fatTonal Bureau of SiiTraarK

jbrarv. E-01 Admin. BIdg. AUG 2 3 1967 -

NBS MISC. PUBL. 280-13

STANDARD REFERENCE MATERIALS:

lyiOSSBAUER SPECTROSCOPY STANDARD FOR

THE CHEMICAL SHIFT OF IRON COMPOUNDS

^? U.S. Department of Commerce

National Bureau of Standards
THE NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards^ provides measurement and technical information services

essential to the efficiency and effectiveness of the work of the Nation's scientists and engineers. The

Bureau serves also as a focal point in the Federal Government for assuring maximum application of

the physical and engineering sciences to the advancement of technology in industry and commerce. To

accomplish this mission, the Bureau is organized into three institutes covering broad program areas of research and services: THE INSTITUTE FOR BASIC STANDARDS . . . provides the central basis within the United

States for a complete and consistent system of physical measurements, coordinates that system with the measurement systems of other nations, and furnishes essential services leading to accurate and uniform

physical measurements throughout the Nation's scientific community, industry, and commerce. This

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includes Radio Standards Physics and Radio Standards Engineering—Office of Standard Refer- ence Data. THE INSTITUTE FOR MATERIALS RESEARCH . . . conducts materials research and provides

associated materials services including mainly reference materials and data on the properties of materials. Beyond its direct interest to the Nation's scientists and engineers, this Institute yields services which are essential to the advancement of technology in industry and commerce. This Institute is or- ganized primarily by technical fields: —Analytical Chemistry—Metallurgy—Reactor Radiations—Polymers—Inorganic Materials—Cryogenics-—Office of Standard Reference Materials. THE INSTITUTE FOR APPLIED TECHNOLOGY . . . provides technical services to promote the use of available technology and to facilitate technological innovation in industry and government. The

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20234.

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3 Located at 5285 Port Royal Road, Springfield, Virginia 2215L
UNITED STATES DEPARTMENT OF COMMERCE

Alexander B. Trowbridge, Secretary NATIONAL BUREAU OF STANDARDS • A. V. ASTIN, Director

Standard Reference Materials:

Mossbauer Spectroscopy Standard for

the Chemical Shift of Iron Compounds

Jon J. Spijkerman, David K. Snediker, Fillmer C. Ruegg,

and James R. DeVoe

Institute for Materials Research

National Bureau of Standards Washington, D.C. 20234

National Bureau of Standards Miscellaneous Publication 260-13

Issued July 28, 1967

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. - Price 40 cents
Library of Congress Catalog Card Number: 67-60030
PREFACE

Within the framework of the NBS Institute for Materials

Research the area of standard reference materials Is a broad

and Important one. Including the preparation, characterization

and distribution of a wide variety of materials In such diverse

fields as metallurgy, polymers and Inorganic materials. In

carrying out such a program there Is much Interaction with

representatives of Industry and science, beginning with discussions as to which primary standard materials will do most

to advance technology, the furnishing of materials and fabrication of samples, and the characterization and certification

of the materials by cooperative efforts. The many groups participating In a standards program are very Interested In detailed Information on specific aspects of the program — but

to date there has been no publication outlet for such written

discussions

.

To meet this need, NBS Miscellaneous Publication 260 has

been reserved for a series of papers In the general area of

"standard reference materials". This series will present the

results of studies and Investigations undertaken within the

Institute for Materials Research with emphasis on the preparation and characterization of standard reference materials.

This subject-oriented series will provide a means for rapid

dissemination of this detailed Information and we hope will

stimulate the use of standard reference materials In science

and Industry,

W. Wayne Melnke, Chief

Office of Standard Reference Materials

111
OTHER NBS PUBLICATIONS IN THIS SERIES

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1964. 30 cents.

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1964. 35 cents.*

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1965. 20 cents.*

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of Solution X-Ray Spectrometrlc Analysis of Copper-Base

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of a Standard Lead-Silica Glass. November I966. 25 cents.*

iv
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Remittance from foreign countries should Include an additional

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V
TABLE OF CONTENTS

PAGE

1. INTRODUCTION 1

2. PREPAEATION AND DESCRIPTION OF THE STANDARD ... 4

Preparation 4 Chemical Description 4 Physlcal Description 5 Electronic Structure ... 7

5. MOSSBAUER SPECTROSCOPY MEASUREMENTS 8 Description of Equipment 8 Measurement of Mossbauer Spectrum Parameters ... 11

Chemical Shift 11

Electric Quadrupole Splitting 11

Llnewldth 12

Magnitude of Resonance Effect 12 Gamma Ray Attenuation 12 Computations ..... 12

4. ANALYSIS OF RANDOM AND SYSTEMATIC ERRORS 13

Random Errors In the Calibration Procedure .... 13

Optical Spectrometer Drift . 15

Counting Statistics l6

Systematic Error in the Determination of the

Electric Quadrupole Splitting l6

Summary 17

5. THE USE OF THE STANDARD l8

Procedure for Measuring Chemical Shift and

Reporting Differential Chemical Shift l8

6. SUMMARY 19

7. ACKNOWLEDGMENTS 20

8. REFERENCES 23

APPENDIX A - COMPUTER CURVE FITTING FOR

MOSSBAUER SPECTRA 26

APPENDIX B - ANGULAR DISTRIBUTION OF RADIATION

IN THE MOSSBAUER EFFECT 33

vi
TABLE OF CONTENTS (Con't)

PAGE

APPENDIX C - FORMAT FOR PRESENTATION OF EXPERIMENTAL

MOSSBAUER SPECTRA AND PARAMETERS 57

APPENDIX D - PHYSICAL CONSTANTS AND CONVERSION FACTORS

FOR IRON-57 MOSSBAUER SPECTROSCOPY .... 4^

APPENDIX E - ATTENUATION AND LINE BROADENING FOR ^^FE

ABSORBERS 45

LIST OF FIGURES

FIGURE NO.

1. Chemical shift of sodium nitroprusside for

different source matrices 2

2. Single crystal of sodium nitroprusside, showing habit and orientation of platelet 6

3. Photograph of single crystal of sodium nitroprusside with platelet shown in proper

orientation 6

4. X-ray stereographic projection of sodium nitroprusside single crystal along the ool axis . . 7

5. Optical system for accurate measurement

of velocity 9

6. Peak intensity assymmetry for the ^5/2 -1/2

doublet in iron compounds as a function of the

angle between the electric field gradient and

the incident radiation 36

7. Attenuation coefficients for l4.4 keV gamma

radiation as a function of element 46

8. Plot of effective source thickness 47

vii
MOSSBAUER SPECTROSCOPY STANDARD

FOR CHEMICAL SHIFT OF IRON COMPOUNDS

Jon J. Spijkerman, David K. Snediker^

Flllmer C. Ruegg^ and James R. DeVoe

Institute for Materials Research

National Bureau of Standards

ABSTRACT

The preparation, calibration, and use of the Standard

Reference Material for chemical shift of iron compounds in

Mossbauer Spectroscopy is described. This standard is a properly oriented single crystal of sodium pent acyanonitrosylferrate(ll) dihydrate ( sodium nltroprusside ) . Primary standards were calibrated with a high accuracy optical Mossbauer

spectrometer and secondary calibrations were made with a tandem Mossbauer spectrometer. The midpoint between the two absorption peaks in the spectrum at 25.0 "^C provide a useful

velocity scale calibration of the spectrometer. Descriptions

of the spectrometers used and the error analysis associated

with the data are given. Suggested format for reporting

Mossbauer spectra and their parameters is also presented.

