V) J

NBS SPECIAL PUBLICATION 260-62

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Standard Reference Materials:

SRM 768:

TEMPERATURE REFERENCE STANDARD

FOR USE BELOW 0.5 K
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The

Bureau's overall goal is to strengthen and advance the Nation's science and technology and

facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is performed by the National Measurement Laboratory, the National Engineering Laboratory,

and the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

Agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities2 — Radiation Research — Thermodynamics and

Molecular Science — Analytical Chemistry — Materials Science.

THE NATIONAL ENGINEERING LABORATORY provides technology and technical

services to users in the public and private sectors to address national needs and to solve

national problems in the public interest; conducts research in engineering and applied science

in support of objectives in these efforts; builds and maintains competence in the necessary

disciplines required to carry out this research and technical service; develops engineering data

and measurement capabilities; provides engineering measurement traceability services;

develops test methods and proposes engineering standards and code changes; develops and

proposes new engineering practices; and develops and improves mechanisms to transfer

results of its research to the utlimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering2 — Mechanical

Engineering and Process Technology2 — Building Technology — Fire Research —

Consumer Product Technology — Field Methods.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal Agencies in the selection,

acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759),

relevant Executive Orders, and other directives; carries out this mission by managing the

Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal Agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following divisions:

Systems and Software — Computer Systems Engineering — Information Technology.

'Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

J Some divisions within the center are located at Boulder, Colorado, 80303.

The National Bureau of Standards was reorganized, effective April 9, 1978.
national Burean of Stands;

APR 2 7 1979

rvoir bee- Cl

Standard Reference Materials:

SRM 768: TEMPERATURE REFERENCE STANDARD

l

FOR USE BELOW 0.5 K

^

R. J. Soulen, Jr.,

and

R. B. Dove

Center for Absolute Physical Quantities

National Measurement Laboratory

National Bureau of Standards

Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued April 1979
Library of Congress Catalog Card Number: 79-600014

National Bureau of Standards Special Publication 260-62

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-62, 47 pages (Apr. 1979)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1979

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-02047-8 Price $2.30

(Add 25 percent additional for other than U.S. mailing).

6 US. GOVERNMENT PRINTING OFFICE : 1 979 O—28 1-069 (85)
PREFACE

Standard Reference Materials (SRM's) as defined by the

National Bureau of Standards are well-characterized materials,

produced in quantity and certified for one or more physical

or chemical properties. They are used to assure the accuracy

and compatibility of measurements throughout the nation.

SRM's are widely used as primary standards in many diverse

fields in science, industry, and technology, both within the

United States and throughout the world. They are also used

extensively in the fields of environmental and clinical analysis. In many applications, traceability of quality control

and measurement processes to the national measurement system

are carried out through the mechanism and use of SRM's. For

many of the nation's scientists and technologists it is

therefore of more than passing interest to know the details

of the measurements made at NBS in arriving at the certified

values of the SRM's produced. An NBS series of papers, of

which this publication is a member, called the NBS Special

Publication - 260 Series is reserved for this purpose.

This 260 Series is dedicated to the dissemination of

information on different phases of the preparation, measurement, certification and use of NBS-SRM's. In general, much

more detail will be found in these papers than is generally

allowed, or desirable, in scientific journal articles. This

enables the user to assess the validity and accuracy of the

measurement processes employed, to judge the statistical

analysis, and to learn details of techniques and methods

utilized for work entailing the greatest care and accuracy.

These papers also should provide sufficient additional information not found on the certificate so that new applications

in diverse fields not foreseen at the time the SRM was originally issued will be sought and found.

Inquiries concerning the technical content of this paper

should be directed to the author(s). Other questions concerned with the availability, delivery, price, and so forth

will receive prompt attention from:

Office of Standard Reference Materials

National Bureau of Standards

Washington, D.C. 20234

George A. Uriano, Acting Chief

Office of Standard Reference Materials

iii
OTHER NBS PUBLICATIONS IN THIS SERIES

Catalog of NBS Standard Reference Materials

(1975-76 edition), R. W. Seward, ed., NBS

Spec. Publ. 260 (June 1975). $1.50* SN003-003-

01445-1

Michaelis, R. E., and Wyman, L. L., Standard

Reference Materials: Preparation of White Cast

Iron Spectrochemical Standards, NBS Misc.

Publ. 260-1 (June 1964). COM74-1 1061**

Michaelis, R. E., Wyman, L. L., and Flitsch, R.,

Standard Reference Materials: Preparation of

NBS Copper-Base Spectrochemical Standards,

NBS Misc. Publ. 260-2 (October 1964). COM74-

11063**

Michaelis, R. E., Yakowitz, H., and Moore, G. A.,

Standard Reference Materials: Metallographic

Characterization of an NBS Spectrometric LowAlloy Steel Standard, NBS Misc. Publ. 260-3

(October 1964). COM74-11060**

Hague, J. L., Mears, T. W., and Michaelis, R. E.,

Standard Reference Materials: Sources of

Information, NBS Misc. Publ. 260-4 (February

1965). COM74-11059

Alvarez, R., and Flitsch, R., Standard Reference

Materials: Accuracy of Solution X-Ray Spectrometric Analysis of Copper-Base Alloys, NBS

Misc. Publ. 260-5 (March 1965). PB 168068**

Shultz, J. I., Standard Reference Materials:

Methods for the Chemical Analysis of White

Cast Iron Standards, NBS Misc. Publ. 260-6

(July 1975). COM74-11068**

Bell, R. K., Standard Reference Materials:

Methods for the Chemical Analysis of NBS

Copper-Base Spectrochemical Standards, NBS

Misc. Publ. 260-7 (October 1965). COM74-

11067**

Richmond, M. S., Standard Reference Materials:

Analysis of Uranium Concentrates at the

National Bureau of Standards, NBS Misc. Publ.

260-8 (December 1965). COM74-1 1066**

Anspach, S. C, Cavallo, L. M., Garfinkel, S. B.,

Hutchinson, J. M. R., and Smith, C. N., Standard Reference Materials: Half Lives of Materials

Used in the Preparation of Standard Reference

Materials of Nineteen Radioactive Nuclides

Issued by the National Bureau of Standards,

NBS Misc. Publ. 260-9 (November 1965)'.

COM74-1 1065**

Yakowitz, H., Vieth, D. L., Heinrich, K. F. J., and

Michaelis, R. E., Standard Reference Materials:

Homogeneity Characterization on NBS Spectrometric Standards II: Cartridge Brass and LowAlloy Steel, NBS Misc. Publ. 260-10 (December

1965). COM74-11064**

Napolitano, A., and Hawkins, E. G., Standard

Reference Materials: Viscosity of Standard

Lead-Silica Glass, NBS Misc. Publ. 260-11

(November 1966). NBS Misc. Publ. 260-11**

Yakowitz, H., Vieth, D. L., and Michaelis, R. E.,

Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards III: White Cast Iron and Stainless Steel

Powder Compact, NBS Misc. Publ. 260-12

(September 1966). NBS Misc. Publ. 260-12**

Spijkerman, J. I., Snediker, D. K., Ruegg, F. C,

and DeVoe, J. R., Standard Reference Materials: Mossbauer Spectroscopy Standard for the

Chemical Shift of Iron Compounds, NBS Misc.

Publ. 260-13 (July 1967). NBS Misc. Publ.

260-13**

Menis, O., and Sterling, J. T., Standard Reference

Materials: Determination of Oxygen in Ferrous

Materials - SRM 1090, 1091, and 1092, NBS

Misc. Publ. 260-14 (September 1966). NBS Misc.

Publ. 260-14**

Passaglia, E., and Shouse, P. J., Standard Refer- ence Materials: Recommended Method of Use

of Standard Light-Sensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for

Colorfastness to Light, NBS Misc. Publ. 260-15

(June 1967). (Replaced by NBS Spec. Publ.

260-41.)

Yakowitz, H., Michaelis, R. E., and Vieth, D. L.,

Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards IV: Preparation and Microprobe Characterization of W-20% MO Alloy Fabricated by

Powder Metallurgical Methods, NBS Spec.

Publ. 260-16 (January 1969). COM74-1 1062**

Catanzaro, E. J., Champion, C. E., Garner, E. L.,

Marinenko, G., Sappenfield, K. M., and Shields,

W. R., Standard Reference Materials: Boric

Acid; Isotopic and Assay Standard Reference

Materials, NBS Spec. Publ. 260-17 (February

1970). Out of Print

iv
Geller, S. B., Mantek, P. A., and Cleveland, N.

