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NBS SPECIAL PUBLICATION 260-59

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

Standard Reference Materials:

ECTRON PARAMAGNETIC RESONANCE

INTENSITY STANDARD: SRM-2601;

DESCRIPTION AND USE
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 divisiqns within the center are located at Boulder, Colorado, 80303.

The National Bureau of Standards was reorganized, effective April 9, 1978.
P 2 5 197S

f cw

Standard Reference Materials:

I ELECTRON PARAMAGNETIC RESONANCE ^

INTENSITY STANDARD: SRM 2601;

DESCRIPTION AND USE

LT. Chang

A.H. Kahn

Center for Materials Science

National Measurement Laboratory

National Bureau of Standards

Washington, D.C. 20234

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

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

OS' NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued August 1978
Library of Congress Catalog Card Number 78-600064

National Bureau of Standards Special Publication 260-59

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-59, 60 page's (Aug. 1978)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1978

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

Stock No. 003-003-01975-5 Price $2.30

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

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

National Bureau of Standards are "well-characterized materials, produced in quantity, that calibrate a measurement

system to assure compatibility of measurement in 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. In many industries

traceability of their quality control process to the national

measurement system is 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 all phases of the preparation, measurement,

and certification 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. It is also

hoped that these papers will 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

J. Paul Cali, 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-

1 1063**

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). COM74-1 1060**

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-

1 1067**

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**

C(

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

K

Michaelis, R. E., Standard Reference Material ' Homogeneity Characterization on NBS Spectn i

''

metric Standards II: Cartridge Brass and Lo\j ^

Alloy Steel, NBS Misc. Publ. 260-10 (Decemb U

1965). COM74- 11064** »

Napolitano, A., and Hawkins, E. G., Standai "(

Reference Materials: Viscosity of Standai

Lead-Silica Glass, NBS Misc. Publ. 260-1 w

(November 1966). NBS Misc. Publ. 260-1 1** 11

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

JJ Standard Reference Materials: Homogener

Characterization of NBS Spectrometric Stani

ards III: White Cast Iron and Stainless Ste Powder Compact, NBS Misc. Publ. 260-; (September 1966). NBS Misc. Publ. 260-12*'

Spijkerman, J. 1., Snediker, D. K., Ruegg, F. C and DeVoe, J. R., Standard Reference Mat

rials: Mossbauer Spectroscopy Standard for

Chemical Shift of Iron Compounds, NBS Mis

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

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

Materials: Determination of Oxygen in Ferroi

Materials - SRM 1090, 1091, and 1092, NB

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

Publ. 260-14**

Passaglia, E., and Shouse, P. J., Standard Refe ence Materials: Recommended Method of U

of Standard Light-Sensitive Paper for Calibra

ing Carbon Arcs Used in Testing Textiles f< Colorfastness to Light, NBS Misc. Publ. 260-1 (June 1967). (Replaced by NBS Spec. Put 260-41.)

Yakowitz, H., Michaelis, R. E., and Vieth, D. I Standard Reference Materials: Homogeneii'

f«r

Characterization of NBS Spectrometric Stani Stan ards IV: Preparation and Microprobe Chara< kn

terization of W-20% MO Alloy Fabricated t Spec Powder Metallurgical Methods, NBS Spe US Publ. 260-16 (January 1969). COM74-11062* hrid Catanzaro, E. J., Champion, C. E., Garner, E. I ft,

a

Marinenko, G., Sappenfield, K. M., and Shield Male W. R., Standard Reference Materials: Bor 5RM" Acid; Isotopic and Assay Standard Referent lopp.

Materials, NBS Spec. Publ. 260-17 (Februai k\.

1970). Out of Print I

E*r,S

Jai

Feb

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 Interlaboratory 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**

apolitano, 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**

riicho, 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**

ylartin, 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

Jarner, 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**

>Ieinrich, 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**

eller, 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). COM7 1-50282**

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). COM7 1-50283**

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

v

I
Cooperative Study (SRM 758, 759, 760), NBS

Spec. Publ. 260-40 (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, K.. 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. 260-45 (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). SN003-003-0 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.

260-49 (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:

vi

Electrolytic Iron, SRM's 734 and 797 from

1000 K, NBS Spec. Publ. 260-50 (June 19' 1.00* SN003-003-0 1425-7

Mavrodineanu, R., and Baldwin, J. R., Stanc

Reference Materials: Glass Filters As a Stanc

Reference Material for Spectrophotome

Selection; Preparation; Certification; Use-S

930, NBS Spec. Publ. 260-51 (November 19 $1.90* SN003-003-01481-8

Hust, J. G., and Giarratano, P. J., Standard Rt ence Materials: Thermal Conductivity and E

trical Resistivity Standard Reference Mate:

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

260-52 (September 1975). $1.05* SN003-1

01464-8

Durst, R. A., Standard Reference Materi

Standardization of pH Measurements, I Spec. Publ. 260-53 (December 1975, Revis

$1.05* SN003-003-01551-2

Burke, R. W., and Mavrodineanu, R., Stanc

Reference Materials: Certification and Us

Acidic Potassium Dichromate Solutions a; Ultraviolet Absorbance Standard, NBS S

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

01828-7

Ditmars, D. A., Cezairliyan, A., Ishihara, S., Douglas, T. B., Standard Reference Mater

Enthalpy and Heat Capacity; Molybden

SRM 78 1 , From 273 to 2800 K, NBS Spec. P

.

260-55 (September 1977). $2.20* SN003I

01836-8

Powell, R. L., Sparks, L. L., and Hust, J. Standard Reference Materials: Stand

Thermocouple Material, Pt.-67:SRM1967, f Spec. Publ. 260-56 (February 1978). $2.' SN003-003-0 18864

Cali, J. P. and Plebanski, T., Guide to Un!

States Reference Materials, NBS Spec. P

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

01883-0

Barnes, J. D. and Martin, G. M., Standard Re ence Materials: Polyester Film for Oxygen 1 ' Transmission Measurements. SRM 1470, N

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

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

Materials: Electron Paramagnetic Resom

Intensity Standard: SRM 2601, NBS S< Publ. 260-59 (in press).

Velapoldi, R. A., Paule, R. C, Schaffer, • Mandel, Jr., and moody, J. R., Standard Re ence Materials: A Reference Method for : Determination of Sodium in Serum, NBS Sj

Publ. 260-60 (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.

vii
Contents Page

1. Introduction 2

2. Theory 4

2.1 Ruby Crystal 4

2.2 The Cr3+ Spectrum r with H Parallel to the c-axis 4 o

2.3 The Cr 3+ Spectrum r with H Not Parallel to the c-axis ... 5 o

2.4 Polarization of the Microwave Field and the

Integrated Intensity 5

2.5 Tabulations and Graphs 6

3. Description of the Ruby EPR SRM 27

3.1 Physical Description 27

3.2 Packaging 27

3.3 Handling 27

3.4 Cleaning

.

. 2m

4. Positioning the SRM in the Cavity 28

4.1 The Microwave Cavity 28

4.1.1 Rectangular cavity, TE102 mode 28

4.1.2 Cylindrical cavity, TE 0 n mode 29

4.1.3 Cylindrical cavity, TM110 mode 29

4.2 Adhesives . U

4.3 Sample Mounting and Associated RF Polarization 29

4.4 Test Run with the Ruby SRM 38

5. Measurement of the Number of Spins 39

5.1 Area under the Absorption Curve 39

5.2 Comparison of Integrated Areas 41

5.2.1 Use of the ruby SRM with H parallel to the

c-axis; test sample with spin 1/2 . 42

viii
5.2.2 Use of the ruby SRM with H perpendicular to the

c-axis; test sample with spin 1/2 42

5.2.3 Arbitrary orientation of the ruby SRM; test sample

with spin 1/2 43

5.2.4 Arbitrary orientation of the ruby SRM; test sample

of arbitrary spin 44

5.3 Calibration and Use of a Working Standard 44

5.4 Use at Other than Room Temperature 44

5.5 Precautions Concerning Visible, UV, X-ray and

Nuclear Radiations 45

List of Symbols 46

References 47

Appendix 1. Magnetic Field Units 48

Appendix 2. Use of the Ruby SRM with a Large Test Sample 49

List of Tables Page

3+ Table 1. EPR spectrum and intensities of Cr in ruby

at 6.000 GHz 7

Table 2. EPR spectrum and intensities of Cr^

+ in ruby

at 9.500 GHz. < . 8

Table 3. EPR spectrum and intensities of Cr*^ + in ruby

at 14.500 GHz 10

Table 4. EPR spectrum and intensities of Cr^

+ in ruby

at 18.000 GHz ... .' 12

Table 5. EPR spectrum and intensities of Cr^

+ in ruby

at, 24.000 GHz 14

Table 6. EPR spectrum and intensities of Cr^

+ in ruby

at 35.000 GHz 1'6

Table 7. EPR spectrum and intensities of Cr^

+ in ruby

at 50.000 GHz 18

ix
List of Figures Page

Fig. 1. Paramagnetic resonance spectrum of Cr^

+ in ruby for

a transition frequency of 6.0 GHz 20

Fig. 2. Paramagnetic resonance spectrum of Cr^

+ in ruby for

a transition frequency of 9.5 GHz 21

Fig. 3. Paramagnetic resonance spectrum of Cr^

+ in ruby for

a transition frequency of 14.5 GHz 22

Fig. 4. Paramagnetic resonance spectrum of Cr'^ + in ruby for

a transition frequency of 18.0 GHz 23

Fig. 5. Paramagnetic resonance spectrum of Cr^

+ in ruby for

a transition frequency of 24.0 GHz 24

Fig. 6. Paramagnetic resonance spectrum of Cr^

+ in ruby for

a transition frequency of 35.0 GHz . . . 25

Fig. 7. Paramagnetic resonance spectrum of Cr^

+ in ruby for

a transition frequency of 50.0 GHz 26

Fig. 8. Rectangular cavity, TE^^ m°de 30

Fig. 9. Rectangular cavity, TEj^ m°de 31

Fig. 10. Cylindrical cavity, TE^^ mode 32

Fig. 11. Cylindrical cavity, TM^^ mode 33

Fig. 12. Relative orientation of the wafer SRM and the laboratory

coordinate system x'y'z' 34

Fig. 13. Relative orientation of the bar SRM and the laboratory

coordinate system x'y'z' . . 3~

Fig. 14. Relative orientation of the wafer SRM and the laboratory

coordinate system x'y'z' 36

Fig. 15. Relative orientation of the bar SRM and the laboratory

coordinate system x'y'z' 37

Fig. 16. Paramagnetic resonance absorption of Cr"^ +

, (1/2,-1/2)

transition 40

x
Standard Reference Materials:

ELECTRON PARAMAGNETIC RESONANCE INTENSITY STANDARD: SRM-2601;

Description and Use.

