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National Bureau of Standards Technical Note 1053

Nat. Bur. Stand. (U.S.), Tech. Note 1053, 76 pages (March 1982)

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CONTENTS

Electrical Properties of Materials

and Their Measurement at Low Temperatures

F. R. Fickett

Electromagnetic Technology Division

National Bureau of Standards

Boulder, Colorado 80303

ABSTRACT

A review^ is^ given of the electrical resistance of materials at cryogenic temperatures,

Measurement techniques, the data base, and uses of the data are presented. The emphasis

is on metals and alloys of technological importance; a topic which covers a large range of

materials. Similarly, the treatment of theory and of measurement techniques is primarily

for the user interested in the more practical aspects of (^) the subject. In every instance, however, references are given (^) which allow the reader to pursue the subject at any level.

Key words: alloys; conductivity; electrical property; metals; polymers; resistance; resistivity; review.

^Funded in part by DoE Division of High Energy Physics,

copper is well within the specification. The message is clear: if the low temperature resistivity is an important parameter for the job at hand, it must be measured on (^) the specific material to be used.

To indicate the^ large^ range^ of^ values^ covered^ by^ the electrical resistivity, consider figure 1.1, which presents typical resistivity data as a function of temperature for (^) a

number of metals and figure 1.2, which indicates the resistive behavior of a variety (^) of

copper products^ [2]. In^ table^ 1.1^ ice^ point^ values^ for^ the^ resistivity^ of^ several common

metals and alloys are listed. The^ measurements are^ reasonably recent except for some of

those referenced to Hall which are "best values" derived from an extensive literature survey. In each case the materials are very well characterized in the references. (^) A

value of the residual^ resistivity^ ratio^ RRR^ is^ also^ given^ in^ the^ table.

Most of the figures presented here are prepared using data from the literature.

Often it^ was^ necessary^ to^ extract^ those^ data^ from^ small^ graphs,^ so^ that^ the^ exact^ numeri-

cal values shown here may^ not^ be^ very^ accurate.^ These^ curves are intended to indicate general behavior only; for accurate data, the referenced sources should be consulted.

RRR -^ Residual^ Resistivity^ Ratio^ =^ p(273 K)/p(4^ K)^.^ In^ metals^ of^ commercial^ purity^ or

better, the numerator depends essentially only on the thermal vibrations of^ the lattice

and not on the impurities. The denominator depends only on the impurities and defects for

most metals, and thus the ratio is a sensitive indicator of purity; in fact, it is capable

of detecting impurity levels far below those which can be seen by most analytical tech- niques. To first order, the ratio is independent of shape factor, i.e., it is equal to the ratio of the resistances. In highly alloyed metals, the ratio is not as meaningful

and is useful only in comparing samples of nominally similar composition.

10 6x

10

E

I— vi CO uu

< o cc 10"

IQ-^U

-T~rr 1 I I I I^ M "1^ r

STAINLESS STEEL (AISI 300 SERIES)

BRASS

Be

AI(IIOG)

Cu (CDA (^) 102) Oxygen (^) Free'

10"^ (^) l I J I I I I I (^) J L 10 100

TEMPERATURE, K

400

Figure 1.1. Resistivity of several common metals as a function of temperature

10

CS 10"'

(/ CO LU CC

cc I—

10 -

1-

5x10"

1 1 1 1 II 1 1 1 1 1 1 1 11 1 1

BRASS ___^

"""^^^

Cu (06 atomic % Mn)/// /V

Cu (CDA 150) __.^-^ //

Zirconium Copper //

Cu (CDA (^) 102) (^) y / OxygenFree' (^) /

/cu (High Purity) / 'Five-Nines'

'J

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 100

TEMPERATURE, K

400

Figure 1.2. Resistive behavior of a number of "pure" coppers and copper copper alloys.