G., Standard Reference Materials: Calibra

tion of NBS Secondary Standard Magnetic Tape

(Computer Amplitude Reference) Using the

Reference Tape Amplitude Measurement

"Process A," NBS Spec. Publ. 260-18 (November

1969). (See NBS Spec. Publ. 260-29.)

Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlab oratory Measurements on the Vapor Pressure of Gold (Certification of Standard Reference Material 745), NBS

Spec. Publ. 260-19 (January 1970). PB190071**

Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressures of Cadmium and

Silver, NBS Spec. Publ. 260-21 (January 1971).

COM74-11359**

Yakowitz, H., Fiori, C. E., and Michaelis, R. E.,

Standard Reference Materials: Homogeneity

Characterization of Fe-3 Si Alloy, NBS Spec.

Publ. 260-22 (February 1971). COM74-1 1357**

Napolitano, A., and Hawkins, E. G., Standard

Reference Materials: Viscosity of a Standard

Borosilicate Glass, NBS Spec. Publ. 260-23

(December 1970). COM71-00157**

Sappenfield, K. M., Marineko, G., and Hague, J.

L., Standard Reference Materials: Comparison

of Redox Standards, NBS Spec. Publ. 260-24

(January 1972). COM 72-50058**

Hicho, G. E., Yakowitz, H., Rasberry, S. D., and

Michaelis, R. E., Standard Reference Materials:

A Standard Reference Material Containing

Nominally Four Percent Austenite, NBS Spec.

Publ. 260-25 (February 1971). COM 74-1 1356**

Martin, J. F., Standard Reference Materials:

National Bureau of Standards-US Steel Corportion Joint Program for Determining Oxygen and

Nitrogen in Steel, NBS Spec. Publ. 260-26

(February 1971). 85 cents* SN003-003-00786-2

Garner, E. L., Machlan, L. A., and Shields, W. R.,

Standard Reference Materials: Uranium

Isotopic Standard Reference Materials, NBS

Spec. Publ. 260-27 (April 1971). COM74-

11358**

Heinrich, K. F. J., Myklebust, R. L., Rasberry, S. D., and Michaelis, R. E., Standard Reference

Materials: Preparation and Evaluation of

SRM's 481 and 482 Gold-Silver and GoldCopper Alloys for Microanalysis, NBS Spec.

Publ. 260-28 (August 1971). COM71-50365**

Geller, S. B., Standard Reference Materials: Calibration of NBS Secondary Standard Magnetic

Tape (Computer Amplitude Reference) Using

the Reference Tape Amplitude Measurement

"Process A-Model 2," NBS Spec. Publ. 260-29

(June 1971). COM71-50282**

Gorozhanina, R. S., Freedman, A. Y., and

Shaievitch, A. B. (translated by M. C. Selby),

Standard Reference Materials: Standard

Samples Issued in the USSR (A Translation

from the Russian), NBS Spec. Publ. 260-30 (June

1971). COM71-50283**

Hust, J. G., and Sparks, L. L., Standard Reference

Materials: Thermal Conductivity of Electrolytic

Iron SRM 734 from 4 to 300 K, NBS Spec. Publ.

260-31 (November 1971). COM71-50563**

Mavrodineanu, R., and Lazar, J. W., Standard

Reference Materials: Standard Quartz Cuvettes,

for High Accuracy Spectrophotometry, NBS

Spec. Publ. 260-32 (December 1973). 55 cents*

SN003-003-01213-1

Wagner, H. L., Standard Reference Materials:

Comparison of Original and Supplemental

SRM 705, Narrow Molecular Weight Distribution Polystyrene, NBS Spec. Publ. 260-33

(May 1972). COM72-50526**

Sparks, L. L., and Hust, J. G., Standard Reference

Materials: Thermoelectric Voltage, NBS Spec.

Publ. 260-34, (April 1972). COM72-50371**

Sparks, L. L., and Hust, J. G., Standard Refer- ence Materials: Thermal Conductivity of

Austenitic Stainless Steel, SRM 735 from 5

to 280 K, NBS Spec. Publ. 260-35 (April 1972.)

35 cents* COM72-50368**

Cali, J. P., Mandel, J., Moore, L. J., and Young, D.

S., Standard Reference Materials: A Referee

Method for the Determination of Calcium in

Serum, NBS SRM 915, NBS Spec. Publ. 260-36

(May 1972). COM72-50527**

Shultz, J. I., Bell, R. K., Rains, T. C, and Menis,

O., Standard Reference Materials: Methods of

Analysis of NBS Clay Standards, NBS Spec.

Publ. 260-37 (June 1972). COM72-50692**

Richmond, J. C, and Hsia, J. J., Standard Refer- ence Materials: Preparation and Calibration of

Standards of Spectral Specular Reflectance,

NBS Spec. Publ. 260-38 (May 1972). COM72-

50528**

Clark, A. F., Denson, V. A., Hust, J. G., and

Powell, R. L., Standard Reference Materials:

The Eddy Current Decay Method for Resistivity

Characterization of High-Purity Metals, NBS

Spec. Publ. 260-39 (May 1972). COM72-50529**
McAdie, H. G., Garn, P. D., and Menis, O., Standard Reference Materials: Selection of Thermal

Analysis Temperature Standards Through a Cooperative Study (SRM 758, 759, 760), NBS

Spec. Publ. 26(M0 (August 1972.) COM-72

50776**

Wood, L. A., and Shouse, P. J., Standard

Reference Materials: Use of Standard LightSinsitive Paper for Calibrating Carbon Arcs

Used in Testing Textiles for Colorfastness to

Light, NBS Spec. Publ. 260-41 (August 1972)

COM72-50775**

Wagner, H. L., and Verdier, P. H., eds., Standard

Reference Materials: The Characterization of

Linear Polyethylene, SRM 1475, NBS Spec.

Publ. 260-42 (September 1972). COM72-

50944**

Yakowitz, H., Ruff, A. W., and Michaelis, R. E.,

Standard Reference Materials: Preparation and

Homogeneity Characterization of an Austenitic

Iron-Chromium-Nickel Alloy, NBS Spec. Publ.

260-43 (November 1972). COM73-50760**

Schooley, J. F., Soulen, R. J., Jr., and Evans, G. A.,

Jr., Standard Reference Materials: Preparation

and Use of Superconductive Fixed Point

Devices, SRM 767, NBS Spec. Publ. 260-44

(December 1972). COM73-50037**

Greifer, B., Maienthal, E. J., Rains, T. C, and

Rasberry, S. D., Standard Reference Materials:

Powdered Lead-Based Paint, SRM 1579, NBS

Spec. Publ. 260^5 (March 1973). COM73-

50226**

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and

Electrical Resistivity Standard Reference Materials: Austenitic Stainless Steel, SRM's 735 and

798, from 4 to 1200 K, NBS Spec. Publ. 260-46

(March 1975). SN003-O03-0 1278-5

Hust, J. G., Standard Reference Materials: Electrical Resistivity of Electrolytic Iron, SRM 797,

and Austenitic Stainless Steel, SRM 798, from 5

to 280 K, NBS Spec. Publ. 260-47 (February

1974). COM74-50176**

Mangum, B. W., and Wise, J. A., Standard Refer- ence Materials: Description and Use of Precision

Thermometers for the Clinical Laboratory,

SRM 933 and SRM 934, NBS Spec. Publ. 260-48

(May 1974). 60 cents* SN003-003-0 1278-5

Carpenter, B. S., and Reimer, G. M., Standard

Reference Materials: Calibrated Glass Standards for Fission Track Use, NBS Spec. Publ.

260^9 (November 1974). SN003-003-0 1344-7

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials:

Electrolytic Iron, SRM's 734 and 797 from 4 to 1000 K, NBS Spec. Publ. 260-50 (June 1975).

1.00* SN003-003-0 1425-7

Mavrodineanu, R., and Baldwin, J. R., Standard

Reference Materials: Glass Filters As a Standard

Reference Material for Spectrophotometry;

Selection; Preparation; Certification; Use -SRM

930, NBS Spec. Publ. 260-51 (November 1975).

$1.90* SN003-003-01481-8

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials

730 and 799, from 4 to 3000 K, NBS Spec. Publ.

260-52 (September 1975). $1.05* SN003-003-

01464-8

Durst, R. A., Standard Reference Materials:

Standardization of pH Measurements, NBS

Spec. Publ. 260-53 (December 1975, Revised).