Key words: Mossbauer, Spectroscopy, standard, differential

chemical shift, quadrupole splitting, random error, systematic

error, sodium nltroprusside, iron compounds, optical Mossbauer

spectrometer, tandem Mossbauer spectrometer, velocity calibration.

viii
1. INTRODUCTION

While the Mossbauer effect was first used to resolve a number of problems in physics it has now found a definite

application in chemical structure analysis. The Importance

of Mossbauer spectroscopy to chemical structural analysis was recognized in I962 but received little attention until 1964.

The early efforts made to explain the parameters obtained in

Mossbauer spectroscopy were qualitative or at most in a semiquantitative sense. Only since I965 have attempts been made

to be quantitative. Such attempts have brought about realization of a serious shortcoming with data published in scientific

periodicals. The Mossbauer chemical shift for a given series

of compounds is rarely reported with respect to the same source

(see figure l). Consequently, normalization of data taken by

different laboratories is necessary. One additional difficulty has been found. Even if the source used in two different laboratories is nominally the same,, serious descrepancies

occur in the chemical shift reported. This presumably is a consequence of the method of preparation of the sources which

usually are made by diffusing a radioisotope into a metal

substrate. Proper annealing is very important and doing this

reproducibly to give the same structural environment is

difficult

.

The most practical solution is to measure the chemical

shift of an unknown compound with respect to a reference compound. This was anticipated by the attendees of a symposium

on Mossbauer Effect at the 1964 Gordon Research Conference on inorganic chemistry. The compound sodium pentacyanonitrosylferrate(ll) dihydrate (sodium nitroprusside ) was suggested at this conference. Other materials were also suggested. A particularly interesting one appeared to be iron foil, but

studies at NBS have indicated that its reproducibility with

respect to both production of the standard and stability of

1
Figure 1. Chemical shift of sodium nltroppusslde for

different source matrices.

It was necessary to develop a philosophy for the production and calibration of this standard which would maintain

Its usefulness during the foreseeable future. The system decided upon Is like that of many of the standards developed at NBS. Ten primary standards were made from the best obtainable

single crystal of sodium nltroprusslde . These crystals were then calibrated with a spectrometer that has very high accu- racy and precision. Fifty standards were then randomly sara-
pled from a lot of 500. The sample of fifty was then calibrated against the primary standards using the NBS tandem

spectrometer. The ten primary standards will he measured

periodically with the high accuracy spectrometer to detect

any possible changes in the chemical shift as a function of

time. Any subsequent lots of standards will be calibrated

against the ten primary standards. In addition, if standards

for compounds other than those containing iron should be desired, these standard reference materials would be calibrated

against the primary standard for iron.

This report describes the theory and procedures for calibration and use of the Standard Reference Material for chemical shift of iron compounds. It has not been found practicable to include all of the detail on the single crystal preparation, on the Mossbauer spectrometers, or on the computer

programs used to resolve the spectra. Pertinent references

on these subjects are giveno

It is important that this new and powerful spectroscopy

receive the benefit of standardization so that the spectrum

parameters can be used with confidence. In conjunction with

this, a format for reporting Mossbauer spectra and for re- porting spectrum parameters along with their nomenclature is

suggested

.

3
2. PREPARATION AND rFSCRIPTION OF THE STANDARD

A. Preparation

Sodium nitroprusside^ ^R^[Fe{m)^m]'2E^0, is prepared

by the action of ^0% (vol) nitric acid on sodium ferrocyanide

or ferricyanlde [5], or by the reaction of nitride ion on either sodium ferrocyanide or ferricyanlde in acid solution

[^.5,6].

Single crystals were grown from a saturated aqueous so- lution of ACS reagent grade material [7] at a pH of 6.5 - 6.8^

using glass equipment. Thin platelets 1 cm x 1 cm x .O78 cm were cut from the single crystals. The platelets were cut with a string saw along the 100 plane within t 2° . The re- quired thickness of 0.0775 - O.OO3O cm with a parallelism

within 0.001 mm and a surface finish of 20 microns was achieved by polishing the platelets. A stock of 500 platelets was produced by the Isomet Corporation for the NBS standard [8].

B. Chemical Description

Sodium nitroprusside Is stable at room temperature under

normal laboratory conditions [9]. The compound with two water

molecules of hydration is stable up to 100° C. At higher temperatures (near 450°C), the salt is transformed [10] to sodium

ferrous ferrocanlde, sodium ferrocyanide^ nitric oxide and

cyanogen. At higher temperatures^ nitrogen is evolved. To

determine the stability of the standard reference crystal in

a laboratory atmosphere, a platelet was exposed for a prolonged period of time. The relative humidity was 50-70^ and the

temperature 25 ± 2°C. No change in weight of the platelet was observed within 10"'^ g after a six month period. For stability

with respect to the Mossbauer spectrum, see section 3. The solid salt is stable in air, but the solutions are

not [11], In alkaline solutions [3,12] the salt Is converted

into pentacyanonltrltof errat e (ll), and in acid solution

hydrocyanic acid is liberated at high concentrations. The

solubility of the salt is 40 mg/lOO ml H^O at l6°C [13] and

4
57 mg/100 ml at 43° C [8], The salt transforms slowly In direct sunlight [l4] to Fe^(CN)^g, NO and Prussian blue.

The specification for reagent grade sodium nitroprusside

is as follows

Sodium nitroprusside, Na2[Fe( CN)^NO] •2H2O, Formula

wt. 297.97

Insoluble matter: Not more than O.i Chloride (Cl"): Not more than 0 Sulfate (SO^): To pass test (limit about 0.01^).

Microchemical analysis on three single crystals taken at random was performed at NBS;, with the results -[15]:

Iron 18.74 + 0.05^^

Carbon 20.2 t 0 ,3%

Hydrogen 1.4 t 0 .1%

Nitrogen 28.0 + 0.3^.

The analyses confirm that the theoretical composition

may be used in any calculations required with this material.

C . Physical Description

The salt crystallizes in deep red orthorhombic crystals,

12 belonging to the space group

'^^yT

"^^^ cell constants,

for four formula weights per unit cell, are [15]:

a = 6.17 + 0.03 A b = 11.84 + 0.06 A

c = 15.43 - 0.08 A. The x-ray density [I7] is I.76 g/cm3, a figure which is in

agreement with the macroscopic determination [l8j of 1.72 't 0.02 g/cm^.

The faces are the (110) primary rhombic prism, the (010)

primary brachy-pinakoid and the (Oil) primary brachydomal

prism. The platelets are cut along the 100 plane as shown in

figure 2 and 3j in the x-ray st ereographic projection shown

in figure 4.

5f Unless otherwise specified, all error limits are standard

deviations of a single observation.

5

D. Electronic Structure

The bonding In the nltroprusslde anion has been described

by Manoharan and Gray [19] In terms of molecular orbital theory

with the configuration 3d^*^^^ 4s ^'^"^^^p 0.251^ rj.^^ 44.9^ 4s

character differs with the 60fo 4s character obtained from the

Walker, Werthelm, Jaccarlno plot [20]. This discrepancy Is under current Investigation In several laboratories [20,21,22],

The quadrupole splitting Is consistent with the assignment

of a low spin configuration for Fe(ll). From the asymmetry

of the Intensity of the 2 transitions, ±3/2 ±1/2, ±1/2 ±1/2,

the electric field gradient Is axlally symmetric and positive

In sign [23] (see Appendix B)

Figure 4. X-ray stereographlc projection of sodium nltroprusslde single crystal along the 001 axis.