Chapter 2. EXPERIMENTAL (^) TECHNIQUES AND CONSIDERATIONS

Resistivity is one of the easiest of all physical properties to measure. The basic techniques and apparatus are described in detail by Meaden (^) [1] and by Gerritsen [19] as

well as in many electrical measurements texts such as those by Stout (^) [20], Gregory (^) [21]

and Wolf (^) [22]. The Kelvin bridge (^) method and (^) the potentiometer method are two of the most

useful classical^ measurement techniques. They both offer better than 1% accuracy in

micro-ohm level measurements. Most of the textbook methods are quite time consuming, and

the approaches actually used in most laboratories are somewhat less sophisticated, since time is often of the essence and high precision is not usually required. Several of these easier techniques are described here; the more esoteric ones are left to the authors

referenced above. The equation from which the resistivity, (^) p, is most often calculated is

p =^ RA/Ji^ =^ VA/I£^ (2.1)

where (^) R is the resistance of the specimen, V the voltage measured, I the current, A the

cross sectional area of the specimen and £ the length between the voltage probes. With reasonable care, both A and i can be determined to 0.5% and, of course, to greater preci- sion in a carefully designed experiment. The usual technique of determining an average

wire diameter for the calculation of A will (^) lead to incorrect results if there are signi-

ficant variations in (^) diameter along the specimen. Most experiments are designed such that

the voltages to be measured are on the order of microvolts or greater. This leads to

practical specimen sizes and current levels, as well as giving a voltage measurable with

good accuracy by relatively inexpensive equipment. Furthermore, equipment such as this is easily adapted to the many modern computer control methods for automated operation.

2.1 Direct current measurements

A direct current (dc) system, which has been used successfully for routine measure-

ments, is shown in figure 2.1. The current source can be anything from an automobile

battery to a precision current calibrator. It should be stable over the time required for a measurement. The standard resistor is (^) chosen primarily to have a sufficiently low

resistance that it will not suffer any significant heating at the highest^ currents.

Allowable power dissipation limits are stated by the manufacturers —^ they are^ lower^ than

one might expect, so it is well to check them. Reversal of the current is essential to eliminate thermoelectric voltages, a complication to be discussed shortly. The use of a commercial nanovoltmeter with its output read by a relatively inexpensive digital volt- meter provides good precision ('^1%) (^) with minimum cost and allows for greater flexibility in an environment where instruments (^) must often be shared among several experiments. The use of (^) a four-probe system for (^) the leads (i.e., separate sets for current and voltage) is the (^) best approach to low level (^) dc resistance measurement; two-lead systems introduce too many possible sources of error.

standard

Resistor

Current

Source

leads

twisted

and/or

'Shielded

leads thermally

anchored.

near sampleF I

^AAAAAAAAA- Sample

Low Temperature Region

Figure 2.1. Block diagram of a system for low temperature resistivity measurements,

2.2 Alternating current measurements

At first glance, alternating current (ac) techniques, particularly those involving

modern lock-in amplifiers seem (^) to offer (^) many advantages in low temperature resistance

measurements, particularly in the elimination of thermal voltages. In practice, however,

rather heroic techniques are necessary to make accurate measurement of resistances smaller

than 1 Q, (^) [23]. On the other hand several very nice ac bridge circuits have been developed for relatively high- resistance (^) thermometry applications at low temperatures (^) [24,25]. The

only source of detailed information on lock-in measurement techniques applicable to low

temperature resistivity measurements appears to be in the manufacturers' literature. Shielding and grounding, along with the correct use of transformers, are the major prob-

lems in such an application and are discussed in detail by Morrison (^) [26].