$1.05* SN003-O03-O1551-2

Burke, R. W., and Mavrodineanu, R., Standard

Reference Materials: Certification and Use of

Acidic Potassium Dichromate Solutions as an

Ultraviolet Absorbance Standard, NBS Spec.

Publ. 260-54 (August 1977). $3.00* SN003-003-

01828-7

Ditmars, D. A., Cezairliyan, A., Ishihara, S., and

Douglas, T. B., Standard Reference Materials:

Enthalpy and Heat Capacity; Molybdenum

SRM 781, From 273 to 2800 K, NBS Spec. Publ.

260-55 (September 1977). $2.20* SN003003-

01836-8

Powell, R. L., Sparks, L. L., and Hust, J. G.,

Standard Reference Materials: Standard

Thermocouple Material, Pt.-67:SRM1967, NBS

Spec. Publ. 260-56 (February 1978). $2.20*

SN003-003-0 18864

Cali, J. P. and Plebanski, T., Guide to United

States Reference Materials, NBS Spec. Publ.

260-57 (February 1978). $2.20* SN003-003-

01883-0

Barnes, J. D. and Martin, G. M., Standard Refer- ence Materials: Polyester Film for Oxygen Gas

Transmission Measurements. SRM 1470, NBS

Spec. Publ. 260-58 (in press).

Chang, T. and Kahn, A. H., Standard Reference

Materials: Electron Paramagnetic Resonance

Intensity Standard: SRM 2601, NBS Spec.

Publ. 260-59 (August 1978). $2.30* SN-003-

003-01975-5

vi
Velapoldi, R. A., Paule, R. C, Schaffer, R.,

Mandel, J., and Moody, J. R., Standard Refer- ence Materials: A Reference Method for the

Determination of Sodium in Serum, NBS Spec.

Publ. 260-60 (August 1978). $3.00 SN-003-003-

01978-0

Verdier, P. H. and Wagner, H. L., Standard Refer- ence Materials: The Characterization of Linear

Polyethylene (SRM 1482, 1483, 1484), NBS

Spec. Publ. 260-61 (December 1978). $1.70

SN-003-O03-O2006-1

Soulen, R. J. and Dove, R. B., Standard Reference

Materials: Temperature Reference Standard

for Use Below 0.5 K (SRM 768), NBS Spec.

Publ. 260-62 (in press).

Velapoldi, R. A., Paule, R. C, Schaffer, R.,

Mandel, J., Machlan, J. L., and Gramlich, J. W.,

Standard Reference Materials: A Reference

Method for the Determination of Potassium in

Serum, NBS Spec. Publ. 260-63 (in press).

* Send order with remittance to: Superintendent

of Documents, US Government Printing

Office, Washington, DC 20402. Remittance

from foreign countries should include an

additional one-fourth of the purchase price for

postage.

** May be ordered from: National Technical

Information Services (NTIS), Springfield,

Virginia 22151.
TABLE OF CONTENTS

PAGE

I. INTRODUCTION 2

II. SAMPLES 5

III. FABRICATION OF SRM 768 7

IV. MEASUREMENT TECHNIQUES 9

A. CIRCUITRY 9

B. HEATING: THE EFFECT OF AC MAGNETIC FIELDS 14

C. THE EFFECT OF DC MAGNETIC FIELDS ON SRM 768 17

V. PERFORMANCE OF SRM 768 24

A. CRYOGENIC TESTING APPARATUS 24

B. ANALYSIS OF DATA 30

VI. CONCLUSION 34

VII. ACKNOWLEDGMENTS 35

VIII. REFERENCES 37

viii
LIST OF TABLES

TABLE NO. PAGE

I. Summary of Properties of SRM 768 3

II. Properties of Materials Used in SRM 768 6

III. Heating in SRM 768 16

IV. Magnetic Values of SRM 21

V. Reproducibility of Early SRM 768 Units

(Serial No. 1, 2, 3) 31

VI. Reproducibility of Later SRM 768

Units (Serial No. 7, 8, 9, 10, 11) 32

VII. Variation in T Observed for SRM 768

Units 1, 2, 3^ 7, 8, 9, 10, 11 34

LIST OF FIGURES

FIGURE NO. PAGE

1. SRM 768 8

2. Mutual Inductance Bridge for SRM 768 10

3. Standard Mutual Inductance 11

4. Iridium Phase Transition 13

5. The Effect of Magnetic Field

on the Transition in Be 20

6. Bottom of Dilution Refrigerator

with Thermal Platform 27

ix
1
SRM 768: Temperature Reference Standard for Use Below 0.5 K

R. J. Soulen, Jr., and R. B. Dove

Temperature Measurements and Standards Division

Center for Absolute Physical Quantities

National Bureau of Standards

Washington, D. C. 20234

Abstract

Cryogenic temperature scales are now available (viz., the newly

created EPT-76 [1]) which are quite accurate and which extend deep into

the cryogenic region (as low as 0.5 K) . It is the region below 0.5 K

where no formal scale exists which is of concern here. By developing a compact device which provides five reference temperatures from 0.015 K

to 0.21 K, the authors hope to provide a lingua franca by which experimental results from different laboratories involving the parameter

temperature may be meaningfully compared.

Such a device, designated SRM 768, is now available and consists of

a self-contained assembly of coils and five samples which can be used to

provide in situ temperature calibration. Simple room temperature

electronics readily permit the observation of the five narrow and highly

reproducible superconducting phase transitions. These phase transitions

have been assigned temperature values by means of fundamental thermometers used at the National Bureau of Standards. Provided that care is

exercised in reducing the magnetic field acting upon the device, the

user can confidently expect to achieve a temperature reproducibility and

traceability to the NBS temperature scale of ±0.2 mK.

Key Words: AuA£ 2 ; Auln 2 ; Be; cryogenic temperature scale; fixed points;

Ir; superconductivity; thermometry; W.

1
I. INTRODUCTION

Cryogenic temperature scales are now available (viz., the newlycreated EPT-76 [1]) which are quite accurate and which extend deep into

the cryogenic region (as low as 0.5 K) . It is the region below 0.5 K

where no formal scale exists which is of concern here. By developing a compact device which provides five reference temperatures from 0.015 to

0.21 K, the authors hope to provide a lingua franca by which experimental results from different laboratories involving the parameter

"temperature" may be meaningfully compared.

Such a device, designated SRM 768, is now available* and consists

of a self-contained assembly of coils and five samples which can be used

to provide in situ temperature calibration. Simple room temperature

electronics readily permit the observation of the five narrow and highly

reproducible superconducting phase transitions. These phase transitions

have been assigned temperature values by means of primary thermometers

used at the National Bureau of Standards. Provided that care is exercised in reducing the magnetic field acting upon the device, the user

can confidently expect to achieve a temperature reproducibility and

traceability to the NBS temperature scale of ±0.2 mK. Table I provides

the salient information about SRM 768. Since the variation in T

c (typically ±1 mK) among different specimens of the same material is

larger than the reproducibility of a given sample (±0.1 mK) , each SRM

768 unit is accompanied by a calibration certificate.

*From the Office of Standard Reference Materials, National Bureau of

Standards, Room B-311, Chemistry Building, Washington, D. C. 20234.

2
TABLE I

Summary of Properties of SRM 768

Material Transition Temperature Typical Typical

Will Lie Between Transition Reproducibility

Width Upon Thermal

Cycl ing

mK mK mK

U 15.0 - 17.0 0.7 0.20

Be 21 .0 - 24.0 0.2 0.10

Ir 98.5 - 99.5 0.8 0.10

AuAl

2 160.0 - 161 .0 0.3 0.10

Auln 0 205.0 - 208.0 0.4 0.15

The values given are the averages of the standard deviations of several

sampl esRECOMMENDED OPERATING CONDITIONS

1) Peak-to-peak magnetic field applied in primary coil: 2.3 uT (23 mG)

for W transition, 0.46 uT (4.6 mG) for the others.

9 -11

2) Heating generated with above conditions: 1.8 x 10 W and 7-5 x 10 W,

respectively.

3) Ambient magnetic field kept below 1 uT.

3
This certificate specifies each T" c in the unit to ±0.1 mK on an NBS

temperature scale which is believed to be thermodynamical ly accurate

within a few tenths of a percent from 0.01 to 0.5 K.*

In many ways SRM 768 is similar to SRM 767 [2], a device containing

five superconductors whose transitions have been adopted as fixed points

for EPT-76. There are significant differences between them, however,

arising chiefly from the requirement of better thermal contact for SRM

768. The remainder of this publication describes in greater detail the

operating conditions and instructions particular to SRM 768.