7
3. MOSSBAUER SPECTROSCOPY MEASUREMENTS

A. Description of Equipment

For the calibration of the standard two types of Mossbauer

spectrometers were used: the tandem spectrometer ^ using a multiplex technique for Int er-comparlson of the platelets, and

a high accuracy spectrometer using an optical Interferometer

for the velocity measurements.

The tandem spectrometer operates In the constant acceleration mode. The Doppler velocity Is generated by an electromechanical transducer, using a loudspeaker to produce the motion,

that Is mechanically coupled to a velocity sensor Incorporated

In a feedback loop. The spectrum is accumulated In a multichannel analyzer operating in a multlscaler mode [24]. The

analog voltage signal, varying linearly with time in a saw tooth fashion. Is taken from the address scaler to provide the

input signal for the transducer. This method guarantees synchronization of the Doppler drive velocity with the channel

number of the analyzer. In order to improve the accuracy of

the spectrometer, two spectra are accumulated simultaneously

(multiplex). The Doppler velocity that is used for both source- absorber combinations is provided by one electromechanical drive

unit [25]. For the calibration, the standard platelets were compared with the primary standard in the multiplex system.

Cobalt-57 in a two mil palladium matrix (0.25 in diameter) was used for the source. The l4.4 keV radiation was detected by a gas flow proportional counter, using a 10^ methane, SOfo argon

(P-IO) gas mixture^ A moving source geometry was used, with a 0.125 in aperature, in order to reduce any error due to the

cosine effect [2?].

The systematic error with respect to velocity of the abovedescribed spectrometer is usually not within the attainable

limits of random error. Since it is desirable to use the standard for calibration of Doppler velocity as well as for chemical

shift, a high-accuracy spectrometer was designed to measure

8
the quadrupole splitting of sodium nitroprusside . An interferometer can be used with minor modifications to measure the

velocity directly in terms of the primary standards of length

(green line of "^^^Hg) and time (WW NBS standard frequency),

since velocity is determined by a measurement of distance and

time

The interferometer consists of a stationary light source, beam splitter, reflector, a movable second reflector, and a photomultiplier (see figure 5). The light Intensity produced

by the interferometer varies sinusoidally with the optical

path difference (AS) between the two reflectors-.

Figure 5. Optical system for accurate measurement

of velocity.

9
The current produced by the photomultiplier Is represented by the equation:

I(AS) = + Iq cos ^^^^ , where (1) = dark current

Iq = signal current.

If the second reflector is not stationary^ but moving with a velocity v, the photomultiplier current will be time dependent:

I(t) = Ip + Iq cos 27r (-^H , where (2)

. 2v frequency = .

^ For a velocity of 1 um/s, using the Hg green line (X. = 5460.7^ a), this frequency corresponds to 3663.5 hertz. This

interferometer thus allows velocity to be determined by a frequency measurement. To provide the feed-back signal for

the electromechanical transducer, the fringe count frequency

is compared with the driving frequency of a General Radio

Company model 1162A. synthesizer* (standardized against WW) by means of a one to one frequency correlator [28]. With this

arrangement, the velocity can be controlled and measured with

high precision and accuracy. In this constant velocity mode,

the spectrum of a primary standard was obtained by varying the

frequency synthesizer through the range of 0 to 5 khertz in

100 hertz steps. Gating circuits were used to control the

fringe and standard frequency counters for positive and negative velocities and to stop the radioactivity counting scalers

during the spectrometer reversing interval. The detector system is identical to the one used in the constant acceleration

mode. More detailed descriptions of this spectrometer appear

in reference [29],

The identification of commercial equipment in this paper does

not imply recommendation or endorsement by the National Bureau

of Standards; nor does it imply that the equipment identified

is necessarily the best available for the purpose.

10
B. Measurement of Mossbauer Spectrum Parameters

From a lot of 500 platelets, 60 were randomly selected,

and of the 60, ten were chosen as primary standards. The ten

platelets were determined to be the best of the 60 by visual

examination. After calibration of the primary standards with

the optical spectrometer, one of the ten was selected for use

as a comparator in the calibration of the 50 sample platelets.

The platelet selected was determined to be the one closest to the average of the quadrupole splitting of the ten primary

standards

.

The spectrum parameters of chemical shift, quadrupole

splitting, percent effect and linewidth were measured. All of

these parameters were calculated with the mathematical technique described in Appeddix A. 1. Chemical Shift

The chemical shift of the sodium nitroprusside platelet

measured with the Incident radiation perpendicular to the 100

crystal plane, at 25.0°C is zero cm/s by definition, and is

determined by the center of the doublet described below. The

shift of an iron compound measured relative to sodium nitroprusside is called the differential chemical shift 5^, while

designates the chemical shift for the standard. The

SL Q

relationship for calculating differential chemical shift is

6 =6 - 6 , , o X std

where 6 is the chemical shift of the unknown compound. The

temperature dependence of the chemical shift is 3 x 10 cm

s""^ °K"^ [3O].

2. Electric Quadrupole Splitting

The nitrous ligand in sodium nitroprusside produces an electric field gradient at the iron nucleus, which results in

the observed doublet spectrum [31]. The average quadrupole

splitting, AE„, for the ten primary standard platelets has been

determined to be O.I726 ± 0.0002 cm/s at 25.0° C with a temperature dependence [30] of 10"^ cm s °K

11
For the 100 crystal plane^ the doublet Is symmetric

energy [32] (Appendix B) . A misalignment of 2 degrees in

the 100 crystal plane of the standard from a perpendicular to the gamma ray produces an asymmetry of S =0.1.

3. Llnewidth

The linewidth (r) measured for the standard is 0,0305

- 0.0004 cm/s. The effective absorber thickness for the

14.4 keV gamma radiation [33,34] is T^ = 3.77 mg/cm^.

a Corrections for cosine effect [32] were made. Using

Margulies' method [33] the thick absorber line broadening is

1.51, yielding a corrected line width of 0.0202 - 0.0004 cm/s

(Appendix E). For powered sodium nitroprusside with absorber

thickness of 25 mg/cm iron, the halfwidth is 5^ larger than

the theoretical width.

4. Magnitude of Resonance Effect

The standard absorber exhibits a percent effect (£) of

(TV 17 ± 2fo using 10 mCi -^'Co on a Pd matrix, with an argon-methane

(P-IO) gas flow proportional counter. The single channel

analyzer was set to pass 9Q% of the l4.4 keV radiation.

5 . Gamma Ray Attenuation

The attenuation of the crystal for l4.4 keV (0.864 A)

radiation is Q^fo, as determined using standard y-spectrometric

techniques. Prom Appendix E the attenuation can be seen to be

due to the iron mass absorption.

C. Computations

Mossbauer spectra are particularly suited to resolutipn

by mathematical methods. Machine digital computation is being

used, hence errors in data manipulation are minimized and

comprehensive random error estimates can be made of the spectrum parameters. The mathematical techniques used for resolving the Mossbauer spectra are described in Appendix A. An

example of the output of the computer program called PARLORS

IV is given in Appendix C.

12
4. ANALYSIS OF RANDOM AND SYSTEMATIC ERRORS

Since the chemical shift of this standard reference

material Is defined to be zero there Is no systematic error associated with It, Therefore, systematic errors are associated only with the quadrupole splitting. Since we define the

midpoint between two peaks of the spectrum of the standard as zero differential chemical shift , the random error in the quadrupole splitting reflects that associated with the measurement

of the zero point for differential chemical shift. Ten primary

standards were selected to be calibrated on the high accuracy

optical spectrometer. The average quadrupole splitting of

these ten results Is the value reported on the certificate.

