NatFonal Bureau of Standards

Library, E-01 Admin. BIdg.

NOV 2 3 1970

NBS TECHNICAL NOTE 365-1

Survey of Electrical Resistivity

Measurements on 8 Additional

Pure Metals in the Temperature

Range to 273 K
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Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

NBS TECHNICAL NOTE 365-1

ISSUED AUGUST 1970

Nat. Bur. Stand. (U.S.), Tech. Note 365-1, 85 pages (Aug. 1970)

CODEN: NBTNA

Survey of Electrical Resistivity

Measurements on 8 Additional Pure Metals

in the Temperature Range to 273 K

I

L. A. Hall and F. E. E. Germann

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

'""CAU O*

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide

a means for making available scientific data that are

of transient or limited interest. Technical Notes may

be listed or referred to in the open literature.

'or sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. (Order by SD Catalog No. 013.46:365-1), Price $1.0020402

CONTENTS

Abstract INTRODUCTION

GENERAL DISCUSSION OF RESISTIVITY

PRESENTATION OF DATA HOW TO USE THE DATA ELECTRICAL RESISTIVITY DATA SHEETS 12 cadmium . chromium

manganese titanium

tungsten

vanadium

zinc . . zirconium

(Data Memorandum No. M-26) 13 (Data Memorandum No. M-27) 23 (Data Memorandum No. M-28) 33 (Data Memorandum No. M-29) 39

(Data Memorandum No. M-30) 49

(Data Memorandum No. M-3I) 63 (Data Memorandum No. M-32) 71

(Data Memorandum No. M-33) 79

I

SURVEY OF ELECTRICAL RESISTIVITY MEASUREMENTS ON & ADDITIONAL PURE METALS

ra THE TENtPERATURE RANGE TO 273 K

L. A. Hall and F. E. E. Germann

Experimental electrical resistivity data for 8 pure metals have been compiled

tabulated, and graphically Illustrated for a temperature range of to 273 K. A section has been prepared for each particular metal -which includes references , brief comments concerned with preparation of sample, purity, and any other pertinent information, tabulated data, and graph.

Key words: cadmium; chromium; compilation; electrical resistivity; low temperatiure; manganese; titanium; tungsten; vanadium; zinc; zirconium.

1. INTRODUCTION

This survey is a continuation of the task of collecting experimental electrical resistivity

data for pure metals. The first group of metals studied were Al, Be, Co, Cu, Au, In, Fe , Pb, Mg,

Mo, Ni, Nb, Pt, Ag, Ta, and Sn.** As in the previous survey, we found many articles describing

experimental measurements of electrical resistivity in the open literature. Many presented results

of straight -forward temperature -dependent resistivity measurements on wires or rods of high-purity

metals. Some dealt with the effects of irradiation, plastic deformation, magnetic fields, and

alloying on resistivity, while others showed the variation in resistivity due to unusual shape of the sample, e.g., whiskers or thin films. In the recent literature, superconductivity was also studied extensively. Because the amount of literature in this field is so large, we have restricted

this sui*vey to the temperature -dependent resistivity measurements on very pure metals.

All of the data from this one area of resistivity measurements have been organized into a relatively concise and useful form. For the experimentalist, we have tried to present a complete

picture of what data are already available so that he may plan his work in such a manner as to fill

in "gaps" in existing data or to check or "reinforce" existing measurements. For the engineer, we have presented a method of predicting the electrical behavior of a metallic specimen of known

purity. When the purity is not known, the resistivity of the metal may be predicted by measuring

its residual resistivity, which can be measured at k,2 K, and applying Matthiessen's rule, as will

be explained below. With these objectives in mind, we have reviewed carefully all of the pertinent

articles and noted in a "comments" section the purity of the metals studied, their residual resistivity value , any mechanical treatment of the sample and its final form during measiirements , and any

other facts which might help explain the character of the experimental data.

* This study was supported in part by the National Aeronautics and Space Administration, Office

of Advanced Research and Technology, Contract R-06-006-Oij-6. ** "Survey of Electrical Resistivity Measurements on l6 Pure Metals in the Temperature Range of

to 273 K," L. A. Hall, Natl. Bur. Stds. Tech. Note 365 (Feb I968)

.
An earlier compilation* presented experimental resistivity data for 53 metallic elements. From the time of that publication to the present, the Compilation Unit of the Cryogenic Data Center

has been actively acquiring electrical resistivity articles. These articles were entered into our Storage and Retrieval System together with all the other cryogenically oriented documents that have

come to our attention by a systematic scanning of the primary journals, and secondary publications

such as Chemical Abstracts, Physics Abstracts, NASA STAR, Nuclear Science Abstracts, DDC TAB, and International Aerospace Abstracts . A computer search of this Storage and Retrieval System was the basis for this compilation. All pertinent articles from the references listed in this search were obtained and reviewed.

2. GENERAL DISCUSSION OF RESISTIVITY**

The measured resistivity p is a function of temperature, but on approaching absolute

zero it approaches a constant residual resistivity Po . The quantity po arises from the presence

of impurities, defects, and strains in the metal lattice. However, in pure annealed metals it is only a small fraction of the total resistivity at room temperat-ure . Subtraction of po from the measured resistivity gives a value of the resistivity appropriate for a perfectly pure, strain-free

specimen. The temperature -dependent resistivity thus obtained is called the ideal or intrinsic

resistivity pj . It is caused by the interaction of the conduction electrons with the thermally

induced vibrations of the lattice ions, and, if present, with the magnetic structure of the lattice. The separation of the total resistivity p^p into temperature dependent (Pi) and temperatureindependent (po) contributions in this way is known as Matthiessen's rule, which may be written

P = Po + Pi •

This rule is a good approximation for all engineering purposes.

The ideal resistivity due to lattice vibrations may be expressed by the Gruneisen-Bloch

relation

_ C /' T \^ r Sr/T z^dz

Pi = iS7 V 67^ Jo (e^ - 1)(1 - e-^)

where M is the atomic weight, C is a constant, and T is in the Kelvin scale. 9r is an empirical temperature characterizing the metal's lattice resistivity in the same way the Debye

temperatiire 6p characterizes a solid's lattice specific heat. It is often true that 6r ?a Sq , typically about 300 K for most metals. Below .about 0.1 6^ this relation reduces to pj °= T^ relation closely. It is found that a few of the metals follow the t'^ relation closely. The exponent of T for most nonmagnetic metals generally lies between k.^ and 5-

* A Compendium of the Properties of Materials at Low Temperatures (Phase II)", R. B. Stewart and

V. J. Johnson, editors, Natl. Bur. Standards, Cryogenic Eng. Lab., WADD Tech. Rept. 6O-56, Part IV (1961) DDC AD 272 769. ** A more complete discussion of electrical resistivity can be found in Electrical Resistance of Metals by G. T. Meaden, Plenum Press, New York, I965.
A metal with a cubic crystal structure has the same resistivity whether in polycrystalline

or single crystal form, apart from a small extra contribution in a polycrystal that may sometimes

be caused by grain boundaries since the cubic structure is isotropic. But in a single crystal of

a noncubic metal, the resistivity is often very anisotropic , its value depending on the direction

of the flow of current. Likewise, polycrystalline specimens of such metals, if preferentially

oriented, as by rolling or drawing, for instance, will have direction-dependent resistive properties.

In anisotropic metals, the electrical resistivity parallel to the principle crystalline axis

is designated p and electrical resistivity perpendicular to the principle axis is designated

p . When values for p and p have been determined for single crystals , one may calculate a

J. . II JL value of p for a polycrysta3-line sample using the equation of Voigt*

3Px

2p + p

II X

I

I

Superconductivity is observed in at least 30 elements. At temperatures less than their

"superconducting transition" temperatures, these elements lose all resistance to electric current. Articles dealing with superconductivity were not reviewed here and only the transition temperatures

are noted for each metal. The curves on our graphs should not be extrapolated below this transition temperature.

In the residual resistance range, approximately below 20 K, trace quantities of certain

impurity atoms in a nominally pure metal can cause resistance minima and other temperature

dependent effects. These are generally quite small and have been neglected in this survey. Along with related magnetic effects, they are commonly classed as a manifestation of the "Kondo effect," occurring in the neighborhood of the "Kondo temperature." The interested reader should refer to the review article by Daybell and Steyert for further infonnation,

3. ERESEMTATION OF DATA A separate section has been devoted to each metal. These sections have been prepared in the format of our regular preliminary compilations and have been numbered consecutively with other worksheets dealing with other properties of materials at cryogenic temperatures. With the collec- tion in this format, the user may easily remove any memorandum on a particular metal that he is studying from the group. The sections contain the following:

a) Sources of data - references for the articles from which we have taken the data.

b) Additional references - other articles dealing with electrical resistivity of the metal which may be of interest to the reader.

c) Comments - a concise discussion of any factors influencing the character of the experimenter's

resistivity data, such as purity, heat treatment, shape of sample, crystal structure, etc.

* Voigt, W. , Lehrbuch der Kristallphysik (Teubner, Leipzig, I928) , p. 959. ** M. D. Daybell and W. A. Steyert, Rev. Mod. Fhys. kO, 38O-89 (1968).
d) Tables - tabiolated experimental data. When the experimenters presented their resixlts graphically, an attempt was made to read values from the graphs and put them into tabular form.

e) Graph - the data have been plotted as ratios p /ps73 > that is, the resistivity at a given

temperature divided by the resistivity at 273 .15 K. Many of the investigators have not given

their ps73 value, and in these instances we have used a value whicu we believed to be the most accurate value of Ps73 in calculating Pm/Psys • Table 1 shows pgya values given by

the investigators and the value chosen as the most accurate. The data are plotted on logarithmic

coordinates which tend to emphasize the differences in the values reported by the several experi- menters at the lower temperatures

.

In Table 1 on pages 6-11, all experimental values of pg^g have been tabulated for the eight metals. The "selected" value is in most instances the lowest available value of Ps73 for that particular metal.

h. HOW TO USE THE DATA

As has been stated before, this is an attempt to gather all experimental data from tempera

-

tiore -dependent electrical resistivity measiorements into a relatively concise form. The graph presents at a glance the amount of work done on a particular metal; however, for some of the more popular metals not all the tabular data are plotted because their cixrves would be superimposed on

others. The annotated bibliography gives an insight into the character of the data.

An engineer, wishing to predict the resistivity of a particular metal, could:

1. review the comments section to find out if measiirements have been made on a sample

similar to his. If he succeeds in finding such measurements he can then refer to

the tabular data and expect his metal to perform similarly.

2. apply Matthiessen's riile, p_ = po + Pi . The residual resistivity, Po , could

be found by measuring the resistivity at 4.2 K of the particular metal being

used. The ideal resistivity, pj , would be estimated from the graph by drawing

a straight line downward from the portion of the lowest curve where p

"^ T

(shown in figure l)

.

TEMPERATURE

Figure 1. Relationship between ideal resistivity.

residual resistivity, Pj and measured

resistivity at a given temperature, p T"
It is also possible to estimate the piority of a metal by measuring its residual resistivity at k.2 K, finding its position on the graph, and referring to the comments section to find

statements of purity for curves in the same region of the graph.

On each graph an additional scale in degrees Rahkine has been added at the top border.

The appropriate conversion is: Kelvin times 1.8 = °R. For example, the ice point 273-15 K is equivalent to ^91. 67 °R.

Table 1 starts on the following page.
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OJ o t>^^ o fd CU rn oo^-- o -d -P ^-v VO

ON oo On OJ ,y <u ON On on OJ ,M <U CO (U VO H ON'-^ rH ^ CO +^ rH rH -—.H d CO -P !h ?I ON

OJ

r-\ <0 ^-^ H -^tHCO —- v-^d) —' r-\ --iH a O H H

CO v_^ ;i! id CO '-^- H CO p! d CO^-^- H 3 !> VoS M d PH<u>cviOo C! 4JHCU!>cv^PO

4-^ bD CO (0 VO Ph CU bD CO CO M3 Pi (U _^ H

O OJ

0,-^.H ^-H-dCTNoS Sh 5,.^-H J>-HrdC7No8 ;^ O VO O (U OJ H 0)

CO -d rH H

ti ^D O (1) 0) H (U CO 0) CO rH '-^ OJ>'d C!4J !>-P , CM > -d d +J^-^ !> -P CU -P bD <U CJN

CD oSon cu3co!>OC! o8c3N Cu3c0!>O!d HcShj Sh oh-h

fl-— cooojj'fc!-— (U ^ in H Pi "a id

CO CUCUPoSShCcO'--

•H CO > VO ^ CO -p

OJ CO

<XS -P ''^

0) -P ^ CO

HoS+2 U r-{ O U -A

CD fn !h H Ph 3 d

CO (UCUPoSMdCO^^

Q iH K O ON 9 , P^ '-I H

CO >

rao uit[o 01 X (^ o8 Pi o8 --^ '^ CO - +J •rHdsdcj ojcocoro •Hsdido cucococv-) fH O fn 4«i CO -p

+^H

>

•rH

<D CO coH co-p co^vD (U cocoHco+Jco^VD CU O 4J CU (U -H

Cl cocococ!d,M(UON d cococoflp!.MajcT\ bOCJN X r-j ^ :S P -H -H O (L) -H (U H H CU rH <U 13 H <U c5 s S o <;

P -H -H O <U tH CU iH H

^1 CU CU'Q —'rH<5 —

OSS c5 5

CO ^_"_- CO -H O

•P +3 -H O CO

0)

C7N CO LfN oo OJ c:iN t- CJN C3NVD H m rv-)^ J- ^ CO CO CJN LTN l>- VO O On i/N m

0)

^1 LTN LTN UfN LTN UTN LP^ LTN LTN LTN ITN LTN VD U^ l/N K

H uio ratio gOT X cl CT\ CJN

U-N

LTN t CO (9^6t)uss^TJ:JSB \r\ LTN LTN

0) ri , a o M

+3 fv-i CO I^ H <M mo uiqo 01 x d COro

CO

LTN

LTN

•H

Pi -P (S-t|6T)a3STaimjo LTN Lr\ ITN ff CO O H ;3

0) ^ H

(D CO 44 >

rao luqo gOT ^ ^cl ON

CV-) C7S

LfN LTN

ffl -PO (596T)uspeaw LTN Lf% U-N EH

^^ ,_^ ,_,

rt CV-) oo '^ _, ^ ro oo oo rd H On C3N C3N (U

CO> H _H H -P ^-^ CO ^-^

0)

CO 1

9 d Si

-P ro S)H CO 1

o ir-

(U CM rao uiqo gOT x d •rH •H

rd CO !> HO

H m FQ m 1

_C0 CO " NO

CO CO

C3N "5 11

4^ en UN -* 1

g

LfN LTN T

CO P

(U

^d I'd Axod^

ou-fz e

10 1
CO

CM 08 ONH -P d 0) ^^ MH -d- O >

CM O O

(J\ > W

08o

Sh '-^ (U CJN M

oj a H iJ rH M -H H

(D CJ ^^ ^ O ;h H ;3 ^

fl 0) ^ 0) l-^

t- ^—

s

cr> CM <u --^MD

CJN rv-1 -p (U CJN H •H ^ H

H rj H^--

ra V ^ ^ '-^ CO f-l •H +2 a\ > (u ^ M ^-^ 08 UA +^

?3 •H (M C^N t:) ft

l(N 0) H 0) S s > ^ <r\ d -P (U H H fl) -P CO M

08 08 -cj- H

CJ\ -P (11 ^71^

hD fH H Ti d

ft

fl (1) 0) ^ s Jh nd •H d ^H +J vo d (D fH CD Cfl (1) m *» ir\ •H +^ CO

?! ra -p a &CT\H fl d

CO •H +J <i) H ^^ -H tH

rH Ji Tl (1) (D--^H ^ P4 <; M pq

p

COH

CM

VD

ON

VD

OJ

CM

>5

d

o

C3N

CI Lr\

iiinTuoojT:2

11
5. ELECTRICAL RESISTIVTK DATA SHEETS

cadmium . chromium manganese titanium

tungsten

vanadium

zinc . . zirconium

(Data Memorandum No. M-26) 13 (Data Memorandum No. M-27) 23 (Data Memorandum No. M-28) 33 (Data Memorandum No. M-29) 39 (Data Memorandum No. M-30) h9

(Data Memorandum No. M-31) 63

(Data Memorandum No. M-32) 71 (Data Memorandum No. M-33) 79

I

12
CRYOGEN C DATA MEMORANDUM

PROJECT NO. 2750422 FILE NO. M-26

ELECTRICAL RESISTIVITY OF CADMIUM, Cd (page 1 of 10

)

(Atomic Number kQ)

Sources of Data :

Aleksandrov, B. N., "Size effect in electrical resistivity of high-purity metals," Soviet Phys. JETP l6, No. 2, 286-94 (Feb I963).

Aleksandrov, B. N. , and D'Yakov, I. G. , "Variation of the electrical resistance of pure metals

with decrease of temperature," Soviet Ehys. JETP I6, No. 3, 6O3-O8 (Mar I963)

.

Bridgman, P. W. , "The effect of pressure on the electrical resistance of single metal crystals

at low temperature," Proc. Am. Acad. Arts Sci. 68, 95-123 (1933).

Eucken, A., and Gehlhoff, G. , "Elektrisches , thermlsches leitvermogen und Wiedemann-Franzsche

zahl der antimon-cadmiunlegierungen zwischen und -190°C," (Electrical, thermal conductivity

and the We idemann-Franz constant for antimony-cadmium a3J.oys between and -190°C), Verhandl.

Deut. Physik. Ges. 14, I69-I82 (1912).

Goens, E. , and Griineisen, E., "Elekrrizitats und warmeleitimg in zink und cadmiumkristallen,

(Electrical and thermal conductivity in zinc and cadmium crystals), Ann. Physik l4, l64-80 (1932).

Gruneisen, E., "Elektrische leitfahigkeit der metalle bei tiefen temperatiiren," (Electrical

conductivity of metals at low temperatures), Ergeb. Exakt. Waturw. 21, 5O-II6 (1945)

•

Gruneisen, E. , and Goens, E., "Untersuchungen an metallkristallen. II. Spezifische warme und

elektrischer widerstand von zink xmd cadmium," (Tests with metal crystals. II. Specific heat

and electrical resistivity for zinc and cadmium), Z. Physik 26, 250-73 (1924).

Holborn, L. , "Uber die abhangigkeit des widerstandes reiner metaJJLe von der temperatur," (About the dependence of resistance of pure metals on the temperature), Ann. Physik 59, 145-69 (l919)»

Jaeger, W. , and Diesselhorst , H. , "Warmeleitimg elektricitatsleitung, warmecapacitat und

thermokraft einiger metalle," (Heat conduction, electrical conductivity, specific heat and

thermal power in metals), Wiss. Abhandl. Physiko-Tech. Reichasanstalt 3) 269-424 (19OO).

Mc Lennan, J. C, and Niven, C. D. , "Electrical conductivity at low temperatures," Phil. Mag.

4, 386-404 (1927)-

Meaden, G. T-, Electrical Resistance of Metals , Plenum Press, New York (1965) 2l8 p.

Meissner, W. , "Messungen mit hilfe von flussigem helium. 2. Widerstand von gold, zink, cadmium,

platin, nickel, eisen und silber bis herab zu 1.3° Abs," (Measurement with the help of liquid

helium. 2. Resistance of gold, zinc, cadmium, platinum, nickel, iron and silver down to about

1.3 K), Z. Physik 38, 647-58 (1926) Abbreviated version appearing in Physik. Z. 27, 725-30

(1926)

.

Meissner, W. , and Voigt, B. , "Messungen mit hilfe von flussigem helium. XI. Widerstand der reinen metalle in tiefen temperaturen , " (Measurements using liquid helium. XI. (a) Resistance

of pure metals at low temperatures), Ann. Physik ]_, No. 5, 761-97 (1930)-

Onnes, H. K. , and Hoist, G. , "On the electrical resistance of pure metals etc. IX. The resis- tance of mercury, tin, cadmiutE, constantin and manganin down to temperatures, obtainable with

liquid hydrogen and with liquid helium at its boiling point," Commun. Phys. Lab. Univ. Leiden

No. 142A (1914) Transl. from Verslag Gewone Vergader. Afdel. Watuurk. Koninkl. Ned. Akad. Wetenschap. , 506-II ( Jun 1914)

.

13
(page 2 of 10) Electrical Resistivity of Cadmium

Cryogenic Data Memorandum No. M-26

Schimank, H. , "Uber das verhalten des elektrlschen widerstands von metallen "bei tiefen

temperaturen , " (The behavior of the electrical resistance of metals at low temperature), Ann. Fhysik k^, 706-36 (191^).

Schott, R., "Uber das warmeleitvermogen einiger metalle bei tiefen temperaturen/' (Thermal

conductivity of some metals at low temperatures), Verhandl. Deut. Ehysik. Ges. I8, No. 1,

27-3ij- (1916).

Tsui, D. C, and Stark, R. W. , "Evidence for anisotropic electron-phonon scattering probabilities from the galvanomagnetic properties of cadmium," Ehys. Rev. Letters 19, No. 23, 1317-9

(Dec 1967).

Tuyn, W. , "Measurements on the electrical resistance of some metals below the boiling point of oxygen," Commun. Ehys. Lab. Univ. Leiden No. I96B (I929) Reprinted from Eroc. Kon. Ned. Akad. Wetensch. 32, 115 (Feb I929).

Tuyn, W. , and Onnes, H. K. , "Nouvelles experiences avec 1 'helium liquide. AB. Nouvelles

mesures relatives a la resistance electrique des metaux a\ax temperatures de I'heli'um liquide,"

(New experiments with liquid helium. AB. New measurements of the electrical resistance of metals at liquid heliixm temperatures), Communs. Ehys. Lab. Univ. Leiden No. I8I (1926)

,

Reprinted from Arch. Neerl. Sci. IIIA 10, 5-4l (1926).

Vtorov, F. P., and Dmitrenko, I. M. , "Superconducting bolometric current modulator," Cryogenics

7, No. k, 207-8 (Aug 1967) Instr. Exptl. Tech. (USSR), No. 3, jh8-30 (May-Jun I966) Transl. Pribory I Tekhn. Eksperim., No. 3, 223-ij- (May-Jun I966).

Other References :

Aleksandrov, B. N., "Effect of dimensions and purity on the electrical resistance of metals in

a longitudinal magnetic field at (liquid) helium temperatures," Soviet Phys. JETP I6, No. k, 871-8 (Apr 1963), Transl. of Zhxir. Eksptl. I Teoret. Fiz. h3, 1231-'4-l (1962).

Alekseevskii, N. E., and Gaidukov, Yu. P., "Open cross sections of cadmium, zinc and thallium

fermi surfaces," Soviet Phys. JETP I6, No. 6, 1481-88 (jun 1963)-

Borovik, E. S., "Change of resistance of metals in a magnetic field at low temperatijres ,

Zh. Eksptl. lo Teoret. Fiz. 23, 91-100 (1952).

Bridgman, P. W. , "The resistance of 72 elements, alloys and compounds to 100,000 kg/cm ," Proc. Amo Acad. Arts Sci. 8I, No. h, I69-25I (Mar 1952).

Bridgman, P. W. , "Miscellaneous measurements of the effect of pressure on electrical resistance,"

Proc. Am. Acad. Arts Sci. 82, No. 2, 83-IOO (Apr 1953).

Dewar, J., and Fleming, J. A., "The electrical resistance of metals and alloys at temperatures

approaching the absolute zero," Phil. Mag. 36, 271-99 (I893).