T. Chang and A. H. Kahn

Ceramics, Glass, and Solid State Science Division

Center for Materials Science

National Measurement Laboratory

National Bureau of Standards

Washington, D. C. 20234

Abstract

This publication provides information concerning the use of ruby

samples, of known Cr 3+ concentration, supplied as a Standard Reference

Material (SRM) for intensity measurements in electron paramagnetic

resonance (EPR) experiments. By comparing the measured intensities of

EPR absorption lines of a test sample and of the SRM, it is often possible for the user to obtain a determination of the number of spins in the

test sample. Procedures and data on ruby necessary for carrying out this

process are presented. Examples of the use of the SRM in typical cases

are offered.

Keywords: Absolute measurement; intensity standard; paramagnetic

resonance; spin concentration; Standard Reference Material

(SRM); ruby

1
1. Introduction

This instruction manual is supplied as an aid in using the NBS

Electron Paramagnetic Resonance (EPR) Intensity 'Standard Reference

Material (SRM) . It provides suggestions for use of the SRM for measuring

the number of active paramagnetic centers in a test sample. This measur*

ment is performed by comparison of the area of the test EPR absorption

line with that of an EPR absorption line of the ruby SRM. This method i: satisfactory if the test resonance is reasonably narrow (about 100 Oe or less) and is describable by a spin Hamiltonian. Even if the test spectrv

is not well understood, comparisons of resonance line areas can be used

to obtain relative measurements of the number of spins in test samples.

The nature of the EPR experiment is outlined so that the nomenclatuj

and symbols used may be defined unambiguously. For a more detailed description, the user is referred to any standard text [1-6] . For further

details concerning the spectrum of ruby and the research leading to the

preparation of the Ruby SRM, the user is referred to a publication by

the authors [7]

.

In the conventional EPR measurement, the sample to be tested is

placed in a sample cavity at a site of uniform microwave magnetic field,

Hi. The cavity is located in a uniform static field, H , at right angle;

to Hj. The field H is modulated at a low frequency (typically 30 Hz to

200 kHz) for signal detection. The static field is slowly varied until

the spins in the sample satisfy the resonance condition, that the

difference of energy, AE, of two of their energy levels in the magnetic

field, coincides with the microwave radiation according to the relation,

AE = hv, (1)

where h is Planck's constant and v is the microwave frequency. A recording of the change of cavity power dissipation, induced by the spins

going into resonance as H is varied, is referred to as the EPR absorption curve. The usual experimental arrangement produces a recording of

the derivative with respect to H of the absorption curve, and one

integration is necessary to obtain the absorption curve. A further

integration with respect to H yields the area under the absorption

curve (see section 5.1). Tfiis area is the measure of the intensity of

the particular resonance absorption being studied. The EPR spectrometer,

as commonly used, gives the data in arbitrary units. By comparing the

absorption signal of the test sample with the signal from a. standard

sample having a known number of spins and a well-understood spectrum, it

is possible, in many cases, to determine the number of the unknown spins

The area under the absorption curve of an EPR line can be written

as a product of four factors, as follows:

Numbers in brackets refer to literature references at the end of

the paper.
Area = [Spectrometer gain factor] x [Filling factor]

x [Concentration of spins]

x [Integrated intensity per spin in unit RF field] (2)

a) The first factor depends on spectrometer conditions. This

factor will include detection efficiency, demodulation efficiency,

amplifier gain, etc. When comparing two different resonances, it is

desirable to hold this factor constant.

b) The second factor is the filling factor, defined by

<H.

2

> V

_ 1 s s n = 5 (3)

<H"> V

1 c c

where V is the sample volume, V the cavity volume, and the brackets

indicate the average of H^ 2 over the sample(s) or cavity (c) . This

factor accounts for the fact that the absorption intensity is proportional to the square of the microwave field amplitude acting on the

spins. Filling factors are tabulated in reference [3].

c) The third factor corresponds to the fact that the absorption

per unit volume of the sample is proportional to the concentration of

spins

.

t d) The last factor is the absorption per single spin, per unit

microwave field amplitude. This factor depends in detail on the nature

of the absorbing center, its spin, energy levels, and the direction of

applied fields. This factor has been computed for Cr 3+ in ruby [7] for

a wide range of conditions and the results are available from tables

supplied in this manual.

On performing a slight rearrangement of the second and third factors,

we obtain the form,

Area = [Spectrometer gain factor] x j— y—

<H • > c

1 c

x [Total number of spins]

x [Integrated intensity per spin] (4)

which explicitly demonstrates that the area is proportional to the

number of spins in the sample.

3
The area under the EPR absorption curve must be used for the

measurement of the number of spins. The product of the square of the

linewidth and the peak-to-peak height is an approximation to the area and

may not give an accurate value. It is important that the user have avail

able the facility for performing the double integrations numerically,

either by computer or by graphical methods; otherwise, the measurement of

the number of spins can not be accomplished.

The EPR standard sample made of ruby is one of the Standard Reference Materials (SRM's) certified and issued by the National Bureau of

Standards. Hence, we shall call the standard sample the EPR SRM.

Wherever we mention the SRM in this publication, we mean the EPR SRM

only and do not refer to any other types of SRM's. We use the terms

standard samples, ruby standards, ruby specimen, or simply SRM, inter

changeably

.

2. Theory

2.1 Ruby Crystal

The EPR SRM specimens were cut from single crystal ruby, i.e.,

chromium (Cr) doped corundum (AI2O3) . These crystals possess trigonal

symmetry. The trigonal axis is a unique axis of the crystal and is calle

the c-axis.

The chromium ions in ruby are substitutional for the aluminum ions,

and assume the trivalent state Cr 3+

. They are the active ingredient

which provides the EPR absorption centers. The Cr 3+ ions experience the

same crystalline environment as the aluminum ions. As a consequence of

the crystalline symmetry and the properties of the Cr3+ ions, the EPR

spectrum of the Cr 3 + in ruby is strongly dependent on the angle, 9,

between the static field, H , and the c-axis. The spectrum does not

vary when the static field, H , is rotated in a plane which is normal to

the c-axis.

In the next two sections, we give a brief description of the energy

levels of the Cr 3+ ion in ruby. Formulas are presented for completeness,

but the user can obtain all needed information from the tables, as

explained in section 2.5.

2.2 The Cr 3+ Spectrum with H Parallel to the c-axis r o

The EPR spectrum for H parallel to the c-axis, i.e., 6 =0°, is

the simplest. In this case the energy levels of the Cr 3+ ions of

concern in the EPR experiment are given by the expression

E = g y D H m + D (m

2

-5/4) (5)

m

&

n B o

v J

4
where y n is the Bohr magneton, H is the static field, g„ is the

p o II parallel g-factor, D is the zero field splitting factor, and m is the

magnetic quantum number. Cr 3+ has spin 3/2 and thus m can assume any of

the four values of 3/2, 1/2, -1/2, and -3/2. Whenever the applied

microwave frequency satisfies the relation

hv = AE = E .-E = g,,y DH +(2m+l)D , (6) m+1 m nl B o

v J K J

resonance absorption can occur. We may denote the transition by pairs

of indices (m+l,m), i.e., (3/2,1/2), (1/2,-1/2), and (-1/2,-3/2). There

are three allowed transitions.

2.3 The Cr 3+ Spectrum r with H Not Parallel to the c-axis

o

When the c-axis and the static magnetic field are not parallel,

there are still four energy levels for Cr 3+ ions, but they can not be

described in the simple form of Eq. (5); also, another parameter g^ , the

perpendicular g-factor, is needed. In this case, the energy states may

not be described by the simple quantum numbers m; we choose to label the

levels by the numbers 1,2,3,4 from the highest energy in sequence downward. In general, there are six possible distinct transitions and we

label them (1,2), (1,3), etc. A particular transition in this notation

is referred to by the symbol (a, 6). Not all transitions will be strong

enough to be observed.

When the field H is parallel to the c-axis, we may use either the

labelling method of tRis section or of the previous section.

From our measurements, the values of the constants for Cr 3+ in

ruby are

a. = 1.9817 ± 0.0004

gj_ = 1.9819 t 0.0006 (7)

2D/h = -11.493 ± 0.004 GHz

2.4 Polarization of the Microwave Field and the Integrated Intensity

The values of the resonance fields for a given microwave frequency

depend on the angle between H and the c-axis of the ruby crystal.

However, the intensity of a particular resonance line further depends on

the direction of the RF field, \\\ , i.e., on its direction of polarization.

(We remember that Hj is always perpendicular to the static field, H

q

.)

To specify the orientation of the various field vectors with

respect to the crystalline c-axis of the ruby SRM, we introduce a set of

mutually perpendicular reference axes x', y', and z', which will be

called the laboratory coordinate system. The z'-axis is chosen to lie

along the direction of the static field, H

q

. The x'-axis, perpendicular

5
to H , is selected to lie in the plane of the crystalline c-axis and the

z'-axis. (If the c-axis is parallel to the z'-axis, the direction of

the x'-axis will be arbitrary.) Lastly, the y'-axis is chosen normal to

the x'- and z'-axes. EPR experiments are usually performed with the RF

field, Hi, parallel to the x'- or y

1 - axes. In these cases we refer to

the RF field as having x'- or y

1 - polarization, respectively. The two

polarizations will induce the same EPR transitions at a given static

field, H , but the line intensities will be different. Information

concerning the polarizations for particular cavities and crystal mounting will be given in Sec. 4.3.