The secondary standards were then calibrated from one of the

primary standards with the use of the tandem spectrometer to determine the random error of both the quadrupole splitting

and the zero point of differential chemical shift for the 50

samples that represent the lot of 500 platelets. The random

errors In the chemical shift and quadrupole splitting are the

standard deviations of a single determination.

A. Random Errors In the Calibration Procedure

Random errors resulted from the comparison technique and

the optical spectrometer measurements. The random errors In the latter will be analyzed first.

For velocity measurements using the high accuracy spectrometer, the distance that the absorber traversed in a unit of

time was determined. Since the Mossbauer transition takes

-7 place In a time Interval of the order of 10 s, the unit of

time for this measurement should be of this magnitude. An Interferometrlc technique using visible light reduces the

measurement of velocity to a frequency measurement. For this

method the unit of length is the "^^^Hg green line (y = 5460.74

± 0.01 A corrected for air) [32]. By comparing the NBS standard frequency (accuracy of 1 part in 10^) with the fringe13
count frequency generated by the interferometer using the

198Hg green line the velocity can be measured. To evaluate

the accuracy^ the relationship between velocity and fringecount frequency (f) is

v=^ (1)

since the optical path is twice the traverse of the spectrometer. The fractional error in velocity, E(v), is given by:

E(v) = [E{\f + E{ff]K vJhere (2)

E(\) = fractional error in wave

length = 2 X 10-6

E(f) = fractional error in frequency.

The interferometer is capable of measurement to within

1/2 fringe, therefore the fractional error in the frequency

is given by:

E(f) =^ = i

(^) =^ (3)

substituting into equation 2 E(v) = [4 X 10-12 ^ (^)2ji

.^^ for

V = 1 cm/s

E(v) = 2 X 10"^

Equation (4) is an expression for the limiting random error. This expression also indicates that the interferometric method

will not work at zero velocity because the error becomes

infinite.

The above consideration does not take into account the

limitations on the traverse of the spectrometer, due to visible

light coherent path length and the Inverse square law of radiation losses if long traverses are used.

Therefore, a more realistic estimate of the error can be

obtained from the error in the fringe counts. Since the

electronic circuitry is capable only of counting to the nearest

14
fringe, the error In velocity Is then dependent upon the number of fringe pulses (f) per centimeter of travel (d).

^ = (\/2Hl/2} (5)

The factor l/2 arises from the fact that the electronics

count half-cycles. For the one centimeter distance of travel

used In this work, equation (5) yields 8 x 10 fringe pulses.

Hence the random error In velocity for one centimeter travel

Is one fringe pulse.

The above considerations assume the velocity correction

circuitry to be capable of Instant correction when a velocity

error Is sensed. However, the mass of the moving system re- duces the correction time, which produces a random error If

the velocity corrections are random, and a systematic error If

the correction signs are largely positive or negative. This

systematic error will be discussed below. The random error could only Increase the line width determination, and the

amount of Increase In line width does not significantly in- crease the random error in the quadrupole splitting determination

Since the tandem system was used, only the differential

linearity (e.g., the line width divided by the separation of

the doublet) is important. This differential linearity was found to contribute an insignificant amount to the total ran- dom error for the calibration measurements [24],

1. Optical Spectrometer Drift

The optical spectrometer drift would contribute the

largest error in the calibration measurements, since this

would be directly reflected in the random error of the chemical

shift. Evaluation of the magnitude of this error by measuring

one of the primary standards over a one month period indicated

a standard deviation of the chemical shift of ± 0.02 cm/s from

50 measurements. However, by using the tandem spectrometer

this error due to drift was reduced to a negligible amount.

15
2 , Counting Statistics

Prellmlnapy measurements on the sodium nltroprusslde

crystals, and the economics of data accumulation time dictated

that a maximum of ^ x 10^ counts per channel (N^) for 200

channels be accumulated for each platelet. This would correspond to a standard deviation of a single determination of

10 cm/s due to counting statistics. This was further con- firmed by the residuals obtained from a least squares fitting

of the experimental data points to a Lorentzlan line profile,

discussed In Appendix A. B. Systematic Error In the Determination of the Electric

Quadrupole Splitting

The error In the velocity measurement Is limited by the

Instrumentation, due to the resolution of the one to one frequency comparator and the time response of the system. The

open loop gain as a function of frequency decreases 6 dB per

octave and the slgnal-to-nolse ratio limits the response to 300 hertz. The frequency correlator response time Is Inversely

proportional to the frequency, but the response time can be

Increased by an Integrating network at the output of the com- parator so as to match the decrease In response of the drive

unit

The error due to the system response could be measured

directly from the comparison (beat) of the fringe frequency

with the reference frequency, using an oscilloscope or by

counting the y radiation at a velocity of 0.5 T away from

resonance as a function of the velocity correction signal.

These random fluctuations never exceeded 10^ of the reference

frequency, which would correspond to a maximum error of 0.1 x 1/4X • f or typically 2fo of the line width of the standard In

the worst case. Since the best frequency was random, this error could only Increase the line width determination, and

not the separation of the peaks. The systematic error as determined from the total fringe count with respect to the

16
reference frequency counts was found to be within the standard

deviation of ± 5 in 10^ fringes.

The cosine effect was minimized by using the proper

aperture. For the measurements on the primary standards, a 0,25" diameter source and detector, separated by 2.0" were

used, and the cosine effect correction was made for this

geometry. The alignment of source and absorber gave negligible

error

In order to determine any long term stability effects on the standard, a series of spectra were taken with the high

accuracy optical Mossbauer Spectrometer over a period of one

year. No detectable changes in any of the parameters were

observedo However, it is always considered advisable to store

the crystal in a dark place away from any sources of extreme

heat, cold or humidity.

C, Summary

A systematic study of the sources of random errors indicates that this error is represented entirely by the limitation

in the total number of Mossbauer gamma rays detected. A lower

random error can be obtained at the expense of increased measuring time. The limiting random error would be that caused

by spectrometer drift. A similar study of systematic errors indicates that the accuracy is well within the limits imposed

by the random error; consequently it can be said that if any

systematic error exists it is less than 0.0002 cm/s for the

quadrupole splitting.,

17
5. THE USE OF THE STAITOARD Procedure for Measuring Chemical Shift and Reporting

Differential Chemical Shift

The standard crystal can be used to calibrate the spectrometer before or after a measurement, or the standard spectrum and the spectrum to be calibrated can be accumulated

simultaneously If a tandem spectrometer Is available. Since

the unknown Is measured relative to the standard, the source parameters do not affect the determination of the differential

chemical shift. For comparison, the various sources and their

respective chemical shifts are shown In figure 1. For detailed directions on the use of this standard, see the Certificate of Calibration on page 22.

18
6 . SUMMARY

The characteristics of sodium nitroprusside fully meet

the requirements for an acceptable Mossbauer standard. Its chemical stability, uniformity and doublet spectrum give the

required accuracy needed for this spectroscopy. The results of this study are best summarized in the Certificate of

Calibration which follows this page.

The use of this standard and the use of consistent re- porting procedures of the spectrum parameters should provide

stability to the growing field of Mossbauer spectroscopy. In addition, it should accelerate efforts to quantitatively unde: stand the spectrum parameters by providing the theoretician

with highly reliable data.