Hilsch, R., and Von Minnigerode, G. , "He3 cryostat for investigation of condensation films

below 1 K," Kaltetechnik ik, No. 12, 39i+-96 (Dec I962).

Meissner, W. , "Widerstand von metallen bei der temperatur des flussigen heliums," (Resistance

of metals at the temperatixre of liquid helium), Z. Instrumentenk. i+6, 103-5 (1926).

Onchi, M. , "Conductivity and surface potential change of cadmium films due to adsorption,"

Transactions of the Natl. Vacuum Symp. of the AVS 10th, I963, MacMillian Co., New York (1964)

5 pp. I

14
Electrical Resistivity of Cadmi-um (page 3 of lO)

Cryogenic Data Memorandum Wo. M-26

Panova^ G= K. , and Samoilov, B. K., "Effect of isotopic composition on the electrical conductivity of cadmiiom," Sov, Ehys. JETP 26, No. 5, 888-90 (May I968) Transl. of Zh. Eksp. Teor. Fiz.

53, 1539-^+^ (Nov 1967)

.

Peiffer, H. R. ^ "Effect of deformation and recovery on the subsequent resistivity increase in cold-worked cadmium/' Rias , Inc.^ Baltimore, Md. , Tech. Rept. No. 7 (1963) Contr. Wo. WOWR3707(0O) 7 PP, DDC AD k3^ 8t|0.

Pelffer, H. , and Maycock, J. W. , "An Investigation of the defect solid state/' Rias, Div. of Martin Co., Baltimore, Md. , Final Rept. (1964) Contr. Wo. WOWR-3707(00) , k8 pp, WASA

N65 19021.

Perez-Alhuerne, E. A., Clendenen, R. L. , Lynch, R. W. , and Drlckamer, H. G. , "Effect of very

high pressure on the structure of some HCP metals and alloys," Phys. Rev. l42. Wo. 2, 392-99

(Feb 1966).

Ruhl, W« , "Zur oxydation von metallen bei sehr tiefen temperaturen , " (On the oxidation of metals at very low temperatures), Z. Physik I76, Wo. 4, 409-20 (Wov I963).

Sharp, J. v., Mitchell, A., and Christian, J. W. , "The recovery of deformed cadmium, magnesium,

zinc and cobalt," Acta Met. I3, 965 -7I (Sep I965).

Stevenson, F. R., and Peiffer, H. R., "Recovery of defects following deformation of high purity

cadmium at 78 K," Rias, Baltimore, Md., Tech. Rept. Wo. h (Jul I963) Contr. No. WOWR-3707(00) 17 PP, DDC AD 410 358

.

Stevenson, F. R., and Peiffer, H. R., "Effect of impurities on the electrical resistivity

increase during elongation of cadmium at 78 K," Rias, Baltimore, Md. , Tech. Rept. Wo. 5 (Jul 1963) Contr. Wo. WOWR-3707(00) 5 pp, DDC AD 4lO 357.

Stevenson, F. R., and Peiffer, H. R., "Effect of impurities on the electrical resistivity

increase during elongation of cadmium at 71 K," Wature 200, 771-72 (1963)

.

Stevenson, F. R. , and Peiffer, H. R., "Recovery of defects following deformation of high purity

cadmium at 78 K," Phys. Status Solidi 4, 4ll-l8 (1964).

Comments :

The data for this graph were taken from the references cited above under "Sources of Data". The tabular values are ratios of electrical resistivity with respect to the resistivity at the ice point temperature (pgys).

Since cadmium is an anisotropic metal, we list suggested values of pg^g for Cd II , Cd ± , and polycrystalline cadmium to be used in calculating electrical resistivities from the ratios

whenever the original investigators did not state such values for their samples. These suggested values are:

p( II )373 = 7'73 X 10~® ohm cm, p(l)s73 = 6.35 x 10"® ohm cm,

and P/ _ N = 6.73 X

10" ® ohm cm. (P0ly)273

These values are from Goens and Gruneisen (1932) . It should also be noted that cadmium

becomes superconducting below 0.52 K.

In instances where data points were quite widely separated or areas where data did not exist,

symbols were used to show the available data points so that the reader will know where

arbitrairy position or shape of the graph was made.

15
(page k of 10) Electrical Resistivity of Cadmium

Cryogenic Data Memorandum No. M-26

Brief descriptions of sample preparation, purity, etc. for each data source follow in chronological order.

Jaeger and Diesselhorst (I9OO) gave two experimental values for electrical conductivity at l8°C and 100°C. An extrapolation of the data gives a resistivity value of pg73 = 7-2 x 10~® n cm.

Eucken and Gelhoff (1912) measured the electrical conductivity of a polycrystalline bar.

Onnes and Hoist (l91^) cast their polycrystalline sample in a glass tube. The impuritiep were < OoOlfc.

Schimank (191'4-) measured the resistances of two samples of high purity cadmium wire. -The first

sample (Cd I) was cold drawn and the second (Cd II) was extruded. The impurities were < O.Ol/o.

Schott (1916) measured the electrical conductivity of a chemically piore rod which had been

previously annealed in a vacuum.

Holborn's (1919) samples were 2 mm diameter wires. The cadmium was purified at the Reichsanstalt and taken from the fourth purity stage (impurity was < O.Olfo). Cd 2 was heated to 220 K for a lengthy period of time.

Griineisen and Goens (1924) determined resistivities of very pure cadmium at 81+° and 0° angles to the hexagonal axis . Ko further information is given about the samples.

Meissner (1926) measured resistance ratios of four samples: Cd II was 3»2 mm dia., 5 cm long

and the measurements were made at 10° to the hexagonal axis; Cd 1 was 3"9 nm dia., 5 cm long

and the measurements were made at 84° to the hexagonal axisj Cd(poly)l was 0.2 mm dia.,

5 cm long and not annealed; Cd(poly)2 was 0.2 mm dia., 5 cm long and annealed.

Tuyn and Onnes (1926) and Tuyn (1929) report measurements on a 99»99fo pure polycrystalline

cadmium wire which was 0.22 mm dia. The superconducting portions of the ciorves are probably

due to the presence of O.OOjfo lead in the samples.

Mc Lennan and Niven (1927) wound strips of cadmium on a piece of pyrex glass. The aged

samples were annealed for 3-5 hours at 200 °C.

Meissner and Voigt (1930 ) stated that their cadmium samples were impure. The polycrystalline

wire was 55 t^^ long, 0.2 mm dia. and had been aged. The single crystals had the following

dimensions: Cd II was 55 mm long, 3«2 mm dia.; Cd ± was 55 mm long, 3-9 mm dia. The data presented here are the same as the data in Meissner (1926).

Goens and Griineisen (1932) determined the resistivity of ideal, pure, undeformed cadmium both

parallel and perpendicular to the hexagonal axis. Polycrystalline resistivity at 273 K can be

calculated from the following: p( II )a73 = 7 '73 x 10"^ ohm cm and p (1)37 3 = ^•3'? x 10" ® ohm cm. We find p, ^ = 6.73 x 10"^ ohm

(poly)

cm. S73 Bridgman (1933) used 1 mm dia. rods of approximately 2.5 cm length -which were cast in pyrex

tubing by slowly lowering out of a furnace. He used iCahlbaum grade cadmium. The data, in the table below were taken at zero pressure.

Griineisen (1945) used the Goens and Griineisen (1932) data to determine the resistivity values

at 0°C.

p II = 7.73 X 10"^ ohm cm,

p X = 6.35 X 10~® ohm cm, and by averaging the two using Voigt 's equation, he calculated for the polycrystal:

p , = 6.73 X 10"^ ohm cm. poly

16
Electrical Resistivity of Cadmium

Cryogenic Data Memorandum No, M-26

(page 5 of 10)

Aleksandrov (I963) and Aleksandrov and D'Yakov (1963) report electrical resistivity measurements on 3.5 mm dia. and I50 mm length samples. The cadmium was purified by zone melting

(99.999994'/o pure) and the samples were annealed in air at 120-130°C for one day following

each change of mounting. They present measurements at both parallel and perpendiciiLar

orientation to the primary axis. Ps73 's were calculated using the pgga 's from Aleksandrov

(1963). Their values are: Cd II has P373 = 7.8 x 10"^ ohm cm, Cd± has P273 = 6.55 x 10"® ohm cm.

The "ideal" resistivity values tabulated in the lower right-hand comer of the graph were taken from Meaden (1965). His book presents a comprehensive review of the literat^lre dealing with experimental determinations of electrical resistivity together with a relatively concise account of the modern theory of the electrical resistance of metals and

alloys

.

Tsui and Stark (1967) measured resistivity of high purity single crystal specimens with

residual resistivity ratios in excess of 150,000. The data in the table are for zero magnetic

field. p273 is calculated to be 7-05 x 10"^ ohm cm.

Vtorov and Dmitrenko (1967) measured resistance of a very pure large-grain specimen of- cadmium.

(residual)'"^- is 1.1 X 10

Tables of Values of Electrical Resistivity

p = resistivity, (ohm cm); pgy^ = resistivity at 273 K, (ohm cm) R = resistance, (ohm); Rs^g = resistance at 273 K, (ohm).

Eucken and Gelhoff (1912)

Temp. K

Resistivity

p X 10^ ohm cm

P/P273*

83 194

273

1.978

5.45 7.76

0.254

0.703

1.0

* These values were not plotted on

the Electrical Resistivity of Cadmium graph.

Onnes and Hoist (I9l4)

Temp.

K

Resistance R X 10^ ohm

R/Rs7 3**

4.2 14.8

20.2 71.9

89.9 273.1*

0.032 0.58

1.45 15.7

20.9

71.0 *

0.00045 0.00817

0.0204

0.221

0.294

1.0

* Interpolated value

.

** These values were not p Electrical Resistivity

graph.

lotted on the

of Cadmium

Schimank (l9l4)

Temp. K

R/Rs73

Cd I Cd II*

20.2 0.0232 0.0217

82.7 0.2584 - 82.9 - 0.2581

90.0 0.2872 0.2860

133.9 0.4949 0.4637

. 161.5 - 0.5644

163.6 0.5742 - 180.4 - 0.6376

182.1 0.6434 - 200.6 0.7149 - 202.3 - 0.7200

226.4 - 0.8137

227.3 0.8203 - 273.09 1.0000 1.0000

* These values were plotted on

the K.ectrical Res istivity of

Cadmiijm graph.

17
(page 6 of 10) Electrical Resistivity of Cadmium

Cryogenic Data Memorandum No. M-26

Schott (1916)

Temp. K

20.4

87. 273.

Resistivity

p X 10® ohm cm

0.1473

1.866

6.849

p/Pe

0.0215 0.272

1.00

Gruneisen and Goens (1924)

Temp. K

P/P2 73*

Cd II Cd 1

20.43 82.0

83.0

85.0 88.3 89.7

130

195

O.O22O4 0.258

0.263

0.282

_ 0.439 0.694

0.0187

0.250

0.262

0.283

0.435 0.693

* For Cd II , p3,3 = 7.79 X 10~® ohm cm; Cd 1 , pg^a = 6.54 X 10"® ohm cm. These values were not plotted on the Electrical Resistivity of Cadmium

graph

.

Holborn (1919)

Temp. K

R/Ro*

Cd 1 Cd 2

80.6

80.8 194.7

194.8

0.2533

0.6906

0.2522

0,6917

* These values were not plotted

on the Electrical Resistivity

of Cadmium graph.

Meissner (1926)

Temp. K

R/Rs7 3 Cd II * Cd± * Cd (poly) 1* Cd (poly) 2* not annealed annealed

1-35 0.000157 0.000475 „ „ 1.68 - 0.000594 0.000736

4.20 - 0.000614 0,000760

4.21 0.00018s O.OOO5O7 - - 20.42 O.O2O0 0.01976 0.0209o 0.0209i 82.48 0.2617 0.2542 0.2579 0.2575

273-20 1.000 1.000 1.000 1.000

* These values are not plotted on t he Electrical Resi stlvity of Cadmium

graph 1because they a re the same data as the Meissne:c and Voigt (1930

)

data.

18

I

I
Electrical Resistivity of Cadmium

Cryogenic Data Memorandum No. M-26

(page 7 of 10)

Tuyn and Ormes (1926) and Tuyn (1929)

Temp. K

I^/Rs73 Cd-1919-I Cd-1920-I cd-1924-I

1-43 1.46

1.74 1.87

2.01

2.30

2.40 2.62

2.80 2.81

0.00000

0.0000s

0.00063

0.00l4o

0.00l4o

0.00004

0.0000a

0.0001s

0.00026

0.00046

2.90 2.98

3.04 3-11

3.20 3.26

3.30 3-39 3-42

3-42

0.0009g

o.ooi4s

0.0015s 0.00174

0.00193

0.00209

0.00237

0.0023c

0.0014^

0.00081

3-46

3-48

3-51 3-77

3-96 4.18

4.22 4.24

14.22 16.53

0.0024a

O.0025o

0.00274

0.0029o

0.0029s 0.00997

0.01424

0.0014^

0.00143

0.00907

0.01331

0.00l2g

0.0014^

0.01022

0.01450 18.06

20.51

56.77

65-99 73-05 73-06 81.01

81.02

90.40 90.41

0.01759

0.02362

0.15572

0.19251

0.22060

0.25219

0.28913

0.01666

0.02267

0.15^^75 0.19158

0.21967

0.25125

0.28820

0.01786

0.02386

0.15581

0.19256

0.22061

0.25218

0.28907

19
(page 8 of 10) Electrical Resistivity of Cadmium

Cryogenic Data Memorandum No. M-26

McLennan and Niven (1927)

Temp. K

R/Ro

Cd I* Cd I* Cd II (unaged) (aged) (aged)

3.6 0.000924

3.8 0.00492

4.2 0.00496 0.00073 0.000939

8.2 0.00087 9.2 0.00120 9.8 0.00127

11.5 0.00221 20.6 0.0262 0.0207 0.0242

80 0.257

81 0.311

83 0.270 273 1.000 1.000 1.000

* These ivalues were plotted on the Electrical 1 Resist Lvity of Cadmium graph.

Melssner and Voigt (1930)

Temp. K

R/Rs73 ca (poly) Cd II Cdl

1.35 _ 0.000157 0.000475 1.68 0.000736 - - 4.20 0.000760 - - 4.21 - 0.00018a O.OOO5O7 20.42 0.0209i O.O22O1 0.01976 82.47 0.2575 0.2617 0.2542

273.16 1.000 1.000 1.000

Goens and Gruneisen (1932)

Temp. K

p X 10^ ohm cm P/P273**

Cd 1 Cd II Cd 1 Cd 11

21.2 83.2

273.2

0.1346

1.626 6.35 *

0.1881 2.024 7.73 *

0.0210 0.254

1.000

0.0241

0.259

1.000

* Interpolated value. ** These values have not been plotted on the Electrical

Resistivity of Cadmium graph.

20
Electrical Resistivity of Cadmium

Cryogenic Data Memorandum No. M-26

(page 9 of 10)

Bridgman (1933)

Temp. K

P/P373 1 Cd II Cd 1

90.35

19i+.85 273.15*

0.2891

0.6903

1.000

0.2850 0.6899

1.000

* At 273.15 K, pii = 7.593 X 10-^ ohm cm

and pj. = 6.289 X 10"® ohm cm.

Aleksandrov (I963) and Aleksandrov and D'Yakov (1963)

Temp. K

P/P2 73*

Cd II Cd J.

.0000107 0.0000162

1.65 0.0000114 0.0000163

3.4 0.0000144 0.0000208

3.7 .0000164 0.0000232

I1.22 0.0000217 0.0000298

7.2 .000192 - Ik 0.00590 0.00596

20.4 0.0212 0.0197

58 0.161 0.160

63.5 0.185 0.181

77.4 0.243 0.238

90.31 0.291 0.289 111.6 0.376 0.373

273 1.0 1.0

* Ps73 was calculated using the pggg values for Cdll and Cdl

Aleksandrov (1963). For Cdll , P273 = 7. 8 X 10"® ohm cm; Cd± , P273 = 6. 55 X 10~® ohm cm.

Vtorov and Dmitrenko (1967)

(read from graph)

Temp. Resistance * K R X 10^ ohms

1.9 2.2 2.4 2.2

3.13 2.5

3.5 2.75

3.7 3.0

293 191818.0

* These data do not appear on the Electrical Resistivity of

Cadmivmi graph.

Tsui and Stark (1967)

(read from graph)

Temp. KResistivity

p X 10® ohm cm

P/PS73

Cd II Cd II

1.35

2.0

3.0

3.5

4.0 4.2

273

0.000047

.000048 0.000065 0.00009

.00013 0.000155

7.05 *

0.0000066

0.0000068

.0000092

.000013

.000018

.000022 1.00

* Calculated value

.

21
(page 10 of 10) Electrical Resistivity of Cadmium

Cryogenic Data Memorandum No. M-26

cvi

I-<

>->

Ico

CO

UJ

oc_J<

o

a:o

LU

_J

UJ

2 4 6 8 10 20 40 60 80 100 200 400 600

1.0

1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1

1

1 ' ' J' '1

1 1 1 1 1 1 1 1 1 1 1 sr ELECTRICAL RESISTIVITY RATIO

FOR CADMIUM

-6

yO(l 1)2^3 = 7.73x10 ohm cm

^0(1)273 = 6.35 X 10'^ ohm cm

/O(poly) = 6.73 xlO ohm cm

J^

J^ Xy X

Ir >r

lo' 1 /

i /r Y //

10^

1 ' '1

Tuyn and Onnes /D(poly)

\

//a

1 V \

\ X ml \ \A

"y' \\ ^^ ^.^ \\ ^MClpnnnn nnrl Niven Ofnnlv)

^K^'''/V

1 1 1 r

--•"

1 1 —

^^

\ff /IHi

/

m

/

', Vi7/

/ f^

^

/

'/ I

1

Id' // / i 1/ \

p 1 -/^^

,^- -^ '—i--^Meissner and Voiqt p(poly - — ^

7

—

'

^^ — — —

7 -tV / / —f "V /

/

^s

1 A I

^Meissner and Voigt (1)

/

/ /\ 1

V'

/

^ Mejssner and Voigt (II)

1 1 1 1 1

10^ / / "Ideal" Resistivity*

of Cadmium /- - Aleksandrov and D'Yakov (±) /-—f- ,

= -6 —

Temp. K

p, X 10= ohm cmPi/Pe73

(9 / \ p„„ = 6.55 X 10 ohm cm / \

~273

1 . 1 / ^ 20

5080

100 150

200

250 273-15

0.13 0.87

1-7

2-3 3-6 ^9

6.2 6.73

0.0193 0.129

0.253

0.3if2 0-535 0.728

0.921

1.0

Jj

1

1

1 Alekson Hrnu nnH D'YnUnu Ml )

' 1

A - Pziz

'sui and \

= 7.8 X 10" ohm cm —

'

i 1 Stark

-/ ©2^3 = 7.05 X IO'°ohm c T1 — * from Meaden (1965)

see text. , -5 > () 1 1 1 1 1 1 1 1 Ill 1 1 4 6 8 10 20 40 60 80 100 TEMPERATURE, K

200 400

22
CRYOGENIC DATA MEMORANDUM

PROJECT NO. 2750422 FILE NO. M-27

ELECTRICAL RESISTIVITY OF CHROMIUM, Cr

(page 1 of 9) (Atomic Wianber 2k)

Sources of Data :

ArajSj S., Colvin, R. V., and MarclrLkowski, M. J., "initial study of electrical resistivity of

a chromi\iin single crystal," J„ Less-Common Metals h, No. 1, 46-51 (I962).

Arajs, S., and Dunmyre, G. R. , "Electrical resistivity and transverse electrical magnetoresistivity of chromixan," J. Applo Hiys. 36^, No. 11, 3555-59 (Nov I965).

Arajas, S., and Dunmyre, G. R. , "Electrical resistivity of chromium-rich chromium- iron alloys

between k and 320 K," J. Appl. Ehys. 37, No. 3, 1017-19 (1966).

Bridgman, P. W. , "Compressibilities and pressure coefficients of resistance of elements, com- pounds, and alloys, many of them anomalous," Proc. Am. Acad. Arts Sci. 68, 27-93 (1933)°

Clinard, F. W. , Jr., and Kempter, C. P., "Low-temperature electrical properties of some transition metals and transition-metal carbides," J. Less-Common Metals 15_, No. 1, 59-73 (May I968).

Erfling, H. D. , "Studies of the thermal expansion of solids at low temperatures II. (Cr,

Beta-Mn, Mo, Rh, Be, Graphite, Tl, Zr, Bi, Sb, Sn, and Beryl), (in German)," Ann. Physik 3k, 136-60 (1939).

Fine, M. E,, Greiner, E. S., and Ellis, W. C, "Transitions in chromium," J. Metals I89, 56-58

(1951).

Goff, J. F., "The thermal conductivity of chromium above and below the Neel temperature - an analysis," Thermal conductivity (Proc. of the Conference on Thermal Conductivity 7th,

Gaithersburg, Md. , Nov I3-I7, I967) National Bureau of Standards Spec. Publ. 302 (Sep I968) pp 311-21.

Harper, A. F. A., Kemp, W. R. G. , KLemens , P. G. , Tainsh, R. J., and White, G. K,, "The thermal

and electrical conductivity of chromium at low temperatures," Phil. Mag. 2, 577-83 (May 1957)

»

Mc Lennan, J. C., and Niven, C. D. , "Electrical conductivity at low temperatures," Phil. Mag.

k, 386-404 (1927).

Mc Lennan, J. C, Niven, C. D. , and Wilhelm, J. C, "The resistance of caesium, cobalt, and chromium at low temperatures," Phil. Mag. 6, 672-7 (1928)

.

Meaden, G. T., Electrical Resistance of Metals , Plenum Press, New York (1965) 2l8 p.

Meissner, W. , and Voigt, B., "Messungen mit hllfe von flussigem helium. XI. wlderstand der reinen metalle in tiefen temperaturen," (Measurements using liquid helium. XI. Resistance of pure metals at low temperatures), Ann. Ehysii 7, Wo. 5, 892-936 (I93O).

Moore, J. P., Williams, R. K. , and Mc Elroy, D. L. , "Physical properties of chromium from 77 to 400 K," Thermal Conductivity (Proc. of the Conference on Thermal Conductivity 7th, Gaithersburg,

Md., Nov 13-17, 1967) National Bureau of Standards Spec. Publ. 302 (Sep I968) pp 297-310.

Moore, J. P., Williams, R. K. , and Mc Elroy, D. L. , "Fiorther comments on transport properties

of chromium," Thermal Conductivity (Proceedings of the Conference 8th, Purdue Univ.. Lafayette,

Ind. , Oct 7-10, 1968) C. Y. Ho, et al., Eds, Plenum Press, New York (1969) PP 303-13.

Newmann, M. M. , and Stevens, K. W. H. , "Magnetic susceptibilities of iron-chromium alloys,"

Proc. Phys. Soc. (London) 74, 29O-96 (1959).

Potter, H. Ho, "Electrical resistance and thermoelectric power of the transition metals," Proc.

Phys. Soc. (London) 53, 695-705 (l94l).