The integrated intensity associated with a single Cr 3+ ion is

theoretically determined if the particular transition and direction of

polarization are specified. The intensity has been calculated from the

transition probability rate according to the usual theory of the intensity of spectral lines [7] . This theory gives the result that one would

obtain if line profiles were obtained by sweeping frequency. The areas

would be proportional to the transition probability rates T , or T^i,

for the polarizations x' or y'. However, in the usual EPR experiment

the absorption line profile is obtained by sweeping the field H . In

this, the common case, the integrated intensity (per spin) can Be

obtained from the transition probabilities divided by a weighting factor,

dv

R /dH , the rate of change of resonance frequency with respect to H

for the°(a,$) transition. The field-sweep integrated intensity will Be

denoted by U , or U ,

x' y'

The transition probabilities, T ,, T ,, are normalized so that the

quantities at (1/2,-1/2) are unity. XThe integrated intensities, Ux

i , Uyt,

are also normalized and adjusted so that the values for the (1/2,-1/2)

transition are unity.

2.5 Tabulations and Graphs

The resonance fields, transition probabilities, and the integrated

intensities are listed in Table 1 through Table 7. Each table corresponds to a commonly used microwave frequency. The frequencies are,

respectively, 6.0, 9.5, 14.5, 18.0, 24.0, 35.0, and 50.0 GHz. In each

table the EPR transitions are listed for values of 0, the angle between

H

q

and the c-axis, from 0° to 90° in steps of 10°.

In the tables the microwave frequency is identified in the caption.

The resonances are grouped according to the value of 0, listed in column

1. Within the group for each angle, 0, the resonances are listed in

order of increasing magnetic field, H . The resonance field values are

listed in column 2. The units of magnetic fields are discussed in

Appendix 1. The transitions are identified in column 3 according to the

(a, 3) notation (see Sec. 2.3). For 0 = 0°, the allowed transitions are

also identified by the quantum numbers (m+l,m) (see Sec. 2.2). The

normalized transition probabilities, T T ,, are listed in columns 4

and 5. The integrated intensities, U

* and^U t are listed in columns 6

6
Table 1. The resonance magnetic field, the transition probability,

T, and the integrated intensity, U, of Cr 3+ ion in ruby,

for microwave frequency of 6.000 GHz.

ANGLE (Deg) H (Oe) TRANS. T , T , u , u , X V X V

0.0 721.1 (3,4) .000 .000 .000 .000

990.2 (2,3) .000 .000 .000 .000

1980.5 U,3)&, h) .750 .750 .750 .750

2163.

3

(1,3) 1.000 1.000 1.000 1.000

3153.5 (2,3) .000 .000 .000 .000

6306.6 (1,2) (% A) .750 .750 .750 .750

10.0 732.6 (3,4) .000 .000 .000 .000

996.5 (2,3) .035 .037 .018 .019

2076.6 (1,2) .162 1.630 .311 3.124

2143.7 (1,2) .051 1.441 .113 3.180

3263.7 (2,3) .261 .249 . 149 .142

5737.3 (1,2) .501 .763 .608 .926

20.0 768.9 (3,4) .000 .000 .000 .000

1019.5 (2,3) .096 . 123 .051 .065

1850.0 (1,2) .458 1.235 .417 1.124

3454.3 (2,3) .539 .478 .362 .320

30.0 837.1 (3,4) .001 .001 .000 .000

1072.7 (2,3) .120 .224 .071 .132

1643.0 (1,2) .407 1. 159 .326 .930

3545.3 (2,3) .659 .582 .505 .446

40.0 952.3 (3,4) .003 .003 .001 .001

1178.

1

(2,3) .085 .325 .061 .233

1473.0 (1,2) .364 1. 124 .265 .817

3416.0 (2,3) .615 .628 .565 .577

50.0 1150.4 (3,4) .011 .012 .006 .007

1343.7 (1,2) .335 1. 104 .225 .742

1407.0 (2,3) .015 .434 .017 .490

2947.7 (2,3) .392 .638 .530 .862

60.0 1250.4 (1,2) .317 1.092 .200 .690

1526.6 (3,4) .050 .047 .040 .038

70.0 1187.9 (1,2) .307 1.085 .186 .656

2366.4 (3,4) .290 .174 .372 .223

80.0 1151.6 (1,2) . 302 1 . 082 . 178 . 637

3565.6 (3,4) .935 .321 1.138 .391

90.0 1139.8 (1,2) .300 1.081 .175 .630

4048.4 (3,4) 1.262 .360 1.377 .393

7
Table 2. The resonance magnetic field, the transition probability,

T, and the integrated intensity, U, of Cr 3+ ion in ruby,

for microwave frequency of 9.500 GHz.

ANGLE (Deg) H (Oe) TRANS

0.0 359.4 (2,3)

718.7 (1,3)

1141.8 (3,4)

3425.0 (1,3) (h,

1784 4 (2 3") 7568.8 (1,2) (3j

10.0 360.2 (2,3)

760.2 (1,3)

1160.9 (3,4)

3146.

(1,3)

4042 6 (2 1)

7154.3 (1,2)

20.0 363.7 (2,3)

920.3 (1,3)

1221 .

(3 4)

2730.5 (1,3)

4351.6 (2,3)

5948.2 (1,2)

30.0 373.0 (2.3)

1338.7 (3,4)

4081.2 (1,2)

4532.8 (2,3)

40*+ \J • 0\J 391 4 (2 3}

1544.9 (3,4)

2689.

(1,2)

4519.5 (2,3)

SO 0 4?? 7 (2 3"> 1929.3 (3,4)

2331.2 (1,2)

4277.0 (2,3)

60.0 475.0 (2,3)

2147.7 (1,2)

2716.4 (3,4)

3805.5 (2,3)

70.0 564.8 (2,3)

2035.9 (1,2)

3143.7 (2,3)

3965.6 (3,4)

T , T , u , u , X y X y

.000 .000 .000 .000

.750 .750 .750 .750

.000 .000 .000 .000

1.000 1.000 1.000 1.000

.000 .000 .000 .000

.750 .750 .750 .750

.025 .026 .012 .013

.688 .716 .737 .768

.000 .000 .000 .000

.793 .738 .645 .600

.541 .526 .368 .358

.646 .759 .692 .813

.074 .087 .038 .044

.526 .622 .729 .861

.001 .001 .000 .000

.701 .397 .528 .299

. DJD SI? AQS

.393 .796 .531 1.076

.111 .157 .059 .083

.007 .007 .003 .003

l Si Q97 2 019

.772 .706 .622 .568

.116 .225 .065 .127

.028 .031 .014 .015

1 9 "\ 1 9QQ 1 . ozo

.773 .735 .667 .634

.093 .287 .058 .180

.097 .103 .068 .072

. JUL) 1 91 1 1 . Z 1

987 i i fin I . 1 ou

.709 .756 .673 .717

.053 .346 .039 .254

.337 1. 169 .275 .953

.293 .251 .321 .276

.595 .779 .647 .847

.014 .409 .014 .386

.355 1. 142 .267 .860

.456 .812 .611 1.087

.649 .382 .790 .465

8
Table 2 (con't.)

ANGLE (Deg) H (Oe) TRANS

.

T , T , u , u , X y AV

y

80.0 750.

0

(2.3) .002 .504 . 002 .784

1973.4 (1,2) .363 1.129 .262 .815

2335.9 (2,3) .318 .878 .640 1.769

5006.2 (3,4) .984 .437 1.075 .478

90.0 1953.5 (1,2) .366 1.124 .261 .802

5386.7 (3,4) 1.117 .452 1.162 .470
Table 3. The resonance magnetic field, the transition probability,

T, and the integrated intensity, U, of Cr 3+ ion in ruby,

for microwave frequency of 14.500 GHz.

ANGLE (Deg)

0.0

10.0

20.0

30.0

40.0

50.0

TT f f\ — \ H (Oe) mr» A ITT TRANS

T t X

542.2 (1,4) .000

1084.

(2,4) (-%, - h ) . 750

i "7 / o a 1742./ O / \ (3,4) . 000

/. C O C A (1,3) . 000

C 1 O "7 C 5227 .

(2,3) (h.- i \ ^) 1.000

9371 .

/ 1 O \ / 3 h) . 750

540.6 (1,4) .016

1123.

(2,4) "7 O /

. 724

17/o.U / o / \ (3,4) .003

/ o a o / 439o.

/I O \ (1,3) o o o

. 332

54o2 .

y

/ O O \ (2,3) . 893

yujo.

( 1 , 2 ) . /03

538.7 (1,4) .050

1Z4U. O (2,4) £ £ o. 663

1 Q A 1 A isy l .

/ o /. \ (3,4) A/. A

. 044

jy4i .

t 1 O \ (1,3) O A 1

. 391

5o2z.

(2,3) . 86 /

O 1 A "7 /. ol07 .

(1,2) coo

. 5o3

539.8 (1,4) .077

1 / o c o 1425.

(2,4) .590

01 An £ 2149.

f o / \ (3,4) 1 O O

. lo2

3455.

(1,3) o / o

. 342

604o.

/ O O \ (2,3) O "7 A

6794.

/ 1 O \ (1,2) /CO

. 452

548.8 (1,4) .088

1646.

(2,4)

CAT

* 505

2681 .

/ O / \ (3,4) o / rv

. 340

2914.5 (1,3) O 1 o 21o

5457 .

(1,2) O "7 O

. 372

6099.

/ O O \ (2,3) . boo

568.4 (1,4) .082

1883.2 (2,4) .413

2295.3 (1,3) .090

3599.2 (3,4) .470

4466.4 (1,2) .372

5953.1 (2,3) .844

T , u , u , y X y

.000 .000 .000

.750 .750 .750

.000 .000 .000

.000 .000 .000

1.000 1.000 1 .000

.750 .750 .750

.017 .008 .008

.736 .744 .756

.003 .001 .001

.322 . 198 .193

.880 .801 .790

.757 .723 . 778

.055 .024 .027

.707 .721 .769

.045 .017 .018

.333 .240 .205

.833 .753 .724

.779 .650 .869

.097 .038 .047

.672 .650 .741

.195 . 102 . 109

.198 .210 . 121

.825 .760 .721

.827 .560 1 .026

.134 .043 .065

.621 .506 .623

.359 .297 .313

.028 .145 .018

.911 .494 1 .208

.831 .773 .742

.164 .041 .082

.552 .368 .491

.023 .072 .019

.447 .525 .499

1.010 .461 1 .253

.846 .782 .784

10
ANGLE (Deg)

60.0

70.0

80.0

90.0

Table 3 (con't.)