*This scale dubbed NBS-CTS-1 (NBS Cryogenic Temperature Scale-1) was

obtained by intercomparing Co-60 gamma-ray aniosotropy and Josephson

junction noise thermometers from 0.011 to 0.050 K. From 0.05 to 0.5 K

the noise thermometer was used alone. The data obtained by these

methods was then "smoothed" with a paramagnetic salt thermometer (cerium

magnesium nitrate) to arrive at NBS-CTS-1. This scale is maintained at

the NBS via secondary thermometers (germanium resistors) and two units

of SRM 768 which were calibrated at the same time as the gamma-ray and

noise thermometers. For a discussion of these thermometers, see H.

Marshak and R. J. Soulen, Jr., Journal de Physique 39, C6-1162 (1978)

and references therein.

4
II. SAMPLES

The physical dimensions, metallurgical state (e.g., crystall inity

and state of anneal), purity and method of preparation of the five

samples incorporated in the superconductive thermometric fixed-point

device are quite disparate and are dictated by such considerations as

toxicity and melting points of the starting materials. The relevant

information on each material (W, Be, Ir, AuA£ 2 and Auln 2 ) is summarized

in TABLE II. The purity of the Ir is notably low compared with the

purity of the other four materials (20% Ru impurity). In fact, our

experiments on different samples of all five materials have shown that

specimens of higher purity can be made (at greater expense and effort!)

and that in some cases the transition temperatures were different. Thus

the T values reported for SRM 768 are not necessarily to be taken as

representing the pure materials. The specific materials used for the

SRM device were not chosen necessarily for their high metallurgical

quality but rather for the availability of enough homogeneous material

to produce many reproducible SRM units for wide distribution at a reasonable cost.

The samples were spark cut from an ingot or "boule" of each material. The surface damage caused by the cutting was removed by gentle

abrasion with 600 grit silicon carbide sandpaper followed by final

polishing with 20 and 2 ym diameter aluminum oxide powder. The exception to this rule was the processing of Be, which, owing to the toxicity, was used in its as-received condition. In an effort to reduce

supercooling (an effect to be explained later) of the superconductive

transition, small pieces of Ail were spot welded to one end of the Be and

W samples.

5
00

r-~ z:

or

ca

s-3

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Cl <L> E E

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03 > 3 -rO C -P'i-

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so>

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oo *

01

— i- o • +-> 1

c

•r—

o 1— S_ -i— r—

13 CO

c CL •r- Z3

•r—

E • • " in OT

E •r- OJ

o

o s_ in lo CL&S c O) ro E O i— c -z. O CM x ^-z: (J

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•ro

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cn TJ u Cl C 3

0J

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00

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=3c CJ i. 3 TJ o C O)

00 s- oo

X >-

+ 03

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03 oo >- OJ 00 5. 3 CO <— CO CL

•t~ +J i— 00 03 Oi CO =t CO

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03 CJ

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s: s- S.

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n- o.

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oo

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X

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roO

coCM

OLOOLO

c

OI

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r— 3 3o

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cn3

03 XOi T3

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T3

01

5-

0JCL

OIs_ o_ 6
III. FABRICATION OF SRM 768

This device is a self-contained assembly of samples and coils

permitting the observation of five superconductive transitions with a reasonable signal-to-noise ratio without generating appreciable heating,

while at the same time maintaining good overall thermal equilibrium

among its parts. Fig. 1 shows the arrangement which has been found to

satisfy these requirements.

Two holes are drilled through a cylindrical OHFC copper block, the

other end of which has been machined to form a 6-32 screw. Into each of

the two holes is inserted a bundle of 300 bare AWG 40 copper wires. Each

bundle is welded in place, and the surface facing the 6-32 screw is then

remachined flat.* A serial number is stamped into the side of the unit

near the screw. The whole assembly is electroplated with pure gold to

an approximate thickness of 0.5 urn. Samples of W, Be, Auln 2 , AuA£2 and Ir are each bound at the positions shown in the figure with GE

7031** varnish and cotton thread. Two sets of copper coils (a primary

and secondary) mounted on thin phenolic tubes are slipped into the two

holes in the copper block and enclose the samples. The spare goldplated copper wire is then folded back over the coils and lashed down

with thread and more GE 7031 varnish. As a consequence of this design,

the coils and samples were found to be in thermal equilibrium even at

the lowest transition temperature.

*Please note that the copper stud has been so annealed by the welding

that care must be exercised to avoid damage (e.g., shearing off) during

installation.

**Use of brand names throughout this article does not imply our endorsement; the particular products were used for convenience and are not

necessarily optimum.

7
SRM 768

794 DIA.

COPPER WIRE WELDED

GOLD PLATED OX-FREE COPPER

PRIMARY: 2 layers 036 AWG COPPER

SECONDARY: 040 awg

COPPER (4000 TURNS)

300 0 40 AWG RARE COPPER WIRES

(GOLD PLATED)

NOTE: DIMENSIONS IN CENTIMETERS w

Ir

CZD Auln

Be

AuAI.

Figure 1. SRM 768. The symmetric unit is composed of two similar

parts, each one consisting of two or three samples bound in

copper wires inside a pair of coils (primary and secondary).

The four coils are connected in series opposition so as to

minimize the total mutual inductance. The serial number

of the unit (in this case, 7) is stamped on the end

designed for attachment to a cryostat which is terminated

with a 6-32 threaded stud. The threads are relieved near

the body of the device so that it will bottom properly

when screwed in, thereby establishing good thermal contact.

CAUTION: Due to welding carried out in a step of

manufacture, the 6-32 copper stud is well annealed and

may be snapped off if too much torque is applied in

mounting. "Finger tight" is sufficient.

8
IV. MEASUREMENT TECHNIQUES

A. Circuitry

As is shown in Fig. 1, each unit is provided with two sets of

coils, each set consisting of a primary and secondary coil. The eight

leads from these sets are interconnected in series opposition, however,

thus requiring only four leads for measurement. The uniformity of a

given pair of primary and secondary coils is such that, even though a

given pair has a mutual inductance of 3 mH, the mutual inductance of the

combination is generally less than 100 pH. The resistance of the

combined primary coil set is about 30 Q at room temperature and drops to

0.4 Q at 4 K. The coil calibration of each primary coil was found to be

B = 0.0158 I (1)

where the current I passing through the coil is given in amperes and the

resulting magnetic field, B, is given in teslas. The coefficient was

obtained in two ways: (1) by sending a known dc current through the

coil and measuring B with a Bell gaussmeter (accurate to a few percent);

and (2) by calculation using the equation for an solenoid of dimensions

given in Fig. 1 knowing the turns per unit length. The two methods

agreed to within 10%, and the aforementioned coil constant was taken as

the average of the two values obtained.

The superconductive transitions are observed as changes in the

mutual inductance of the coils which occur when the magnetic field

generated by the primary coil is expelled from the interior of the

sample as it enters the superconducting state (the Meissner effect). The

mutual inductance change may be observed using either a Hartshorn bridge

[3] or a much simplier circuit developed by one of the authors (RJS) in

collaboration with J. F.Schooley and G. A. Evans [4]. The latter bridge,

designed for use with SRM 767, was difficult to use with SRM 768, however.

The reason for this is that the secondary coil in SRM 768 is wound

directly on the primary coil in order to maintain thermal equilibrium

throughout the unit. The resulting capacitance between the coils

9
Figure 2. Mutual inductance bridge for SRM 768. The circuit shown in

dashes represents the SRM 768 coils at cryogenic temperatures which are actually four coils arranged in series

opposition. A switch selects one of two secondary coils of

the reference mutual inductance; the one with fewer turns

provides a reference mutual inductance of 0.22 mH suited

for use with SRM 768, the other one gives a mutual

inductance of 5.1 mH for use with SRM 767. A ten-turn

potentiometer (total resistance, 100 Q,) reduces the voltage

developed by the standard mutual inductance until bridge

balance is achieved. A TRIAD G-4 transformer with a turns ratio of - 90, couples the circuit to a phasesensitive detector, N. We have used a PAR Model 120

phase-sensitive detector with a PAR Model 112 preamplifier

as well as preamplifiers and amplifiers of our own design

with equal success. Provision of a circuit to balance the

small out-of-phase component of the voltage has not proved

necessary

.