2.4 Low level measurements

The relatively easy methods just described do not always suffice. The most frequent failing occurs when voltages well below the microvolt level must be measured. In fact,

nanovolt signals are commonly encountered in physics experiments on (^) pure metals. (^) In spite

of the availability of commercial nanovoltmeters and potentiometers on the market, measure-

ments at this level are very difficult and measurements with 1% accuracy require (^) very

specialized apparatus. A nanovolt detection system using commercial (^) components is described

by Clark and Fickett [30]. An extensive discussion of techniques using SQUID (Supercon-

ducting Quantum Interference Devices) detectors is given by Gifford, Webb, and Wheatley

[31]. Other devices,^ which^ convert the low level dc voltage to ac in the cryostat and

subsequently amplify the resulting signal, have been described in the literature. Magnetic

amplifiers (^) [32], Hall effect amplifiers (^) [33], superconducting modulators (^) [34], and relay

modulators [35] have all been used in this manner.

2.5 Additional considerations

Low temperature measurements introduce other special problems of a technical nature that must be considered:

a. The temperature^ of^ the specimen must be accurately measured^ and^ precisely controlled

b. At low^ temperatures, joining techniques for^ current and^ voltage^ leads^ are^ more critical than at room temperature. c. Voltage leads traverse a large temperature gradient, leading to spurious thermal

voltages and creating unwanted paths for heat conduction.

d. Uneven thermal contraction of parts of the apparatus can stress the sample. In addition to these, there are more basic phenomena which can create havoc for the

unwary, such as size effects and large resistance changes due to magnetic fields^ or^ phase transformations. These are covered in later chapters. Here we discuss only the four topics listed above.

Temperature control. When resistivity measurements as a function of^ temperature^ are necessary, the experimental setup becomes much more complex. In some instances, one can take an easy (^) way out by immersing (^) the specimen in various constant temperature baths. The

most common baths are liquified gases and slushes (solid-liquid mixtures) of^ organic

fluids, usually prepared by mixing with liquid nitrogen (^) [36]. Some of the temperatures

attainable by this method are listed in table 2.1. The temperatures of^ the^ liquid^ gas baths are dependent on pressure and, thus, on elevation; for example, liquid helium^ boils at 4.0 K at Boulder, Colorado (elevation 1610 m) vs. 4.2 K at sea level. It should not need emphasis (^) that liquid hydrogen and liquid oxygen should be used only by those familiar

with their unique capabilities for total destruction of the laboratory. Some^ caution^ is also necessary with many of the organics. It is common practice to mix crushed dry ice^ • with either acetone or alcohol (^) to make a liquid bath at dry ice temperature. Any cryo- genic bath (^) should be contained in an insulated container for stability and longevity. Vacuum pumping (^) of cryogenic liquids, combined with some form of pressure control, such as

a (^) manostat system, allows attainment of '^-l K with (^) helium, 14 K with hydrogen, (^25) K with

neon and 64 K with nitrogen, but the (^) resulting system complexity seldom justifies (^) such an approach except for the case of helium, (^) where only more complex options (^) (e.g., dilution refrigerators) are available. The (^) entire range of specialized (^) techniques for producing and measuring temperatures (^) below 1 K is described (^) by Betts [37] and not discussed here. In all other cases (^) the heater temperature control (^) techniques described below are (^) more practical.

Table 2.1. Liquified gas and slush bath temperatures.

Substance Temperature (K)^ (^) Bath Type

Ice water 273.15 Slush

Isobutane 262.9 Liquid B.P.

Carbon tetrachloride 250 Slush

Propane 230.8 Liquid B.P.

m-xylene 226 Slush

Trichloroethylene 200 Slush

Carbon dioxide 194.6 Solid

Methanol 175 Slush

n-pentane 142 Slush

Iso-pentane 113 Slush

Methane 111.7 Liquid B.P.

Oxygen 90.1 Liquid B.P.

Nitrogen 77.3 Liquid B.P.

Neon 27.2 Liquid B.P.

Hydrogen 20.4 Liquid B.P.

Helium (He^) 4.2 Liquid B.P.

Helium (He^) 3.2 Liquid B.P.

^All temperatures given at 0.1 MPa (^) (1 atm).