23
(page 2 of 9) Electrical Resistivity of Chromium

Cryogenic Data Memorandum No. M-27

Semenenko, E. E. , "Minimum electric resistivity of antiferromagnetic metal (chromium)," JETP

Letters 3, No. 11, 291-3 (jun I966) Transl. of Zh. Eksp. I Teor. Fiz., Pisma V Redaktsiyu 3, No. 11, f43-7 (Jun 1966)0

Sochtig, H. , "Untersuchungen an relnem chrom im anomaliegebiet. Elektrischer und thermischer

widerstand, thermokraft, warmetonung, magnetische suszeptibilitat und gitterstmktur , " (Research

on pure chromium in the anomalous region. Electrical and thermal resistance, thermopower,

thermalhue, magnetic susceptibility and lattice structure), Ann. Ehysik 38> No. 2, 97-120 (19^4-0).

White, G. K. , and Woods, S. B., "Electrical and thermal resistivity of the transition elements

at low temperatures," Ehil. Trans. Roy. See. London A251 No. 995, 273-302 (1959).

Other References :

Arko, A. J., Marcus, J. A., and Reed, W. A., "High-field galvanomagnetic effects in antiferromagnetic chromium," Phys. Rev. I76 , No. 2, 67I-83 (Dec I968)

.

Bastow, T. J., and Street, R. , "Transverse magnetoresistance of high-purity chromium foils,"

Phil. Mag. 10, No. lOij-, 269-76 (196^4-)

.

Brenner, A., Burkhead, P., and Jennings, C, "Physical properties of electrodeposited chromium,"

J. Res. Natl. Bur. Stds. kO, 31-59 (19^8).

Brldgman, P. W. , "The electric resistance to 30,000 kg/cm of twenty nine metals and intermetallic compounds," Proc. Am. Acad. Arts Sci. 79, 1^4-9-79 (l95l)

.

Bridgman, P. W. , "The resistance of 72 elements, a3J.oys and compounds to 100,000 kg/cm ,

Proc. Am. Acad. Arts Sci. 8I, No. h, I69-25I (Mar 1952).

Erfling, H. D. , "Zur anomalie des elektrischen widerstands von chrom. Nachtrag zu untersuchungen von H. Sochtig," (An anomaly in the electrical resistance of chromium. Supplement to studies

by H. Sochtig), Ann. Physik la, 100-2 (19^2).

Kostina, T. I., Kozlova, T. N., and Kondorskil, E. I., "Dependence of the electric and magnetic

properties of chromium on the magnetic field strength and temperature," Zhur. Eksptl. I Teoret

Fiz. 1+5, No. 5, 1352-55 (1963).

Matsumoto, T., Sambongi, T., and Mitsui, T. , "Anomaly in the electrical resistivity of chromium

metal in the vicinity of spin-flip temperature," J. Phys. Soc. Jap. 26, No. 1, 209 (jan 1969)-

Mc Whan, D. B. , and Rice, T. M. , "Pressure dependence of itinerant antiferromagnetism in

chromitmi," Phys. Rev. Letters 19, No. I5 , 846-9 (Oct I967)

.

Milgram, A. A., and Lu, Chih-Shun , "Field effect and electrical conduction mechanism in discontinuous thin metal films," J. Appl. Phys. 37, No. I3, 4-773-9 (Dec I966)

.

Milgram, A. A., and Lu, Chih-Shun , "Preparation and properties of chromium films," J. Appl.

Phys. 39, No. 6, 285I-6 (May I968)

.

Mitsui, T., and Tomizuka, C. T. , "Effect of hydrostatic pressure on the Neel temperature in

chromiirai," Phys. Rev. 137, No. 2A, A564-65 (Jan I965).

Powell, R. W. , and Tye, R. P., "The influence of heat-treatment on the electrical resistivity

and the thermal conductivity of electrodeposited chromium," J. Inst. Metals 85_, I85-92 (1957)

•

24
Electrical Resistivity of Chromium (page 3 of 9) Cryogenic Data Memorandum Wo. M-27

Sambongi, T., and Mitsui, T», "Electrical resistivity of antiferromagnetic chromium," J. Fhys.

Soc. Jap. 24, No. 5, 1168 (May I968)

.

Ulyanov, R. A., and Kovtun, S. F., "Effect of alloying on the volume resistivity of titanium,"

Ehys. Metals Metallog. 17, No. k, 24-30 (1964) Transl. of Fiz. Metal. I Metalloved. 17, No. k, 505 -U- (1964).

Comments:

The data presented here were taken from the references cited above under "Sources of Data" and

are listed as ratios of electrical resistivity with respect to resistivity at the ice point

temperature. When actual values of P273 for the samples used by the investigators are not

available, a datum value reported by White and Woods (p373 = 12.155 x 10"^ ohm cm) is suggested

for calculating the values of electrical resistivity from these ratios.

In instances where data points were quite widely separated or areas where data did not exist,

symbols were used to show the available data points so that the reader will know where arbitrary

position or shape of the graph was made.

Brief descriptions of sample preparation, purity, etc. for each data so-urce follow in chrono- logical order.

Mc Lennan and Niven (1927) measured the resistance of 3/16 in. wide and I-I/2 in. long strips

of chromium cut from an electrolytically deposited sheet. The aged sample was heated for

2 hours at high temperatures.

Mc Lennan, Niven and Wilhelm (I928) continued the measurements of Mc Lennan and Niven (1927)

adding some low temperature values for the "aged" sample.

Melssner and Voigt (l930) used a 99"5?^ pure chromium sample with the following dimensions;

21 mm long and 2.5 mm x 2.5 mm cross section. No further information is given for the sample.

Bridgman (1933) reported values (at one atmosphere pressure) of resistance for a swaged rod,

4 cm long and 2.5 mm dia. idiich was of "exceptional degree of purity". His Ps^s = l8-9 x

10"

®

ohm cm.

Sochtig (1940) measured resistances of high purity chromium with the following dimensions;

0,58 X 0.23 X 0.21 cm. He also reported P273 = 21 x 10"^ ohm cm. He also reports values by

Erfling (1939) which were made on the same sample and extend to lower temperatures.

Potter (1941) measured resistances of a 99'99fo pure chromium rod approximately 1 cm long which

had been annealed at 600°C.

Fine, Greiner and Ellis (l95l) used a wrought chromium specimen, consisting of powder filings

"sAiich had been cleaned magnetically and annealed 2 ho-urs at 800°C in vacuum.

Harper, Kemp, KLemens, Tainsh and White (1957) and White and Woods (1959) report resistivity

values for a 99 .998/0 piore chromium rod, 8 cm long and 3 nTM dia. This recrystallized sample

had been annealed in vacuo at 1050°C for 4 hours. The residual resistivity was

Pq = 0.055 X 10~® ohm cm.

Newmann and Stevens (1959) report resistivities for 2 cm long pure chromium rods which had

been annealed in vacuum at about 1200 K for a month.

25
(page 4 of Electrical Resistivity of Chromium

Cryogenic Data Memorandum No. M-27

Arajs, Colvin and Marcirikowski (1962) made resistivity measurements on a single crystal specimen

parallel to the [lOO] axis. The sample dimensions were 0.254 cm x 0.235 cm x O.9OO cm. At

one time measurements were made on the sample after it had been left overnight at 3IO K. Another time the sample was heated to 373 K, then cooled rapidly to 78 K and left for a period

of time before measurements were taken. The residual resistivity was 1.04 x 10~® ohm cm.

Arajs and Dunmyre (1965, I966) used 99.9953fo chromium sample cut from an arc-melted ingot

and the final shape, O.478 cm x O.476 cm cross section and 5 cm long, was obtained by surface

grinding. The residual resistivity at 4.2 K was O.O81I x 10~® ohm cm. The values in the table

are for zero magnetic field.

The "ideal" resistivity values tabulated in the lower right-hand corner of the graph were taken from Meaden (1965). His book presents a comprehensive review of the literature dealing

with experimental determinations of electrical resistivity together with a relatively concise account of the modern theory of the electrical resistance of metals and alloys.

Semenehiso (1966) presents data showing resistance minimums below 10 K. No quantitative

analysis was made of the impurities in the three samples. He states that "even the purest

one contained O.Olfo Fe, 6 x 10"^ f Ni, and ~ 5 x

10"''^

fo Mn. The samples were annealed in a vacuum of less than 10" '^ mm Hg at ~ 1300°C. The data were not plotted on the Electrical

Resistivity of Chromium graph.

Goff (1968) measured ideal resistivities of a 99.92fo pure sample (4 mm x 4 mm x 35 mm) which

had been annealed in vacuum at 900°C for 24 hrs prior to measurement. The residual resistivity

was 0.1834 X 10"^ ohm cm.

Moore, Williams and Mc Elroy (1968) made resistivity measurements on two samples Cr A and

Cr Bo Cr A was prepared by using vacuum compacted crystals for extruding a rod 60 cm long

and 1.6 cm dia. This sample had a purity of 99 "98^0. Cr B was prepared by arc melting

crystals into an ingot which was drop cast into a rod 15 cm long and 1.6 cm dia. This

sample had a purity of 99.992/0. The values in the table are smoothed.

Clinard and Kempter (1968) measured resistivity of annealed polycrystalline rods about 0.25 in. dia. and 1 in. long. The purity was 99.656 fo.

Moore, Williams and Mc Elroy (I969) borrowed Goff 's (I968) sample for these resistivity

measurements. There is a large disagreement between Goff 's results and these resiilts on the

same sample.

Tables of Values of Electrical Resistivity

p = resistivity, (ohm cm); P273 = resistivity at 273 K, (ohm cm). R = resistance, (ohm); ^273 = resistance at 273 K, (ohm).

McLennan and Niven (1927)

Temp. K

Resistance R X 10® ohm

R/I^2 73

Cr (unaged) Cr (aged) Cr (unaged) Cr (aged)

2.35 4.2 20.6

80

83 273

25.9 26.2

26.7

29.2 42.0*

0.90

2.01

15.0 *

0.617

0.624

0.636

0.695

1.00

0.060 0.134

1.000

* Interpolated value.

26
Electrical Resistivity of Chromium

Cryogenic Data Memorandum No. M-27

(page 5 of

McLennan, Niven and Wilhelm (1928)

Temp. K

Resistance R X 10® Ohm

I^/Ks73

Cr (aged) Cr (aged)

2.25 4.2 20.6

80 273

0.79

0.79

0.80

2.01 15.8 *

0.05

0.05 0.051

0.127

1.00

* Interpolated value

.

Meissner and Volgt (1930

)

Temp. K

R/Rs73

1.41

4.20

20.45 78.42 86.14

273.16

0.833 0.834 0.842 0.8507

0.8561

1.000

Bridgman (1933)

(read from graph)

Temp. KR/R273

193

213

233 253 273*

0.885 0.903 0.962

0.99

1.00

* Ps73 = 18.9 X 10~® Ohm cm.

Sochtig (1940) and Erfling (1939)

(measurements on the same sample)

Temp. K

P/P2 73

20.36

79.00

77.69

90.09

0.0188 n ^^, . 0.0874 J ^^^^S

0.0868 n ^ ^^. 0.122 J

sochtig

Potter (1941)

Temp. KR/E273*

2077

90 173

273

0.021

0.074

0.119

0.508

. 1.00

* These values were not plotted

on the Electrical Resistivity

of Chromium graph.

Fine, Greiner and Ellis (1951)

(read from graph)

Temp. K

Resistivity

p X 10® ohm cm P/P273*

78

123 173

223

273

1.8

4.1

7.0 10.4

13.0

0.14

0.32 0.54

0.80

1.00

* These values were not plotted on the Electrical Resistivity of Chromiijm

graph

.

27
(page 6 of 9) Electrical Resistivity of Chromium

Cryogenic Data Memorandum No* M-27

Harper, Kemp^ KLemens , Tainsh and White (1957)

White and Woods (1959)

Temp. Ideal resistivity Resistivity P/PS73 K Pi X 10® ohm cm P = Pi + Po

Po = 0.055 X 10~® ohm cm

15 0.0027 0.0577 0.004.7 20 0.007s 0.0622 0.0051

25 0.015b 0.0705 0.0058

30 0.029 O.OSlj. 0.0069

IK) 0.078 0.133 0.0109

50 0.165 0.220 0.0181

60 0.3o 0.355 0.0292

70 0.53 0.575 0.0473

80 0.81 0.865 0.0712

90 l.lg 1.235 0.102

100 1.6s 1.675 0.138

120 2.66 2.715 0.223

140 3.9 3.955 0.325

160 5.2 5.255 0.432

180 6.4 6.455 0.531

200 7.75 7.805 0.642

220 9.0s 9.105 0.749

250 10.95 11.005 0.905

273 12.1 12.155 1.00

Newman and Stevens (1959)

(read from graph)

Temp. KResistivity

p X 10® ohm cm P/P273*

90 150

200 273

2.5

6.3

9. 13.

0.19

0.48

0.69

1.00

* These values were not plotted on the Electrical Resistivity of Chromium

graph

.

Arajs, Colvin and Marclnkowski (1962) ] (read from graph)

Temp. Resistivity P/p273 K p X 10® ohm cm

10 1.04 0.085

50 1.3 0.11

100 2.8 0.23

150 5.7 0.46

200 8.5 0.69

250 11.3 0.92

273 12.3 1.0

Arajs and Dunmyre (1965, I966)

(read from graph)

Temp. Resistivity P/p2 73 K p X 10® ohm cm

4.2 0.0811* 0.0066

20 0.085 0.0070

40 0.2 0.016

60 0.4 0.033

100 1.8 0.15

l4o 4.0 0.33

200 7.9 0.64

273 12.3 1.00 * from text

28
Electrical Resistivity of CHiromium Cryogenic Data Memorandum No. M-27

(page 7 of 9)

Semenenio (1966)

(read from graph)

Temp. K

R/RsooK *

Sample 1 Sample 2 Sample 3

1.5 0.00681 0.008006

4.0 0.07617 0.006799 0.008002

6.0 0.07612 0.006798 0.008005

6.5 0.07608 0.006797 0.00801

10.0 0.07602 0.006796 - 12.0 0.07603 0.006797 - 15.0 0.07609 0.006801 - i6.o 0.07616 -

* These values were not plotted on the Electrical

Resis"bivity of Chromium graph.

Clinard and Kempter (1968)

(read from graph)

Temp. Resistivity P/P373 K p X 10® ohm cm

k.2 0.1 0.0080

20 0.1 .0088

50 0.4 0.032

IOC 2.0 0.16

150 5.0 0.40

200 8.0 0.64

273 12.5 1.00

Goff (1968)

(read from graph;

Temp. ideal resistivity resistivity P/pS73 K Pj X 10® ohm cm P = Pi + Po^

Po = 0.1834 X 10"® ohm cm

20 0.011 0.1944 0.016

50 0.2 0.3834 0.032

70 0.7 0.8834 0.073

100 2.0 2.1834 0.18

200 7.6 7.7834 0.64

273 12.0 12.1834 1.00

29
(page 8 of 9) Electrical Resistivity of Chromiinn Cryogenic Data Memorandum No. M-27

Moore, Williams and McElroy (I968)

Temp. Resistivity P/P373** K p X 10® ohm cm

Cr A Cr B Cr A Cr B

80 0.860 1.060 0.0729 0.0876

90 1.225 1.445 0.104 0.119

100 1.630 1.860 0.138 0.154

120 2.605 2.860 0.221 0.236

li).0 3.7& 4.050 0.319 0.335

160 5.000 5.295 0.424 0.438

180 6.315 6.575 0.535 0.543

200 7.545 7.830 0,639 0.647

220 8.790 9.100 0.745 0.752

240 10.015 10 . 300 0.849 0.851

260 11.095 ia.385 0.940 0.941

273 11.8 *

- 12.1 * 1.00 1.00

* Interpolated value

.

** These5 values were not plotted on the Electrical

Resistivity of Chromium graph.

1

Moore, Williams and McElroy (1969)

(using Goff 's (1968) sample)

Temp. Resistivity p/pS73** K p X 10® ohm cm

90 1.495 0.120

100 1.935 0.155

120 2.935 0.235

140 4.190 0.335

160 5.515 0.441

180 6.830 0.546

200 8.130 0.650

220 9.460 0.757

240 10.755 0.860

260 11.895 0.952

273 12.5 * 1.00

* Interpolated value. ** These values were not plotted on the Electrical Resistivity of Chromium

graph.

30 I
Electrical Resistivity of Chromium

Cryogenic Data Memorandum Ho. M-27

(page 9 of 9)

TEMPERATURE, °R

O

I-<

I-w

(/) hia:<

o

oc

\-

o

UJ_l

2 4 6 8 10 20 40 60 80 100 200 i*00 600

1.0

V

1

1

^

^^^^——— - —— - " ^^

^ MpiciQnpr nnrt Vnint ^-

MC Lennan and Niven^ -

— ^^--"^/

1 1 ——1

———^ {

ELECTRICAL RESISTIVITY RATIO

FOR CHROMIUM

/D273 =12.155x10' ohm cm

/

10-

Ara

/

js

^2

,C(

73

)lv in

2.

1and Marcin

3 X 10'® oh

kowsk m cmi (II

K Y

/

A

/

\

1

) 7 ii (h // M

y. \

MCLennan.Niven.and Wilhelm^ ^^ /

^ p

/.\ 1 \ ^ ^

c III r 5ochtig and Erfling

11

\

1 1 1 Mc Lennan and Niven

/3-^,= 2lxlO"^ohi

^^^

. 1 1n cm \ A(j

Pz73^

Goff 1

12.2 xlO'^ohm cm \ .^

fl

ll

10^

C inard

3= '2-^

and

)xlC

Ke mp

oh

te mr

orn h\ \i

)

\ Jly , / / \ —-^' '^ / /

^j r^./

\ ^ ^^ y

1

1

\—

1

1 ^.—

1

, "Ideal" Resistivity*

of Chromium

1

1 1 Arais and Dunmvre \ j^^ y

Pr>-ri = 12.3x10'^ ohm c m

\ -^

^ Temp. K

p, X 10^ ohm cm

Pl/P^73 ~273

1 1 ®

\ 20

5080 100 150

200 250 273.15

0.007a

0.166

0.8, i.6p

^•55 7.75 10.95 12.1

0.00060 0.0136

0.0669

O.I3U 0.376 - o.6to

0.905

1.0

Whit e and Woods

, -^

* from Meaden (1965) see text. 10 1 Ill 1 8 10 20 40

TEMPERATURE, K

60 80 100 200 400

CRYOGENIC DATA MEMORANDUM

PROJECT NO. 2750422 FILE NO. M-28

ELECTRICAL RESISTIVITY OF MANGANESE, Mn ^^^^ 1 of 5) (Atomic Number 25)

Sources of Data:

Brunke, F., "Untersuchungen an reinem alpha-, beta- und gammamangan

, " (investigation of pure

alpha-, beta- and gamma manganese), Ann. Hays. 21, 139-68 (193^+).

Erfling, H. D. , "Studies of the themal expansion of solids at low temperatures II. (Cr,

Beta-Mn, Mo, Rh, Be, graphite, Tl, Zr, Bi, Sb, Sn, and beryl), (in German)," Ann. Physii 3k,

136-60 (1939).

Erfling, H. D. , "Anderung der thermischen ausdehnung und des elektrischen widerstandes von- mangan beim ubergang zur alpha-phase," (Change in thermal expansion and electrical resistance

of manganese in transition to alpha-phase), Ann. Ehysii 37, I62-8 (19'j-O).

Jaeger, W. , and Diesselhorst, H. , "Warmeleitung elektricitatsleitung, warmecapacitat und

thermokraft einiger metalle," (Heat conduction, electrical conductivity, specific heat and

thermal power in metals), Wiss. Abhandl. Ehysik.-Tech. Reichasanstalt 3, 269-^24 (I9OO).

Meaden, G. T., "An alpha-manganese resistance thermometer for the measurement of low temperatures," Cryogenics 6, No. 5, 275-8 (Oct I966)

.

Meaden, G. T. , Electrical Resistance of Metals , Plenimi Press, New York (I965) 2l8 p.

Meaden, G. T., and Pelloux-Gervais, P., "The electrical resistivity of alpha -manganese between

2 and 325 K," Cryogenics 5, No. h, 227-28 (Aug I965)

.

Meissner, W. , and Voigt, B., "Messungen mit hilfe von flussigtcm helium. XI. Widerstand der reinen metalle in tiefen temperaturen, " (MeasTirements using liquid helium. XI. Resistance of pure metals at low temperatures), Ann. Physik 7, No. 5, 892-936 (193O).

Reddemann, H. , "Wiedemann -Franzsche shal von 3-mangan bei -190°C," (The Wiedemann-Franz

coefficient of beta-manganese at -190°c), Ann. Physik 22, 28-3O (1935).

White, G. K. , and Woods, S. B. , "Conductivity of alpha-manganese," Can. J. Phys. 35.^ 3^6-8

(1957).

White, G. K. , and Woods, S. B. , "Electrical and thermal resistivity of the transition elements

at low temperatures," Phil. Trans. Roy. Soc. London A251,No. 995, 273-302 (1959).

Other References : p Bridgman, P. W. , "The resistance of 72 elements, alloys and compounds to 100,000 kg /cm ," Proc. Am. Acad. Arts Sci. 8I, No. k, I69-25I (Mar 1952).

Griffiths, D. , and Coles, B. R., "Magnetic brillouin zone effects in the thermoelectric power and magnetoresistance of alpha-manganese," Proc. Phys. Soc. (London) 82, No. 525, Pt. 1, 127-32 (1963).

Mendelssohn, K. , Griffin, G. S., Sutcliffe, P. W., et al., "Low temperature properties of actinide metals," Low Temperatiire Physics and Chemistry (Proc. of International Conf . on Low

Temperature Physics and Chemistry lOth, Moscow, USSR, Aug 3I - Sep 6, I966) IV. Antiferromagnetism,- A. S. Borovik-Romanov , et al., Eds., Viniti, Moscow, USSR (1967) pp 117-21.

33
(page 2 of 5) Electrical Resistivity of Manganese

Cryogenic Data Memorandum No. M-28

Comments:

The data for this graph were taken from the references cited above under "Sources of Data" and

are listed as ratios of electrical resistivity with respect to the resistivity at the ice point

temperature (psva). Manganese is an allotropic metal and measurements have been made on samples of three different crystal structures. The suggested values of Pays , to be used if the experimenter did not give one for his sample, follow:

For a-Mn, pa 73 = II+3.5 x

10" ® ohm cm (Meaden I965 , I966);

fbr S-Mn, pg73 = 91"0 x 10"^ ohm cm (Bruhke 193^); for Y-Mn, pgvg = 22.7 x 10~® ohm cm (Bruhke 1934).

Brief descriptions of sample preparation, purity, etc. for each data source follow in chrono- logical order.

Jaeger and Diesselhorst (19OO) measured conductivity at 18 and 100 °C. By extrapolating the data to 0°C and calculating resistivity we have PS73 = 1+2.04 x 10~® ohm cm. They do not describe the crystal structure of their sample.

Meissner and Voigt (193O) used a sample 1.0 mm x 1.8 mm x 11 mm which was 93»65f» pure. The values are for a-manganese.

Brunke (1934) measured conductivity of pure a, S, and Y"Mn» Ths calculated resistivities are in the table.

Reddemann (1935) give one value of resistivity for 3-manganese at -190°C. The other values

are resistance ratios. The sample was 5 inni dia. and I6 mm long with no statement of purity.

Erfling (1939) states that his 8-manganese sample was pure and had been annealed in vacuum

at 1100 °C.

Erfling (l94o) gives two values of pg73 for y-manganese and a-manganese. The y-Mn was cut from an electrolytically deposited sample, approximately 2.3 cm long and 0.2 to O.3 cm wide.