10
BRIDGE MUTUAL INDUCTANCE STANDARD

T

1.6 cm

^^^^^^^^

S3^^^^^^^^^^^^^^^^^

SECONDARY 2 : 100 TURNS #32

COPPER WIRE

SECONDARY 1 : 2500 TURNS #38

COPPER WIRE

PRIMARY : 1100 TURNS #32

COPPER WIRE

PHENOLIC COIL FORMERS

4.0 cm

5.6 cm

Figure 3. Standard mutual inductance. The primary coil (innermost

coil) is wound on a phenolic coil former which has an

inner diameter (i.d.) of 0.64 cm and an outer diameter

(o.d.) of 0.80 cm. The secondary coil of 2500 turns is

wound on a second phenolic former with an i.d. of 1.1 cm

and an o.d. of 1.3 cm. The 100-turn secondary is wound

on top of the latter coil. The mutual inductance

between the primary and the 2500 turn coil is 5.1 mH,

while the mutual inductance between the same primary and

the 100 turn secondary is 0.22 mH.

11
introduces a large phase shift into the circuit which renders balancing

of the bridge difficult. To circumvent this problem, the authors

developed a third bridge which is relatively immune to such capacitances,

performs just as well as the previous two and is as simple to build as

the second. This new bridge is shown schematically in Fig. 2. It

injects a current at a frequency of 400 Hz from the reference voltage of

a phase-sensitive detector into the primary coil of the SRM unit as well

as into the primary of a simply-constructed standard mutual inductance

(see Fig. 3). The voltage induced in the secondary coil of the standard

inductor is reduced by means of a ten turn potentiometer which can be

adjusted to null the voltage induced in the secondary of the SRM unit.

The null condition is observed with a phase-sensitive detector which is

coupled to the circuit by a transformer, T. The circuit parameters used

here are not necessarily optimized, but the authors have found that this

bridge performs as well as the two aforementioned bridges.

A typical superconductive transition is shown in Fig. 4. The

output from the phase-sensitive detector, which is proportional to the

change in mutual inductance of the coil set (in arbitrary units), is

plotted on the Y axis of an X-Y recorder, while on the X axis is registered the offset of an ac resistance bridge which monitors a calibrated

germanium resistance thermometer. The width, W, of the transition is

defined as the temperature range over which 80% of the change in mutual

inductance occurs, while the T

Q

is defined as the midpoint of the mutual

inductance change. For this sample of iridium, W - 0.9 mK, and T

c -

0.098 K. Two traces of the transition are generally obtained, one as

the sample is slowly warmed through the transition, and a second as the

sample is cooled back through T . The hysteresis could be due either to

lack of thermal equilibrium between the sample and the resistance

thermometer or to supercooling effects. Experiments quickly showed that,

as long as heating (cooling) rates were slower than 0.5 mK/min, the

hysteresis which appeared in all the materials was due to supercooling

and not to lack of thermal equilibrium. All data reported here were

obtained with heating (cooling) rates less than this value.

12
CO

DC

H-1 mK-H

X

-3.0 -2.0 -1.0 0 1.0

T-T c (mK)

2.0 3.0

Figure 4. Iridium phase transition. The change in mutual inductance

AM as observed by the circuit in figure 2 is plotted in

arbitrary units versus the output of an ac resistance

bridge monitoring a calibrated germanium resistance

thermometer. The transition temperature is chosen as the

midpoint of the transition, while the width W of the

transition is defined as 80% of the change AM centered

about T . This transition was plotted out in a time of

approximately five minutes. The slight amount of

hysteresis present is due to supercooling.

13
It is worth pointing out that a simplification in the measurement

process ensues from this particular arrangement of samples and coils.

Note in Fig. 1 that the samples are placed in the coils so that, as the

temperature is raised or lowered, the occurrence of a superconductive

transition will alternate back and forth between the two coil sets.

Since the change in mutual inductance produced by four of the samples

(W is the exception) is about the same magnitude, and since the coils

are arranged in series opposition, the output on the Y axis of the X-Y

recorder will be displaced first in one direction by the first transition, then returned approximately to the original position by the

second, and so on. This means that rebalancing of the bridge after each

transition and changing of the amplifier gain are not really necessary

in order to measure the transitions of Be, Ir, AuA£ 2 and Auln 2 . The

mutual inductance change accompanying the transition in the tungsten

sample is about a factor of 25 less than the others, however, and the

gain must be increased accordingly.

B . Heating: the effect of ac magnetic fields

Since SRM 768 is intended for use at very low temperatures

where even very small amounts of heat are perceptible, a natural question concerning the use of the device is, "How much current can be used

in the primary coil to observe the transition and, How much heat is

generated?" Actually, introduction of current into the primary coil

generates heat in three ways: the familiar I R loss in the primary

coil, eddy current heating in the samples, and eddy current heating in

the gold-plated copper wires used to enclose the samples. Calculation

of the first is obvious: the eddy current heating can be calculated

from the equation [5]

' _V_ B

2 d

2 10" 16

W (2)

g 32p

14
where V is the sample volume exposed to a time-varying magnetic field,

B. The resistivity of the sample is given by p and d is the diameter of

the sari

obtain

sample. Assuming B = B

Q

e

la)t

, and averaging over one cycle, we

- B

2

B

2

B = -§- 4/v2 = -g££ 4tt

2

v

2

(3)

Here we have used the peak-to-peak value, B , instead of B , since

pp 0

peak-to-peak voltages are easy to determine from oscilloscope traces.

Equation (2) thus becomes

V B

2

2

Q = ^

v

2

d

2 10- 16

W (4)

The eddy-current heating was calculated for two values of magnetic

field because these are the ones recommended for observation of the

superconductive transitions in SRM 768. That is to say, a value of

Bpp = 0.46 yT has been found to produce a voltage change of between 20

and 50 yV at the output of the coupling transformer (see Fig. 2) when

the Be, Ir, AuA£2 and Auln 2 transitions occurred. This signal produces

a trace on the Y axis of the recorder with a signal-to-noise (S/N) ratio

of at least 10/1 when a time constant of 1 s is used. Since the signal

induced by the W transition is about a factor of 25 weaker, both the

amplitude of the magnetic field and amplifier gain can be increased by

factors of five. In this case, the vertical axis signal of the X-Y

recorder was observed to have a S/N ratio of at least 5/1 and thus the W

transitions were readily observable. Equation 4 was used to estimate the

three heating terms of these two values of magnetic field, and the

results are summarized in TABLE III.

15
Material

TABLE III

Heating in SRM 768

,++

I

v = 400 Hz

= 29 U A

PP

B = 0.46 uT+++

v = 400 Hz 140 wA

PP

i 2.3 M T+++

cnr cm Q cm W

w 8 .0 X lO"

3 0 .13 5 X lO"

9

1

.

,4 X io- 1?

3..6 X lO' 11

Be 7 .3 X lO"

2

0.,40 4 X 10" 8

3.,1 X 10" 11

7.,9 X lO' 10

Ir 1 ! .8 X lO'

2

0..20 4.,4 x 10~ 6

8..6 X 10" 15

2.,2 X 10" 13

AuAl

2

3,.5 X 10" 2

0. 20 2 X lO" 7

3.,8 X 10* 13

9. 3 X 10" 12

Auln,, 3.,5 X lO"

2

0. 20 2 X lO"

7

3. 8 X lO"

13

9. 3 X 10" 12

SUBTOTAL 3.3 x 10" 11 8.4 x 10" 10

600 #40 AWG

copper wires 1.3 x 10 7.5 x 10

t2 d u • ++++

I R Heating

3 x 10" 8

SUBTOTAL

Kp_j(_LO

3.3 x

10'

it. 2 x

10'

-13

11

11

2 .6 x 10

8.4 x 10

12

-in

9.6 x 10

-in

TOTAL 7.5 x 10

11 1.8 x 10"

+ Sample volume, V, calculated from dimensions given in TABLE II.

++ If the sample did not have a circular cross section, a fictional diameter d was obtained by setting A = ttcI 2 /4 , where A is the cross-sectional area of the samole.

+++ Obtained from the coil constant, B = 0.0158 I.

++++ The resistance, R, of the two primary coils at 4.2 K is 0.4 Q; the average power

per cycle is I 2 R = I J R/8.

16
Several approximations render entries in TABLE III somewhat uncertain. We have approximated non-cycl indrical rod samples by a simulated cylindrical geometry of the same cross section. Variation of

resistivity and volume of the samples could cause the estimate of eddy

current heating in the samples to vary by as much as 20%. Moreover, the

calculation of the eddy-current heating generated in the 300 copper

wires assumes that all wires are electrically insulated from each other.