This Standard Reference Material can be purchased from

Office of Standard Reference Materials

National Bureau of Standards

Washington, D. C. 20234

Attention:

Standard Reference Materials Unit.

19
7 . ACKNOWLEDGMENTS

The characteristics of sodium nitroprusside as a possible

Mossbauer standard for chemical shift were first pointed out by G. K. Wertheim in a discussion with R. H. Herber, from the

parameters published by Kerler and Neuwirth. During the Gordon

Conference on Inorganic Chemistry in 1964, the need for a standard was discussed by Professors J. Danon, J. F. Duncan,

V. I. Gol'danskll, R. H. Herber, and N. N. Greenwood. Many of

the specifications for a standard were pointed out by these

persons and their assistance is deeply appreciated.

The initial single crystals were prepared by Dr. J. Torgesen and Mr. A. Horton; the x-ray analysis which led to the position of the 100 plane was conducted by E, Farabarough,

all of the Inorganic Materials Division, NBS. The final crystals were prepared at the Isomet Corporation and the interest

of Dr. I. W. Ruderman greatly facilitated the prompt delivery.

The assistance of Mr. R. W. Shideler, (Analytical Chemistry

Division) with the electronic instrumentation, Mr. J. M. Cameron of the Applied Mathematics Division, NBS with the

mathematical statistics, Mr. E. Rhodes (Analytical Chemistry

Division) with the computer programming, and Mrs. R. S. Maddock

(Analytical Chemistry Division) with the preparation of the

report is also gratefully acknowledged. The calculation by

Mr. Paul Black (Analytical Chemistry Division) of the angular

dependency of the electric quadrupole asymmetry is gratefully

acknowledged.

20
U. S. Departn]y|j)^ of Commerce

John T. ^orjjoaC ?lecretary

Standards

Directo, (^j^j^iifi^^i^ QIaltbrattnn

Standard Reference Material 725

for

Mossbauer Differential Chemical Shift for Iron-57

Sodium Pentacyanonitrosylferrate(II) Dihydrate*

(Sodium Nitroprusside)

This Standard Reference Material was prepared from a single crystal of the compound sodium pentacyanonitro9ylferrate( II) dihydrate , Na[Fe(CN)5N0] • 2H2O. The purity of this compound, also known as sodium

nitroprusside, meets the specifications of the American Chemical Society for reagent-grade materials as

verified by quantitative analysis of the main constituents , but should not be considered as entirely free from

impurities such as heavy metals. It is in the form of a platelet of dimensions 1 x 1 x 0.0775 ± 0.003** cm

that has been cut from a large single crystal. The 1 x 1 cm surface is parallel to the 100 crystal plane within

± 2 degrees of arc. The opposite 1 x 1 cm surfaces are parallel to within 0.001 cm with a surface finish of 20

microns. The natural iron concentration is 25.0 ± 1 mg/cm2. The chemical shift of this Standard is compared

to that of the National Bureau of Standards Primary Standard which has the value of zero cm/s differential chemical shift. This Standard has an average value for the chemical shift of 0.0000 ± 0.0002 cm/s at 25.0°C. This uncertainty is expressed as the standard deviation of a single determination derived from single measure- ments on 50 platelets. The National Bureau of Standards dual-spectra Mossbauer spectrometer [l,2] was

used. The resonant spectra have considerable line-broadening due to the thickness of the absorber. The

experimental line width (full width at half maximum) is 0.0305 ± 0.0004 cm/s. The line width corrected for thickness broadening is 0.0202 cm/s. The Mossbauer effect is 17 percent. To allow the user to calibrate the velocity scale of a Mossbauer spectrometer, the electric quadrupole

splitting of the Standard Reference Material was measured. The velocity scale of the dua'-spectra comparison

spectrometer was calibrated by measurement of the electric quadrupole splitting of the Primary Standards

using an optical interferometric technique. The average value of the electric quadrupole splitting for this Standard is 0.1726 ± 0.0002 cm/s at 25.0°C where the uncertainty is expressed as the standard deviation of a single determination derived from single measurements on 10 platelets. The details of the instrumentation and of preparation and measurement of the sodium nitroprusside

crystals are given in NBS Miscellaneous Publication 260-13 entitled "Mossbauer Spectroscopy Standard for Chemical Shift of Iron Compounds."

The single crystal platelets of sodium nitroprusside were prepared by the Isomet Corporation of Palisades

Park, New Jersey. The calibrations of the crystals were made within the National Bureau of Standards

Institute for Materials Research, by J. J. Spijkerman, F, C. Ruegg, D. K. Snediker, and W. L. O'Neal of the Radiochemical Analysis Section , James R. DeVoe, Chief.

* This nomenclature is based upon the structure of this compound as determined by Mossbauer spectroscopy.

** Unless otherwise specified all uncertainties are standard deviation of a single determination. References:

[1] Radiochemical Analysis: Activation Analysis, Instrumentation, Radiation Techniques , and Radioisotope Techniques, July 1963 to June 1964, James R. DeVoe, Editor, NBS Tech. Note 248 , pp 25-37 (1964). Available from Superintendent of Documents , Government Printing Office, Washington, D.C. 20402, 50 cents a copy.

[2] Radiochemical Analysis: Activation Analysis, Instrumentation, Radiation Techniques , and Radioisotope Techniques, July 1964 to June 1965 , James R. DeVoe, Editor , NBS Tech. Note 276 , pp 74-1 10 ( 1966). Available from Superintendent of Documents, Goviemment Printing Office, Washington , D.C. 20402, $1.00 a copy.

Washington, d. c. W. Wayne Meinke, Chief January 30, 1967 Office of Standard Reference Materials (This certificate supersedes certificate of 4-6-66)

(over)
Directions for Use

The Standard Reference Material in the form of a single crystal platelet is sandwiched between two

pieces of a 4 mil polyethylene film. Due to the advisability of keeping it free from moisture it is recom- mended that the platelet not be removed from this container. A suitable mounting consists of two concentric aluminum rings approximately 1.25 inches in diameter. The crystal, encased in the plastic envelope,

is placed between the rings and the assembly is fastened together with small screws, therelDy clamping the envelope firmly between the rings. Both rings have an inside diameter of 0.75 inch to expose the crystal and

to prevent crushing of its edges. This was the procedure used in taking all of the data at NBS on this Standard Reference Material. Place the Standard Reference Material as the absorber at 25.0° C in the Mossbauer spectrometer and

take sufficient transmitted counts of the 14.4 kev gamma-ray from an iron-57 source to obtain counting

statistics to the required degree of uncertainty. Determine the peak position of the electric quadrupole

splitting. The use of digital computation techniques are recommended. Divide the distance between the peaks by two and assign this as the value for chemical shift indicated above. Replace the Standard crystal with the compound whose chemical shift is to be measured as the absorber in the spectrometer. Measure

the peak position parameters as a difference between that of the unknown compound and the mid-point be- tween the peaks of the Standard.
8 . REFERENCES

[I] Christ, B. W., Private Communication.

[2] Schechter, H., Ron, M., Niedzwiedz, S., Herber, R. H.,

Nucl. Instr. Methods 44, 268 (1966).

[3] Ford-Smith, M. H., The Chemistry of Complex Cyanides , Her Majesty's Stationery Office, London (1964) p. I8.

[4] Sidgwick, N, V,, Chemical Elements and Their Compounds , Oxford University Press, Oxford (I950).

[5] Brauer, G,, Handbuch der Praparativen Anorganischen

Chemle, Enke Verlag Stuttgart (1954).