White and Woods (1959) present data based on the experiments of White and Woods (1957) for

a-Mn. The table contains smoothed values taken from large-scale graphs. Three samples were

used: Mn 1, of high purity, was annealed in vacuo at 600°C for some hours; Mn 2, a 99 •99^0 pure sample, was not annealed; Mn 3; a 99'99f<' pure sample, was annealed in vacxmm at 600°C. Their cross sections were ~ 3 x O.7 mm, ~ 3 x 1.1 mm, and ~ 3-3 x 1.4 mm, respectively. Only

the residual resistivities of Mn 1 and Mn 3 were given. I averaged the two values to obtain

po to add to the ideal resistivities from their table.

Meaden (1965, I966) used an electrolytically prepared sample of 99»995fo pure manganese -which had been annealed under a vacuum of 10"^ to 8 x

10"^ torr for 7 hours at 625°C.

The "ideal" resistivity values tabulated in the lower right-hand corner of the graph were taken

from Meaden (1965). His book presents a comprehensive review of the literature dealing with

experimental determinations of electrical resistivity together with a relatively concise accoxmt of the modern theory of the electrical resistance of metals and alloys

.

34
Electrical Resistivity of Manganese

Cryogenic Data Memorandum No . M-28

(page 3 of 5)

Tables of Values of Electrical Resistivity

p = resistivity, (ohm cm); Pa73 = resistivity at 273 K, (ohm cm) R = resistance, (ohm); R273 = resistance at 273 K, (ohm).

Jaeger and Diesselhorst (19OO)

Dg73 = 42.04 X 10~® ohm cm

( extrapolated)

Brunke (1934)

a

BY

- Mn, ps73 = 714 X 10"^ ohm cm

- Mn, P273 = 91 X 10"^ ohm cm

- Mn, p273 =22.7 X 10~® ohm cm

Reddemann (1935)

6 - Manganese

Temp. K

K/E2 73

78.0

83.0*

90.0

194.6

273.1**

0.731

0.750 0.891

1.0

* One experimental value is given

at this temperature;

pga = 100 X

10" ® ohm cm. ** Using the pgs and reading the ratio from the graph, R/R273 or

p/Ps73 ) "we can estimate

P373 = 135.5 X 10~® ohm cm.

Meissner and Voigt (1930) a - Manganese

Temp. K

P/P273

1.41

4.20 20.46

77.82

88.9 273.16*

0.9581

0.9765

1.0020 0.9807 0.9776

1.0

* Ps73 = 150 X 10"^ ohm cm.

Erfling (1939)

8 - Manganese

Temp. K

R/R3 73*

78

78 0.731 (measured in 1935)0.774 (measured in 1937)

* These values are not on the Electrical

Resistivity of Manganese graph.

Erfling (l94o)

Mn, P273 = 627 X 10" ® ohm cm

Mn, P373 = 39.2 X 10"® ohm cm

35
(page ^ of 5) Electrical Resistivity of Manganese

Cryogenic Data Memorandum No. M-28

White and Woods (1957, 1959) a - Manganese

Temp. Ideal Resistivity Resistivity P/PS73 K Pi X 10^ ohm cm P = Pi + Po

Po = l4 X 10~® ohm cm

k 1.9 15.9 0.106

6 ^.3 18.3 0.122

8 8 22 0.147

10 12 26 0.173

15 28 i^2 0.280

20 kG 60 0.400

25 65 79 0.527

30 82 96 0.640

ko 105 119 0.793

50 117 131 0.873

60 122 136 0.907

70 122 136 0.907

80 121 135 0.900

90 120 I3i^ 0.893

100 121 135 0.900

120 123 137 0.913

Ito 125 139 0.927

160 127 ll^l 0.940

180 130 11+4 0.960

200 131 145 0.967

220 131 145 0.967

250 133 147 0.980

273 136 150 1.00

Meaden (1965, 1966) a - Manganese

Temp. Resistivity P/pS73 K p X 10^ ohm cm

6.9 0.0481

4.2 9 0.0627

10 19 0.132

20 54 0.376

30 92 0.641

40 118 0.822

50 128 0.892

60 132 0.920

70 133 0.927

80 132.5 0.923

90 132 0.920

100 132.5 0.923

150 137 0.955

200 140.5 0.979

250 143 0.996

273.15 143.5 1.00

36
Electrical Resistivity of Manganese

Cryogenic Data Memorandum Wo. M-28

(page 5 of 5)

6 8 10 TEMPERATURE, °R

20 40 60 80 100 200 400 600

lO

hCVJ

<

>->

H

CO

(O

cc<

o

o

llJ _lUJ

1.0

10

10

n

1

1 ELECTRICAL RESISTIVITY RATIO

FOR MANGANESE

-6 a - Mn, y0273= 143.5x10 ohm cm P-Mn, p^^^= 91 xlO'^ohm cm y-Mn, yOg^j =22.7xlO~^ohm cm

Re< PzizJd

= i:

smo

35.e

nn

) >

\

(yS-Mn

-6 10 ohm

\

cm —~" " 1 rf^ ^

-(Xh- ^ P^ J, "^X.,.---^

/' N- --'^

Meissner and Voigt (Q-Mn) y / \

yO„, = 150 X 10 ohm cm / \ r 27 i /

^Erfling (/8-Mn)

//r //

//

//

^^ ^

X

y

/

( \w

P

hite ( 273^'and 50 >Wo(

10

Dds

-6

C

(

)hrn

-^

cr

/In n

)

t f /

/ /

A--y 1 "Ideal" Resistivity*

of -Manganese

\ Temp. K

P, X 10^ ohm cm

Pi /P27a \ ®

\ Meaden (a-Mn) 20

5080 100

150

200 250 273-15

^3- 123- 127.5

127-5

132. 135.5

138. 138.5

0.35^^ _ 0.888

0.921

0.921

0.953 - 0.978 0.996

1.0

Pz 73

= 1 4:5.J3 -6

X 10 ohm cm

* from Meaden (I965) see text.

1 1 1 1 1 1 6 8 10 20 40

TEMPERATURE, K

60 80 100 200 400

ROW 3/70

37

CRYOGENIC DATA MEMORANDUM

PROJECT NO. 2750422 P'LE NO. ^.gg

(page 1 of 9) ELECTRICAL RESISTIVITY OF TITAHIUM, Ti

(Atomic Number 22)

Sources of Data:

Berlincourt, T. G. , "Hall effect resistivity and magnetoresistivlty of Th, U, Zr, Ti, and KTd," Ehys. Rev. Uh, No. h, 969-77 (1959)=

Bostrom, W. A., "Electrical resistance of zirconium and titanium," Westinghouse Elec. Corp.,

Atomic Power Div., Pittsburgh, Pa., Rept. No. WAPD-T-I76 (Apr 195i|) Contr. No. AT-11-l-GEN-lij-, 13 pp.

Cape, J. A., and Hake, R. R. , "Localized magnetic impurity states in Ti, Zr, and Hf," Phys. Rev. 139, No. lA, Pd.h2-k9 (Jul I965).

Clausing, P., and Moubis, G. , "Over den electrischen weerstandvan titaan en zirkoon bij lage

temperaturen , " (The electrical resistance of titanium and zirconium at low temperatures),

Physica ]_, No. 7, 245-50 (1927)-

Clinard, F. W. , and Kempter, C. P., "Low-temperature electrical properties of some transition metals and transition-metal carbides," J. Less-common Metals 15_, No. 1, 59-73 (May I968).

De Haas, W. J., and Van Alphen, P. M. , "The change in resistance of graphite, thoriian, titaniumzirconium between 20.4 K and 1.1 K," Commun. Phys. Lab. Univ. Leiden No. 212E (l93l) Reprinted

from Proc. Kon. Ned. Akad. Wetensch. 34, 70 (1931).

Kemp, W. R. , KLemens, P. G. , and White, G. K. , "Thermal and electrical conductivities of iron,

nickel, titanium, and zirconium at low temperatures," Australian J. Phys. 9, I8O-88 (jun I956).

McLennan, J. C, Howlett, L. E., and Wilhelm, J. 0., "On the electrical conductivity of certain

metals at low temperatures," Trans. Roy. Soc. Can. Sec. Ill, 23, Part I, 287-306 (jan 1929).

Meaden, G. T., Electrical Resistance of Metals , Plenum Press, New York (1965) 2l8 p.

Meissner, W. , Franz, H. , and Westerhoff, H. , "Measurements with the help of liquid helium. XV. Resistance of barium, indiun, thallium, graphite, and titanitim at low temperatures," Ann. Physik

(5) 13, 555-63 (1932).

Meissner, W. , and Voigt, B. , "Messxmgen mit hilfe von flussigem helium. XI. Wlderstand der reinen metalle in tiefen temperaturen," (Measurements using liquid helium. XI. Resistance of pure metals at low temperatures), Ann. Physik 7, No. 5, 892-936 (1930).

Mendelssohn, K. , Sharma, J. K. N. , and Yoshlda, I., "Heat conductivity of pure metals below

1 K," Bull. IIR Annexe I965-2, pp 49-56 (Meeting of Commission 1, Grenoble, France, Jun 8-11,

1965).

Potter, H. H. , "Electrical resistance and thermoelectric power of the transition metals,"

Proc. Phys. Soc. (London) 53.5 695-705 (l9^l) •

Roesch, K. C, "The influence of temperature and preferred orientation on Hall coefficient and

resistivity of pure titaniimi," Calif. Inst. Technol., Pasadena, Rept. (Nov I962) Contr. AF

49(638) 1034, 111 pp, DDC AD 289 535.

Rosenberg, H. M. , "Thermal conductivity of metals at low temperatures," Phil. Trans. Roy. Soc. London A247 , No. 933, 441-97 (1955).

Wasilewski, R. J., "Observations on electrical resistivity of titanium," Trans. Met. Soc. AIME

224, 5-8 (1962).

39
(page 2 of 9) Electrical Resistivity of Titanium

Cryogenic Data Memorandum No. M-29

Webber, R. T. , and Reynolds, J. M. , "Incipient superconductivity in titanium," Phys. Rev. 73, GkO (Mar 1948).

White, G. K. , and Woods, S. B., "Electrical and therinal resistivity of the transition elements

at low temperatures," Phil. Trans. Roy. Soc. London A251, No. 995, 273-302 (1959).

Other References :

Brehm, C, and Lehr, P., "Influence de la deformation par traction du zirconium et du titane

sur la resistivite residuelle et sur la densite de dislocations," (Effect of zirconium and

titanium tensile deformation on the residual resistivity and dislocation density), Compt. Rend. Ser. 0,265, No. l8, 97'+-6 (1967).

Fast, J. D. , "Uber die darstellung de reinen metalle der titangruppe durch thermische

zersetzung ihrer jodide. V. Titan," (On the preparation of pure metals in the titaniiim group from thermal dissociation of their iodides. V. Titanium), Z. Anorg. u. allgem. Chem. 2^1,

h2-^6 (1939).

Koftun, S. F., and Ulyanov, R. A., "Influence of alloying of the physico-mechanical properties

of titanium," Physical Metallurgy of Titanium, Izdatelstvo Nauka, Moscow, SSSR (1964) Transl. by Foreign Technology Div. , Wright-Patterson AFB, Ohio, No. FTD-HT-66-354 (Dec I966) pp I58-8I, DDC AD 655 033.

Strothenk, H., "Messungen der differentiellen sorptionswarmen und der elektrischen

leitfahigkeit im system titan-wasserstoff in abhangigkeit von der wasserstoff-konzentration,"

(Measurements of the differential sorption temperat\ires and electric conductivity of the titanium-hydrogen system as functions of hydrogen concentration) , Hannover Technische

Hochschule, West Germany, Ph.D. Thesis (1965) IO8 pp NASA 68-IO909.

Volienshteyn , N. V., and Galoshina, E. V., "Hall effect in transition metals with low number

of d-electrons , " Phys. Metals Metallog. 20, No. 3, I66-69 (1965) Transl. of Fiz. Metal. I Metalloved. 20, No. 3, 475-8 (I965).

Wedler, G. , Brocker, F. J., Kock, H. G. , and Wolfing, C, "Der einfluss von ordnungszustand

imd schichtdicke auf die struktur und die elektrische leitfahigkeit aufgedampfter metallfilme - nickel, titan, silver," (influence of the order-disorder state and film thickness on the structure and electrical conductivity of evaporated nickel, titanium, and silver films),

Basic Problems in Thin Film Physics (Proc. International Symp. , Clausthal-Gottingen, West

Germany, Sep 6-11, I965) Gottingen, Vandenhoeck and Ruprecht (1966) pp 566-73.

Comments :

The data for this graph were taken from the references cited above -under "Sources of Data" and

are listed as ratios of electrical resistivity with respect to the resistivity at the ice point temperature (psvs). When the actual values of pg^g are not available for the polycrysta3JLine samples used by the investigators, a datum value reported by Clinard and Kempter

(1968) (P273 = 39.4 X 10~® ohm cm) is suggested for calculating values of electrical resistivity from these ratios. Only one investigator (Wasilewski, I962) has determined resistivity

for titanium single crystals with directions of the current being both parallel and perpendicular to the primary axis. His results are:

for Ti( II ), pg73 = (48.0 ± 0.7) X 10"*^ ohm cm; for Ti(x), P373 = (45.35 ± 0.5) X 10"^ ohm cm.

It should also be noted that titaniiim becomes superconducting at O.39 K. 40
Electrical Jteslstivity of Titanium

Cryogenic Data Memorandum No. M-29

(page 3 of 9)

In instances where data points were quite widely separated or areas where data did not exist

,

symhols were used to show the available data points so that the reader will know where arbitrary position or shape of the graph was made.

Brief descriptions of sample preparation, purity, etc. for each data source fo3J.ow in chrono- logical order.

Clausing and Moubis (I927) measured the resistivity of a 99 •QW" Pure titanium sample. No further information is given for the preparation of the sample

.

Mc Lennan, Howlett and Wilhelm (1929) used a wire specimen which had been baked in vacuo at

a high temperature for a number of hours to remove as much as possible of the occluded gases.

Meissner and Voigt's (I930) sample was a rod 2 mm dia. and 33'5 mh long with a purity of

99. Hi.

De Haas and Van Alphen (193I) did not report method of preparation or purity of their sample;

however, they did state that the purity was not high enough to obtain reproducible data. Their titanium became superconducting at I.63 K.

Meissner, Franz and Westerhoff (1932) used two very pure single crystals (Ti 3 and Ti k) which

were grown from the gas phase. The lower residual resistance of Ti k is probably not due to higher purity but rather due to better crystalline structure of the sample

.

Potter (19^1) measured resistivities on a 1 cm long specimen. No other information is given

about the sample.

Webber and Reynolds (19^8) report resistance measurements in zero magnetic field for a 99 •89/0 pure wire sample, 0.055 in diameter.

Bostrom (195^+) used a high purity crystal bar 2 to 2-I/2 in. long and ~l/8 in. diameter. He compared the resistivity of this high piority bar to the resistivity of commercial titanium.

Rosenberg (1955) measured resistivities of a single crystal, O.O306 cm dia. and 1.6 cm long,

which had a purity of 99.99fo.

Kemp, KLemens and White (1956) used a 98^0 titanium rod, 3 nm dia., which had been annealed

at 950 °C for 5 hours in vacuo.

Berlincourt (1959) made five sets of measurements.

cut from a rolled sheet

2.3 cm long and O.32 cm

wide and 0.0127 cm thick

sample

Ti lu

Ti la

Ti 2u

Ti 2a

Ti 3 crystal bar O.O361 cm thick

purity

99.912/0

99.902i4.'/o

99-79/»

99.83fo

99.987/0

annealing

1 hr at 1200 °C at

7 X

10"'' mm Hg

1 hr at 1200 °C at

7 X 10" ^ mm Hg

White and Woods (1959) measured electrical resistivities of five samples.

sample purity ^ diameter (mm) Ti 1 98 3 Ti 2 high 2.6 x 0.1

Ti 3 99.99 1.6 X 3.1

TI k 99.99 1.6 X 3.1 Ti 5 99.99 ^.9 X 3.1

treatment

annealed in vacuo at 950 °C

" " " 700 °C

" " " 800°C,60 hours

as rolled,

annealed in vacuo at 800°C,60 hours

The residual resistivity was estimated to be 2.3 x 10"^ ohm cm. The values in the table are smoothed (from large-scale graphs) values of pi.

1^1
(page h of 9) Electrical Resistivity of Titanium

Cryogenic Data Memorandum No. M-29

Roesch (1962) measured resistivities of three specimens. All were cut from the same polycrystalline sheet. No quantitative analysis was made of the impurities. All surfaces were cleaned and samples were placed in pyrex tubes filled with heliiim. The lower resistivity of specimen 3 is most likely due to fewer lattice defects.

specimen 1

dimensions, cm

12.72

3.86 0.0066

12.08

0.0093 12.08

k.lk 0.0093

heat treatment

1 hour at 500°

C

1 hour at 500°

Specimen 2 was heated an additional

1 hour at 950 °C to produce Specimen 3.

Wasilewskl (1962) reports resistivity measurements on zone refined, high purity titanium

single crystals. The Ti II and Ti -L samples had a cross section of ~ 2 mm^ and a length of

15 mm. The polycrystalline sample had the dimensions 50mmx5mmx0.5 mm. Ps73 values

are given.

Cape and Hake (I965) used pure titanium specimens, 1 in. x 0.1 in. x 0.01 in. from buttons arc -cast in an inert atmosphere.

which were cut

The "ideal" resistivity values tabulated in the lower right-hand corner of the graph were taken from Meaden (I965). His book presents a comprehensive review of the literature dealing

with experimental determinations of electrical resistivity together with a relatively

concise account of the modern theory of the electrical resistance of metals and alloys.

Mendelssohn, Sharma and Yoshida (I965) measured resistivity of a single crystal sample of unknown purity and dimensions.

Clinard and Kempter (1968) made measurements on a polycrystalline sample l/4 in. dia and

1 in. long, which had been annealed prior to measurement. The titanium was of commercial

grade and not specifically of high purity.

Tables of Values of Electrical Resistivity

resistivity, (ohm cm); resistance, (ohm); Pa73 = resistivity at 273 K, (ohm cm). Rs73 = resistance at 273 K, (ohm).

Clausing and Moubis (I927)

Temp. p/P373 K

78.i^8 0.2150

90.20 0.2547

158.5 0.5176

194.1 0.6674

222.2 0.7828

273.09* 1.0

* Ps73 = 82 X 10~® ohm cm

** Thsse values were not plotted

on the Electrical Resistivity

of Titanium graph.

McLennan, Hewlett and Wilhelm (1929)

Temp. KR/R373

2.4

4.2 20.6

80.0 273.1

0.755

0.755 0.772

0.831

1.0

42
Electrical Resistivity of Titanium

Cryogenic Data Memorandum No. M-29

(page 5 of 9)

Meissner and Voigt (1930

)

Temp. K

P/P273*

1.13

1.17 1.26

1.30 4.21 20.46 77.61

88.19 273.16

0.0014

0.154

0.203 0.211

0.215 0.2180 0.3180

0.3505

1.00

* P273 = 54 X 10~® ohm cm.

De Haas and Van Alphen (l93l)

Temp. K

R/R273*

1.63

1.73 1.78

1.88

2.01

4.22 20.41

superconducting

0.0011

0.0433

0.1018

0.1047

0.1048

0.1051

* These values were not plotted on

the Electrical Resistivity of Titaniim graph.

Meissner, Franz and Westerhoff (1932)

Temp.

K

R/Rs73

Ti 3 Ti 4

1.21 0.0797 —

1.30 0.088s 0.00001*

1.68 _ 0.000086*

1.73 O.Uo 0.00034*

1.75 - 0.0034

1.82 - 0.1036 3.24 0.159 0.102

20.44 0.158 0.101^ 78.76 - 0.210s 79.11 0.259s 0.211

273.16 1.0 1.0

* These three points were not plotted on the Electrical Resistivity of Titanium | graph. 1

Potter (1941)

Temp. K

R/Re7 3

20

90 173

273

0.26

0.39

0.65

1.0

Webber and Reynolds (1948)

(read from graph)

Temp. K

r/r^*

1.1

1.5

2.0

2.5 3.0

3.5 4.23

.088** 0.092

0.102

0.150 0.175

0.180

0.180

* R^^ is room temperature. ** These values have not been

plotted on the Electrical

Resistivity of Titanium

graph.

Bostrom (1954)

Temp. K

Resistivity

p X 10® ohm cm

P/P3 73*

77

273 16.9452.27 0.324

1.00

* These values have not been plotted on the Electrical Resistivity of Titanium graph.

43
(page 6 of 9) Electrical Resistivity of Titanium

Cryogenic Data Memorandum No. M-29

Rosenberg (1955)

(read from graph)

Temp. K

Resistivity

p X 10^ ohm cm

p/pS73

h.5

10.0

20.0

30.0

37.5

2.1^1

2.i^2

2.63

2.88

0.0612

0.0615 0.0622

0.0668

0.0731

Kemp , KLemens and White (1956)

(read from graph)

Temp. Resistivity P/P273 K p X 10® ohm cm

2 23 0.3^3

20 23 0.343

^5 25 0.373

70 28 O.lj-18 100 35 0.522

150 kk 0.657

200 54 0.806

273 67 1.00

Berlincourt (1959)

Temp. Resistivity P/PS73** K p X 10® ohm cm

Ti lu Ti la* Ti 2u Ti 2a Ti 3* Ti la Ti 3

k.2 4.43 3.91 5.83 8.18 1.46 0.095 0.0336

77.0 8.81 8.07 10.5 12.5 6.00 0.197 0.138 273.0 - 41.0 - - 43.5 1.00 1.00

295.0 - - - 50.0 - 296.0 - - 48.8 - - 296.5 48.7 - - - - 297.0 - - - - 49.2

297.5 - 47.3 - - -

* Only the resistivity ratios for Ti la and Ti 3 were plotted on the ]Hectrical Resistivity

of Titanium graph. ** For Ti 3, P273 = 43.5 X

10"® ohm cm and

Ti la, pg73 = 1).1.0 X 10" ® ohm cm. (interpolated values)

44
Electrical Resistivity of Titanium

Cryogenic Data Memorandum No. M-29

(page 7 of 9)

White and Woods (1959)

Temp. Ideal resistivity Resistivity P/PS73 K Pi X 10® ohm cm P = Pi + PQ

Po = 2.3 X 10" ohm cm

20 0.02o 2.32 0.0562

25 0.075 2.37b 0.0575

30 0.2o 2.5 0.0605

40 0.65 2.9e 0.0714

50 1.4 3.7 0.0896

60 2.3 4.6 O.IU.

70 3.5 5.8 0.140

80 4.85 7.3^ 0.173

90 6.3s 8.6, 0.209

100 7.9 10.2 0.247

120 11.2 13.5 0.327

140 14.8 17.1 0.414

160 18.5 20.8 0.504

180 22.1 24.4 0.591

200 25-7 28.0 0.678

220 29.3 31.6 0.765

250 34.8 37.1 0.898

273 39.0 41.3 1.0

Roesch (1962)

(read from graph)

Temp. KResistivity

p X 10^ ohm cm

P/P273

4.2 77.4

273.