H (Oe) TRANS. T . x

?

601 .

6

(1 .4) • 064 \J \J *T 1716.8 (1 ,3) .031

2151.2 (2 ,4) .326

3902 3 (1 ,2) 408

4819 5 (3 ,4) 626

5624.0 (2 ,3) .808

653.5 (1 .4) .042

1298.4 (1 ,3) .008

2460.2 (2. 4) .235

3603.5 (1 ,2) .437

5173.8 (2 3) mill 111

6039.

1

(3.,4) .805

730.

9

(1 ,4) .021

1025.8 (1 ,3) .000

2775.0 (2 ,4) .110

3454.

7

(1 ,2) .454

4724.2 (2.,3) .774

6918.9 (3 ,4) .953

832.0 (1 ,4) .011

864.8 (1 ,3) .000

2936.7 (2 ,4) .000

3409.4 (1 ,2) .459

4507.8 (2 ,3) .790

7237.3 (3 4) 1.010

T TTu t TT V u 1 X y

1 ftQ on OQ7

.113 .027 .099

.470 .270 .389

1

1

. OAA uoo A18 iX

1 A S AQO 797 . JO7

• 870 / j 78Q 8^9

90Q 0? 114 1 1 4

.167 .006 .138

.359 .185 .283

X1 . 080 uou . 490 H*CU X 018

Q9 1

. 81O X 0\J SI 9 887

233 01 9 1 17

.179 .000 .133

.174 .081 .128

1 081 41 0 976

1-L • 001 \J\J ± 874 1 1 10

S9A QQ1 . J4J SAS

007 971

. uuu . OOO UUU OOO

.000 .000 .000

1.080 .407 .956

1.062 .941 1 .265

.527 1.027 .536

11
Table 4. The resonance magnetic field, the transition probability,

T, and the integrated intensity, U, of Cr 3 + ion in ruby,

for microwave frequency of 18.000 GHz.

ANGLE (Deg)

0.0

10.0

20.0

30.0

40.0

50.0

H (Oe) TRANS

T , T , u , u , x

? y' x' y

1

1173.0 (1,4) .000 .000 .000 .000

2163.3 (2,4) .000 .000 .000 .000

2346.1 (3,4) (-h,~ h) .750 .750 .750 .750

5316.9 (1,3) .000 .000 .000 .000

6489.7 (2,3) (hr-h) 1.000 1.000 1.000 1 .000

10633.8 (i,2)(%,h) .750 .750 .750 .750

1165.6 (1,4) .012 .013 .006 .006

2202.9 (2,4) .054 .055 .020 .020

2420.3 (3,4) .725 .731 .728 .734

5110.8 (1,3) N 7 ' .158 .154 .085 .083

6657.2 (2,3) .957 .948 .913 .904

10329.

(1,2) \ 7 ~ ' .718 .756 .731 .770

1150.

(1,4) .037 .041 .018 .019

2287.9 (2,4) .240 .250 .108 .113

2687.5 (3,4) .645 .662 .641 .658

4685.9 (1,3) .257 .231 .146 .132

6951.7 (2,3) .921 .896 .844 .821

9482.4 (1,2) .636 .774 .681 .828

1139.5 (1,4) .057 .069 .027 .032

2404.3 (2,4) .315 .342 .164 .178

3192.2 (3,4) .582 .601 .603 .623

4200.8 (1,3) \ 7 ' .253 .183 .145 .105

7172.9 (2,3) \ 7 S .910 .876 .825 .794

8286.6 (1,2) .542 .809 .617 .921

1143.0 (1,4) .065 .093 .030 .042

2563.7 (2,4) N 7 * .319 .366 .181 .208

3685.9 (1,3) \ 7 ' .188 .080 . 109 .046

3973.4 (3,4) .572 .569 .629 .627

7027.3 (1,2) .476 .864 .564 1 .024

7240.7 (2,3) .902 .873 .825 .799

1166.0 (1,4) .061 .111 .028 .050

2773.8 (2,4) .291 .355 .175 .214

3146.

(1,3) .101 .007 .061 .004

5032.2 (3,4) .618 .557 .701 .632

5981.4 (1,2) .456 .931 .531 1 .083

7127.9 (2,3) .888 .884 .831 .827

12
Table 4 (con't.)

ANGLE (Deg.)

60.0

70.0

80.0

90.0

H (Oe) TRANS. T , T , u , u , X V X

1213.

7

(1,4) .050 .125 .023 .057

2623.0 (1,3) .038 .008 .024 .005

3035.9 (2,4) .244 .315 .153 .197

5271.5 (1,2) .469 .985 .510 1 .069

6254.9 (3,4) .713 .556 .795 .619

6850.

6

(2,3) .869 .908 .843 .881

1291.2 (1,4) .034 .136 .016 .064

2181.2 (1,3) .009 .037 .006 .023

3335.2 (2,4) .172 .232 .109 .147

4851.6 (1,2) .490 1 .013 .493 1 .021

6469.

7

(2,3) .857 .949 .871 .965

7405.3 (3,4) .831 .558 .887 .595

1404.3 (1,4) .019 . 154 .009 .076

1849.6 (1,3) .000 .050 .000 .030

3613.3 (2,4) .070 .096 .043 .059

4634.0 (1,2) .504 1.024 .483 .982

6106.

4

(2,3) .863 1.006 .923 1 .077

8221.7 (3,4) .928 .560 .952 .574

1514.5 (1,4) .013 .230 .006 .111

1667.

6

(1,3) .000 .000 .000 .000

3739.

1

(2,4) .000 .000 .000 .000

4567.2 (1,2) .509 1.027 .479 .968

5944.3 (2,3) .873 1.040 .961 1 .145

8516.0 (3,4) .966 .561 .976 .567

13
Table 5. The resonance magnetic field, the transition probability.

T, and the integrated intensity, U, of Cr 3+ ion in ruby,

for microwave frequency of 24.000 GHz.

ANGLE (Deg)

0.0

10.0

20.0

30.0

40.0

50.0

H (Oe) TRANS. T , U , U , x' y' x

f V

2254.7 (1,4) .000 .000 .000 .000

2884.4 (2,4) .000 .000 .000 .000

4509.4 (3,4) (-k, -h) .750 .750 .750 .750

6398.4 (1,3) .000 .000 .000 .000

8653.3 (2,3) (Jg,-h) 1.000 1.000 1.000 1.000

12796.9 (1,2)(% , h) .750 .750 .750 .750

2220.

(1,4) .008 .008 .004 .004

2963.3 (2,4) \ 7 * S .004 .004 .001 .001

4609.4 (3,4) .742 .743 .749 .750

6245.6 (1,3) \ 7 J .059 .058 .030 .030

8759.3 (2,3) .985 .980 .967 .963

12521.5 (1,2) .731 .754 .738 .762

2155.9 (1,4) .023 .024 .010 .011

3153.7 (2,4) .033 .035 .013 .014

4928.1 (3,4) .719 .720 .744 .745

5871.8 (1,3) .134 .125 .071 .066

8983.4 (2,3) .961 .946 .919 .905

11755.9 (1,2) \ 7 y .681 .768 .706 .797

2104.7 (1,4) .033 .039 .014 .017

3396.

(2,4) \ 7 ' / .089 .096 .040 .043

5397.0 (1,3) .155 .128 .084 .069

5502.0 (3,4) .694 .686 .738 .729

9177.7 (2,3) .947 .925 .893 .872

10664.6 (1,2) .620 .793 .665 .850

2083.2 (1,4) .037 .050 .015 .021

3667.6 (2,4) .138 .155 .067 .075

4883.2 (1,3) .132 .087 .071 .047

6350.6 (3,4) > 7 ' .687 .652 .744 .706

9252.0 (2,3) \ 7 ^ / .938 .918 .884 .865

9475.6 (l\ 7s 2)^ .572 .829 .626 .907

2097.3 (1,4) .035 .058 .014 .024

3965.2 (2,4) .158 .184 .083 .097

4359.0 (1,3) .086 .035 .046 .019

7428.7 (3,4) .713 .627 .773 .680

8407.2 (1,2) .549 .871 .598 .949

9172.9 (2,3) .930 .924 .887 .881

14
Table 5 (con't.)

;LE (Deg) H (Oe) TRANS. T , T , u , u , x' y' x' y

1

60.0 2149.6 (1,4) .028 .063 .012 .026

3853.9 (1,3) .043 .006 .023 .003

4285.

9

f r\ I \ (2,4) .145 . 175 .079 .096

7590.8 (1,2) .547 .910 .579 .963

8606.0 (3,4) .769 .612 .820 .652

8953.1 (2,3) .923 .942 .900 .919

70.0 2241.4 (1,4) .019 .066 .008 .027

3407.8 (1,3) .015 .000 .008 .000

4606.6 (2,4) . 100 . 124 .056 .069

7049.8 (1,2) .555 .938 .565 .956

8651.4 (2,3) .921 .972 .925 .976

9676.8 (3,4) .838 .604 .870 .627

80.0 2365.0 (1,4) .011 .072 .004 .030

3060.5 (1,3) .002 .003 .001 .001

4867.

2

(2,4) .036 .045 .020 .025

6749.0 (1,2) .563 .953 .557 .943

8376.5 (2,3) .927 1.005 .959 1.040

10425.8 (3,4) .895 .601 .907 .609

90.0 2448.8 (1,4) .007 .082 .003 .033

2900.8 (1,3) .000 .000 .000 ,000

4972.3 (2,4) .000 .000 .000 .000

6653.3 (1,2) .566 .957 .554 .937

8261.2 (2,3) .932 1.022 .978 1.073

10695.3 (3,4) .917 .600 .921 .603

15
Table 6. -The resonance magnetic field, the transition probability,

T, and the integrated intensity, U, of Cr 3 + ion in ruby,

for microwave frequency of 35.000 GHz.