[6] Mellor, D. P. and Craig^ D. P., Proc . Roy. Soc . , New

South Wales I8, 25 (1944).

[7] Reagent Chemicals , ACS Specifications, American Chemical

Society, Washington, D. C. (196O) p. 476.

[8] Ruderman, I. W., Isomet Corporation, Pallisades Park,

New Jersey,

[9] Playfair, C, Proc. Roy. Soc. (London) 74, 328 (I85O).

[10] Perret, A. and Gislon, A., Bull. Soc. Chim. 53, 283 (1933).

[II] Sidgwick, op cit, p. 287.

[12] Kazo, Noji., J. Pharm. Soc. Japan, 67, 6 (1947).

[13] Handbook of Chemistry and Physics, 45th ed.. Chemical

Rubber Company, Cleveland, Ohio (1964).

[14] Justin-Muellex, P., Bull. Soc. Chem. 55, 2, 1932 (1935);

Overbeck, K., Pogg. Ann. 87, 110 (1935).

[15] Taylor, J. K., Analysis and Purification Section,

Analytical Chemistry Division^ National Bureau of

Standards, Private Communication.

[16] Cooke, P. W., Nature 157 , 5l8 (1946).

[17] Manoharan, P. T. and Hamilton, W. C, Inorg. Chem. 2_, 1043 (1963).

[18] Mears, T., Private Communication.

[19] Manoharan, P. T. and Gray, H. B., J. Am. Chem, Soc. _87, 3340 (1965).

23
[20] Spijkerman, J. J.^ Ruegg, F. C, and May, L., "The Use

of Mossbauer Spectroscopy in Iron Coordination Chemistry",

Mossbauer Effect Methodology, _2, I. Gruverman, editor.

Plenum Press, New York, 1966, po 85

[21] Danon, J., "Mossbauer Effect and Chemical Bonding in

Transition Metal Complexes", Technical Report Series No. 50, International Atomic Energy Agency, Vienna (1966)

P. 89.

[22] Gol'danskii, V. I., Private Communication, Lecture "On the

problem concerning the correlation of chemical shift and

quadrupole interaction in NQR spectra for the electronic

structure of iron atoms". International Atomic Energy

Agency International Conference on Hyperfine Interactions,

Wellington, New Zealand (October I966).

[23] Danon, J., J. Chem. Phys . 4l, 3378 (1964).

[24] Ruegg, F. C, Spijkerman, J. J., and Devoe, J. R., Rev.

Sci. Inst. 36, 356 (1965).

[25] DeVoe, J. R., ed., "Radiochemical Analysis: Activation

Analysis, Instrumentation, Radiation Techniques, and

Radioisotope Techniques", NBS Technical Note 4o4 (in

press )

[26] DeVoe, J. R., ed., "Radiochemical Analysis: Activation

Analysis, Instrumentation, Radiation Techniques, and

Radioisotope Techniques", NBS Technical Note 276 (Jan.

1966) p. 89.

[27] DeVoe, J. R., Ibid ., p. 101.

[28] DeVoe, J. R., Ibid ., p. I6. [29] DeVoe, J. R., Ibid ., p. 84. [30] Fluck, E., Kerler, ¥., and Neuwirth, W., Ange. Chem. 2_, 277 (1963).

[31] Costa, N. L., Danon, J., and Xavier, R. M., J. Phys. Chem.

Solids, 23, 1783 (1962).

24
[32] Spljkerman^ J. J.j Ruegg, P. and DeVoe, J. R., "A Standard Reference Material for Mossbauer Spectroscopy

of Iron and its Compounds Technical Report Series No. 50 J International Atomic Energy Agency, Vienna (I966),

P. 254.

[33] Margulies, S. and Ehrman, J. R., Nuclear Instr. Methods

12, 131 (1961).

[3^] Peshkin, M„, Phys. Rev. 139, A717 (I965).

[35] Kaufman, V., Jo Opt. Soc . Am. 52, 866 (I962).

[36] Blatt, J. M. and Weisskopf, V. F., Theoretical Nuclear

Physics , John Wiley and Sons., Inc., New York (1952), p. 37.

[37] Gol'danskii, V. I., Karyagin, S. V., Makarov, E. P. and

Khrapov, V. V., Transactions of the Conference on the

Mossbauer Effect (Dubna), Joint Institute of Nuclear

Studies (1962).

[38] Bearden, J. A., Private Communication.

[39] Nuclear Data Sheets, Nuclear Data Group, Oak Ridge

National Laboratory, Oak Ridge, Tennessee (1965).

[kO] Isaak, G. R. and Isaak, U. , Phys. Letters 17, 51 (I965).

[4l] Locher^ P. R. and Geschwind, S., Phys. Rev. I39 , 722

(1965).

[42] Hanna, S. S. and Preston, R. S., Phys. Rev. I39 , 722

(1965).

[43] Bearden^ J. A., "X-Ray Wave Lengths", U. S. Atomic Energy

Commission Report NYO-IO586 (1964).

[44] Compton, A. H. and Allison, S. K. , X-Ray s in Theory and

Experiment , D. Van Nostrand Co., Inc., Princeton, N. J. (1955).

[45] Heinrich, K. P. J., "An Outline for Cooperative Action

on the Determination of X-Ray Mass Attenuation Coefficients in the Wavelength Range from O.5 to 100 A (25 to 0.12 KeV)", NBS Technical Note 284 (Peb. I966).

25
APPENDIX A COMPUTER CURVE FITTING PGR MOSSBAUER SPECTRA

The mathematical analysis described, below resolves a series of Mossbauer peaks superimposed on a baseline parabola.

Lorentlzlan functions are used for the Mossbauer absorption

profile, and since the equations Involved In finding the best

fit are non-linear, a solution cannot be obtained. However,

by making several approximations and substitutions, linear

equations result which can be solved for approximate results.

The nature of these approximations requires initial estimates

of peak position and half width (half width at half maximum)

to be made manually. Once the equations are solved, results

of the first solution can be used as new input estimates, and

the solution procedure repeated. By iterating in this fashion,

a solution is obtained.

The basic form of a curve consisting of n Lorentzlans and

a parabola is

where the first bracketed term is the sum of the n Lorentzlans

and the second term the equation for the parabola. Here A^, P^^ and B. are the amplitude, position, and half width of the ith

(Lorentlzlan)^ and E, F and G have their usual meaning . These

3n+3 parameters are the unknowns to be solved for by the program. Since a successive-approximation method is used, input to the computer must Include a convergence criterion, specifying the

lower limit parameter corrections desired in the solution^ and

This method is used in a series of computer programs called

PARLORS written in FORTRAN 4.1 for the CDC 36OO [25].

26
a maximum number of iterations (e.g. a limit on the number of

times the program will iterate in the event of diverging solutions) as well as the required estimates.

Once a suitable number of iterations is obtained the

program prepares:

1) a subtract matrix,, containing distance between any two

peaks above the diagonal, peak position along diagonal and the

centroid of any two peaks below the diagonal;

2) an area fraction matrix, containing the ratio of the

area under two peaks off the diagonal, and the fraction of the

area under one peak to the total area on the diagonal;

3) an error analysis; and

4) several types of plots.

METHOD OF SOLUTION

To find the best least square fit to a set of data (x ,

. J y.) the quantity

J k

^ = ^

[^j(obs)-yj(theor)]^

J-^1 must be minimized. (For most sets of data, k is equal to 200

channels.) From (1) the expression for Y^(^-^YieoT)

substituted:

k

0=1

y j(obs)'

1 +

+ E + Fx Gx 2

To linearize the equation the following definitions are made

h.