Specimen 1 Specimen 2 Specimen 3** 1 2 3**

1.80

6.10

41.0

1.56

5.85

38.0 *

1.23

5.60

36.5 *

0.044

0.149

1.00

0.041

0.154

1.00

0.034

O.X53

1.00

* Interpolated value. ** Only the values for Sp

graph.

ecimen 3 were plotted on the Electri cal Resistivity of Titanium

Wasilewski (1962)

Temp. K

P/pS73*

Till Ti 1 Ti(poly)

4.2 19.6

77 196

273

0.1786

0.6355

1.00

0.2086

0.6450

1.00

0.0306

0.0309

0.15 0.67

1.00

* For Ti II , p273 = (48.0 ± O.7 ) x 10"® ohm cm, Til , Ps73 = (45.35 ± 0.5 ) X 10"® ohm cm, Ti(polj^ p273 = (42.67 + 0.05) X 10~® ohm cm. These values have not been plotted on the Electrical Resistivity of Titanium graph.

45
(page 8 of 9) Electrical Resistivity of Titanium

Cryogenic Data Memorandum No. M-29

Cape and Hake (I965)

(read from graph)

Temp. Resistivity P/PS73 K p X 10® ohm cm

5.5 1.40 0.0355

8.0 1.39 0.0353

15.0 1.38 0.0351

18.5 1.39 0.0353

21.0 1.40 0.0355

2i)..0 1.43 0.0363

28.5 1.52 0.0386

30.1 1.61 0.0409

35.2 1.75 0.0444

Mendelssohn, Sharma and Yoshida (I965)

(read from graph)

Temp. K

Resistivity

p X 10® ohm cm

P/pS73

0.4

0.8

1.2

0.91

0.91

0.91

0.0231

0.0231

0.0231

Clinard and Kempter (1968)

(read from graph)

Temp. Resistivity P/P3 73 K p X 10® ohm cm

2 2.0 0.0508

10 2.0 0.0508

25 2.0 0.0508

50 3.4 0.086

75 5.8 0.147

100 9.4 0.239

150 18.4 0.467

200 27.5 0.698

250 37.0 0.939

273 39.4 1.0

46
Electrical Resistivity of Titanium

Cryogenic Data Memorandum Wo. M-29

ro

O

<

(T. >

>

H

(/)

(/) UJ

a:

_i

<

o

(r. h-o

LJ

_JLU

TEMPERATURE, °R

20 40 60 80 100

(page 9 of

400 600

8 10 20 40

TEMPERATURE , K

60 80 100 200 400

ROW 3/70

47

CRYOGENIC DATA MEMORANDUM

PROJECT NO. 2750422 ^"-E NO. ^_^q

ELECTRICAL RESISTIVITY OF TUNGSTEN, W (page 1 of 13)

(Atomic Number 'Jk)

Sources of Data:

Backlund, N. G. , "Measurement and analysis of the thermal conductivity of tungsten and

molybdenum at 100-ii-OO K," J. Ehys . Chem. Solids 28, No. 11, 2219-23 (Nov I967).

Berthel, K. H. , "Der spezifische elektrische widerstand von elektronen-strahlzonengeschmolzenem

wolfram zwischen l.k and 27 K," (The specific electrical resistance of electron beam zone melted tungsten between l.lj- and 27 K) , Phys. Status Solidi 5, No. 2, 399-406 (1964).

Berthel, K. H. , "Uber den einfluss verschiedener streuprozesse auf den spezifischen

elektrischen idealwiderstand von reinem wolfram bei tiefen temperaturen," (influence of various scattering processes on the specific electric ideal resistance of pure tungsten at low temperatures), Realstrixktur und Eigenschaften Von Reinststoffen (Internationales

Symposium Reinststoffe in Wissenschaft und Technik, Dresden, Germany, 2nd, Sep 28 - Oct 2, 1965, Pt. 3), J. Kunze, et al. Editors, Akademie-Verlag, Berlin, Germany (1967) pp 875-84.

Clinard, F. W. , and Kempter, C. P., "Low-temperature electrical properties of some transition metals and transition-metal carbides," J. Less-Common Metals 15_, No. 1, 59-73 (May 1968)

.

Cox, M. , "Thermal and electrical conductivities of tungsten and tantalum," Ehys. Rev. 64 , No. 7/8, 241-47 (Oct 1943).

De Haas, W. , and DeNobel, J., "The thermal and the electrical resistance of a tungsten singlecrystal at low temperatures and in magnetic fields," Physica 5.> 449-63 (1938)

.

De Robel, J., "Thermal and electrical resistivity of some tungsten single crystals at low

temperatures and in strong magnetic fields," Physica 23, 26I-69 (1957)-

Gruneisen, E. , and Adenstedt, H. , "Einfluss transversaler magnetfelder auf elektrizitats und

warmeleitung reiner metalle bei tiefer temperatur," (The effect of a transverse magnetic

field on the electrical and thermal conduction of pure metals at low temperature), Ann. Physik 31, 714-44 (1938)

.

Gruneisen, E., and Goens , E. , "Unterschungen an metalUsristallen. V. Elektrlzitats- und

warmeleitung von ein- un vielkristallinen metallen des regularen systems," (investigations

of metal crystals V, Electrical and thermal conductivity of single and poly crystalline

metals of regular system), Z. Physik 44, 615-42 (1927).

Henning, F., "Gasthermometrische messungen zwischen -193 und -258 degrees," (Gas thermometry

measurements between -193 and -258 degrees), Z. Physik 4, 264-79 (l92l)

.

Holborn, L. , "Uber die abhangigkeit des widerstandes reiner metalle von der temperatur,"

(About the dependence of resistance of pure metals on the temperature) , Ann. Physik 59, 145-69 (1919)-

Kannuluik, W. G. , "The thermal and electrical conductivities of several metals between

-183°C and 1C0°C," Proc. Roy. Soc . (London) Al4l, I59-68 (1933).

Mc Lennan, J. C, Howlett, L. E., and Wilhelm, J. 0., "On the electrical conductivity of certain metals at low temperatures," Trans. Roy. Soc. Can. Sec. HI, 23, Part I, 287-30^

(Jan 1929).

Meaden, G. T., Electrical Resistance of Metals, Plenum Press, New York (1965) 2l8 p.

49
(page 2 of 13) Electrical Resistivity of Tungsten

Cryogenic Data Memorandum No. M-30

Meissner, W. , "Messungen mit hilfe von flussigem helium III. Widerstand von metallen. Supraleitfahigkeit von tantal/' (Measurements with the help of liquid helium. III. Resistance

of metals. Superconductivity of tantaltim) , Physik. Z. 29, 897-904 (1928).

Meissner, W. , and Voigt, B. , "Messungen mit hilfe von flussigem helium. XI. Widerstand der reinen metalle in tiefen temperaturen/' (Measurements using liquid helium. XI. Resistance

of pure metals at low temperatures), Ann. Physik 7, No. 5, 892-936 (I93O).

Moore, J. P., McElroy, D. L. , and Barisoni, M. , "Thermal conductivity measurements between

78 and 3^0 K on aluminum, iron, platinum, and tungsten," Proc . 6th Conf. on Thermal Conductivity, Dayton, Ohio (Oct 19-21, I966) Air Force Materials Lab., Wright-Patterson AFB, Ohio, PP 737-78.

Powell, R. L. , Harden, J. L. , and Gibson, E. F., "Low-temperature transport properties of commercial metals and alloys. IV. Reactor grade Be, Mo, and W," J. Appl. Phys . 31; No. 7, 1221-24 (Jul i960).

Shukovsky, H. B. , Rose, R. M. , and Wulff, J., "The low temperature electrical resistivity

of lattice defects in deformed tungsten single crystals," Acta Met. 14, No. 7, 82I-3O

(Jul 1966).

Van den Berg, G. J., "The electrical resistance of potassium, tungsten, copper, tin, and lead at low temperatures," Physica 14, III-38 (Apr 1948).

VoUsenshtein, N. V., Starostina, L. S., et al., "Temperature dependence of electric con- ductivity of molybdenum and tungsten mono crystals in low temperature region," Phys. Metals

Metallog. 18, No. 1, 85-9O (1964), Fiz. Metal. I Metalloved. I8, No. 6, 888-94 (1964).

White, G. K. , and Woods, S. B. , "Low temperature resistivity of the transition elements - cobalt, tungsten and rhenium," Can. Jo Phys. 35., 656-65 (1957).

White, G. K. , and Woods, S. B. , "Electrical and thermal resistivity of the transition

elements at low temperatures," Phil. Trans. Roy. Soc. London A251, No. 995, 273-302 (1959).

Wiese, J. R., "The flow and fracture of zone refined tungsten," Franklin Inst.,

Philadelphia, Pa., Labs, for Research and Development, Quart. Prog. Rept. No. Q-B1973-3;

Tech. Rept. No. WAL TR 834. 2/11-2 (Mar I963) Contr. No. DA-36-034-ORD-3747 RD, 10 pp, DDC AD 407 426.

Other References:

Berthel, K. H., "Restwiderstandsverhaltnis , durchmesser-effekt und stromabhangigkeit des widerstandsverhaltnisses von zonengeschmolzenem wolfram bei tiefen temperaturen," (Residual

resistance ratio, diameter effect and current dependence of the resistance ratio of zone- melted tungsten at low temperatures), Phys. Status Solidi 5., No. 1, 159-68 (1964).

Borovik, E. S., "Change of resistance of metals in a magnetic field at low temperatures,"

Zh. Eksptl. I Teoret Fiz. 23, 9I-IOO (1952).

Bridgman, P. W. , "Electrical resistance under pressure, including certain liquid metals,"

Proc. Am. Acad. Arts Sci. 56, 61-154 (1921)

.

50
Electrical Resistivity of Tungsten (page 3 of I3)

Cryogenic Data Memorandum No. M-30

Bridgman, P. W., "The electric resistance to 30,000 kg/cm^ of twenty nine metals and intermetallic compounds/' Proc. Am. Acad. Arts Sci. 79, 114-9-79 (1951)

,

Bridgman, P. W. , "The resistance of 72 elements, alloys and compounds to 100,000 kg/cm^,"

Proc. Am. Acad. Arts Sci. 8I, Wo. h, I69-25I (Mar 1952).

Conte, R. R. , and Dural, J., "Dispositif d ' irradiation aux neutrons a 20 K," (Apparatus for neutron irradiation at 20 K) , Rev. Ehys . Appl. 2, No. 1, 1-6 (1967).

De Nobel, J., "Thermal and electrical resistance of a tungsten single crystal at low

temperatiH-es and in high magnetic fields," Physica I5, 532-40 (Jul 1949).

Dobson, P. J., and Hopkins, B. J., "Electrical conductance of thin ultrahigh-vacuum

evaporated films of tungsten on glass," J. Appl. Phys. 39, No. 7, 3074-8I (jun I968)

.

Engelhardt, J. J., Webb, G. W. , and Matthias, B. T., "Superconductivity and the d-shell,"

Science I55, No. 3759, 191-3 (Jan I967)

.

Geiss, W. , Van Liempt, J. A. M. , "Das eirweiterte gesetz von Matthiessen," (The extended law

of Matthiessen), Z. Physik 41, 867 -71 (1927)

.

Gibson, J. W. , and Hein, R. A., "Superconductivity of tungsten," Phys. Rev. Letters 12,

No. 25, 688-90 (jun 22, 1964).

Goree, W. S., "Electrical conductivity of metals at high pressures and low temperatures,"

Florida Univ., Gainesville, Ph.D. Thesis (1964) I66 pp (Abstr. in Dissertation Abstr. 12,

7344, Jun 1965). (Available Univ. Microfilms, Ann Arbor, Mich., Order No. 65-5985).

Goree, W. S., and Scott, T. A., "Pressure dependence of electrical conductivity at low

temperatures," Proceedings of the Intern. Conf . on Low Temperature Physics 9th, Pt. B, Plenum Press, New York (1965) pp I205-9.

Goree, W. S., and Scott, T. A., "Pressure dependence of electrical conductivity of metals

at low temperatures," J. Phys. Chem. Solids 27, No. 5, 835-48 (May I966)

.

Ibragimov, Sh. Sh., "Effect of neutron bombardment on certain properties of tungsten,"

Phys. Metals Metallog. (USSR) 23., No. 2, 175-8 (I967) Transl. of Fiz. Metal. Metalloved.

23, No. 2, 354-7 (1967).

Justi, E. , and Scheffers , H. , "Die elektrische anisotropic von wolfram-einkristallen bei

tiefen temperaturen in starken magnetischen transversalfeldern," (Electric anisotropy of single crystal tungsten for low temperatures in strong transverse magnetic field), Phys.

Z. 37, 700-9 (1936).

Justi, E. , and Scheffers, H. , "Die elektrische leitfahlgkeit von wolframeinkristallen bei

tiefen temperaturen in straken magnetischen quer- und langsfeldern," (Electrical conductivity of single crystal tungsten at low temperatures in strong magnetic cross and longitudinal

fields), Physik. Z. 38, 891-6 (1937)-

Kammerer, 0. F., and Strongin, M. , "Superconductivity in tungsten films at temperatures

near 4 K," Brookhaven National Lab., Upton, N. Y. , Rept. No. BNL-9479, (1965) Contr. No. AT(30-2)-GEN-l6, 17 pp. Presented at Intern. Symp. on Basic Probl. in Thin Film Phys.,

1st, Clausthal-Gottingen, Germany, Paper No. CONF-650936-I, NASA N66-17545.

Kapitza, P. L. , "The change of resistance of metals in magnetic fields," Leipziger

Vortrage, S. Hirzel, Leipzig, Germany (1933) Reprinted in Collected Papers of P. L. Kapitza. Volume I (1916-I934), Pergamon Press, Ltd., Oxford, England (1964) pp 472-8.

Krautz, E., and Schultz, H., "Der einfluss von gitterbaufehlern auf den elektrischen widerstand und den Hall-effekt von wolfram und tantal," (The influence of lattice structure

faults on the electrical resistance and Hall effect of tungsten and tantalum), Z. Angew.

Phys. 15, No. 1, 1-4 (Jan 1963)-

51
(page h of 13) Electrical Resistivity of Tungsten

Cryogenic Data Memorandum No. M-30

Kuhlmann, H. H. , and Schiiltz, H. , "Erholimgsstufe III in entkohltem wolfram nach

neutronenbestrahlung bel k.3 K," (Recovery state III In decarbonized tuingsten after neutron irradiation at h.^ K) , Acta Met. Ih, No. 6, 798-8OO (jun I966)

.

Mlmeault, V. J., and Hansen, R. S., "Flash desorption and isotopic mixing of hydrogen and

deuterium adsorbed on tungsten, iridium, and rhodium," J. Chem. Ehys. h^, No. 6, 22ifO-50 (Sep 1966).

Mostovetch, N., and Vodar, B. , "Variations, en fonction du potentlel applique, de la resistance electrique des depots metalliques tres minces aux basses temperatures," (Variations as function of applied potential of the electrical resistance of very thin metallic

deposits at low temperatures), Compt. Rend. 23O , 93^-6 (Mar I95O).

Nachtigall, E. , "Eigenschaften von molybdaen und wolfram bel niedrlgen und mittleren

temperaturen , " (Properties of molybdenum and tungsten at low and medium temperatures),

Z. Metallk. I+3, No. 1, 23-26 (jan 1952).

Thomas, J. G., and Mendoza, E., "The electrical resistance of magnesium, aluminimi,

molybdenum, cobalt, and tungsten at low temperatures," Ehil. Mag. h3) 900-10 (Aug 1952).

Tye, R. P., "Preliminary measurements on the thermal and electrical conductivities of molybdenum, niobium, tantalum, and tungsten," J. Less-Common Metals 3.j No. 1, I3-I8

(Feb 1961).

Van Witzenburg, W. , and Laubitz, M. J., "Magnetoresistances and the phonon conductivity

of metals," Can. J. Phys . i|;6, No. 17, ldQ'J-9k (Sep I968).

Vodar, B. , Mostovetch, Mo, Barbaron, M. , and Spondlin, R., "Electrical conductivity of

• thin metallic films at liquid helium temperatures," Proc . Intern. Conf . Physics Very Low

Temp., Mass. Inst. Technol., Cambridge, II3 (Sept 19^9).

Comments

:

The data for this graph were taken from the references cited above under "Sources of Data" and are listed as ratios of electrical resistivities with respect to the resistivity at the ice point temperature (psvs). When the actual values of P373 are not available for the samples used by the various investigators, a datum value reported by Moore, McElroy, and Barison (l967)(pg,3= 4.839x10"^ ohm cm) is suggested for calculating values of electrical

resistivity from these ratios. Gibson and Heln (l96i<-) reported that superconductivity had

been observed in a sample of high-purity tungsten at a temperature below 0.011 K.

In Instances where data points were quite widely separated or areas vAiere data did not

exist, symbols were used to show the available data points so that the reader will know

where arbitrary position or shape of the graph was made.

Brief descriptions of sample preparation, purity, etc. for each data source follow in chronological order.

Holborn (I919) measured the resistance of 0.1 mm dla. wire which had been annealed a long

time in vacuum at temperatures at which the metal glowed. There was no purity statement.

No information is given on the Hennlng (1921) sample.

52
Electrical Resistivity of Tungsten (page 5 of 13) Cryogenic Data Memorandum Wo. M-30

The Gruneisen and Goens (1927) sample was a "very pure" single crystal deposited from the vapor. Resistivity values for a less pure sample were determined but have not been

included in this compilation. '

Meissner (1928) used an annealed tungsten sample 5I nim long and O.O3 mm diameter.

The Mc Lennan, Hewlett and Wilhelm (I929) sample was in wire form, baked in vacuo at a high temperature for a nimiber of hours to remove as much as possible of the occluded gases.

Meissner and Voigt (I93O) had two samples; W-1 was a wire O.O3 ram dia. and 60 umi long and

W-2 had the dimensions 4 mm x 4 mm x 65 mm. Both samples were annealed.

Kannululk (1933) measured resistivities of 99.83^ pure tungsten crystals. W-1 had a cubic

configuration, a cross-sectional area of O.OIO53 cm^ and a lengtK of 7.8'46 cm. W-2 had a hexagonal configuration, a cross sectional area of 0.01022 cm^ and a length of 7>9'<0 cm.

De Haas and De Nobel (1938) single crystal rod with a hexagonal cross section. They

ass-umed that the axis of the rod was parallel to the (ill) direction. The sample was of high purity. All the values in the table were taken in zero magnetic field.

Gruneisen and Adenstedt (1938) measured resistivities of a cubic body centered crystal

rod para3J.el to [lOO] axis. The cross sectional area was O.O25I cm^ and the length was

5.6 cm.

Cox (19^3) reported resistivity values for two wires, 0.010 in. diameter and kO cm long. W-2 was aged at "temperatures of 2^100° and 2600°C for 370 hours. W-8 was aged at temperatures of 2300 °C for 370 hours.

Van den Berg (19^8) had two single crystal samples (thick rods) of different orientations.

W^ had its length parallel to the rib of the lattice cube. W^ had its length parallel to the body diagonal of the lattice cube.

De Nobel (1957) measured resistivities of a single crystal rod whose axis made an angle

of at most 5° with the [lOO] direction. No purity statement is given. The values in the table were measured with a magnetic field strength of zero.

White and Woods (1957> 1959) measured resistivity values for three samples of 99'99fo pure

tungsten. W-la was annealed at 1350 °C in vacuo for some hours, then at 600°C for some hours, then cooled. W-lb was the same as W-la except heavy copper leads were attached

instead of thin copper leads. W-2 was electropolished to 1 mm dia. then annealed at 1300 °C in vacuo. The smoothed values in the table may have an error of about ± Vfo due to uncertainty in the geometry of the specimen.

Powell, Harden and Gibson (196O) had, a 98/0 pure tungsten rod 3 '67 mm dia. and I3 cm long. The sample was not annealed after machining.

Wiese (1963) used two electron-beam zone-refined rods of high purity tungsten. Probes were

set at varying intervals along the rod. Probes 6-7 were on the polycrystalline ends of the sample. All other probes are on the single crystal portion.

Berthel (196^4-) made resistance meas\irements on ten (single crystal) rods with diameters

ranging from I.5 "to 4.3 mm. No purity statement was given. They were prepared by

electron beam zone melting. The values in the table are the average of all measurements.

Volienshtein, et al. (196*4-) measured resistances of both single crystal and polycrystalline

samples. The single crystals were produced by zone melting by electron bombardment, with

dimensions of 3 to 4 mm dia. and 25 mm long rods. About 100 data points were taken and

presented graphically.

53
(page 6 of 13) Electrical Resistivity of Tungsten

Cryogenic Data Memorandum No. M-30

The "ideal" resistivity values tabulated in the lower right-hand corner of the graph were taken from Meaden (I965). His book presents a comprehensive review of the literature

dealing with experimental detemiinations of electrical resistivity together with a relatively concise account of the modern theory of the electrical resistance of metals and alloys

.

Moore, Mc Elroy and Barison (1966) report smoothed values of electrical resistivity for

two rod samples; one is stated as "high purity" and the other "radial". The "high purity"

saniple was prepared by electron-beam melting and has a ratio Ps'73/P 4:.^ o^ -^ 400. The

"radial" sample is 99. 98/0 pure.

Shukovsky, Rose and Wulff (I966) measured resistivities of single crystals which were seeded for a [lOO] axial orientation and were grown by a floating-zone electron-beam

technique in vacua of 2 x 10"^ torr and 2 x 10"^ torr at a rate of 2 mm/min. The starting

material was 99.99fo pure. The values in the table are for an undefonned sample. Residual

resistivity p^ = 4.8 x

10" '° ohm cm.

Backlund (1967) had two sample bars, 10 cm long and 4 and 5 nTM diameters, state the purity of his samples

.

He does not

Berthel (1967) used 99.999^° pure tungsten rods with diameters between I.5 and 4.5 ram. residual resistance value was not given.

Clinard and Kempter (1968) measured resistivities of a pure tungsten cylinder, l/4

in. dia. and 1 in. long. The residual resistivity, Po , was 0.1 x 10

Tables of Values of Electrical Resistivity

ohm cm.

p = resistivity, (ohm cm); R = resistance, (ohm);

P273 = resistivity at 273 K, (ohm cm) Rs73 = resistance at 273 K, (ohm).

Holborn (1919)

Temp. K

R/R273*

80.4

81.1

194.85 273.0

0.1529

0.1554

0.6509

1.0

* These values were not plotted

on the Electrical Resistivity

of Timgsten graph.

Henning (l92l)

Temp. K

R/B273*

81

90 197

273

0.1564

0.1942

0.6523

1.00

* These values were not plotted

on the Electrical Resistivity

of Tiingsten graph.

Gruneisen and Goens (1927)

Temp. K

P/PS73

21.2 83.2 273.2*

.00120 0.1387

1.00

* P373 = 4.91 X 10"^ Ohm cm

'

Meissner (1928)

Temp. K

R/I^2 73

1.31

4.22 20.44

78.24

273.20

0.0307

0.0307

0.0317

0.1478

1.00

5h
Electrical Resistivity of Tungsten

Cryogenic Data Memorandum No. M-30

(page 7 of 13)

McLennan, Howlett and WiUielm (1929)

Temp. K

Resistance R X 10^ ohm

R/Ks7 3*

2.k k.6

20.6

85.0 273.1

k.6

k.6 k.l

28.3

1^1-9.0

0.031

0.031

0.032

0.190

1.0

* These values were not plotted on the Electrical Resistivity of Tungsten

graph

.

Meissner and Voigt (1930)

Temp. K

r/bS73 W-1* W-2

0.00 0.0307 0.000516

1.31 0.0307 0.00053

I1.2I - O.OOOjif

if. 22 0.0307 - 20. U 0.0317 0.00108

77.60 - 0.1156

78.23 O.lij-78 - Q-J.kO - 0.1565

273.16 1.0 1.0

* These values were from

Meissner (1929)

.