ANGLE (Deg)

0.0

10.0

20.0

30.0

40.0

50.0

H (Oe) TRANS

T , u , X y X y

A9AA 9 aaa . UUU aaa . UUU aaa . UUU AAA

. UUU

4237.5 (2,4) .000 .000 .000 .000

8381.3 (1,3) .000 .000 .000 .000

8475.6 (3,4) (-3s, -h:) .750 .750 .750 .750

12619.1 (2,3) (3s,-h) 1.000 1.000 1.000 1.000

16762.7 (1,2) (

3^ , h) .750 .750 .750 .750

OQQ1 Q (1,4) . UUz . uuz . 001 .001

4507.4 (2,4) .004 .004 .002 .002

8259.8 (1,3) .019 .019 .010 .010

8603.0 (3,4) .747 .746 .751 .749

12684.6 (2,3) .995 .993 .989 .986

16515.4 (1,2) .740 .753 .743 .757

o q o a "5 JoZU. J U ,4; aa7 . UU/ aaq . UUo aao.

. UUJ . UUJ

4839.1 (2,4) .018 .019 .008 .009

7933.6 (1,3) .054 .052 .028 .026

8990.7 (3,4) .741 .733 .753 .745

12835.9 (2,3) .984 .977 .966 .959

15822.8 (1,2) .713 .763 .725 .776

O. 7 A£ A J 1 uo . O U ,4; . miUl 1 . Ul O

nn/, . UU4 AA ^

. UUD

5206.

(2,4) .041 .044 .019 .020

7479,0 (1,3) .074 .067 .038 .034

9644.5 (3,4) .736 .714 .759 .736

12982.9 (2,3) .975 .963 .947 .936

14819.3 (1,2) .679 .779 .700 .804

ai o.

. Ul J m 7 . Ul / AA . UUJ AAA . UUo

5595.2 (2,4) .064 .070 .031 .034

6962.2 (1,3) .072 .058 .037 .030

10545.4 (3,4) .741 .692 .770 .720

13049.8 (2,3) .968 .957 .938 .927

13689.5 (1,2) .649 .802 .675 .835

3644.7 (1,4) .013 .020 .005 .007

5994.6 (2,4) .075 .085 .038 .043

6429.7 (1,3) .055 .037 .028 .019

11624.5 (3,4) .759 .673 .790 .700

12613.3 (1,2) .629 .827 .655 .861

12999.0 (2,3) .964 .960 .938 .934

16
Table 6 (con't.)

ANGLE (Deg) H (Oe) TRANS

.

T , T , u , u , y

VA J

60.0 3690.4 (1,4) .010 .021 .004 .008

5919.4 (1 3) 033 017 • 017 W X / • 009 WW-/

6386.0 (2,4) .069 .080 .036 .041

f 11722.2 (1,2) .621 .852 .639 .877

12750.0 (3,4) .791 .658 .815 .678

12840.8 (2,3) .962 .970 .947 .956

70.0 3777.3 (1,4) .006 .020 .002 .008

5472.

2

(1 3) 014 005 • 007 WW/ • 003 w W -J 6736.1 (2,4) .045 .053 .024 .028

11080.1 (1,2) .621 .871 .629 .883

12624.0 (2,3) .963 .987 .964 .987

13744.6 (3,4) .827 .648 .842 .660

80.0 3879.1 (1,4) .003 .019 .001 .007

5142 6 (1 3) 003 . 001 .002 .000

6989.7 (2,4) .015 .018 .008 .009

10700.2 (1,2) .623 .884 .622 .883

12433.6 (2,3) .967 1.003 .981 1.018

14429.7 (3,4) .856 .643 .862 .647

90.0 3930.9 (1,4) .002 .019 .001 .007

5012.7 (1,3) .000 .000 .000 .000

7084.2 (2,4) .000 .000 .000 .000

10575.2 (1,2) .624 .888 .620 .883

12356.9 (2,3) .969 1.010 .990 1.032

14673.8 (3,4) .867 .641 .869 .642

17
Table 7. The resonance magnetic field, the transition probability,

T, and the integrated intensity, U, of Cr 3+ ion in ruby,

for microwave frequency of 50.000 GHz.

ANGLE (Deg.)

0.0

10.0

20.0

30.0

40.0

50.0

n v*-'e ) 1 Jt\fUN O . TV

TTu » TTU 1 X y

6009.0 (1,4) .000 .000 .000 .000

6QA 1 Q O L} 000 . ooo UUU . uuu . uuu

1 1 OftS L \ l , -J/ ooo . ooo UUU . uuu . uuu

1

1 JOO 9ftR9J . s7 "iO . 7/ JURO Ten . / jU 7 =;n

. / DU

lOUi ift097/ • J9 f9 Q\ (l, _-5) ±

1

. OOO UUU 1

1

. ooo uuu 1

1

. OOO uuu 1

i

. nnn uuu

Z99Z 1l 70/ U • Qy 7^0 7 RO 7 7 ^n . / JU

5938.0 (1,4) .000 .000 .000 .000

lC\lf\ 1 U / O • LH f9\1,h)L~\ . 001 UU J . 009 UU J 00 9 . uuz . nn9 uuz

10Q77 ^ ( 1 9^ 007 • 007 UU / . OOA UU4 . nnA UUh

1A09Q 9 C\ L} 7AQ 1 LI . 7^1 / j 1 . 7/ AQHj

18070 lOU /U.J1 (1 9^ QQft QQ7 QQ R . 77J QQA

9 1 QA1 A n 9"» ki ,z; ILL . 7^9 / D Z 7Afi • / HO 7 =;a . / J4

5803.7 (1,4) .001 .001 .000 .001

79Q6 S O L\ 01 1

. 019 U J. z . OOft UUD OOfi • UUD

1UO 10A7A ft / D . O C\ 9^ 099 . 099 UZZ Ol 9 . Ul Z Ol 1

. U 1

1AAA9 A ( 9 L\ 7AQ 79Q 7 ^ R . / J J . / tJ

1 Q 1 7 C Q (0 9"\

vz, j; QQ 9 . yoy Qft/i

. yon Qftl . y oi

9 1 9Q 1; A . 79Q / zy 7. / jy . 79^ / J J . 7/ AADD

5689.2 (1,4) .003 .003 .001 .001

/ ouo .

CO A\ (.z,4; . UZ J . UZ4 . Ul 1 m 9 . U 1 z

i r>9 ft 1 UZ J / . O U ,3; 09 ^ . 099 UJJ Ol ft

. Ul o 01 7 . U 1 /

1 J 1 Do .

(.3,4; 7 ^O . / JU . 79A / ZD 7 A 1

. / D 1 • 7/ j97/

1 R9R9 7 I OZOZ . / ^9^ . yoo . QR9 yoz • Q7A y / h QAft . yoo

Ofil/.A 7 iUj'tD . /

/"U1 9 \ ,z; 70ft . /UO 771 7 1 Q . / 1 y

7 ft9 o / OZ

5622.1 (1,4) .004 .005 .001 .002

on C7 o OZ J / . j

f9 /

"\ 099 09 A . UjD Ol A . Ul D n i ft

. uio

Q 7 9 1 9 y / zi . z u

,

09ft . U JO . 099 Ujj Ol Q . ui y 01 7 . U 1 /

l 0 1UJ .

(.3,4; 7^7 . / J / . 719 / 1 Z .III. 779 79fi . / ZD

loJJj .

^9 t *\ Q7ft . y / O OAS . yoo QA9 . yoz

i yz jz .

f 1 9"\ U ,z; AftQ . ooy 7ftfi . 709 / U j . ROI OU1

5608.2 (1,4) .004 .006 .001 .002

8717.3 (2,4) .038 .042 .019 .021

9180.2 (1,3) .031 .025 .016 .013

17182.6 (3,4) .771 .698 .786 .711

18173.8 (1,2) .674 .802 .688 .818

18301.8 (2,3) .981 .979 .967 .965

18
Table 7 (con't.)

ANGLE (Deg)

60.0

70.0

80.0

90.0

H (Oe) TRANS. T , T , u , u , A. y X. y

5643.8 (1,4) .003 .006 .001 .002

8663 6 ei 3^ 0?1 01 s 01 0 008

9153.3 (2,4) .034 .038 .017 .019

17242.2 (1,2) .666 .819 .676 .830

18187.5 (2,3) .981 .985 .973 .977

18274.4 (3,4) .790 .686 .802 .697

5714.4 (1,4) .002 .006 .001 .002

ft??0 7 n 31 01 0 OOfi 00 ^ OO -}

9523.4 (2,4) .021 .024 .011 .012

16541.0 (1,2) .663 .832 .667 .838

18031.8 (2,3) .982 .994 .982 .993

19218.7 (3,4) .811 .678 .818 .683

5789.3 (1,4) .001 .005 .000 .002

7Q1 f) 6 ( 1 3^1 • 003 \j \j 001 001 • 001 \J\J 1 9777.

1

(2,4) .007 .008 .003 .004

16110.8 (1,2) .662 .841 .662 .841

17897.9 (2,3) .984 1.002 .991 1.009

19861.3 (3,4) .827 .673 .830 .675

5823.2 (1,4) .000 .005 .000 .002

7796.

4

(1,3) .000 .000 .000 .000

9868.2 (2,4) .000 .000 .000 .000

15966.8 (1,2) .662 .844 .661 .842

17844.7 (2,3) .985 1.005 .995 1.015

20088.9 (3,4) .833 .671 .834 .671

19
20 40 60

Q (degrees)

80

Fig. 1. Paramagnetic resonance spectrum of Cr 3+ in ruby for a transition

frequency of 6.0 GHz. Plots give the values of the resonance fields, H0

as a function of 8, the angle between the c-axis of the ruby SRM and the

direction of the field, H0 .

20
8

XJ

CP

0) Oi o

o

X

Freejuency = 9.5C;hz

\

0 20 40 60

Q (degrees)

80

Fig. Paramagnetic resonance spectrum of Cr~ in ruby for a transition

o frequency of 9.5 GHz. Plots give the values of the resonance fields,

as a function of 6, the angle between the c-axis of the ruby SRM and the

direction of the field, HQ

.

21
10

0 20 40 60

6 (degrees)

80

Fig. 3. Paramagnetic resonance spectrum of Cr 3+ in ruby for a transition

frequency of 14.5 GHz. Plots give the values of the resonance fields, H0 , as a function of 9, the angle between the c-axis of the ruby SRM and the

direction of the field, HQ

.