Continuous temperature control (^) may be performed by a variety of (^) techniques. White

[38] discusses^ several^ methods^ in^ general outline and includes references (^) to the litera-

ture. The technique of (^) electrically heating a copper block in good (^) thermal contact with

the specimen, but partially (^) isolated from the coolant bath by a (^) properly chosen heat leak,

is the usual choice. (^) The electronics for temperature control (^) are available commercially

A complex, but successful technique for increasing this precision involves: coating the specimen with varnish, curing, drilling a 0.2 mm diameter hole to the metal surface, inserting a 0.12 mm flux coated ball of low melting point solder (available commercially), heating to melt the solder, and inserting a pre-tinned potential (^) lead. Spot welding (^) can

be used^ for^ nearly^ any^ combination^ of^ metals,^ but it^ is easiest for higher resistivity materials. Often an intermediate metal such as nickel must be employed. Some arrange-

ments, such as joining a small diameter copper wire to one of large diameter, will tax the

skill and patience of the most accomplished welder. The major problem with spot welding leads is the possibility of major damage to the specimen by mechanical deformation or arc burn. Welding, usually used for joining fine wires, is (^) a reliable technique if (^) a small

oxy-hydrogen torch is^ available.

Table 2.2, Thermometers for^ the^ measurement^ of low^ temperatures

Type Temperature Range (K)

Comments

Liquid in glass

Toluene Pentane

Thermocouple

Type E Type KP or EP vs, Au.07at.%Fe

4- (^20)

An impure pentane,

Useful also above room temperature. Can be used to room temperature^

Metal resistor

Platinum

Copper Indium

Semiconductor

Germanium Thermistor

Carbon resistor

4- 4-

4-

Can be used to 1200 K^ -^ usual appli' cation (^) is above 50 K. Not commercially available. Not commercially available.

Very (^) sensitive to magnetic fields, Very sensitive to magnetic fields.

Inexpensive, less field sensitive than the semiconductors.

a. AuFe is not a standardized thermocouple type but is available commercially. Tables are given by Sparks and Powell^ [47].

11

Thermal considerations^ for^ lead^ wires^.^ The^ conduction^ of^ heat^ to^ the^ specimen^ by the leads can occasionally be troublesome. In such cases leads of high thermal resistance alloys, such as constantan, Evanohm, or manganin are sometimes used. The alloys have similarly high electrical resistances. Theoretical aspects of the problem and some

practical calculations^ are^ presented^ by^ Mercouroff^ [50]. A^ more^ common^ solution^ is^ to use

copper wire, but to anchor a reasonable length of^ the lead^ to a heat sink block which

approximately tracks the specimen in temperature [51]. This technique has the added

advantage of^ minimizing^ spurious^ thermal^ emf's.^ These^ thermoelectric^ voltages,^ generated

in the presence of thermal gradients, arise from contacts between dissimilar metals and from inhomogeneities in the lead material. Spurious voltages in a well-designed experi-

ment should be stable at the submicrovolt level over short time periods. All dc potential

measurements should be an average^ of^ two readings taken before and after reversing the

sample current.

Thermal contraction^.^ Relative^ thermal^ contraction^ may^ cause^ serious^ problems^ in electrical measurements at low temperatures due to the wide range of behavior exhibited for various classes of common materials (^) [2]. Clearly, a pure metal rigidly attached to a

plastic substrate will be strongly compressed on cooling. The usual result of such an

arrangement is that the metal tends to buckle. The obvious solution is to allow some

motion of the specimen in the holder. Another is to make the entire holder from the same

type of materials^ as^ the specimen,^ e.g.,^ a^ copper holder^ for^ pure metals,^ and^ rely^ on^ thin

varnish coatings and polymer films for electrical insulation. A final possibility is that

of matching the expansion coefficient of the holder material to that of the specimen.

This can be accomplished by the use of filled epoxies [52] or, possibly, graphite-epoxy

composites of suitable composition (^) [53].

12