Kannuluik (1933)

Temp. KResistivity

p X 10^ ohm cm

P/PS73*

W 1 W 2 W 1 W 2

90.0

19i^.5 273

0.892

3.22

if. 98

0.81f3 3.17 k.9k0.1790

0.6if6if 1.00

0.1706

0.6if2if 1.00

* These values were not plotted on the Electrical

Resistivity of Tungsten graph.

De Haas and De Nobel (1938)

Temp. Resistivity P/PS73* K p X 10^ ohm cm U.14 0.0023® 0.000486

17.55 0.0031^ 0.000650

20.36 .0041"^ 0.000860

20. if 2 0.0042^ 0.000870

50.55 0.142^ 0.0294

63.50 0.323° 0.0666

65.20 0.347^ 0.0715

65.80 0.356^ 0.0735

68.20 0.394^ 0.0813

69.80 0.423° 0.0872

71.30 0.446° 0.0920

74.30 0.499° 0.103

74.95 0.511° 0.105

77.40 0.559^ 0.115

80.10 0.606^ 0.125

85.05 0.704° 0.145

90.15 0.807° 0.166

* The value of p2 73 used in tllis calculation

was 4 . i539 X 10"^ ohm cm. E e Haas and

De Nobe 1 did not report a pj,73 value.

Gruneisen and Adenstedt (1938)

Temp. K

R/R2 73 (Wll )

20.33 78.94 273.15*

.00216 0.1230

1.0

* pg^3 = 4.86 X 10"^ ohm cm

55
(page 8 Of 13) Electrical Resistivity of Tungsten

Cryogenic Data Memorandum No. M-30

Cox (1943)

Temp. K

Resistivity

p2 73 X 10® ohm cm

P/P2 73*

W 2 W 8 W 2 W 8

77.36

77.4

90.2

193 273.2

0.6736

0.9132

3.18 5.034

0.6135

0.8558

5.035

0.134

0.181

0.632

1.0

0.122

0.170

1.0

* These values were not plotted on the Electrical

Resistivity of Tuagsten graph.

Van den Berg (1948)

Temp. K

K/Rg73

W,^ w,*

1.29 .00045* _ 1.30 - 0.00071^ 2.01 0.00044^ 0.00071^

3.00 0.00045"^ 0.00072*

4.40 0.00045^ - 4.49 - 0.00072^ 7.68 0.00047^ - 8.05 - 0.00074^ 11.27 0.00052^ - 15.14 0.00062^ - 18.06 0.00078^ 0.00109^ 20.41 0.00097^ 0.00129^

* Wy had its length parallel to the rib

of the lattice cube.

Wj had its length parallel to the body

diagor^l of the lattice cube.

De Nobel (1957)

Temp. K

Resistivity

p X 10® ohm cm

p/p273

14.50

20.42

55.35

63.95 68.51

72.97

77.35

273

0.0123

0.0141

0.2155 0.3551

0.4297

0.5087

0.5921

5.423 *

0.00227

0.00260

0.0397

0.0655 0.0792

0.0938

0.109

1.0

* Calculated value

56
Electrical Resistivity of Tungsten

Cryogenic Data Memorandum No. M-30

(page 9 of 13)

White and Woods (1957, 1959)

Temp. Ideal resistivity Resistivity P/PS73 K pj X 10 ohm cm P = Po + Pl^

Po = 0.0303 X 10" ohm cm

15 0.0024 0.0327 .00674

20 0.005s 0.0359 .00740

25 O.OII5 0.0418 0.00862

30 0.022 0.0523 0.0108

to 0.0^ 0.0963 0.0199

50 0.15i 0.1813 0.0374

60 0.27i 0.3013 0.0621

70 0.425 0.4553 0.0939

80 O.6O0 0.6303 0.130

90 0.82o 0.8503 0.175

100 1.02 1.0503 0.217

120 1.44 1.4703 0.303

l4o l.Ss 1.9103 0.394

160 2.33 2.3603 0.487

180 2.78 2.8103 0.579

200 3.22 3.2503 0.670

220 3.66 3.6903 0.761

250 4.33 4.3503 0.897

273 4.82 4.8503 1.0

Powell, Harden and Gihson (196O)

(read from graph)

Temp. K

Resistivity

p X 10® ohm cm P/P273*

410

20

40

6080 100

0.16

0.16

0.17

0.22

0.43

0.8

1.2

0.0330 0.0330

0.0350 0.0454

.0886 0.165 0.249

* The value of P373 used in this calculation

was 4.839 X 10-^ohm cm. Powell, Harden and

Gibson did not report a psyg value.

The values in this colimn were not plotted

on the Electrical Resistivity of Tungsten

graph.

57
(page 10 of 13) Electrical Resistivity of Tungsten

Cryogenic Data Memorandum Wo. M-30

Wiese (1963)

Temp. K

Resistance*

R X 10^ ohm

probes 1-2 2-3 3-4 4-5 6-7 1 Sample W-1

295774.2

61.20 6.37 0.039

61.57

6.29 0.001

56.90

5.83 0.003

44.74

4.62 0.033

43.91 4.97 0.369

Sample W-2

30077

4.2

62.22 6.61

.0101

57.29

6.03 59.63 59.806.28 6.29 probes broke -

47.50

5.85 0.602

* These values have not been plotted on the Electrical Resistivity of Tungsten graph.

Berthel (1964)

Temp. Ri/Rs73* Temp. Ri/R273* K K

14.00 0.0000785 24.57 .001028 14.50 0.000090 24.62 0.001036

15.00 0.000103 25.00 0.001126

15.50 0.0001175 25.08 0.001145

16.00 0.0001335 25.51 0.001246

16.50 0.0001525 25.78 0.001319

17.00 0.0001735 25.99 0.001373

17.50 0.000197 26.29 0.001459

18.00 0.000223 26.49 0.001514

18.50 0.000253 26.79 0.001602

19.00 0.0002855 26.98 0.001666

19.50 0.000323 27.06 .001690 20.00 0.000365

20.25 0.0003875

* These i/•alues were not pl(Dtted on the I]lectrical

Resist Lvity of Tungsten j^raph

.

58
Electrical Resistivity of Tungsten

Cryogenic Data Memorandum Wo. M-30 (page 11 of 13)

Volkenshtein, et al. (1964)

(read from graph)

Temp. K

K/Rs73

single crystal poly crystal

5 10

15

20

25

3033

40

506070 100

150

200

250 273

0.0001

0.0001

0.0002

0.00045 0.0009

O.QO25 0.0043

0.03

0.22 0.46

0.68

0.9

1.0

0.037

0.040 0.042

0.0525

0.0670 0.089 0.16

0.26

0.48

0.68

0.90

1.0

Moore, McElroy and Barison (1966)

Temp. Resistivity P/PS73** K p X 10^ ohm cm

"High purity" "Radial" "High Purity" "Radial"

80 0.60 0.76 0.124 0.152

100 1.04 1.20 0.215 0.240

120 1.48 1.64 0.306 0.328

140 1.92 2.08 0.397 0.416

160 2.36 2.52 0.488 0.504

180 2.80 2.96 0.579 0.592

200 3.24 3.40 0.670 0.680

220 3.68 3.84 0.760 0.768

240 4.12 4.27 0.851 0.854

260 4.56 4.71 0.942 0.942

273 4.839* 5.002* 1.0 1.0

* Taken from text. ** These values were not plotted on the Electrical Resistivity of Tungsten

graph

.

59
(page 12 of 13) Electrical Resistivity of Tungsten

Cryogenic Data Memorandum No, M-30

Shiikovsky, Rose and Wulff (1966)

(read from graph)

Temp. Pj X 10® ohm cm Resistivity p/pE73 K P = Po + Pi po = 0.0004 X 10" ® ohm cm

7.3 0.0000552 0.0005352 .000111

8 .000072 0.000552 .000115

9 .000096 0.000576 .000120

10 0.00013^+ 0.000614 0.000128

15 O.OOOlj-S 0.00098 0.000204

20 0.00163 0.00211 0.000440

25 0.00528 0.00568 0.00118

30 0.0178 0.01828 0.00381

35 0.0408 0.04128 0.00860

ko 0.0816 ,08208 0.0171

* PS73 = k.Q X 10~® ohm cm

Berthel (1967)

(read from graph)

Temp. Ri/Rs73* K

2 0.0000007

4 0.0000027

10 0.000024

16 0.00013

20 0.00035

26 0.0013

* These values have not been

plotted on the Electrical

Resistivity of Tungsten

graph

.

Backlund (1967)

(read from graph)

Temp. Resistivity P/PS73 K p X 10® ohm cm

4.2 0.2 0.04

20 0.2 0.04

50 0.3 0.06

100 1.1 0.27

150 2.1 0.42

200 3.3 0.66

273 5.0 1.00

Clinard and Kempter (1968)

(read from graph)

Temp. Resistivity p/Pe73 K p X 10® ohm cm

4.2 0.1 0.02

20 0.1 0.02

50 0.3 0.06

100 1.2 0.24

150 2.2 0.44

200 3.5 0.70

250 4.5 0.90

273 5.0 1.0

60
Electrical Resistivity of Tungsten

Cryogenic Data Memorandum Ko. M-30

(page 13 of 13)

TEMPERATURE. °R

ro

CVJ

COW

liJ

<O

o

LJ

_l

UJ

2 4 6 8 10 20 40 60 80 100 200 400 600

1.0

fST' j^

yOj/f y^

yg

ELECTRICAL RESISTIVITY RATIO

FOR TUNGSTEN

/©g.^^ = 4.839 X lO"^ ohm cm

/

f

lo' ^

i

1 1 1 1 1 1 f/i ^

1 1 1 1 1 1 Voikenshtein ,et al. (poly)^ J

Meissner W

\ - \ \ r^ J^ ^ Ly fi

10^ n

Ba ck

5.0

un

Y 1

do

5 nhm rm /i

I\ Clinard and Kempter

c

/ ?7^ A p„„ = 5.0x10 "

1 ^y^ ohm cm

1 1 1

1 u . / White and Woods Ue iNOuci

. -6

Tl \ //i

\ n cm —

/°273 =

^-'itii>x u Oh

U 11

cm^

y(Jj

r273

10^ Van der1 Berg (W, )^ A1\

1 1 1 Gruneisen

H 1

1

and Adenstedt

5x10 ohm cm

\ f // '273

\ ^^^^^^ >^ //

1 :l_ , _. i.^ -- —^ ^ » II — —_-"'^y A

— — — — -V-

^——='

i /\ ^' ,.

1 11—

1

WN

\ —

V

^ UP Mnns nnn ue ixinnei \ \

_

1 MpiccnAi' n

1 1 nr\ \/r\'u3t / 1 \

1 1 1 1 I , / 1 1 1

1

1 / "Ideal" Resistivity*

of Tvingsten

Van den c

1

ery K V 'y'

10^ -\'/ Temp. K

p, X 10^ ohm cm

Pl/P273

\ . ® :

\, \

' —

20

5080 100 150

200

250 273-15

0.0056

0.15i O.6O0 1.02

2.10 3.22

4-32

4.8^

0.0012 " 0.0313 0.124

0.212 0.436

0.668 0.896

1.0

\

\ 5hukovskv. Rose and Wulff \

_ ^ =4.8x10 ohm cm

1 1 1 .-J

1

1 \

(Single Crystal

1 1 L_

k

1

-5

* from Meaden (I965) see text. 10^ J [11 I i 6 8 10 20 40 60 80 100

TEMPERATURE, K

200 400

61

CRYOGENIC DATA MEMORANDUM

PROJECT NO. 2750422 PILE NO- J4-3I

ELECTRICAL RESISTIVITY OF VANADIUM, V (page 1 of ?) (Atomic Number 23)

Sources of Data:

Amitirij E. B. , Kovalevskaya , Yu. A., and Kovdrya, Yu. Z. , "Hall effect and electrical resistivity of vanadium at 20-300 K," Soviet Ehys. -Solid State 9, No. 3, 704-6 (Sep I967) Transl.

of Fiz. Tverd. Tela % No. 3, 905-8 (Mar I967).

Burger, J. P., and Taylor, M. A., "Anomalies in the magnetic susceptibility and electrical

resistivity of vanadium," Biys . Rev. Letters 6, No. k, I85-87 (Feb I961)

.

Hren, J. A., and Wayman, C. M. , "Some properties of vanadium at subatmospheric temperatures,"

Trans. Met. Soc . ABffi 2l8, 377-9 (Feb I960)

.

Loomis, B. A., and Carlson, 0. N. , "Investigation of the brittle-ductile transition in vanadium," Reactive Metals (Proceedings of the Annual Conference 3rd, Buffalo, N. Y. , May

27-29, 1958) W. R. Clough, Ed., Interscience Publishers, New York (1959) 2, pp 227-4-3.

Meaden, G. T. , Electrical Resistance of Metals , Plenum Press, New York (1965) 2l8 p.

Meissner, W. , and Voigt, B. , "Messungen mit hilfe von flussigem helium. XI. Widerstand der reinen metalle in tiefen temperaturen," (Measurements using liquid helium. XI. Resistance of pure metals at low temperatures), Ann. Physik ']_, No. 5> 892-936 (1930).

Meissner, W. , and Westerhoff, H. , "Messungen mit hilfe von flussigem helium. XXIII. Supraleitfahigkeit von vanadium," (Measurements using liquid helium. XXIII. Superconductivity of vanadium), Z. Physik 87, 206-9 (1933).

Potter, H. H. , "Electrical resistance and thermoelectric power of the transition metals,"

Proc. Phys. Soc. (London) 53; 695-.705 (l94l)

.

Rostoker, W. , and Yamamoto, A. S., "A contribution to the vanadium-oxygen phase diagram,"

Trans. Am. Soc. Metals 47, 1002-17 (1955).

Smirnov, Yu. M. , and Finkel, V. A., "Crystal structure of tantalum, niobium and vanadium at 110-400 K," Soviet Phys. JTBTP 22, No. 4, 75O-3 (Apr I966) (Transl. from Zh. Eksperim. I Teor.

Fiz. 49, 1077-82, Oct 1965).

Taylor, Mo A., and Smith, C. H. L. , "The electrical resistivity of vanadium and vanadiumchromium solid solutions," Physica 28, No. 4, 453-60 (Apr I962)

.

Westlake, D. G. , "Anomalies in the physical properties of vanadium. The role of hydrogen,"

Phil. Mag. 16, No. 143, 905-8 (Nov I967).

Westlake, D. G. , "A resistometric study of phase equilibria at low temperatiires in the vanadium-hydrogen system," Trans. Met. Soc. AIME 239, No. 9, 1341-4 (Aug 1967).

Westlake, D. G. , and Alfred, L. C. R. , "Determination of the Debye characteristic temperature

of vanadium from the Bloch-Gruneisen relation," J. Phys. Chem. Solids 29, No. 11, 1931-4

(Nov 1968).

White, G. K. , and Woods, S. B. , "Low temperature resistivity of transition elements - vanadium,

niobium, and hafnium," Can. J. Phys. 35, 892-9OI (1957)-

White, G. K. , and Woods, S. B. , "Electrical and thermal resistivity of the transition elements

at low temperatures," Phil. Trans. Roy. Soc. London A251 No. 995, 273-302 (1959)-

63
(page 2 of 7) Electrical Resistivity of Vanadlimi Cryogenic Data Memorandum No. M-3I

Other References :

Blades, J. D. ^ Gerber, J., and Thompson, C. T., "Initial studies of the preparation and

properties of vanadium thin films," Solid State Electron. 1, No. k , 319-22 (1960) Office of Naval Research, Washington, D. C, Symposium Rept. No. ACR-50, 121-29 (May I960) DDC AD 2^1.6 916.

Bridgman, P. W. , "The resistance of 72 elements, alloys and compounds to 100,000 kg/cm ," Proc. Am. Acad. Arts Sci. 8I, No. k, I69-25I (Mar 1952).

Engelhardt, J. J., Webb, G. W. , and Matthias, B. T., "Superconductivity and the d-shell,"

Science 155, No. 3759, 191-3 (Jan 1967)

.

Frerichs, R. , and Kircher, C. T., "Superconductive fi3-ms of the transition metals, niobium,

titanium and vanadium made by 'protected sputtering'," Low Temperature Physics LT 8, Proc. 8th Intern. Conf. on Low Temp. Phys., London, I962, 376-77 (I963) Butterworths , Washington,

D. C.

Martin, R. B., and Rose-Innes, A. 0., "Superconductivity of vanadium," Phys. Letters I9,

No. 6, i^67-69 (Dec 1965).

Meyers, L., and Little, W. A., "Apparent lack of long-range order in superconducting vanadium,"

Phys. Rev. Letters I3, No. 11, 325-27 (Sept 1964).

Noer, R. J., and Knight, W. D. , "Nuclear magnetic resonance and relaxation in superconducting

vanadium," Rev. Mod. Phys, 36, No. 1, 177-85 (Jan 196k).

Sirota, N. N., Ovseichuk, E. A., and Stribuk, E. K. , "Effect of the degree of deformation on

the superconducting properties of niobium and vanadium," Soviet Phys. Doklady 11, No. 11, 976-8 (May 1967) Transl. of Dokl. Akad. Nauk SSSR I7I, No. 1, 88-90 (Nov I966)

.

Smirnov, Yu. M. , and Finkel, V. A., "Crystal structure of tantalum, niobium and vanadium at 110 - too K," Soviet Phys. JETP 22, No. k , 750-3 (Apr I966) , Transl. of Zh. Eksperim. I Teor. Fiz. 49, 1077-82 (Oct 1965).

Suits, J. C, "Vanadium films evaporated onto liquid-He -cooled substrates in ultra-high

vacuum," Natl. Symp. Vacuum Technol. Trans. 9, 74-80 (1962)

.

Suzuki, H. , Minomura, S., and Miyahara, S., "Effect of pressure on the anomaly of vanadl\im,"

J. Phys. Soc. Japan 21, No. 10, 2089 (Oct I966)

.

Thompson, C. T., and Gerber, J. F., "A note on superconducting vanadium thin films,"

Burroughs Corp., Paoli, Pa. Rept. No. TR61-20 (Mar I96I) Contr. No. NONR-214500, k pp

DDC AD 253 747.

Van Gijrp, G. J., "The effect of structure on the superconducting properties of vanadium and niobium foils," Philips Res. Repts. 22, No. 1, IO-35 (Feb I967)

.

Comments

The data for this graph were taken from the references cited above under "Sources of Data" and are presented here as ratios of electrical resistivity with respect to the resistivity

at the ice point temperature (P273). When the actual values of pgyg for the samples used

by the several investigators were not available, a datum value reported by Taylor and Smith

(1962) (p273 = (19.54 ± 0.2) X 10"^ ohm cm) is suggested for calculating values of electrical

resistivity from these ratios. These data should not be extrapolated to temperatiires below

5.03 K as vanadium becomes superconducting around that temperature.

6k
Electrical Resistivity of Vanadium (page 3 of T) Cryogenic Data Memorandum Wo. M-3I

In instances where data points were quite widely separated or areas where data did not exist,

symbols were used to show the available data points so that the reader will know where arbitrary position or shape of the graph was made.

Brief descriptions of sample preparation, purity, etc. for each data source follow in chronological order.

Meissner and Voigt (1930) used a 99-79fo pure vanadiim rod whose cross section was 2 mm x 2 mm

and whose length was 19.5 nnn.

Meissner and Westerhoff (1933) made three sets of resistance measurements. Only one set of data is presented in the tables. Their sample was a 99'3^o pure vanadium rod which had been

pulled from a melt. No further information is given about the sample.

Potter (1941) measured resistance of a specimen about 0.6 mm square and 6 mm long. The resistivity at 273 K is roughly estimated to be l8.2 x 10~® ohm cm.

In White and Woods (1957^ 1959), two of the samples (V2 and V4) were ~99>9/o pure vanadium

rods with 3-55 nim diameters. One of these {yk) had been annealed at 1300°C in vacuo. A third sample (Vl) was 99-7^o p\H"e vanadium foil of O.OOO5 in. thickness which was rolled into

a "rod" about I-I/2 in. long with an effective cross -sectional area determined by weighing

to be 0.0037 cm^ . The change of slope of the curve at about 200 K may be connected with an appreciable oxygen content. The residual resistivity, Po , for each of the three samples was:

Sample Po , 10"^ ohm cm

VI 2.97 V2 3.10 V3 ^-83

The values in the table are compiled from the experimental data.

Loomis and Carlson (1959) made electrical resistivity measurements on bomb-reduced vanadium

samples of 99 .'J'^o purity. The cold rolled bars were recrystallized by annealing at 900°C for

5 hours in vacuo. These samples had an average grain diameter of 0.04 mm. They found a discontinuity in the data at ~ 193 K.

The Hren and Wayman (1960) specimen was a 99'li' pure coiled wire with a 0.025 in. diameter

and an 8 cm length. Measurements were made on specimens; l) with no heat treatment of sample,

2) after annealing at 950 °C, and 3) after vacuum degassing at 1500°C. The tabular values

were taken from their graph.

Burger and Taylor (1961) used 99'9fo pure vanadium specimen. No further information about

the specimen is given. The absolute value of the resistivity is only accurate to ± ^<fo.

Taylor and Smith (1962) had specimens of approximately lOmmxlmmxlmm which were annealed at 800°C for 5 hours in a vacuum of about 10"^ mm Hg and quickly cooled. Their

purities follow:

Sample fo Purity

J.M. 99.63

U.S. B.M. 99.85

B.M.I. 99.92

The resistivity data are believed to be accurate to roughly ifo. An anomaly in the temperature dependence of the resistivity of vanadiiim was found at 225, 226, and 227 K for specimens

B.M.I. , J.M. and U.S. B.M.

The "ideal" resistivity values tabulated in the lower right-hand corner of the graph were taken from Meaden (1965). His book presents a comprehensive review of the literature dealing

with experimental determinations of electrical resistivity together with a relatively concise

accoimt of the modern theory of the electrical resistance of metals and alloys.

65
(page 4 of 7) Electrical Resistivity of Vanadium

Cryogenic Data Memorandum Wo. M-31

Smirnov and Finkel (1966) used polycrystalline samples in the form of strips or plates, 0.1

to 0.3 mm thick. Sample VI had a purity of 99-74^0; sample V2 had a purity of 99.20'/o. A transition of the second type was observed at 195 and 23O K for VI and V2, respectively.

Amitin, Kovalevskaya and Kovdrya (1967) report resistivity ratios for two samples. Sample 1 was polycrystalline, 99.63'/o pure vanadium, with dimensions I3.I x 3-7 x 0.8 mm. It was annealed at r^ 10" "^ mm Hg vacuum at 850°C for five hours prior to measurements. Sample 1 has

pg7 3 /po = 11.5. Wo information is given for Sample 2 except that P373/P0 = 15- for Sample 1 are tabulated. Only data

Westlake (1967) and Westlake and Alfred (1968) report resistivity measurements on a 99 •977^0 pure strip, 60 mm long, 4.2 mm wide, and 0.4 mm thick. This sample was annealed in a dynamic vacuum of 2 x 10"^ torr for 30 min. at 1073 K. Westlake 's Phil. Mag. article states that anomalies similar to those reported by previous investigators were found In the samples having

hydrogen present. He suggests that many of the anomalies reported by previous Investigators may be attributable to hydrogen content In the sample. The data In the table are for hydrogen-free vanadium.