22
12

0 I J- 1 1 —J —J 1 L _J

0 20 40 60 80

Q ( degrees

)

Fig. 4. Paramagnetic resonance spectrum of Cr 3+ in ruby for a transition

frequency of 18.0 GHz. Plots give the values of the resonance fields, H0

as a function of 0, the angle between the c-axis of the ruby SRM and the

direction of the field, HQ

• 23
0 1 1 — — — 1 1 1 —L -L- 0 20 40 60 80

Q (degrees)

Fig. 5. Paramagnetic resonance spectrum of Cr i+ in ruby for a transition

frequency of 24.0 GHz. Plots give the values of the resonance fields, H

Q

as a function of 6, the angle between the c-axis of the ruby SRM and the

direction of the field, HQ

.

24
16

14

12

03C

O

' 10

o

oX

8

"

" -

Freq uency : = 35 G^Hz

0 20 40 60

Q (degrees)

80

Fig. 6. Paramagnetic resonance spectrum of Cr 3+ in ruby for a transition

frequency of 35.0 GHz. Plots give the values of the resonance fields, H0 , as a function of 6, the angle between the c-axis of the ruby SRM and the

direction of the field, Hr'o •

25
Fig. 7. Paramagnetic resonance spectrum of Cr 3 in ruby for a transition

frequency of 50.0 GHz. Plots give the values of the resonance fields, H0

as a function of 0, the angle between the c-axis of the ruby SRM and the

direction of the field, H

Q

.

26
For a visual display of the resonance fields versus angle 9, at

each microwave frequency, we have prepared the graphs of Fig. 1 through

Fig. 7. These plots give the resonance fields only. The intensities

and other information can be obtained from the tables.

3. Description of the Ruby EPR SRM

3.1 Physical Description

Each set of EPR SRM consists of two pieces of ruby single crystal.

One piece is a square wafer of dimensions approximately 1.5 x 1.5 x 0.5 mm,

with the c-axis perpendicular to the square surface. The second piece

is a bar of dimensions approximately 0.5 x 0.5 x 4.0 mm, with the c-axis

parallel to the long edge. The orientation of the c-axis, with respect

to the specified direction, has a maximum error of 0.5°. The dimensions

are nominal. The total number of Cr 3+ ions in each piece is given in

the accompanying certificate.

The SRM specimens were cut from a single crystal boule, annealed at

1800 °C, and etched in hot concentrated phosphoric acid at 500 °C. The

surface appears wavy and glazed. The color is a pale pink. The annealing

and etching treatments were necessary for obtaining consistent EPR spectra. Details are discussed in another publication [7]

.

3.2 Packaging

Each ruby SRM specimen is contained in a plastic vial. The two

vials are contained in a plastic bottle. We recommend storing the specimens in the packing containers when they are not in use. This precautionary advice is offered because the specimens, being small and transparent, are easily lost.

3.3 Handling

The ruby SRM should be handled with fine tweezers, preferably

non-magnetic (e.g. brass, German silver, or plastic tweezers). Steel

tweezers may leave undesirable ferrous contamination on the surface of

the ruby.

Instructions for initial inspection are as follows:

1. Remove the two vials from the plastic bottle. The ruby samples

are visible through the walls of the plastic vials.

2. Prepare a shallow glass dish, such as a culture dish or evaporation dish, and place a white or dark background under the dish to provide

contrast for ease of viewing. Provide adequate lighting.

3. Select one of the vials for opening and place it in the dish.

Open the cap smoothly so that the crystal will not fly out.

27
4. The SRM specimen can be taken from the vial with tweezers, or

it can be dumped out into the dish by pressing the mouth of the vial to

the dish and lightly tapping the bottom. Care should be exercised to

prevent the crystal from being lost.

5. Inspect and return the SRM to the containers.

3.4 Cleaning

The surface of the ruby specimen can be cleaned by wiping with paper

or cotton soaked with an organic solvent, such as alcohol or acetone. If

the surface needs to be scrubbed, the sample should be soaked in the

appropriate solvent for easier cleaning.

If there is confirmed metallic contamination on the surface, dilute

hydrochloric acid may be used to remove it. The sample must be throughly

rinsed afterward. However, it is not necessary to wash the samples in

acid routinely.

4. Positioning the SRM in the Cavity

In this chapter, we shall suggest methods for the mounting of the

ruby SRM in the sample cavity. In usual practice the sample cavity is

arranged so that the microwave magnetic field is vertical. The DC

magnetic field produced by the magnet is usually horizontal. From this

assumed configuration, we shall develop a method to determine the orientation of the laboratory coordinate system x'y'z', and hence to determine

the integrated intensity factor, Uxi or Uyi , to be used in the measurement. It is important that the user examine his spectrometer and determine whether there is any difference between the spectrometer configuration and that which is described here. Necessary modifications to suit

the individual case in question should be made.

4.1 The Microwave Cavity

We shall discuss three types of microwave cavities commonly used in

EPR experiments.

4.1.1 Rectangular cavity, TE 10 2 mode. The TE 10 2 rectangular cavity is

essentially a piece of rectangular waveguide stopped at both ends, as

shown in Fig. 8 and Fig. 9. The coupling iris is the hole shown at one

end; this end is connected to the waveguide from the external microwave

system. A variable coupling adjustment is usually placed outside the

cavity in the connecting waveguide. The dashed lines of Figs. 8 and 9

represent the loops of the RF magnetic lines of force. The magnetic

field decreases toward the center of the loops. At the center, the RF

magnetic field is zero, and the RF electric field is a maximum.

28
An experimental sample can be placed at the positions shown. These

positions are the locations of the maximum RF magnetic field. However,

the loops tend to round off at the corners. Hence, unless the sample is

small, there will be a variation of magnetic field over the volume of

the sample.

The TE102 cavity can be used vertically as in Fig. 8, or horizontally as in Fig. 9. In the vertical configuration the sample can be

attached to the cavity wall. In the horizontal configuration a sample

holder is needed. The sample holder can be fashioned from a quartz or

other dielectric rod, a tube, or a square cell.

4.1.2 Cylindrical cavity, TE 0 n mode. The TE 0 n cylindrical cavity is a piece of cylindrical pipe stopped by two end plates as shown in Fig. 10.

The iris can be on the end plate half-way between the center and the

side wall, or on the side wall at half the height of the cylinder. The

quality factor (0J is a maximum when the diameter is equal to the height.

The sample can be placed at the position shown and supported by a sample

holder. This type of cavity usually has a high Q and a large volume. A

large sample access hole can be cut at che center of an end plate without

disturbing the cavity mode.

4.1.3 Cylindrical cavity, TM110 mode. The cylindrical cavity in the

TMuo niode is shown in Fig. 11. It has a microwave magnetic field

pattern that is not cylindrically symmetric, as shown. This mode can

only be excited through an iris on the side wall. The frequency of the

cavity is determined by the diameter only. The length of the cavity is

arbitrary, and it can be very long. This type of cavity can accommodate

a very large sample.

4.2 Adhesives

The SRM can best be attached to a surface or a sample holder with

adhesives. Either varnish or household cement may be used. The adhesive

should be of a type that is removable by washing with an organic solvent.

Cement that can form a permanent bond must not be used. The low temperature glue commonly used in EPR research are satisfactory. We recommend

that a trial application of the adhesive on a similar surface be performed

before it is used on the SRM.

Most adhesives have or tend to form broken chemical bonds or free

radicals that will produce EPR signals. It is advisable to dilute the

adhesives with the appropriate solvent to reduce the amount of cement

used as well as to speed the drying. Of course, this procedure will

only lessen the possible interference from the adhesive. A blank run ; with adhesive only will determine if there is any extraneous signal.

4.3 Sample Mounting and Associated RF Polarization

It is of utmost importance in the use of the ruby SRM that the user

know the orientations of the c-axis, the static magnetic field, HQ , and the direction of polarization of the RF magnetic field, H^ . In the

29
Fig. 8. Rectangular cavity, TE 10 2 mode. Dashed lines represent the RF

magnetic field. The square plate represents the sample which is attached

to the wall. The circle on the top face represents the coupling iris.

30
Fig. 9. Rectangular cavity, TE102 mode. Dashed lines represent the RF

magnetic field. The rectangular block represents the sample, which must

be supported. The circle on the end represents the coupling iris.

31
Fig. 10. Cylindrical cavity, TE on mode. Dashed lines represent the RF

magnetic field. The small cylinder at the center represents the sample,

which must be supported. The circles on the top and side represent

possible locations of the coupling iris.

32
Fig. 11. Cylindrical cavity, TM 110 mode. Dashed lines represent the RF

magnetic field. The rectangular block at the center represents the

sample, which must be supported. The circle on the side represents the

coupling iris.

33
•

Y'

(A)

Y'

t H, -Y' POLARIZATION)

(B)

Fig. 12. Schematic drawings demonstrating the relative orientation of th(

wafer SRM and the laboratory coordinate system x'y'z'. In (A) the c-axis

is parallel to the direction of the DC field, HQ

, and the RF field, Hi,

has Y' -polarization. In (B) the c-axis makes arbitrary angle 9 with the

direction of H and the RF field is shown with Y ' -polarization

o

r 34
Fig. 13. Schematic drawings demonstrating the relative orientation of the

bar SRM and the laboratory coordinate system x'y'z'. In (A) the c-axis

is parallel to the direction of the DC field, HQ

, and the RF field, H T , has Y' -polarization. In (B) the c-axis makes arbitrary angle 6 with the

direction of H

q

and the RF field is shown with Y' -polarization.

35
CD P

<Po f—

H

c

o 10 •H •H p X .—

03 03 CD P •H c O <P

0) •H CD U.

P. D£ o E—

CD

ve Th

•pH N

03 X a

U-» X

H X

CD H

4-* 4-> CD

C/) •H

&0 X<P

C (/) H U

P <U Q

03 P

P 03 <D P C

c/) •H P

C

o p tp

B O O

CD O

-d (J c

o

•H 00 P p

c o CJ •H p CD 03 fH 03 P •H p O T3 T3 X>

03 (D O i—

X. PS •H P C P CD •H

03 X o 4-1 £ P p

CD

f-l H

o 03 CO 03 i—io 0

• H P ^ CO T3 I H C " p <d x

• cd a

DO <4-t U W

•h o3 a) «i

<;
Fig. 15. Schematic drawings demonstrating the relative orientation of

the bar SRM and the laboratory coordinate system x'y'z'. The RF field,

Hi, has X' -polarization.