In actual fact they do touch each other by virtue of the construction

and the resulting increase in heating is hard to estimate. In view of

these uncertainties, an experiment was conducted with five SRM 768 units

connected in series on a common copper platform which also held a calibrated germanium resistance thermometer to determine whether such

heating, though small, could be observed. With this arrangement the

estimates for heating given in TABLE III should be multiplied by an

additional factor of five. The transitions of the five samples each of

W, Be, Ir, AuA£2 and Auln 2 were first recorded on the germanium resistance thermometer (i.e., 25 X-Y recordings) using a peak-to-peak primary

field of 0.46 yT; then all 25 transitions were recorded (with a reduction in amplifier gain) using a field of 2.3 yT. If the aggregate

effect of the terms given in TABLE III were important, the T

c values

should systematically shift when the peak-to-peak field was quintupled.

No shift in temperature greater than the imprecision of the measurement

(about 0.05 mK) was observed in any of the twenty-five samples. We

conclude that the heat generated in the measurement of the T

c

's does not

produce any noticeable temperature gradient between the specimens and

thermometer as long as thermal contact is established via a metallic

link. If, however, a liquid-solid interface (e.g., liquid He 3 -copper)

separates the SRM unit from the desired thermometer, as can commonly

occur in dilution refrigerator applications, greater care may have to be

exercised.

C. The effect of dc magnetic fields on SRM 768

The single most important environmental factor which determines the shape and position of the superconductive transition is the

ambient magnetic field. We discern two distinct effects here.

17
In the first place, the magnetic field H

c (T) which completely suppresses

superconductivity at a temperature T in a sample is given approximately

by [6]

H

C

(T) - H

c (0) (1-(T/TC

) 2

) (5)

The more accurate equation, differing by a few percent from Eqn. 5, is

given by the BCS theory [7]. Thus, if an ambient magnetic field of

value H is present, Eqn. 5 or the more correct BCS function can be

a solved for the temperature T

1 (by necessity, below T ) at which the

superconductive transition will now occur. The effect on the transition

curve shown in Fig. 4 is to uniformly displace the curve to a lower

temperature. Near T this displacement may be calculated from

AT. = V - T. = H =f TTf^V

1 (6)

c c c a \ dT / j_T

c

The slope of the critical magnetic field can be calculated from the BCS

result [7]

/dH \ /M°)\ 2

(dT^)

T=T

- 1-737 (^-)(l-i2

) (7)

c Here a is the average of the energy gap anisotropy parameter which, at

risk of committing errors of 1-2%, we set to zero.

The second effect of the same magnetic field is to cause the sample

to supercool: that is, the sample must be cooled considerably below the

equilibrium T

1 before it can enter the superconducting state. This

effect introduces hysteresis into the transition as it is traced out.

The maximum supercooling that can occur can be calculated from the

equation derived from the Ginzburg-Landau theory [8]

H

sc

H

a

" ZA kH

c

(T) (8)

where the G-L parameter k is given in terms of other solid state parameters of the superconductor [9]

k = k

q + k. (9)

18
where

^ K

Q

= 1.61 x 10 2

* (y

3/2

T

c /N4/3

) (4") (10)

and

= 7.53 x 10 3 p y

h

(11)

Here, y is the linear coefficient of the normal -state electronic

specific heat, N is the number of valence electrons per unit volume,

S is the free area of the Fermi surface, and S

f

is the area of the Fermi

surface for a free-electron gas of density N. Thus k may be evaluated

for each material using normal state values, and the maximum amount of

supercooling (i.e., how low the temperature must be reduced for superconductivity to occur) may be calculated from Eq. (8) and solving for

the supercooling temperature T . Near T . the amount of supercooling can be evaluated by

l / dHr \ 1

s s c 2.4k y dT /j-j a

'

c

We note an important point: this expression gives the maximum

supercooling which can occur. Sample imperfections will cause the

sample to enter the superconducting state anywhere between T

s and T .

Both effects, depression of the transition and supercooling, were

studied for each material used in SRM 768. A typical measurement is

shown in Fig. 5 for Be. The curve with the highest superconducting

transition and minimum hysteresis was recorded by cancelling all three

components of the earth's magnetic field with a three-axis Helmholtz

coil. Curves with depressed transitions and supercooling were generated

by applying known values of magnetic field along the axis of the measuring coil set. From such curves, it was possible to obtain experimental

values of (dH

c/dT) T=T

and k. These are given in TABLE IV along with

the theoretical estimates using the appropriate equations and parameters. Except for the case of AuA£2 , the experimental and theoretical

values for the slope are in good agreement. Thus Eqn. (6) can be used

to calculate the depression in transition with great confidence. We

19
Figure 5. The effect of magnetic field on the transition in Be.

Curve 1 : H = 0.0 T

Curve 2

Curve 3

H = 9.5 yT

H = 19 yT

c

22.7 mK

21 .3

20.0

22.0 mK

18.0

15.4

20
I— CD

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i— CD

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4-

oc

o

c

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s:

orOO

4-o CD

CO il

01

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<t •r- 1— 4-> tuc +J cn Q.

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21
note that the theoretical value for k is always less than its experimental value, which says that none of the samples supercools to its

theoretical maximum. Clearly, in calculating the effect of supercooling

for the samples in SRM 768, Eqn. (12) is to be used with the eccperimental

values for k.

The last two columns in TABLE IV give values for depression of T

c and supercooling which will actually be seen in an ambient magnetic

field of 1 uT. For example, in that magnetic field, the superconductive

transition of tungsten will be depressed by only 0.08 mK, but the sample

will have to be cooled yet another 0.36 mK before it becomes superconducting. Since the supercooling is very much larger than the depression

of T

c for a given value of magnetic field, it is possible for larger

fields to supercool the sample to absolute zero, thereby making observation of the transition impossible even though T

c is finite! The

supercooling is especially large for W and Be so the authors adopted the

procedure of spot welding two small buttons of pure aluminum (99.999

percent pure) to one end of each sample of these two materials.*

*This was accomplished by charging a 4500 yFd capacitor to 30 V and

-2

discharging it through the pure Ail wire (diameter - 2.4 x 10" cm) and

a W or Be sample. This technique deposited an hi hemisphere approximately 2.5 x 10 cm in diameter onto the sample. We found that we

could restrict the superconductor in a more clearly-defined geometry by

this technique than by soldering.

22
Aluminum, possessing a higher T (- 1 K) and H (- 10,000 uT) serves as

c c

a nucleation center to induce superconductivity in the samples. We

observed that the supercooling in samples so treated was reduced by an

order of magnitude. The last column in TABLE IV indicates the supercooling which can actually be expected for SRM 768. To summarize:

a 1 yT field does not produce much supercooling, but it still leads to

significant 3 reductions in T . We would therefore recommend for the

c highest thermometric accuracy that ambient magnetic fields be reduced to

at least this value by techniques to be described in the next section.

23
V. PERFORMANCE OF SRM 768

A. Cryogenic testing apparatus

In this section we describe our experience with eight SRM 768

units which were cycled several times between room temperature

and 0.01 K. These experiments, with a few exceptions, extended only

over a period of several months and therefore provide little information

on long-term performance. These experiments, however, are the culmination of a four year program in which several other samples of these

materials (not necessarily from the same source or boule) have been used

for several years during which no evidence was found to indicate that

reproducibility of a given sample would degrade with age or thermal

cycl ing.

The cryostat used for these experiments is a He 3 - He

1* dilution

refrigerator which can maintain temperatures as low as 0.01 K in its

continuous mode of operation. The general features of the cryostat are:

an outer glass dewar containing liquid N 2 and an inner glass dewar

containing liquid He

1* at a temperature of 4 K. A brass vacuum can, 60

cm long and 8.9 cm in diameter, is immersed in the liquid He

1* and contains a pumped He

1* bath at 1 K and a dilution refrigerator. The remaining volume inside the can (about 30 cm long and 8.9 cm in diameter)

provides the working space for the experimental samples.

The cryostat was cooled in the following way. At room temperature

the vacuum can was pumped to a pressure of approximately 0.13 Pa

(lum of Hg) and then filled with He 3 exchange gas at a pressure of 67

Pa.

24
The liquid nitrogen dewar was filled and maintained full overnight,

thereby cooling the apparatus to 77 K. Subsequent transfer of liquid

He

1

* into the inner dewar reduced the temperature to 4 K. The vacuum can

was then pumped for 30 minutes, after which heaters warmed the 1 K pot

and dilution refrigerator to 10-15 K. This "bakeout" proceeded for

, _4 another 30 minutes to reduce the He^ pressure to 1.3 x 10 Pa as read

on a room temperature ionization gauge. After this the heaters were

turned off and the charge of 3 He - ^He gas was condensed into the

dilution refrigerator. Then circulation of the refrigerator was begun

and the mixing chamber was eventually cooled to - 10 mK.