Tables of Values of Electrical Resistivity

p = resistivity, (ohm cm); R = resistance, (ohm);

P273 = resistivity at 273 K, (ohm cm).

1^273 = resistance at 273 K, (ohm) .

Melssner and Voigt (1930)

Temp. K

R/R2 73

1.25

1.37 4.21

20.45

77.59 83.57 273.16*

0.429 0.511

0.555 0.9540

0.9674

0.9683

1.0

* ps7s = 17 X 10"^ ohm cm.

Melssner and Westerhoff (1933

)

Temp. R/Rs73 K

<4.30 superconducting

4.30 1.7 X

10"^ 4.31 2.9 X 10"^ 4.33 3.1 X 10" = 4.36 3.6 X 10"= 4.39 3.8 X 10" = 4.41 3.7 X 10" = 20.4 3.05 X

10"= 77.5 0.l62s 273.16 1.0

Potter (1941)

Temp. R/^73

K

14* 0.326

20* 0.328

77* 0.421

90* 0.455

173 0.71

273** 1.0

* Experimental values were taken

at these temperatures

.

** Estimated pg^g = l8.2 x 10"® ohm cm.

Rostoker and Yamamoto (1955)

(read from graph)

Temp. K

R , ohms R/R3 73*

221

233

253

273

0.0334

0.0347

0.0373 0.0397

0.841 0.874

0.940

1.0

* These values "were not plotted on

the Electrical Resistivity of Vanadium graph.
Electrical Resistivity of Vanadium

Cryogenic Data Memorandum No. M-31

(page 5 of 7)

White and Woods (l957j 1959)

Temp. Ideal resistivity Resistivity P/PS73 K Pi X 10® ohm cm P = Po + Pi where the average

Po = 3'63 X 10"^ ohm cm

15 O.OI4 3.6^1^ 0.166

20 0.037 3.667 0.167

25 0.076 3.706 0.169

30 O.I4 3.77 0.172

ko 0.3e 4.01 0.183

50 0.75 4.38 0.200

60 1.2v 4.90 0.223

70 1.9o 5.53 0.252

80 2.^ 6.28 0.286

90 3.5o 7.13 0.325

100 k.3 7.93 0.362

120 6.0 9.63 0.439

140 7.75 11.38 0.519

160 9.5 13.13 0.599

180 11.2 14.83 0.676

200 12.9 16.53 0.754

220 l'+.5 18.13 0.827

250 16.65 20.28 0.925

273 18.3 21.93 1.0

Loomis and Carlson (1959)

(read from graph)

Temp. Resistance K/R2 73 K R X 10^ ohms

83 0.6 0.040

93 1.2 0.080

133 4.0 0.267

173 7.2 0.480

193 8.8 0.587

199 11.0 0.733

233 13.0 0.867

273 15.0 1.0

Hren and Wayman (1960)

(read from graph)

Temp. K

Resistivity

p X 10® ohm cm

P/PS73

126

160

200

240 273

13.8

17.0 20.6

23.8

26.4

0.523 0.644

0.780 0.901

1.0

Burger and Taylor (1961)

(read from graph)

Temp. Resistivity P/P3 73* K p X 10® ohm cm

225 18.57 0.807

230 19.10 0.830

235 19.60 0.852

240 20.08 0.873

245 20.55 0.893

273 23.0 1.0

* These v alues were not plotted on the

Electri cal Resistivity of Vanadium

graph.

67
(page 6 of 7) Electrical Resistivity of Vanadium

Cryogenic Data Memorandum No. M-31

Taylor and Smith (1962)

Temp. KResistivity

p X 10® ohm cm

PS73

Sample J.M. Sample B.M.I. Sample U.S.B.M. J.M. B.M.I. U.S.B.M.

20

77 273

4.00 + 0.06

6.48 ± 0.1

22.67 ± 0.38

0.74 ± 0.01

3.18 ± 0.03 19.54 ± 0.20

1.56 ± 0.03

3.98 ± 0.07

20.34 ± 0.31

0.176

0.286

1.0

0.0379

0.163

1.0

0.0767

0.196

1.0

Smirnov and Fihkel (1966)

(read from graph)

Temp. r(t) - r(ij.o k)* K R(110 K) VI V2

110

125 0.1 0.1

150 0.32 0.32

175 0.53 0.56

200 0.72 0.74

225 0.9 0.92

250 1.04 1.13

273 1.18 1.3

*These data were not plotted on the Electrical Resistivity of Vanadium

graph

.

Amltln, Kovalevskaya and Kovdrya (I967)

(read from graph)

Temp. P/P27S* K

Sample 1

20 0.09

50 0.11

100 0.30

150 0.51

200 0.72

250 0.92

273 1.0

* p273 = 24.1 X 10"® ohm cm.

Westlake (I967) and Westlake and Alfred (1968)

Temp. Ideal resistivity Resistivity P/Pe73 K Pi X 10® ohm cm P = Po + Pi where

Po = 1.0 X 10~® ohm cm

8.0 _ 1.0 0.0488

20.0 - 1.0 .0488 22.0 0.04 1.04 0.0507

56.0 1.08 2.08 0.101

59.0 1.24 2.24 0.109

115.6 6.04 7-04 0.343

134.4 7-75 8.75 0.427

169.8 10.91 11.91 0.581

191.0 12.74 13.74 0.670

198.3 13.40 14.40 0.702

213.5 14.67 15.67 0.764

233-6 16.35 17-35 0.846

242.6 17-08 18.08 0.882

260.8 18.52 19.52 0.952

270.0 19.27 20.27 0.989

273-0 19-5 20.5 1.0

68
Electrical Resistivity of Vanadium

Cryogenic Data Memorandum No. M-3I

(page 7 of 7)

TEMPERATURE , "R

20 40 60 80 100 400 600

cvi

oc.

co

CO

<

o

a:

h-oLU

8 10 20 40

TEMPERATURE, K

80 100 400

69

CRYOGENIC DATA MEMORANDUM

PROJECT NO. 2750422 FILE NO. M-32

ELECTRICAL RESISTIVITY OF ZINC, Zn (page 1 of (Atomic Number 30)

Sources of Data:

Aleksandrov, B. W. , "Size effect in electrical resistivity of high-purity metals/' Soviet

Ehys. JETP I6, No, 2, 286-94 (Feb I963).

Aleksandrov, B. N., and D'Yakov, I. G. , "Variation of the electrical resistance of pure metals with decrease of temperature/' Soviet Fhys. JETP I6, No. 3, 603-O8 (Mar I963)

.

Bridgman, P. W. , "The effect of pressure on the electrical resistance of single metal crystals

at low temperature/' Proc. Am. Acad. Arts Sci. 68, 95-123 (1933).

Collings, E. W. , Hedgcock, F. T. , and Muir, W. B. , "Influence of spin ordering on the low

temperature magnetic and electrical properties of the Zn-Mn system, " Low Temperature Physics

LT 8, Proc. 8th Intern. Conf. on Low Temp. Phys . , London, I962, 253-54 (1963) Butterworths

,

Washington, D. C.

Goens, E. , and Gruneisen, E., "Elektrizitats und warmeleitimg in zink und cadmiumkristallen,"

(Electrical and thermal conductivity in zinc and cadmium crystals), Ann. Physik 14, l64-80

(1932).

Gruneisen, E. , "Metallische leitfahigkeit," (Metal conductivity), Handbuch Der Physik I3 , 1-75 (1928).

Gruneisen, E., and Goens, E., "Untersuchimgen an metallkristallen. II. Spezifische warme und elektrischer widerstand von zink und cadmium," (Studies with metal crystals. II. Specific

heat and electrical resistivity of zinc and cadmium), Z. Physik 26, 250-73 (1924).

Holborn, L. , "Uber die abhangigkeit des widerstandes reiner metalle von der temperatur,"

(About the dependence of resistance of pure metals on the temperature), Ann. Physik 59 j 145-69 (1919).

Jaeger, W. , and Diesselhorst, H. , "Warmeleitung elektricitatsleitung, warmecapacitat und

thermokraft einiger metalle," (Heat conduction, electrical conductivity, specific heat and thennal power in metals), Wiss. Abhandl. Physik. -Tech. Reichasanstalt 3) 269-424 (19OO)

.

Meaden, G. T., Electrical Resistance of Metals , Plenum Press, New York (1965) 2l8 p.

Meissner, W. , "Widerstand von metallen bei der temperatur des flussigen heliums," (Resistance

of metals at the temperature of liquid helium), Z. Instrumentenk. 46, IO3-5 (1926).

Meissner, W. , "Messungen mit hilfe von flussigem helium. 2. Widerstand von gold, zink,

cadmium, platin, nickel, eisen und silber bis herab zu I.3 degrees abs," (Measurement with

the help of liquid helium. 2. Resistance of gold, zinc, cadmium, platinum, nickel, iron and silver down to about I.3 K) , Z. Physik 38, 647-58 (1926) Abbreviated version appearing

in Physik. Z. 27, 725-30 (1926)

.

Meissner, W. , and Voigt, B. , "Messungen mit hilfe von flussigem heliian. XI. Widerstand

der reinen metalle in tiefen temperaturen , " (Measurements using liquid helium. XI. Resistance of pure metals at low temperatures), Ann. Physik T, No. 5j 761-97 (1930).

Pawlek, F., and Rogalla, D. , "The electrical resistivity of silver, copper, aluminium, and

zinc as a function of purity in the range 4-298 K," Cryogenics 6, No. 1, 14-20 (Feb I966)

.

Pawlek, F., and Rogalla, D. , "Der elektrische widerstand von silber, kupfer, aluminium,

zink und natriian zwischen 4 und 298 K in abhangigkeit von den verunreinigungen," (Electrical

resistance of silver, copper, aluminum, zinc and sodium between 4 and 298 K in dependence

of the imp\arities), Metall 20, No. 9, 949-56 (I966).

71
(page 2 of 8) Electrical Resistivity of Zinc

Cryogenic Data Memorandum No. M-32

Schimank, H. , "Uber das Verhalten des elektrlschen widerstands von metallen bei tiefen

temperaturen," (The behavior of the electrical resistance of metals at low temperature),

Ann. Physik k3_, 706-36 (191*+).

Tuyn, W. , "Measurements on the electrical resistance of some metals below the boiling point

of oxygen/' Commun. Phys . Lab. Univ. Leiden Wo. I96B (1929) Reprinted from Proc. Kon. Ned. Akad. Wetensch. 32, 115 (Feb 1929).

Tuyn, W. , and Onnes, H. K. , "Wouvelles experiences avec 1' helium llqulde. AB. Nouvelles

mesures relatives a la resistance electrique des metaux temperatures de 1' helium liquide,"

(New experiments with liquid helium. AB. New measurements of the electrical resistance of

metals at liquid helium temperatures), Commun. Phys. Lab. Univ. Leiden No. I8I (1926)

,

Reprinted from Arch. Neerl. Sci. IIIA 10, 5-^1 (1926).

Wilkes, K. E, , Powell, R. W. , and DeWitt, D. P., "Thermal conductivity measurements on cobalt and zinc between 78 and 373 K," Thermal Conductivity (Proceedings of the Conference

8th, Purdue Univ., Lafayette, Ind. , Oct 7-10, I968) C. Y. Ho, et al., Eds, Plenum Press, New York (I969) PP 3-7-

Other References:

Aleksandrov, B. N. , "Effect of dimensions and purity on the electrical resistance of metals

in a longitudinal magnetic field at (liquid) helium temperatures," Soviet Phys. JETP I6,

No. k, 871-8 (1963) Transl. of Zhur. Eksptl. I Teoret Fiz. k3, 1231-^1 (I962).

Alers, P. B. , Spohr, D. A., and Webber, R. T., "The thermal conductivity of metals," Bull. IR Annexe 1955-3 (Presented at Conf. de Physique des Basses Temperatures, Paris, Sept. 2-8,

1955) 3 pp.

Amonenko, V. M. , Kruglykh, A. A., and Paperov, I. I., "Production of zinc of high purity

and method of purity control," Fiz. Metal. I Metalloved. 11, 633-35 (I961)

Beck, P. A., "Annealing of cold worked metals," Advan. Phys. 3, 2k'j>-32k (Jul IS'yh)

Boato, G., Bugo, M. , and Rizzuto, C, "The effect of transition-metal Impurities on the residual resistivity of Al, Zn, In, and Sn," Nuovo Cimento 45B, No. 2, 226-14.0 (Oct I966)

Borovik, E. S., "Change of resistance of metals in a magnetic field at low temperatures,"

Zh. Eksptl. I Teoret Fiz. 23, 9I-IOO (1952).

Bridgman, P. W. , "The resistance of 72 elements, alloys and compounds to 100,000 kg/cm^,"

Proc. Am. Acad. Arts Sci. 8I, No. k, I69-25I (Mar 1952).

Buckel, W. , and Hilsch, R. , "Influence of condensation at low temperatures on the electrical

resistance and superconduction of various metals," Z. Physik I38 , No. 2, 109-20 (l95'<-)-

Desalvo, A., Condi, P., Levi, F. A., and Zighani, F., "Purif icazione dello zinco oltre al limite di 99,999 percent E determinazlone del contenuto di impurita mediante metodi fisici,"

(Preparation of zinc of p\irity 99-999 percent and determination of the amount of impurity

hy physical methods), Metallurgia Italiana 55.J ^°' ^'^ > 511-20 (1963).

Desalvo, A., Condi, P., Levi, F. A., and Zignani, F., "Electrical conductivity of high-purity

zinc." Nuovo Cimento 3I, No. k, 904-13 (1964).

72
Electrical Resistivity of Zinc , (page 3 of Cryogenic Data Memorandum No. M-32

Dewar, J,, and Fleming, J. A., "The electrical resistance of metals and alloys at temperatures approaching the absolute zero," Phil. Mag. 36, 271-99 (1893).

Grenier, C. G. , Reynolds, J. M. , and Zebouni, W. H., "Electron transport phenomena in zinc at liquid helium temperatures," Louisiana State Univ., Baton Rouge, Interin Tech. Rept. No. 2,

(J\£L 1962) Grant No. DA-ORD-31-124-61-G76, Pro j . No. 59901004, 6I pp, NASA n62 II+966.

Haager, M. , and Siebinger, K. , "Orientation dependence of the resistivity increase due to alpha-radiation," Berg. Huettenmaenn. Monatsh. Ill , No. 3; 112-6 (1966)

.

Kan, L. S., and Lazarev, B. G. , "Effect of hydrostatic compression on the electrical con- ductivity of metals at low temperatures," Soviet Ehys . JETP 7, No. 1, I8O-8I (Jul 1958).

Lucasson, A. , and Lucasson, P. , "Experimental results obtained in low temperature electron

irradiation of Pd, Mo, Zn and alpha-U," J. Phys. Chem. Solids 27, No. 9, li).23-9 (Sep I966)

.

Luthi, B. , "Longitudinal magnetoresistance of metals in high fields," Phys. Rev. Letters 2,

503-I1 (1959).

Luthi, B., "Widerstandsanderung von metallen in hohen magnetfeldern , " (Resistance of metals

in high magnetic fields), Helv. Phys. Acta 33, I6I-82 (1960).

Onnes , H. K. , and Tuyn, W. , "Data concerning the electrical resistance of elementary sub- stances at temperatures below -80°C," Commun. Phys. Lab. Univ. Leiden Suppl. No. 58 (1926) 88 pp.

Schofield, F. H. , "The thermal and electrical conductivities of some pure metals," Proc. Roy. Soc. (London) AIO7 , 206-27 (1925).

Skove, M. J., and Stillwell, E. P., "Size effects in residual resistance ratios for zinc whiskers," Appl. Phys. Letters 7, No. 9, 2hl-2 (Nov I965).

Comments

:

The data for this graph were taken from the references cited above under "Sources of Data" and are listed as ratios of electrical resistivity with respect to resistivity at the ice point temperatixre (pg73). Since zinc is an anisotropic metal, we list suggested values of

Ps73 for Zn II , Znl , and polycrystalline zinc to be used in calculating electrical resistivity from the ratios if the p273 is not stated by the author. These values are:

p(ll )273 = 5-589 X 10"® ohm cm, p(l )s-js = 5 .386 X 10~® ohm cm, and

p , = 5 '^6 X 10"^ ohm cm. poly

The first and second values are from Bridgman (1933) and the third value was calculated from

their data using Voigt's equation:

1 ["j^ ^]

3 [P'l "^ P-L P(poly) J

It should also be noted that zinc becomes superconducting at O.85 K.

73
(page k of 8) Electrical Resistivity of Zinc

Cryogenic Data Memorandum No. M-32

In instances where data points were quite widely separated or areas where data did not exist,

symbols were used to show the available data points so that the reader will know ^ere

arbitrary position or shape of the graph was made.

Brief descriptions of sample preparation, purity, etc. for each data source follow in chronological order.

Jaeger and Diesselhorst (I9OO) used a 99.97fo pure zinc rod with dimensions I.805 cm diameter

and 27 cm length. The wire was made from the same starting material. There were no measurements below 0°C.

Schimank (191^) measured the resistance of an extruded, polycrystalline wire. No further Information is given for the sample

.

The Holbom (1919) samples were 0.25 ram diameter wires which had been annealed at 200 and

300 °C. The impurities are < O.Olfo.

Meissner (I926) (the Z. Instrumentenk. article) measured conductivities of a single crystal

sample both parallel and perpendicular to the principle axis. The sample was 99 • 99^0 pure.

Meissner (I926) (the Z. Ehysik article) reported resistance measurements for three samples. The Zn II measurements were made on a single crystal, O.7 mm diameter and 5 cm length, with

its orientation parallel to the hexagonal axis. The Zn J. measurements were for a single

crystal, O.9 mm diameter and 12 cm length, with its orientation perpendicular to the hexagonal

axis. Zn(poiy) was a drawn polycrystalline wire, 0.25 ram diameter and 12 cm length, which

was annealed at 200 °C for 3 hours before measurements were made

.

The Grimeisen and Goens (l92it) measurements were taken with both orientations, parallel and perpendicular to the hexagonal axis. No information is given on shape or heat treatment

of the sample. The samples were of high purity.

Tuyn and Onnes (1926) measured resistances of a wire specimen with impurity content < 0.01^. The specimen was heated for a period of time in the temperature range of I50 to 200 °C.

Tuyn (1929) used the same specimen described by Tuyn and Onnes (I926), designated Zn-1921-I. Another specimen was prepared in the same way, designated Zn-1921-II.

Meissner and Voigt (193O) used Kahlbaxmi zinc, assuming high purity, to make the single

crystal samples. The dimensions were 0.7 mm in diameter and 55 mm long for Zn II , and

1.3 mm diameter and 55 nim long for ZnX.

Goens and Gruneisen (1932) measured resistivities of pure, undeformed single crystal rods. In the actual measurements, the samples' crystal axes were at 3-6°, ^+.9°, 8.7°, and 79-7°

to the current direction. The values in the table are resistivities extrapolated to the parallel and perpendicular orientations

.

Bridgman (1933) determined the effect of pressure on resistivity. The values in the table,

however, are his measurements at zero pressure. The crystals were made from spectroscopically piore zinc which was filtered in the molten condition and thoroughly outgassed in a diffusion pump vacuum. The single crystal samples were 1 mm diameter rods , approximately

2.5 cm long, which were cast in pyrex tubing by slow lowering out of a furnace. The measurements were made perpendicular and parallel to the hexagonal axis

.

Aleksandrov (1963) and Aleksandrov and D'Yakov (1963) report measurements on single crystals,

4 mm in diameter and 200 mm in length, which were grown from seeds in graphite forms by zone melting. The specimens were annealed 1 to 2 days at 100 to 120 °C prior to measuring

resistivities.

Collings, Hedgcock and Muir (1963) measured resistances for pure zinc. No details are given on preparation of sample.

7h
Electrical Resistivity of Zinc

Cryogenic Data Memorandum No. M-32

(page 5 of 8)

The "ideal" resistivity values tabulated in the lower right-hand corner of the graph were taken from Meaden (1965). His hook presents a comprehensive review of the literature

dealing with experimental determinations of electrical resistivity together with a relatively

concise account of the modem theory of the electrical resistance of metals and alloys.

Pawlek and Rogalla (1966) used 99'99595'o pure zinc wires with 2 mm diameters "which were annealed one hour in argon at 200 °C prior to measurements

.

Wi3J£es, Powell, and De Witt (1968) used a 99>999/o pure rod which was 1.207 cm in diameter

and 10.16 cm long. No further information is given for the sample.

Tables of Values of Electrical Resistivity

p = resistivity, (ohm cm); R = resistance, (ohm);

P273 Rs73 resistivity at 273 K, (ohm cm) resistance at 273 K, (ohm).

Schimank (191^) Holborn (1919

)

Temp. K

R/R2 7

3''^ Temp. K

-VR2 73*

20.2

82.0 195-3

273.09

0.015!^. 0.2185 0.6982

1.0

80.5 194.8

273

0.2180 0.6856

1.0

* These values were not plotted on the Electrical

Resistivity of Zinc graph. * These values were not plotted on the Electrical

Resistivxxy 01 ZiXnc grapii.

Gruneisen and Goens (1924)

Temp. P/PS7S** K

Zn 1 Zn II

20.37 0.0074l 0.00757 78.6 - 0.215

81.3 0.207 - 82.0 0.211 0.227

84.0 - 0.236b 89.7 0.246 0.260

130 0.409 0.418

195 0.684 0.681

273 * 1.0 1.0

* For Zni, p273 = 5-39 x 10"^ ohm cm; Zn 11 , Ps73 = 5.83 X 10 ^ ohm cm. ** These values were not plotted on the Electrical Resistivity of Zinc graph.

Meissner (1926)

(The Z. Rhys ik article)

Temp. K

R/Rs73

Znll Zn 1 Zn (poly)

1.67 O.OOI8I3 0.00316 . 4.14 - - .00491 4.20 - 0.00317 - 4.21 .001833 - - 20.42 - - 0.01138

20.45 0.008736 0.00905 - 82.48 - - 0.2254

83.74 0.2351 0.2195 - 273.20 1.0 1.0 1.0

75
(page 6 of 8) Electrical Resistivity of Zinc

Cryogenic Data Memorandiim No. M-32

Meissner (1926)

(the Z. Instrumentenk. article)

Temp. KResistivity

p X 10^ ohm cm P/PS73*

Zn 11 Znl Zn II Zn ±

22.2 89.7

273.2

0.0788

1.52

5.82

0.0524

1.33

5.38

0.0135 0.261

1.0

0.00974

0.247

1.0

* These values were not plotted on the Electrical Resistivity

of Zinc graph.

Tuyn and Onnes (1926)

Temp. K

R/Rs73

1.40

3.38 4.22 273.09

0.00656

0.00656

0.00656

1.0

Tuyn (1929)

Temp. K

r/Rs 73

Zn-1921-I* Zn-1921-II

1.40 0.00378 _ 4.22 0.00378 - 14.24 0.00838 0.00738

16.45 .00984 0.00875

17.99 0.01119 0.01006

20.485 .01383 0.01278

57.83 0.12552 - 57.86 - 0.12505

66.10 0.15901 0.15838

72.71 0.18643 0.18581

81.04 0.22136 0.22078

88.72 0.25367 0.25300

* The v£ lues for Zn-1921-I were plotted

on the Electrical Resistivity of Zinc

graph.