37
following, we follow the convention of the beginning of this chapter,

that H

q

is always horizontal and Hi vertical.

In Figs. 12 through 15 we show two typical mountings of the ruby

SRM specimens. In each case we show how H can be rotated with respect

to the specimen. In two of the cases (Fig. 12 and Fig. 13) angle 9

changes as the field H is rotated; in the other two cases (Fig. 14

and Fig. 15) 6 is fixec! at 90°. In each figure the appropriate polarization x

1 - or y'- is listed. When 6 = 90° the sample may be rotated abo

the x' axis with no change in the spectrum or the intensity. It is impo

tant for the user to be familiar with the mode of the cavity he is using

and to understand the correspondence of the illustrated fields and cryst,

orientations to his own laboratory configurations. If the orientation

of the c-axis is not correctly ascertained, the resonance field will not:

agree with the tabulated values. If the wrong polarization is presumed,

the intensity also will not agree with the tabulation.

4.4 Test Run with the Ruby SRM

The features of the Cr 3+ EPR spectrum that have been described can

be observed by a test run with either piece of the ruby SRM. With the

aid of the graphs and the tabulated information supplied in this publica

tion, the resonance transition should be readily locatable. It is

advisable to start with the angular position of 0 = 0°. At 9.5 GHz, the

(1/2,-1/2) transition is at 3425.0 Oe (see Fig. 16). A slight difference of the microwave frequency from 9.5 GHz, and slight miscalibration

of the control setting of the magnetic field of the spectrometer may

cause the transition to occur at shifted field readings. Slight misalignment from the 6=0° condition will also displace the transition.

This misalignment can be corrected by rotating the sample holder or the

electromagnet with respect to each other. At 9.5 GHz, as seen from the

angular dependence curve (see Fig. 2 and Table 2), the (1/2,-1/2) transition occurs at a maximum. Slight deviation from the 6=0° condition

will cause both the resonance magnetic field and the line intensity to

decrease. Hence, by varying the angular setting the 6=0° position can be located by maximizing the field value and the intensity of the

(1/2,-1/2) transition. This transition should have a line width of abou

15 Oe between points of steepest slope. The two outer halves of the two

outer hyperfine lines should be clearly resolved at room temperature.

For the (3/2,1/2) transition, the two outer halves appear as two extende

wings. At 359.4, 1141.8 and 3784.4 Oe, the positions of forbidden transitions, no signal should be observed. If 9 is set to 90°, the spectrum

will consist of two transitions occurring at 1953 and 5387 Oe. The

intensity ratio of these two transitions will unambiguously verify the

assignment of the polarization of the microwave field. (See Sec. 2.4,

4.3, and 5.2.2.)

For other frequencies, of course, the transitions occur at differen

fields, but the same principle to locate the c-axis as just described

still applies. The verification of the polarization of the microwave

field may have to be more carefully done.

One should become familiar with the Cr 3+ EPR spectrum before put1

the SRM into practical use.

gg
5. Measurement of the Number of Spins

5.1 The Area under the Absorption Curve

The area under the absorption curve can be obtained by digital

computer or by hand calculation. The usual procedure is to sweep the

static field, H

q

, through values from Ha to H^, where the interval from

Ha

to H, contains the entire resonance line being measured. The signal,

S (ri) , obtained, which is proportional to the derivative of the absorption curve, is recorded for n equally spaced values of H . We enumerate

the field values as H a , H2 , H3

. . . , Hn _ 1? H • and the corresponding

measured values of S(H) as S (ty , S(H2 ), S?H 3 ) S(H ), S(Hb

).

The units of H are in oersteds and the units of S(H) are arbitrary and

depend on the sensitivity and gain of the spectrometer. It is assumed

that the scan range, H to H^, completely encloses the line, so that

S(H) vanishes near eacn" end of the interval.

The area, A, is defined by the double integration of the derivative

signal as follows:

H, n

b

A = / dH / dH' S(H') . (8)

H H

a a

In computer controlled EPR instruments there is usually a provision

for calculating this integral numerically, the evaluation involves

calculation of A by the procedure:

[S(H

a

)

+ S(H

a

) + S(H

2

)

+ soy + s(h

2

) + soy

+ S(H

a

) + S(H

2

) + S(H

3

) + ... + S(H

b

)] . (9)

If the EPR spectrometer has no computer associated with it, S(H) can be

recorded by a strip chart recorder and digitized by hand. The integration of Eq. (9) can then be performed by hand. (See Fig. 16.)

Consecutive measurements with both samples placed in the cavity

together is preferable to successive substitution of the samples. If

the scan ranges, H^-H , or the number of points, n, are different for

the two resonances, tlie user must take care to see that the proper

calculation of Eq. (9) is carried out. Users of manufacturer-supplied

computer programs for spin concentration should be sure that changes in

these quantities are given appropriate accounting. Proper adjustment of

the zero line and correction for base line drift should be incorporated

in the integration process [4,7].

39
ZERO LINE

AH =

(A)

AREA= E(AAREA),

(AAREA)j = (AH) 2 2:S(H

BASE LINE

ZERO LINE

Fig. 16. Paramagnetic resonance absorption of Cr 3+

, (1/2,-1/2) transi

tion, with H parallel to the c-axis of the ruby crystal. In (A) the

observed signal, the derivative of the absorption profile vs. applied

field H , as obtained from the spectrometer is shown. The scan range

Hu-H is 95 Oe. In (B) the absorption signal vs. applied field H is

snown, he as obtained from (A) by a single integration

arbitrary units.

Ordinate is in

40
5.2 The Comparison of Integrated Areas of Two EPR Lines

By evaluating the ratio of the areas of two EPR lines it is often

possible to determine the ratio of the number of spins which give rise

to the two lines. The ratio of the two areas, Ai and A2, from Eq. (4),

can be written as the product of four ratios, as follows:

<H

2 > A^ Spect. Gain.^ 1 s^ Integr. Intensity^

A0 Spect. Gain,, x

„ 2 x Integr. Intensity, x NT

Z Z <n 1 > z z

1 S

2

(10)

If the ratio k\j

is measured and if the first three factors of the

righthand side of Eq. (10) are known, then the ratio N1/N2 can be found.

The first factor, the ratio of spectrometer gain factors of the two

resonances can be set-equal to unity if the spectrometer conditions are

the same for the two resonances. If not, this factor can be measured.

The second factor will be unity if both resonances come from the

same value of RF field . This would be the case if two small samples

are used and they are placed in the cavity adjacent to each other. If

the two samples are placed at different sites in the cavity, or if they

are extended, it will be necessary to know the ratio

2 2

<H. > /<FL > . 1 1 s

2

This can be obtained from calculated filling factors [3] or by mapping

the field in the cavity (see Appendix 2)

.

The third factor is the ratio of the integrated intensities per

spin. The integrated intensity per spin for a general transition (a, B)

is given by the quantity [7]

2 2 2 2 1 . i„ i_ |2

[integrated Intensity for

?a general transition

,<a|sjB>|

(2S+1) kT a3

dH

o

where S is the component of the spin angular momentum, S, along^ and

(dv o/dH ) is the weighting factor for the transition. For Cr 3 in

ruby this factor may be put in the convenient form

[Integrated Intensity

for ruby

2 K

£. u

a ' P fl2l

4kT U£ U J

41
i i i 1

a B

l <a l S £l g> l g|,^ B where U ' = -5 — —-— and is obtainable from Table 1 through

I a , g , n Table 7.

•dH 1 o

Details of the passage from Eq. 11 to Eq. 12 may be found in Ref. 7.

The integrated intensity for the unknown sample must be determined for

each particular case. Several examples are given in the next part of

this section.

5.2.1 Use of the ruby SRM with HQ parallel to the c-axis; test sample

with spin 1/2. The simplest use of the ruby SRM for intensity comparison

occurs when the ruby is oriented with the c-axis parallel to the static

field, HQ

. If the test sample has spins with the value S = 1/2 and an

isotropic g-factor (e.g., DPPH) , a very simple measurement of the number

of spins is possible. We assume that the test sample and the SRM experience the same values of RF field amplitude. We compare the area of the

test sample resonance with the area of the (1/2,-1/2) resonance of the

SRM. From the preceeding discussion and Ref. 7, the ratio of the areas

is — . A L I

A

C13J

o

2 N

o «0

where the N's are the total numbers of spins, and the g's are the spectro

scopic splitting factors; unsubscripted symbols pertain to the test

sample and zero-subscripted pertain to the standard sample. In this

case, the tables are needed only to locate the field for the (1/2,-1/2)

transition of the ruby.

If the (3/2,1/2) transition of the SRM is used, the area ratio

becomes

A_ „ _i_ 5_ «_ (14 )

If the test sample has spin higher than 1/2 the discussion of the

general case, Sec. 5.2.4, should be applied.,

The principal objection to using the ruby SRM with H0 parallel to

the c-axis is that the ruby resonance of the (1/2,-1/2) transition

occurs at static fields in the g = 2 region. Thus, in many cases the

EPR lines of the test sample and the standard sample will interfere with

each other. This difficulty can be avoided by using the ruby SRM in a

different orientation.

5.2.2 Use of the ruby SRM with H perpendicular to the c-axis; test

sample with spin 1/2. For x-band radiation (9.5 GHz) the EPR spectrum

of ruby consists of two lines at 1954 Oe and 5387 Oe. Between these two

42
field values is a large "window" in which most commonly occurring resonances can be observed. Hence, this orientation offers convenient use.

In addition, the resonance fields and integrated intensities of the ruby

SRM lines, in the vicinity of 6 = 90°, vary slowly with angle so that

alignment is not critical.

If again, the test sample has spin 1/2 and an isotropic g-factor,

and the RF field amplitudes are the same at the test and standard sample

sites, the ratio of the areas is

A

o 2NoS0 U%e o

' 1

'

where the symbols A, N, and^ g are the same as before, and the factor

a 8

U o o is the normalized integrated intensity given in Table 1 through

cx B Table 7. One finds the value of U o o by identifying the transition

(a ,8 ) observed and the polarization of the RF field,

o o

We offer an example as a demonstration. Let the resonance frequency

be 9.5 GHz and let y' -polarization be used. Assume we have decided to

use the resonance at 5387 Oe as the standard resonance. Then from

Table 2 we find that at angle 9 = 90°, the appropriate U factor is

U^, 3,4

= 0.470 . (16)

(17)

For this case, the ratio of areas is

A_ . N_ g_ _1_

A N g 0.940 ' o o

b0

The value of g is 1.9818.