The ambient magnetic field at the site of the cryostat is approxi-

-5

mately 5x10 T; two means have been used to reduce it to a level

tolerable to the SRM 768 unit. When studies of the magnetic field

dependence were desired, the dewars were surrounded with three Helmholtz

coils arranged on three orthogonal axes. When minimization of the

magnetic field was desired, two annealed concentric mu metal cylindrical

shields were used. The inner one is 60 cm long, fits on the brass

vacuum can, and is thus maintained at 4 K. The outer one is also 60 cm

long and slips on the outside of the N 2 dewar (diameter 20 cm). Assuming a magnetic permeability of 10,000 we calculate that the ambient

field should be attenuated by a factor of 2400 by the two mu metal cans

when they are both at room temperature. Thus the magnetic field at the

o site should be reduced to 2 x 10 T using these cans. A value of 1 x -8

10 T was actually achieved when the cans were removed from the cryostat and separate coils around each cylinder were used to "degauss" the

cans in situ. Unfortunately, when the cans are mounted on this particular

cryostat, there is no room for a coil to surround the inner can, so the

cans must be degaussed in the following sequence: removal of the outer

can from the N 2 dewar; degaussing the inner can; then raising the outer

mu metal can and degaussing both in place. In this situation the

magnetic field inside the cans is found to vary from 0.1 to 0.2 yT

at room temperature. A further degradation in the shielding is expected

to occur when the inner mu metal can is cooled to 4.2 K, because the

permeability drops by a factor of ten. We therefore estimate that the

25
samples are exposed to a residual field of 1 to 2 yT under the conditions

of a degaussing at 300 K followed by cooling of the inner can to 4 K.

This situation could be improved by constructing the inner cylinder from

a material whose permeability is not reduced at 4 K, but inspection of

TABLE IV indicates that a magnetic field of 2 yT is tolerable, though

not desirable.

Some authors have suggested using superconducting shields to reduce

the magnitude of the ambient magnetic field, but we strongly recommend

that this technique not be used. The problem is that thermal gradients

in the shield generate large currents and magnetic fields as the shield

enters the superconducting state. Thus the experimental ist can find

himself confronted with a cryogenic environment "poisoned" by a field of

several mT even though he began the experiment at liquid nitrogen

temperatures with a field of a few yT! [10]. Given the relative ease

in elimination of fields by the other two techniques described above, we

feel that the use of superconductive shields in this context introduces

an unnecessary risk.

In Fig. 6 we show a schematic diagram of the bottom of the mixing

chamber. The dilution refrigerator (i.e., still, heat exchangers,

mixing chamber) is a commercial version in which the bottom of the

mixing chamber has been replaced by one of our own design and fabrication. The bottom used here is a solid piece of OFHC copper which has

been plated to a thickness of 0.5 ym with pure gold after all holes were

drilled and tapped. Several 6-32 holes are tapped in the upper section,

four of which accept doped germanium resistance thermometers (GERT's for

short) which were inserted into gold-plated copper pods made to our

specifications. Two of these resistance thermometers (Serial #2966 and

15151) were usable down to 0.1 K, below which the resistance of the

thermometers grew too large for use (several Mft), while two others

(Serial #RS2 and 1405) were sensitive down to 0.01 K and relatively

insensitive above 0.1 K. The lower section of this assembly consists of

a rod which terminates in a blind hole which can accept a gold-plated

mating post. A nylon compression clamp completes the junction. Since

the bottom of the dilution refrigerator is fabricated from a single

26
MIXING

CHAMBER

GERMANIUM

RESISTANCE

THERMOMETER

— 1 cm

PLATFORM

NYLON CLAMP

SRM 768

UNIT

Figure 6. Bottom of dilution refrigerator with thermal platform.

27
piece of annealed copper, it can be considered isothermal in all thermometry experiments conducted in this apparatus. Furthermore, no perceptible thermal gradients across the connector at the bottom of the rod have

been observed.

The desired experimental apparatus is mounted to the post. For

example, when it was desirable to calibrate the GERT's, a Josephson

junction noise thermometer was clamped around the post and a y-ray

anisotropy thermometer was slipped into the blind hole and clamped. On

other occasions, a paramagnetic salt, cerium magnesium nitrate (CMN),

was mounted to a post which fitted into the blind hole. Over the

course of years and several experiments of this nature, an absolute

temperature scale of high accuracy has been achieved and transferred to

the GERT's. This temperature scale, designated NBS-CTS-1 and to be

fully described elsewhere, was used to assign values to the superconductive transitions in SRM 768. Its maximum thermodynamic inaccuracy is

believed to be a few tenths of a percent over its range of 0.01 K to 0.5

K.

When superconductive transitions were to be measured, the primary

thermometers (noise, y-ray) were removed and a copper platform containing SRM 768 units was attached to the connector. The GERT's,

retaining the temperature scale, were used to define the temperatures of

the transitions. The platform shown in Fig. 6 consists of a solid

copper structure in the form of a copper disk (diameter 7.5 cm; thickness 0.6 cm) terminating in a post which fits into the connector.

Several 6-32 holes are tapped in the disk and a gold plate of 0.5 um

thickness covers all surfaces of the platform.

28
In the experiments reported here, as many as five SRM 768 devices

were screwed into 6-32 tapped holes in the platform and, for economy of

electrical leads, the primary coils were connected in series. To

expedite the measurements five measurement bridges, phase sensitive

detectors, and X-Y recorders were used so that the transitions of a

given material in all five devices could be simultaneously traced out on

a common temperature scale determined by the most senior GERT (Serial

#1405). The width and hysteresis of each transition were thereby

obtained in terms of GERT #1405. After complete tracings were obtained,

the center of one of the transitions was measured versus as many of the

four GERT's as were usable at that temperature. The centers of the

other transitions were then determined relative to the center of that

unit from the X-Y recordings.

The GERT's were measured with an ac Mueller bridge operated at

27 K. Below 0.1 K, a peak-to-peak voltage drop of 80 yV was maintained across the resistors, while above 0.1 K the voltage drop was

increased to 160 yV. At these levels of excitation, no self-heating of

the GERT's to the yK level was observed, yet adequate temperature

sensitivity of approximately 50 yK was maintained. The output of the

preamplifier connected to the bridge was monitored to establish that

extraneous noise (chiefly 60 Hz) was kept below 1 yV (peak-to-peak) even

though the resistances of GERT #1405 and RS2 increase to values as high

as 400 kQ, at 10 mK. Thus extraneous power generated in the resistors

was (1/80) 2 less than that purposely generated by the signal at 27 Hz.

Such low noise was only achieved by careful circuit design, generous use

of mu metal shields around electronic components, and careful location

of electronic equipment.

29
B. Analysis of data

Two groups of prototype SRM 768 units were prepared. The

first group with Serial Nos. 1, 2, 3 contained W and Be samples with no

A£ spot welds to suppress the supercooling. The second group (Serial

Nos. 7, 8, 9, 10, 11) used the Ail spot welds for these two materials and

a different boule of Auln 2 . The results for the first group (1, 2, 3)

are shown in Table V, while the results for the second (7, 8, 9, 10, 11)

are given in Table VI. A typical entry reads as follows: for the

tungsten sample in SRM 768, Serial No. 1, in run I, the transition

temperature was measured to be 15.37 mK, the width of the transition was

0.21 mK and it had a hysteresis due to .supercool ing of - 0.04 mK.

There are some blanks in Table V for the W samples which indicate

that the supercooling was so large on these occasions that the sample

remained in the normal state to the lowest temperature obtainable with

the dilution refrigerator (- 10 mK). No such entries occur for the W

samples in Table VI, indicating that the hysteresis due to supercooling

was successfully reduced by the A£ spot welds. Also note that the

hysteresis (reported in the last column) was significantly reduced for

Be by the application of A& spot welds. It is evident that supercooling

is not a problem for the other materials in SRM 768. In Table VI there

are no entries for Auln 2 samples for runs 1-4 because a new sample

preparation technique was tried here which produced poor samples. In

runs 5-11, samples of Auln 2 were prepared in the original way used for

units 1, 2, 3, except that a new boule of Auln 2 was used.

We note also that the T values of Auln 2 for the first group (1, 2,

3) are about 2 mK higher than for the second group (7, 8, 9, 10, 11)

indicating that there is some variation in T

c from boule to boule. It

is also apparent, however, that each boule yields quite uniform T

values

.