1 where « (5)

27
1

(6)

where and are the estimated values of h^ and P^, the

peak height and position with error 6^ and y^, respectively,

Using (4)

(7)

1 +

to linearize the equations^ (5) and (6) are substituted Into

(7) . The result Is expanded by the binomial theorem, and all

higher terms (non linear) of 6^, y^ are neglectedo

A. A. 1 +

A.. (8)

1 +

1 +

Let

becomes

Ij " ^l(^j"-^l^^^ ^^^^ right side of equation (8)

Substituting (8) Into (3)

k r n

S = j=i 1+1

(9)

28
Letting = 2A^H^y^ and = A^6^

k

J-1 i=l ^Ij ij + (10)

. . 0 E + FXj + GXj

The unknowns are now A^fC^,D^, for 1 = l,2,...n and E,F,G used

in the minimization of S results in a set of 3n+3 simultaneous

linear equations, which are the usual normal equations of least

squares. The following manipulations simplify setting up these

equations, and in fact follow the method used in the computer

program:

Let y' be the row vector (prime denotes transpose)

y' = (yi yg •••yk^ ^^^^ denoting the k observations and let Z' be a row vector

Z = (A-L.C-^.D^.A^.C^oo.A^^C^^D^^E^P^G)

denoting the 3n+3 unknowns and let

T =

1 1 (Xi-P2)^

2

^ 2

'

1 X2-P2 (Xg-Pg)^

«2l'

2 2

^ «22

2Q22

1- V^i (VPi)"" 1 V^2 (V^s)^

'kl 41 ^k2 q:k2 ^k2

(12)

l^X^^X^

(13)

So that the normal equations become

T'TZ = T'y

29

(14)
The matrix equation (l4) Is then solved for the values of Z. Then

A. = Z 31-2

, . ^31-1

^1 2H,Z3,_.2

^31 ^31

(15)

i A. '31-2

3n+l F = Z 3n+2 G = Z 3n+3

From these corrections, y. and 6.^3 better estimate of P. and

h. (and thus B. ) are obtained.

1- - -1 (Note that because of the ap- proximations made the solutions are not exact). If more ac- curacy Is desired, reiterate by replacing the old estimates

with the corrected estimates and repeat the whole procedure.

ERROR ANALYSIS

Once the value of each unknown has been obtained, the

theoretical value of the data points (y^.^heor^ calculated. The mean square residual.

St

M-1

^ ^J-obs" ^j-theor /(k-3n-3)

(16)

describes the precision of fit, (k Is the number of data

points; and 3n+3 the number of parameters solved for.) The

varlance-covarlance matrix for Z Is then

Var(Z) = (T'T)

1 2

a (17)

The variances of A^, E,F, and G are given by the diagonal

terms of (17) and the covarlance of Z. and Z. by the l,j terms

50
Using propagation of error formulae and (15)

Var !!iy+ _ gc°v(Ai,Dj

(18)

Then the approximation Var (h. (6^) Is made and since from

= 1/ h^. Var(B,

)

rdB."]^ Var (6

(19)

Since Yj_ = Var(Yj_) depends on Var (H^). Because

h^ = H^^ the equation

(20)

Is used In the error analysis to take account of the eri-or In

half width.

Because A^^^ C^, and J)^ are determined from the same data

they will Involve the same random errors and hence be correlated.

This correlation Is expressed by the terms of the varlancecovarlance matrix as follows:

M = Var(Aj_) Cov(A^C^)

Cov(A^C^) Var(C^)

Cov(A^D^) Cov(C^Dj_)

The variances and covarlances of

Cov(A^D^) - cov(c^D^

;

Var(D^)

(21)

[0 0]

(22)

31
and

2A^H^-2D^ = [2Hj_ 0 -2]

are given by

0 1 0 0 M 1 2H, 0 -2 0 -2

(23)

(24)

Var(C^) [2H^Cov(A. ,C^)-2Cov(C^,D^)]

[2H^CoV ( , ) -2 Co V (

, D . )][4h . ^Var ( A^ ) -8h^ Gov ( A^ , D . ) + 4Var ( D . )]

Substituting the appropriate matrix elements into equation

(l8) gives

2, Var(Yj_) = (y^)'

Var ( ) H^^'Var ( A^ ) -2H^ Gov ( A^D^ )+Var ( — + o A.H.-D.

(25)

2[H^Cov(A^,C. )-Gov(D^,G. )]

^l^VV^V

Finally the approximation Var (Pj_) = Var ( y j_ ) Is made. By

the above formulas the values and variances of all the para- meters in (1) can be determined.

32
APPENDIX B ANGULAR DISTRIBUTION OF RADIATION IN THE

MOSSBAUER EFFECT

We consider the particular case of the Mossbauer transitions In Pe-57. These transitions occur between the ground

state of spin-1/2 and the first excited state (l4.4 kev) of

spin-3/2.

The spln-3/2 state possesses 4 magnetic substates (^3/2,

^1/2) so that there are 6 possible Mossbauer transitions:

9/4(l+cos^e)

3 sln^e

3/2 -» 1/2 Am = -1 -3/2 -* -1/2 = +1

1/2 -¥ 1/2 = 0 -1/2 -* -1/2 = 0 -1/2 -¥ 1/2 = +1

1/2 -¥ -1/2 = -1

3/4(l+cos^e)

Here Am represents the z-component of angular momentum which

Is carried off by the photon, or gamma ray. In the transition.

The angular distribution of radiation Is derived with the

aid of the theory of multiple fields. In this particular ex- ample we are concerned with transitions which Involve magnetic

dlpole radiation. The angular distribution Is given by the

equation [36]

Z, (e,$) = X* • X, = V2[l-f[^]|Y,^,,,|^l/2[l-f[^]

I Y |2 , |2

55
In this equation 6 Is the angle between the gamma ray and the

quantization axis, and $ is the azimuthal angle about this

axis; I is the multipole of the radiation and m is the z-component of angular momentum of this radiation; the Y^^ (9^^)

called the vector spherical harmonics and are related to the

spherical harmonics by the relation

X (e,$) = 2 Y (e,$) S = iti ? X V m m

where L is the quantum mechanical angular momentum operator.

The physical significance of the vector spherical harmonic

X_^^(0,$) is that it completely determines the angular dependence of the electric and magnetic multipole fields.

The relative transition probabilities of the various

transitions are determined by the Clebsch-Gordon coefficients

(also called vector addition coefficients, Wigner coefficients,

or C-coeff icients) . The probability that a transition will occur

is given by , ( JM;m,m' ) (notation of Blatt-Weisskopf [36]), In this notation I is the spin of the photon (=l) and is

the spin of the ground state; J, M are the spin and z component

of spin for the excited state; m is the z-component of angular

momentum carried off by the photon in the transition and m' is

the z-component of spin for the ground state. Clearly, M = m

+ m' (conservation of z-component of spin). The transitions

and their relative probabilities in the cases when the degeneracy of the ma^^netic substat es is resolved and unresolved

indicated below:

Transition Relative Probability

1/2 3/2, Am = +1, 3 -1/2 -> 1/2, Am = +1, 1 1/2 1/2, Am = 0, 2 -1/2 -1/2, Am = 0. 2 1/2 -1/2, Am = -1. 1 -1/2 -3/2, Am = -1. 3 54
Transition Relative Ppobability

+3/2 ^ ±1/2

±1/2 4* +1/2

11 In the case when the degeneracy is unresolved^ the angular

distribution of radiation and the relative transition probabilities are given by:

Now in the case of single crystals the absorption spectrum

will possess a pronounced asymmetry. This is due to the fact

that the distribution of radiation is affected by the crystal

structure in a complicated way ( Go I'danskii-Karyagin Effect [37],

which varies for different crystals. In this case the distributions given above must be multiplied by the so-called LambMossbauer or Debye-Waller factor f(0) which depends on the angle

6 as well as on the temperature and the energy of transition.