Meissner and Voigt (1930)

Temp. K

1^/1^2 73 Zn II ** Zn 1

1.67 .OOI8I3 .00174d 4.21 0.001833 0.001752 20.42 - 0.00750

20.45 0.008736 - 82.47 - 0.2141

83.73 0.2351 - 273.16* 1.0 1.0

* For Zn II , P273 = 5.99 x 10"^ ohm cm; Znl , P273 = 5.65 X 10~® ohm cm. These are calculated values

.

** The Zn II values were not plotted because they are identical to the Meissner (1926) (Z. Ehysik) values.

Goens and Gruneisen (1932)

Temp. K

Resistivity

p X 10® ohm cm

p/Pe73 ^

Zn II Zn 1 Zn II Znl

2183

273

293

0.044b

1.293 5.57 * 6.05

0.0366

1.155 5.4 *

5.83

0.00806

0.232

1.0

.00678 0.214

1.0

* Interpolated values. ** These values were not plotted on the Electrical

Resistivity of Zinc graph.

76
Electrical Resistivity of Zinc

Cryogenic Data Memorandum No. M-32

(page 7 of 8)

Bridgman (1933)

Temp. K

p/pa73** Zn II Zn 1

90.35

194.85 273.15*

0.3047

0.6807

1.0

0.2459 0.6794

1.0

* For Zn II , payg = 5.589 x 10"® ohm cm; Znl , Ps73 = 5.386 X 10"® ohm cm. ** These values were not plotted on the Electrical Resistivity of Zinc graph.

)

Aleksandrov (1963) and Aleksandrov and D'Yakov (1963)

1 Temp. P/P293* Resistivity P/P2 73 K p x 10® ohm cm

Zn II Zn ± Zn II Zn 1 Zn II Zn 1

1.6 -1.1x10"^ -1.1x10"^ .000068 0.000064 0.0000119 0.0000118

4.22 1.4x10"^ 1.6x10"^ .000086 0.0000935 0.0000151 .0000173 14 1.13x10"^ 1.08x10"^ 0.00695 0.0063 0.00122 0.00117

20.4 6x10" 2 4.96x10"^ 0.0369 .0289 0.00647 0.00535

58 0.120 0.103 0.738 0.70 0.129 0.130

63.5 0.137 0.121 0.842 0.80 0.148 0.148 11-^ 0.195 0.180 1.20 1.05 0.211 0.194

90.31 0.238 0.227 1.465 1.32 0.257 0.244

111.6 0.325 0.318 2.0 1.855 0.351 0.344

273 ** - - 5.7 5.4 1.0 1.0

* For 1

2

Jl II , Pagg = 6.15 X

10"® nl , P293 = 5.83 X

10"® 3hm cmj Dhm cm. ** Inter polated values for this t smperature

.

Collings, Hedgcock and Muir (1963)

(read from graph)

Temp. R/Bs73* K

1 0.001

5 0.002

10 0.002

20 0.010

30 0.029

40 0.055

50 0.085

57 0.107

* These values have not been

plotted on the Electrical

Resistivity of Zinc graph.

Pawlek and Rogalla (1966)

Temp. KResistivity

p X 10® ohm cm

p/pa73

4.2

77

195

273

0.00381

1.16

4.01

5.99

.000636 0.19^

0.669

1.0

Wilkes, Powell and DeWitt (1969)

Temp. KResistivity

p X 10® ohm cm

P/Pa73*

77.8 198.7

273.2

300.9

1.187

3.745 5.56

6.129

0.213 0.674

1.0

* These values were not plotted on the Electrical Resistivity of Zinc graph.

I)

77
(page 8 of Electrical Resistivity of Zinc Cryogenic Data Memorandum EFo. M-32

TEMPERATURE, "R

ro

CVJ

o"<

>->

h-<o

to

UJ

_J<

o

tr

I-o

LU_l

UJ

2 4 6 8 10 20 40 60 80 100 200 ^00 600

1.0 1 1 1 [ 1 1 1 1 1 1 1 j^ 1 1 1 1 1 1 1 1 1 1 1 /^

ELECTRICAL RESISTIVITY RATIO

FOR ZINC

yOdOg^g = 5.589xlO'®ohm cm

p(-i-)2Ti =5.386x10" ohm cm

p{po\y)^^^= 5.46 X lO'^ohm cm

Ah y\

yi //

I

T

10- J

/

F

^ w

jj J /§ mr

/j W

Tuyn and Onnes P (oolv) \ //j

1 1 1 . 1

/ \. ///

Af

10^ -^

M

y^/A Tliun Of nnlv) ^</A/yii luy 1 y^ » K"'//

__,,,^^ y/y. r 7—— ^^^/h

--» ^^ ///L .^ > Meissner n fnolv) Jr-

. . "'' /y\ /w f- T-J-

^j

c o—" ^

\

Meissner \± )

10^ ^ / \kl^Meissner \\\) /

©-

^

—

\

\

1 III

-Pawiek and Rogalla yO(poly \

Meissner ana voigi ix; k / p„,= 5.65xl(D ohm cm p,„ = 5.99 X 10 ohm cr r273 1

1

T1 _J_

"Ideal" Resistivity*

of Zinc Aleksandrov a nH A leksan dr ov

I

10-^ -and D'Yakov (±) -

O = 54- y in nhm r

Temp. K

p, X 10^ ohm cm

' P| /P273

1j m f 20

5080 100 150

200

250 273-15

0.052

o.ks

1.16

1.6,

2.72 3.84

4.93

5.'t5

0.0095 0.0899

0.213

0.297

o.i+99 0.705

0.905

1.0

"273 \\

/

i 7

rvw 1 ^

1

/

\

Aleksandrov and

Alpkt;nnHrn\/ nnri D'VnU 1^ -fi

10^ »

*==^=" P27

1

3"

1 bY X lU oh m crTl * from Meaden (1965)

see text. 6 8 10 20 40

TEMPERATURE, K

60 80 100 200 400

78
CRYOGENIC DATA MEMORANDUM

PROJECT NO- 2750i<-22 FILE NO. M-33

ELECTRICAL RESISTIVITY OF ZIRCONIUM, Zr (page 1 of ?) (Atomic Number hO)

Sources of Data:

Adenstedt, H. K. , "Physical, thermal and electrical properties of hafnium and high piirity

zirconium," Trans. Amer. Sec. Metals kh, 9-^9-73 (1952).

Berlincourt, T. G. , "Hall effect resistivity and magnetoresistivity of Th, U, Zr, Ti, and Nb,"

Phys. Rev. 114, No. h, 969-77 (1959).

Clausing, P., "Over den electrischen weerstand van zirkoon," (The electrical resistance of zirconium), Physica h, 372-5 (1924).

Clausing, P., and Moubis, G. , "Over den electrischen weerstandvan titaan en zirkoon bij lage

temperaturen , " (The electrical resistance of titanium and zirconium at low temperatures),

Physica 7, No. 7, 2^5-50 (1927).

Clinard, F. W.-, and Kempter, C. P., "Low-temperature electrical properties of some transition metals and transition-metal carbides," J. Less-Common Metals 15_, No. 1, 59-73

(May 1968).

De Haas, W. J., and Voogd, J., "The change of the electric resistance of pure hafnium and zirconium between I.3 K and 90 K," Communs . Phys. Lab. Univ. Leiden No. 194c (1928) , Transl. of Verslag Gewone Vergader. Afdeel. Katuurk. Koninkl. Ned. Akad. Wetenschap. 37, 872-4

(Nov 1928)

.

Kemp, W. R. , Klemens, P. G», and White, G. K. , "Thermal and electrical conductivities of iron, nickel, titanium, and zirconium at low temperatures," Aiistralian J. Phys. 9^ I8O-88

(J\in 1956).

Mc Lennan, J. C, Howlett, L. E., and Wilhelm, J. 0., "On the electrical conductivity of certain metals at low temperatures," Trans. Roy. Soc. Can. Sec. Ill, 23, Part I, 287-306

(Jan 1929)

.

Meaden, G. T. , Electrical Resistance of Metals , Plenum Press, New York (1965) 2l8 p.

Meissner, W. , and Voigt, B. , "Messungen mit hilfe von flussigem helium. XI. Widerstand der reinen metalle in tiefen temperaturen," (Measurements using liquid helium. XI. Resistance

of pirre metals at low temperatures), Ann. Physik 7, No. 5, 892-936 (l930).

Potter, H. H. , "Electrical resistance and thermoelectric power of the transition metals,"

Proc. Phys. Soc. (London) 53, 695-705 (l9^l)

.

Renucci, L. , Langeron, J. P., and Lehr, P., "Etude de la resistivite electrique du zirconium.

Application a 1 'etude de la recristallisation du metal apres ecrouissage. Influence de la purete," (Electric resistivity of zirconium. Application to the study of the recrystallization of the metal after cold working. Influence of purity), Mem. Sci. Rec. Met. 58, 699-715

(1961).

Roberts, L. D. , Sartain, C. C, and Dabbs, J. W. T., "Electrical resistance of high-purity

zirconium below 3OO K," Oak Ridge National Lab., Oak Ridge, Tenn. , Progr. Rept. ORNL-I365

(June 1952).

White, G. K., and Woods, S. B. , "Electrical and thermal resistivity of the transition

elements at low temperatures," Phil. Trans. Roy. Soc. London A25I No. 995, 273-302 (1959)-

79
(page 2 of T) Electrical Resistivity of Zirconium

Cryogenic Data Memorandum No. M-33

Other References ;

Bridgman, P. W. , "The electric resistance to 30,000 k^cm of twenty nine metals and intermetallic compo\uids," Proc. Am. Acad. Arts Sci. 79, 1^9-79 (1951).

p Bridgman, P. W. , "The resistance of 72 elements, alloys and compounds to 100,000 k^cm ," Proc. Am. Acad. Arts Sci. 8l, No. k, I69-25I (Mar 1952).

Brehm, C, and Lehr, P., "Influence de la deformation par traction du zirconiiim et du titane

sur la resistivite residue3JLe et sur la densite de dislocations," (Effect of zirconium and

titanium tensile deformation on the residual resistivity and dislocation density), Compt. Rend. Ser. C 265, No. I8, 974-6 (1967).

De Boer, J. H., and Fast, J. D. , "Uber die darstellung der reinen meta]J.e der titangruppe

durch thermische zersetzimg ihrer jodide. III. Hafnium," (Concerning the preparation of pure

metals of the titaniian group by thermal dissociation of their iodides. III. Hafnium), Z. Anorg. Allgem. Chem. I87, 193-208 (1930).

Fehlner, F. P., "Behavior of \iltrathin zirconium films upon exposure to oxygen," J. Appl.

Phys. 38, No. 5, 2223-31 (Apr I967)

•

Finch, R. A., "Measurement of resistivity and heat capacity of metallic conductors," North

American Aviation, Inc., Canoga Park, Calif., Rept. No. NAA-SR-MEMO-5819 (1960) 26 pp.

Renucci, L. , Langeron, J-P. , and Lehr, P., "Sur la conductibilite electrique a basse

temperature du zirconiiim de zone fondue," (On electrical conductivity of zone melted

zirconium at low temperatures), Compt. Rend. 2l+9, No. I3, III3-I5 (Sept 1959).

Swanson, M. L. , "Low temperature recovery of deformed zirconium," Can. J. Phys. hk, No. 12, 3241-57 (Dec 1966).

Swanson, M. L. , Quenneville, A. F., and Schultz, H. , "Stage 1 recovery of deformed zirconium,"

Appl. Phys. Letters 6, No. 3, 4-9-51 (Feb I965).

Comments

;

The data for this graph were taken from the references cited above under "Sources of Data" and are listed as ratios of electrical resistivity with respect to the resistivity at the

ice point temperature (pays). When the actual values of Pg^s are not available for the samples used by the various Investigators, a datum value reported by White and Woods (1959)

(p273 = 38.85 X 10"^ ohm cm) is suggested for calciilating values of electrical resistivity

from these ratios. It should also be noted that zirconium becomes superconducting at O.56 K.

In instances where data points were quite widely separated or areas where data did not exist,

symbols were used to show the available data points so that the reader will know where arbitrary position or shape of the graph was made.

Brief descriptions of sample preparation, purity, etc. for each data source follow in chronological order.

The Clausing (1924) sample had a purity of 99.9fo. No further information is given about

the sample.

Clausing and Moubls (1927) made three sets of measurements on three wire samples; Zr 5 was 99.88fo pure, Zr 6 and Zr 14 were both 99.97/o pure. No further information is given

about the samples

.

1
Electrical Resistivity of Zlrconiiim (page 3 of 7) Cryogenic Data Memorandum No. M-33

De Haas and Voogd (1928) measured resistances of a "very pure" zirconium rod. The rod was, however, too irregularly formed to have its specific resistance determined. No further

information is given about the sample.

Mc Lennan, Howlett, and Wilhelm (1929) used a polycrystalline wire "vrfiich had been baked in vacuo at a high temperature for a number of hours. The piority was not stated.

Meissner and Voigt (I93O) report resistance measurements on two zirconium samples. Zi 1 was a 99-69/0 pure polycrystalling wire with a 5 nun diameter. Zr 2 was a wire of unknown

purity, which had been annealed in a vacuum for 2.5 hours at 500°C.

Potter (19^+1) gave no information on the purity or preparation of the sample.

Adenstedt (1952) used three samples in his resistivity measurements. Two had resistivities

measured over a temperature range of 200 to 1000 °C, and one had resistivities measured below

0°C. The latter sample was a 0.22 in. diameter rod of 10 in. length which had been cold- swaged, machined and vacuum annealed at 7OO °C for two hours. The purity was stated to be

99 •9f'> pure zirconium.

TIhe Roberts, et al. (1952) measurements were made with a crystal bar of high purity. One set of values are for the unannealed sample and another set for the same sample after it had been pickled in an aqueous solution of nitric and hydrofluoric acids and then annealed

in. a vacuum for ijO min. at 796 ± l4°C.

Kemp, Klemens and White (1956) measvired resistivities of a 99 •99fo pure zirconium rod of

3 mm diameter, which had been annealed at 950 °C for five hours in vacuo.

Berlincourt (1959) had three crystal bar samples of ^^.Q&fo pure zirconium which had been

machined from bulk material to a thickness of O.O378 cm- No mention is made of heat treatment

.

White and Woods (1959) present tabular values of ideal resistivity for a 99>95'?^ pure zirconium sample of 0.6 mm diameter. The sample was arc cast, annealed h hours at 1100 °C, swaged at room temperature, annealed for I5 min. at 1000 °C and finally for I5 min. at 800°C

in a vacuum of (l to 2) x 10" ® mm Hg.

Renucci, Langeron and Lehr (1961) measiired resistivities of three samples. Zr 1 and Zr 2 were prepared by thermal dissociation of Zrl^ and had a purity of 99 •85/0 • Zr 1 was re- crystallized at 600 °C for a I5 hour period whereas Zr 2 was used after cold-working with

no heat treatment. Zr 3j resulting from magnesium thermal reduction of ZrCl^ , was 99-71'?^ pure and had been recrystalllzed at 700°C for I5 hours.

The "ideal" resistivity values tabulated in the lower right-hand comer of the graph were taken from Meaden (1965). His book presents a comprehensive review of the literature

dealing with experimental determinations of electrical resistivity together with a relatively

concise account of the modem theory of the electrical resistance of metals and alloys.

81
(page 4 of 7) Electrical Resistivity of Zirconium

Cryogenic Data Memorandum No. M-33

Tables of Values of Electrical Resistivity

p = resistivity, (ohm cm); pgyg = resistivity at 273 K, (ohm cm), R = resistance, (ohm); R373 = resistcince at 273 K, (ohm).

Clausing (1924)

(read from graph)

Temp. R/Rs73 K

80 0.74

100 0.775

150 0.875

200 0.92

250 0.975

273 1.0

De Haas and Voogd (1928)

Temp. r/Ro K

1.35 0.0383s

3.63 0.03836 4.21 0.0383s 14.17 0.03926 18.00 0.04039 20.32 0.04167 61.27 0.1318

78.19 0.1926

90.01 0.2379

Meissner and Voigt (1930

)

Temp. K

p/p2 73*

Zr 1 Zr 2

1.13 1.23

1.36

4.21

4.22

20.45 20.46 77.61

78.42 83.57

86.14

88.19 273.16

0.0388

0.0403

0.0421

0.04436 0.1971

0.2214

0.2380

1.0

0.108g

0.109o 0.1124

0.2648

0.2924

1.0

* For Zr 1, P273 = 60 x 10"® ohm cm, Zr 2, P273 = 49 X 10"® ohm cm.

Clausing and Moubls (1927)

Temp. K

p/pS73*

Zr 5 Zr 6** Zr 14

77. to _ _ 0.1777

78.16 0.2185 - - 78.20 - 0.2264 - 90.20 - 0.2704 - 90.22 0.2626 - - 144.8 - 0.4769 - 178.0 - 0.6084 - 217.6 - 0.7692 - 273.09 1.0 1.0 1.0

* For Zr 5, PS73 = 42.5 X 10"® ohm cm. Zr 6, Ps73 = 42.4 X 10~® ohm cm, Zr 1^^PS73 = 41.0 X 10~® ohm cm. ** Values for Zr 6 were plotted on the Electr Leal Resistivity of Zirconium | graph.

1

Mc Lennan, Howlett, and Wilhelm (1929)

Temp. K

Resistance R X 10* ohms

R/Rs73

2.4

4.2 20.6

84.0 273.1

77.9

78.1

83.0

305. 1079.

0.0722 0.0724

0.0769

0.283

1.0

Potter (1941)

Temp. K

R/R273**

2077

90 173 273*

0.0385 0.196

0.237

,0.567 1.0

* P273 = 17.1 X 10"® ohm cm. ** These values were not plotted on the Electrical Resistivity of Zirconium graph.

82
Electrical Resistivity of Zirconiiim Cryogenic Data Memorandum No. M-33

(page 5 of 7)

Adenstedt (1952)

Temp. K

P/pS73*

90 273 0.228

1.0

* P373 = 39.6 X 10~® ohm cm.

Roberts, Sartain, and Dabbs (1952)

unannealed crystal pickled and annealed crystal

Temp. KResistivity

p X 10® ohm cm

P/P273 Temp. K

R/Rs73

4.2 73.3 273.2 295.72.14 8.68

42.0 *

45.6

0.051 0.207

1.0 1.1

14.01

20.33

68.52

77.50 273.2

0.02279

0.02514

0.14076

0.17356

1.00

* Interpolated value

Kemp, KLemens and White (1956)

Temp. Resistivity P/PS73 K p X 10® ohm cm

5 2 .0445

15 2 0.0445

50 5 o.m

80 9 0.20

100 12 0.267

130 17 0.378

170 24 0.533

200 31 0.689

250 39 0.867

273 45 1.0

Berlincourt (1959)

Temp. K

Resistivity

p X 10® ohm cm

P/PS73

Zr 1 Zr 2 Zr 3 Zr 1 Zr 2 Zr 3**

4.2

77

273 298.6

300.0 300.1

0.224

6.11

37. * 42.6

0.213

6.08

37. *

42.6

0.216

6.08

37. *

42.6

0.00605

0.165

1.0

0.00576

0.164

1.0

0.00584

0.164

1.0

* Interpolated value

** The values for Zr 3 were plotted on the Electrical Resistivity of Zirconium graph.

83
(page 6 of 7) Electrical Resistivity of Zirconium

Cryogenic Data Memorandum No. M-33

White and Woods (1959)

Temp. Ideal resistivity Resistivity P/P37S K Pi X 10® ohm cm P = Pi + Po where po = 0.25 x

10" ® ohm cm

15 0.02s 0.28 0.00721

20 0.09o 0.3lj- 0.00875

25 0.23s O.lj-9 0.0126

30 0.1+, 0.72 0.0185

ho 1.2o 1.^5 0.0373

50 2.25 2.50 o.o6i+ij- 60 3.5o 3.75 0.0965

70 h.% 5.15 0.133

80 G.h, 6.65 0.171

90 7.9o 8.15 0.210

100 . 9.5b 9.80 0.252

120 12.8 13.05 0.336

ll|.0 16.0 16.25 o.in8

l6o 19.3 19.55 0.503

180 22.6 22.85 0.588

200 26.1 26.35 0.678

220 29.14- 29.65 0.763

250 34.6 3i^.85 0.897

273 38.6 38.85 1.0

Renucci, Langeron and Lehr (196I)

Temp. K ^/^73

Zr 1 Zr 2 Zr 3

k.2 Xk.O

20.

U

77.^

273

0.025

0.02511- 0.0278

0.182

1.0

0.0865

0.0870

0.0905

0.21+95 1.0

0.1785 0.1790

0.1815

O.3I160 1.0

Clinard and Kempter (1968)

(read from graph)

Temp. Resistivity P/P273 K p X 10® ohm cm

k.2 0.8 0.0205

20 1.0 0.0256

1+0 2.0 0.0513

50 3.5 .0897 100 9.8 0.250

150 18.0 0.1+62 200 27.0 0.692

250 35.0 0.897

273 39.0 1.0

81+
Electrical Resistivity of Zirconiuiu Ciyogenic Data Memorandum No. M-33

(page 7 of 7)

ro

LU

01<O

a:

I-o

UJ

_l

LU

2 4 6 8 10 TEMPERATURE

20 40

, °R

60 80 100 200 400 600

1

1 11'-^

Clausing — ^Jr""^

^,..-^ \^ A "^ /^

ELECTRICAL RESISTIVITY RATIO

FOR ZIRCONIUM

—6

/Jg.^^ =38.85x10 ohm cm

»

J /ffir /

///Mr

Renucci , Longeron orid Lehr (Zr3)N

1 \ y

/

L \

^

f

J

^

1

Mr\ Clausing and Moubis"!

1

1 Meissner and /?273=49xl( —1—1—1—

r

Voigt(Zr2

D ohm cm

)

\

k^

^73=^2.4x10 ohm cm

lo' ^^y^ Hf\/k ^^ '^/\ w

^MCLennc m -^ nK

1 1 1

1 Renucc .Longeron, and Lehr

)n, nOWicii , uriu vviirie

1 1 1 1 1 1 //, 1

^ (Zr2)

— ^ 'I

i

^De Haas> orid Voogc1 ^

\

1 1 1 1 Kemp.K emens and White

_ . -6 .

1 .\

^ p«,,= 4oxiu Ohm cm ^_-

-^^^ 1 1 1 1 1 1 \ Meissner and Voigt (Zr 1

)

10^

Cli

P273

noH

= 39 X

and

10-^

Ken

oh

npt

Tl <:m /

if. Ren

fucc

'27 3^

.an

60 X

gero

10 ohm c

n and Lehr

m

(Zr!) / /

y /\

^y^ y \

....-•-'' \

"Ideal" Resistivity*

of Zirconium A^

W iA/u:t» A \tJ«-<J. - \

VVIIIIC UIIU vvuuu^ — Tern]K

p. p, X 10^ ohm cm

Pl/pS73

BerlmcourT \ 'A/-__- 273 vJO.OvJ AIW Ulllll

1 Ulll ® , yO„ =37xl0'^c)hm cm 20

5080 100

150

200

250

273

o.09o

2.25 6.i^ ' 9-55 17.6

26.1

3i^.6 15 38.6

0.0023

0.0583 0.166

0.2i^7 0.456

0.676

0.896

1.0

' ^ f o

« )

,,-^

* from Meaden (I965) see text.

It) 1 1 \ 1 1 Mil' 1 1 1 6 8 10 20 40

TEMPERATURE, K

60 80 100 200 400

85

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