30
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31
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32
Two techniques for degaussing the mu metal cans were tried. For

runs 1-4 on units 1, 2, 3 and for runs 1-4 of units 7, 8, 9, 10, 11,

degaussing was not performed until the inner shield was at 4 K. For run

5 of units 1, 2, 3 and runs 5-11 of units 7, 8, 9, 10, 11, the degaussing procedure was done at 300 K with no further degaussing at lower

temperatures. We can see that for samples with Ail spot welds (7, 8, 9,

10, 11) there is no significant difference in T" c or in the standard

deviation of T . When the hysteresis of the curves is examined in some

detail for all units (these data are not included in this report), we

find that there is generally less hysteresis in the transitions when the

second technique for degaussing the mu metal cans is used. We have

therefore decided to adopt the second practice in all future calibrations.

We can distill the information in Tables V and VI into a final

Table VII which indicates the total variation in T observed for all

c specimens of a given material in SRM units 1, 2, 3, 7, 8, 9, 10, 11 and

the expected reproducibility of the T

c of a given specimen. We see, for

example, that the T of a tungsten sample will fall within ±0.8 mK of

15.9 mK and that its reproducibility might be as good as 0.12 mK and as

poor as 0.5 mK. We estimate that the uncertainty in measurement of the

resistance can lead to a variation of ±50 yK which could account for the

lower limit in the last column of Table VII. The evidence suggests that

the upper limit is not due to lack of reproducibility of the GERT itself.

The most likely cause of the large standard deviation for some samples

is lack of uniformity of the magnetic field in the inner shield. Using

the information in the third-to-last column in Table IV, we can calculate that a ±1 yT variation in the remanent magnetic field from experiment to experiment almost exactly gives the largest standard deviation

observed for all materials in Table VII. Unfortunately, the magnetic

field was not measured so this must remain as a conjecture. At any

rate, the user can expect a reproducibility at the worst of ±0.2 mK for

the five transitions given by SRM 768 and possibly some improvement if

greater care is exercised in reducing the ambient magnetic field. The

information contained in Table VII was used as the basis for the entries

given in Table I.

33
TABLE VII

Variation in T" c Observed for SRM 768 Units 1,2,3,7,8,9,10,11

Material Lowest T Highest T

Observed for a Given Material

Range Variation of the

standard deviation

(mK) (mK) (mK) (mK)

W

Be

Ir

AuAl,

Auln,

15.1

21.3

98.4

160.2

204.9

17.1

4.8

99.5

161 .0

207.7

2.0

3.5

1.1

0.8

2.8

0.00 _ 0.45

0.03 - 0.86

0.02 - 0.15

0.02 - 0.25

0.13 - 0.25

VI. CONCLUSION

We have described how five superconducting materials were incorporated into a device which can be used with a simple room- temperature

detection circuit to define five reference temperatures from 0.015 to

0.206 K. If proper electronic detection techniques are used and care is

exercised in reducing the dc magnetic field, the user can expect to

obtain a temperature reproducibility of the transitions to no worse than

±0.2 mK.

34
VII. ACKNOWLEDGMENTS

Many people have made significant contributions to this project

which has culminated in SRM 768. A collaboration with Dr. H. Marshak

resulted in the intercomparison of the noise and nuclear orientation

thermometers which forms the foundation for the temperature scale borne

by SRM 768. Dr. D. B. Utton initiated the exploration which led to the

selection of AuA£ 2 for the device; he also studied the magnetic properties (magnetization and H (T)) of AuA£2 and Auln 2 . Dr. J. F. Schooley

offered several suggestions which were incorporated into the device and

this document. Mr. F. S. Biancaniello developed the necessary sample

preparation techniques and then produced the boules of AuA£2 and Auln 2 .

We thank Mr. L. K. Ives for generously allowing us to use his sparkcutting machine, and Mr. C. H. Brady for making microphotographs of the

gold-compound materials. Mr. R. S. Kaeser developed and built several

electronic circuits which were of great assistance, and his advice on

several experimental matters proved consistently valuable. Mr. S. E.

King assisted in many phases of the experimental program (especially in

data reduction and analysis) for two summers during the course of this

program. Finally, we gratefully acknowledge both the financial support

and encouragement from our colleagues in the Office of Standard Reference Materials: Mr. R. K. Kirby, Mr. R. E. Michaelis, and Mr. G. A.

Uriano.

35
Several individuals were generous enough to lend us test samples of

many materials. In general, the effect of their loans was to assist us

in defining the metallurgical qualities necessary to obtain boules with

the desired superconducting properties. Arranged by the material they

were kind enough to send, they are:

Be

1. D. L. McElroy, Oak Ridge National Laboratory, Oak Ridge,

Tenn.

2. R. L. Falge, Jr. , NBS.

3. W. A. Reed, Bell Laboratories, Murray Hill, NJ.

4. G. J. London, The Franklyn Institute Research Laboratories, Philadelphia, PA.

Ir

1. E. Zysk, Englehard Laboratories, Newark, NJ.

2. S. Hornfeldt, Uppsala University, Uppsala, Sweden.

3. D. U. Gubser, U.S. Naval Research Laboratory,

Washington, D.C.

4. J. Rexer, Union Carbide Corporation, Parma, Ohio.

AuA£2

1 . L. Bennett, NBS.

Auln 2

1. K. Andres, Bell Laboratories, Murray Hill, NJ.

36
VIII. REFERENCES

To be published, Metrologia.

Schooley, J. F., Soulen, R. J., and Evans, G. A., NBS Special

Publication 260-44, U. S. Government Printing Office,

Washington, D. C. 20402 (Catalog No. CI 3. 10: 260-44).

Hartshorn, L., J. Sci. Instru. 2, 145 (1924).

Soulen, R. J., Schooley, J. F., and Evans, G. A.,

Review Sci. Instru. 44, 1537 (1973).

Wheatley, J., Physics 1, 342 (1965).

Gorter, C. J., and Casimir, H. G. B., Phys. Z. 35, 963 (1934);

Z. Tech. Phys. 15., 539 (1934).

Bardeen, J., Cooper, L. N., and Schrieffer, J. R.,

Phys. Rev. K)8, 1175 (1957).

Ginsburg, V. L., and Landau, L. D., Zh. Eksperim.

i. Teor. Fig. 20, 1064 (1950).

Goodman, B. B., IBM J. Res. Develop. 6, 63 (1962).

Pierce, J., J. Appl . Phys. 44, 1342 (1973); see also,

Pierce, J., PhD Thesis, Stanford University.

37
MBS-1 1 4A (REv. s-7ei

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS SP 260-62

No. 3. teciptent's Accession Ho,

4. TITLE AND SUBTITLE

Standard Reference Materials:

Temperature Reference Standard for Use Below 0.5 K: SRM-768

5. Publication Date April 1979

(. Performing Organization Code

7. AUTHOR(S)

R. J. Soulen, Jr. and R. B. Dove

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

10, Project/Task/Work Unit No.

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, state, zip)

Same as Item 9

13. Type of Report & Period Covered

14* Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number:

|

| Document describes a computer program; SF-185, F I PS Software Summary, is attached. 79-600014

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here.)

Cryogenic temperature scales are now available (viz., the newly created EPT-76

[1]) which are quite accurate and which extend deep into the cryogenic region (as

low as 0.5 K). It is the region below 0.5 K where no formal scale exists which is

of concern here. By developing a compact device which provides five reference

temperatures from 0.015 K to 0.21 K, the authors hope to provide a lingua franca

by which experimental results from different laboratories involving the parameter

temperature may be meaningfully compared.

Such a device, designated SRM 768, is now available and consists of a self-contained assembly of coils and five samples which can be used to provide

in situ temperature calibration. Simple room temperature electronics readily

permit the observation of the five narrow and highly reproducible superconducting

phase transitions. These phase transitions have been assigned temperature values

by means of fundamental thermometers used at the National Bureau of Standards.

Provided that care is exercised in reducing the magnetic field acting upon the

device, the user can confidently expect to achieve a temperature reproducibility

and traceability to the NBS temperature scale of ±0.3 mK.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

AuA£ 2 ; Auln 2 ; Be; cryogenic temperature scale; fixed points; Ir; superconductivity;

thermometry; W.

18. AVAILABILITY 9Unlimited

I | For Official Distribution. Do Not Release to NTIS QOrder From Sup. of Doc, U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003-

|

| Order From National Technical Information Service (NTIS), Springfield,

VA. 22161

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