The 90° orientation has a convenient safeguard for checking that

the polarization is correctly identified. If the polarization is of the

y'-type, the resonance at field 1954 Oe should have approximately twice

the integrated intensity of the resonance at 5387 Oe, as is seen from

the U-factors of Table 2, 9 = 90°. If the polarization is of x'-type

the resonance at 1954 Oe should have approximately one-fourth the

integrated intensity of the resonance at 5387 Oe. The difference in

these ratios is so pronounced that the polarization type (x'- or y'-)

is unambiguously verified from the observed signals by inspection.

5.2.3 Arbitrary orientation of the ruby SRM; test sample with spin 1/2.

Eq. (15) of the previous section can be generalized to the case of

arbitrary orientation of the ruby SRM with respect to the static field.

For the case of a test sample with S = 1/2 and an isotropic g-factor,

Eq. (15) applies directly. However, one must use the value of U for the

angle 9 used, and for the appropriate transition and RF polarization.

The user must provide a means of measuring the angle between the c-axis

43
and the static field, H . If an angle other than a multiple of 10° is

desired, graphical interpolation of the resonance fields and U-factors

is satisfactory.

5.2.4 Arbitrary orientation of the ruby SRM; test sample of arbitrary

spin. If one of the resonance lines is from the ruby SRM the ratio of

intensities becomes

irrMst

!8>l

2

A

,|1 d„aB

VdHi1 I

A N g h . O o 6o „a 3

(18.

U o

M o(6)

where zero subscripts refer to the standard resonance (a0

3 0

) and U is

the appropriate normalized integrated intensity found in Table 1 through

Table 7. The user must know the spin Hamiltonian of the test sample in

order to evaluate the matrix element and the weighting factor. If the

resonance spectrum shows fine structure, angular dependence, or both,

the spin Hamiltonian must be examined if a concentration measurement is

to be made.

5.3 Calibration and Use of a Working Standard

ma

In some applications it may not be desirable to use the ruby SRM

and a secondary working standard may be needed. This might occur, for

example, in cases where intense UV radiation is present and the ruby

fluorescence would interfere with the experiment. The working standard

can be of any material that has a suitable EPR signal.

If a working standard is needed, it should be calibrated against

the ruby. The following discussion offers a procedure for the calibration. As an example, we consider the TE102 rectangular cavity, as illustrated in Fig. 9. The working standard might be located on the cavity

wall. (Any location which will produce a good resonance is satisfactory,

Before performing measurements on the test sample, a ruby SRM should be

positioned at the test sample site and the intensity of the working

standard compared with that of one of the transitions of the ruby. From

this comparison one can then transfer the intensity measurement from the

ruby standard to the working standard.

5.4 Use at Other Than Room Temperature

The EPR signal from Cr 3+ in ruby can be observed from the lowest

temperatures attainable (below 1 °K) to above room temperature. Special

designed cavities are needed at extreme temperatures. At low temperatur

saturation [3] of the EPR resonance may be troublesome. Power levels

should be kept low enough to avoid saturation. At high temperatures the

line shape and line width will change.

44
5.5 Precautions Concerning Visible, UV, X-Ray and Nuclear Radiations

It is well known that ruby suffers damage from intense radiation

[8], Usually nuclear radiations are not encountered in EPR experiments.

However, it is possible that x-ray, UV, or strong visible light may be

used in certain applications. This may cause damage or may induce

undesirable fluorescence.

Damage to ruby can be detected by a change of color, from pink to

orange. This can be best observed against a dark background, preferably

by comparison with an undamaged ruby SRM. Exposure to room light at

room temperature for several days will usually bleach the discoloration.

The effects of low levels of irradiation on the EPR signal is small and

reversible [8]

.

In optical EPR experiments- using UV irradiation, the ruby will

asually fluoresce, giving off the prominent R-lines (at 694 nM) . Some

}f the common varnishes or household cements used to attach the SRM to

the cavity or holder, also fluoresce when excited by UV radiation.

Precautions should be taken if this could interfere with the planned

ixperiment

.

45
List of Symbols

A - Area under resonance absorption curve in arbitrary units.

D - Axial crystal field splitting parameter.

- Energy level belonging to state specified by m.

AE - Energy spacing between levels,

g || , gj_ - Spectroscopic splitting factors,

h - Planck's constant.

H

q - DC magnetic field.

- RF magnetic field.

k - Boltzmann's constant.

m - Azimuthal quantum number.

n - Number of equally spaced field points for digitizing the absorption

curve.

N - Total number of spins in a sample.

S - Spin quantum number.

S^ - Component of spin operator along the direction of H^.

S (H) - Experimentally observed signal, proportional to the derivative of

the absorption curve at field H . o T - Absolute temperature.

T^,, T , - Transition probability rates for polarization x' or y'

U , , U , - Field sweep integrated intensity per spin, for polarization

J x or y .

V - Volume of microwave cavity,

c V

g - Volume of sample.

(a, 3) - Specification of transition between states symbolized by a and 6.

n - Filling factor.

u_ - Bohr magneton.

a

v - Frequency of microwave radiation.

v

g - (Ea-Eg)/h, the frequency corresponding to the energy difference

between levels a and 3.

46
REFERENCES

1. CP. Slichter, Principles of Magnetic Resonance (Harper and Row,

New York, 1963)

.

2. C. P. Poole, Jr. and H. A. Farach, The Theory of Magnetic Resonance

(John Wiley § Sons, Inc., New York, 1972).

3. C. P. Poole, Jr., Electron Spin Resonance (Interscience Publishers,

New York, 1967)

.

4. R. S. Alger, Electron Paramagnetic Resonance (Interscience Publishers,

New York, 1968)

.

5. A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of

Transition Ions (Clarendon Press, Oxford, 1970).

6. D.J.E. Ingram, Biological and Biochemical Applications of Electron

Spin Resonance (Plenum Press, New York, 1969).

7. T. Chang, D. Foster, and A. H. Kahn, J. Res. Natl. Bur. Standards

(U.S.) 83, 133 (1978).

8. R. F. Wenzel, J. J. Halpin, and F. J. Campbell, Report NRL-7063

(AD-704069), Naval Res. Lab., Washington, D. C. (20 Feb. 1970).

47
Appendix 1. MAGNETIC FIELD UNITS

A short explanation of the units used in this publication follows.

The energy of an atomic magnetic moment in an applied magnetic field is

determined by the magnetic field strength, H. The most commonly used

unit of H in the practice of magnetic resonance is the c.g.s. electromagnetic unit, the oersted, abbreviated Oe. Accordingly, we use the

oersted in this report. The magnetic induction, B, is measured in the

c.g.s. electromagnetic system in gauss, abbreviated G. For this system

of units, in vacuum B has a numerical value equal to the value of the

field strength, H, and the two are sometimes referred to interchangeably I The SI (Systeme International) unit of H is the ampere/meter (A/m) and

that of B is the tesla (T) . The quantities H and B may be converted

from c.g.s. electromagnetic units to SI units by the formulas:

H(A/m) - H(Oe) x 10

3

/4tt

B(T) - B(G) x

10~ 4

.

48
Appendix 2. USE OF THE RUBY SRM WITH A LARGE TEST SAMPLE

We expect that many users will want to determine the number of

spins in a sample which is so large that the RF field will not be uniform

over the spatial extent of the sample. This may occur when a long flat

quartz cell is used to hold a liquid sample. In this case it is necessary to find the change of signal strength arising from the non-uniformity

of the RF field amplitude.

We shall illustrate the method of accounting for the variation of

field amplitude by considering the use of a flat quartz cell for liquid

samples. Both pieces of the ruby SRM, will be used. One piece is placed

at a fixed position in the cavity and is used as a reference for measuring

the average Hi 2 in the sample cell. The second piece is mounted on the

flat quartz cell and can be moved over the region of the cavity to be

occupied by the experimental sample. The two pieces should be so arranged

that the resonance signals from both pieces can be observed simultaneously. When the movable piece is at the center of the cavity its signal

will be a maximum. When it is moved away from the center, the field H^

will be reduced and the signal will be weaker. By measuring the signal

strength at several positions along the region where the experimental

sample will reside, one can obtain an average of the signal strength.

The ratio of the averaged signal to the maximum signal (with the SRM

at the center of the cavity) is equal to the ratio of the average of H^ 2

to the value at the maximum.

During measurements on test samples, the SRM fixed to the quartz

cell can be used as a standard for comparison with the unknown. The

intensity of the resonance of the test sample should be multiplied by

the factor

(H n

2

) - /(H,

2

) 1 'maximum 1 average

to correct for the fact that portions of the extended test sample see a smaller field than the maximum.

49
NBS-114A (REV. 7-73)

U.S. dept. of comm. | |. PUBLK ATION OK REPORT NO.

BIBl 10GRAPHIC DATA NBS Sp 260-59

SHEET

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE Standard Reference Materials:

Electron Paramagnetic Resonance Intensity Standard:

SRM-2601; Description and Use

5. Publication Date August 1978

6. Performing Organization Code

7. AUTHOR(S)

T. Chang and A. H. Kahn

8. Performing Organ. Report No

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

same

13. Type of Report & Period

Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number 78-600064

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

bibliography or literature survey, mention it here.)

This publication provides information concerning the use of ruby samples,

of known Cr^+ concentration, supplied as a Standard Reference Material (SRM)

for intensity measurements in electron paramagnetic resonance (EPR)

v experiments. By comparing the measured intensities of EPR absorption

lines of a test sample and of the SRM, it is often possible for the user

to obtain a determination of the number of spins , in the test sample.

Procedures and data on ruby necessary for carrying out this process are

presented. Examples of the use of the SRM in typical cases are offered.

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) Absolute measurement; intensity standard; paramagnetic

resonance; spin concentration; Standard Reference Material (SRM); ruby

18. AVAILABILITY [jS Unlimited

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