9 231.6 232.4 249.7

30.32 374.7 374.6 375.6 399.7

39.96 503.7 503.9 505.0 532.8

50.11 639.3 639.5 640.5 671.2

60.29 778.4 779.0 779.8 812.7

69.41 907.7 908.3 908.9 943.6

80.00 1063.2 1064.0 1064.4 1100.7

90.44 1222.8 1224.2 1225.1 1262.0

99.78 1370.4 1371.9 1372.8 1410.7

Calibrations by Cryogenic Calibrations, Pitchcott,Aylesbury, Buckinghamshire, England.

The reels each contained 3 metres of wire, so thatthere are about 50 metres between reels 1 and 17.

each of which entailed cooling from room temperatureand maintaining the apparatus for at least twelvehours at the low temperatures before warming upagain. No change in calibration as great as 0.5 percent was found over the two-year period involved.Our general experience is in line with this observa-tion on the effect of temperature cycling alone.

(b) Sparks and Powell have kinked and stretchedpieces of wire and measured the e.m.f. of thermo-couples made from a deformed with an undamagedlength. This treatment changed the calibration solittle that if the deformed wire were part of a gold-0.03 per cent iron vs. Chromel thermocouple withone junction at the ice point, then all temperaturesdeduced down to 4 K would be unchanged within0.1 K.

(c) Comparisons between adjacent pieces of wiretaken from the same reel suggest that in general thecalibrations do not differ by more than 1 per cent,but specimens taken from three different reels drawnfrom one batch of alloy, measured by Ricketson (8)showed very remarkable agreement, as shown in thetable. Results are shown at about 10 K intervals andonly the results below 100 K are given, because abovethis temperature the Chromel contributes more thanhalf the measured e.m.f., so that any irreproducibilityin the gold-iron is relatively less important.

It appears that the more usual variability betweenreels from one batch of alloy is similar to differencesbetween different batches and between wires pro-duced by different manufacturers. At the lowesttemperatures, the sensitivity of the gold-iron wireis so dependent on iron concentration that largervariations in calibration must be expected. Goulder(9) has recently calibrated, between 0.4 and 2 K,four pieces of gold-0.03 per cent iron wire used atdifferent times in different apparatus in this labora-tory, covering a period of about six years in manu-facture. The sensitivities are shown in Figure 3.

Equipment for the calibrationof low temperature sensorsbetween 2 and 273K has beenspecially set up by CryogenicCalibrations. The sensorsare placed in closely fittingholes in the copper blockat the bottom of the lowtemperature apparatus (showndismantled) on the right,which is contained in adewar holding liquid nitrogenor helium. On the left is anaccurate temperature con-troller and a controlled D.C.output for the heater coil onthe sensor block and a tem-perature controlled box forresistance and voltage stand-ards. On the table is aCryobridge automatic balanc-ing potentiometer for mea-surement with 25 Hz current,and behind the operator aTinsley Staubomatic poten-tiometer for D.C. measure-ments, with galvanometer andcurrent control devices above

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ABSOLUTE THERMOPOWERAu/0.03 at I. Fe

0.4 06 0'-8 1TEMPERATURE K

Fig. 3 Calibration of three Au-4- 0.03at.%Fe vs.superconductor thermocouples below 2K. Ap-proximate years of manufacture:

1-1966, 2-1967, 3-1969, 4-1970

From all these experiments we may conclude thatthe calibration of a gold-iron wire used in a thermo-couple is exceedingly stable during repeated tem-perature cycling and is little affected by normalmechanical handling. As the sensitivity down to-1 K is comparable with that of thermocouples

in common use at normal temperatures, there aremany low temperature applications where they canbe conveniently used, employing standard electricalmeasurement techniques. The differences betweendifferent batches of wire are sufficient to requirechecking of the calibration at a few convenientlyrealised fixed points if a temperature difference isrequired to be known to better than about 1 per cent.However, all the calibrations seem to differ fromone another in a smooth manner so that adjustmentsare not difficult to make.

References1 See, for example, J. K. Hulm, Cryogenics, 1972, 12, 4722 G. Borelius, W. H. Keesom, C. H. Johansson and J. 0.

Linde, Proc. Kon. Akad. Amsterdam, 1932, 35, 103 W. B. Pearson and I. M. Templeton, Canad, Y. Phys.,

1961, 39, 1084; D. K. C. MacDonald, W. B. Pearsonand I. M. Templeton, Proc. Roy. Soc., 1962, A266, 161

4 R. Berman and D. J. Huntley, Cryogenics, 1963, 3, 70;R. Berman, J. C. F. Brock and D. J. Huntley, Cryogenics,1964,4,233

5 R. Berman and J. Kopp, Y. Phys. F: Metal Phys., 1971,1,457

6 L. L. Sparks and R. L. Powell, Measurements and Data,1967, 1, 82;,7. Res. Nat. Bur. Standards, 1972, 76A, 263

7 R. L. Rosenbaum, Rev. Sci. Instrum., 1968, 39, 890;ibid., 1969, 40,577

8 B. W. A. Ricketson, Private communication9 D. P. Goulder, Private communication

A Low Temperature Resistance ThermometerThe well-known platinum resistance thermometer

—widely used in industry and accepted for part ofthe International Temperatures Scale over the rangefrom 13.8K to the ice point—has disadvantages atvery low temperatures in that the resistance to bemeasured is then small, while it is inconvenient tomeasure resistances with values spread over threedecades.

The addition of small amounts of transition metalsto gold has an anomalous effect on its resistivityat low temperatures, and on this basis a new typeof cryogenic resistance thermometer has beendeveloped by Degussa of Hanau, West Germany.This employs a 0.4 per cent manganese-gold alloywhich has proved to be entirely stable and can bedrawn into fine wire.

The addition of this small amount of manganese togold is dramatic in that the resistance of a sensor thatis 50 ohms at the ice point falls to 25 ohms at heliumtemperatures rather than to 0.01 ohm with puregold. Most of this additional resistance is temperatureindependent, but the alloy still has a positive slope ofresistance against temperature from a value that isprobably as low as 0.1K.

The detection voltage for any given accuracy of

measurement is dependent on the maximum currentthat may be passed through the sensor withoutcausing the wire to overheat appreciably and on thevalue of the fractional sensitivity dR/RdT. Themaximum current for this new thermometer in anyparticular thermal environment is likely to be similarto that of platinum thermometers of the sameresistance and construction. The fractional sensi-tivity is better than that of the nickel-manganinstrain gauge type of sensor and appreciably the sameas that of the gallium-arsenide diode. It is at itshighest around 2K, but falls rapidly by nearly amagnitude between 10 and 15K.

Linearisation, an important electronic processthat allows a display of temperature from sensormeasurement, should be comparatively easy between40K and the ice point as the sensitivity alters byonly about 10 per cent.

If the reproducibility of this sensor—marketedunder the name Keltip—proves to be high with timeand thermal cycling, a very useful new instrumentwill have become available for both industrial andlaboratory use, particularly where millikelvin ac-curacy is not essential but where simple and multiplepresentation of temperature is required.

B. W. A. R.

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