It is clear that the factor f(0) acts as a kind of distribution

function which selects only the Mossbauer transitions, i.e.,

only recoil-free transitions.

From figure 6, the electric field gradient vector is at an angle of 54° with the 100 crystal plane. The -5/2 state is of

higher energy that the -1/2 state and the electric field gradient is positive. For the 001 and 010 planes, the intensity

ratio is 1.55 and 0.65, respectively. The calculated values of

figure 6 differ from the experimentally observed values of 1.55

and 0.74, indicating the possibility of a Gol'danskii-Karyagin

±3/2 ±1/2

+1/2 +1/2

3/2(l+cos^e)

1+3/2 sin^e 1

1

Effect.

35
ol \ \ I \ \ \ \ \ \ \ \ \ \ \ \ I \ I \ I 0 20 40 60 80 100 120 140 160 180 200

©(DEGREES) (see tent)

Figure 60 Peak intensity assymmetry for the -3/2->-l/2

doublet in iron compounds as a function of

the angle between the electric field gradient

and the incident radiation.

56
APPENDIX C FOPIMAT FOR PRESENTATION OF EXPERIMENTAL MOSSBAUER

SPECTRA AND PARAMETERS

Typical of every new spectroscopic discipline, there has

been a variety of presentations of spectra using different^

nomenclature and units for the spectrum parameters. For purposes of encouraging spectroscopist s to report their data in

a uniform manner a suggested format and nomenclature are described below. It is hoped that these reporting procedures

will serve as a basis for those accepted by pertinent governing bodies such as the International Union of Pure and Applied

Chemistry.

Nomenclature for the pertinent Mossbauer parameters are presented in Table 1. Certain explanations are necessary.

The electric quadrupole splitting can best be represented by

subscripting the magnetic quantum numbers of the transitions.

Since the separation between two peaks must be represented as the difference between two sets of transition energies, the

value of AEq must be followed by a subscripted matrix indicating the two transitions. The magnetic quantum numbers in the

excited and ground state of transition 1, (rn^jm^) and that of

transition 2,(m^,m2) uniquely define AE^.

The line width r obtained experimentally is to be con- trasted with r the theoretical line width. Corrections for

o thickness of the absorber [33] for the cosine effect [27] and

other effects Including instrument broadening may be applied

to r in order to approach r^. Reporting the magnitude of the effect requires great care

if laboratory Independency on measurement is to be retained.

The expression given requires that h(v) be corrected to the

peak height that a Lorentzian function would have if the peak

were of theoretical width (r ). This eliminates many of the

37
Table 1 — Nomenclature for Experimental Mossbauer Spectrum Parameters.

Name Symbol Units

Differential do cm/

s

Chemical

Shift Quadrupole

Splitting cm/s

Temperature 5^ cm/s/°K

Coefficient of

the differential chemical shift Temperature cm/s/°K

coefficient of the quadrupole splitting Line width F cm/s

Magnitude e percent

of the Effect

Definition Displacement of the center of a singlet or a multiplet, from the center of the doublet

of the standard reference material. The separation of two peaks resulting from two transitions (1 and 2) from the excited

(prime) to the ground state that results from electric quadrupole interaction with an electric field gradient, where m

represents the magnetic quantum number

resulting from this interaction. The variation in So with temperature in degrees Kelvin. The temperature range should be specified.

The variation of AEq with temperature in degrees Kelvin. The temperature range should be specified. The full width at half maximum of the Mossbauer peak.

where h('») = height of resonance base line h(v) = height of peak at absorption

maximum B = background

h(v) is to be normalized to peak height corresponding to theoretical line width.

Asymmetry S^ The ratio of the more positive velocity peak

Coefficient height to the more negative velocity peak

height of a doublet. For normalization see

h(v) above. Sg The ratio of the more positive velocity absorption area to the more negative velocity absorption area.

38
problems of peak area and base line estimation. It is necessary to evaluate the background which results from such non- resonant radiation as Compton scatter, x-ray f lourescence, etc. Such backgrounds are certain to be different for different

spectrometer source-detector configurations. The type of sample matrix will also alter this background correction. It is to be understood that the emphasis is on direct experimental

parameters. It is possible to relate £ to the Debye-Waller

factor for the absorber if such a factor is also known for the source

.

The same normalization of h as for h(v) described above

is required for determining S^. The asymmetry coefficient

which measures areas (S^) can best be obtained by evaluating

a the function parameters of the Lorentzian using a least squares

fit to the experimental data. The area of the peak can then

be obtained by evaluating the function.

An example of a spectrum reporting format is shown on pages kO through 42. The first page contains all the necessary

chemical data such as purity. References on synthesis ^ structure^ and other work on the spectroscopy of the compound are given. On the second page is the spectrum showing a best least

squares fit of Lorentzian functions to the experimental data

points. A parabolic baseline- may have to be subtracted as well.

For transmission spectra the peak should be pointing downward.

On the third page are the calculated parameters and their

random error reported as a standard deviation of a single determination. All of the unprocessed data in the spectrum is given

on this page.

39
SODIUM NITROPRUSSIDE

DISODIUM PENTACYANONITROSYL FERRATE DIHYDRATE

Na Fe(CN) NO

2 5 SINGLE

2H 0

2 CRYSTAL

Supplier — Isomet Corporation Muir

Index No. 62C03

Reference

N. L. Costa, J. Danon

and R. M. Xavier, J. Phys. Ctiem. Solids

23, 1783 (1962)

Temperature Room

8 cm/s

-0.012 ± 0.005

A E cm/s

Q

0.185 ±0.005

62E01 L. M. Epstein, J. Chem, Phys. 36, 2731 (1962)Room -0.0165 ± 0.001 0.176 ±0.001

62K01 W. Kerler and Room -0.0176 ± 0.0008 0.1700 ± 0.0012

W. Neuwirth, Z. -107 °C -0.0567 ± 0.0003 0.1725 ± 0.0006 Physik. 167, 176 -25 °C -0.0592 ± 0.0003 0.1715 ± 0.0006

(1962) 25 °C -0.0607 ± 0.0003 0.1712 ± 0.0006

(9.1 mg/cm^)

60 °C -0.0616 ± 0.0003 0.1712 ± 0.0006

(9.1 mg/cm^)

25 °C -0.0608 ± 0.004 0.1723 ± 0.0008

(24.2 mg/cm^) 62K02 W. Kerler, Z. Physik. 167, 194

(1962)

J. Danon, J. Chem.

Phys. 41, 3378 (1964) P. T. Manoharan and

H. B. Gray, J. Am. Chem. Soc, 87, 3340

(1965)

F. A. Cotton, R. R. Manochamp, R. J. M. Henry, R. C. Young,

J. Inorg. Nucl. Chem.

10, 28 (1959)

25 C -0.06064 ± 0.00007 0.1713 ± 0.0004

40
o

cn

c5dddc3c3c3dc3c5-3

<BOO+LQLOh''\ X SINHDO °WyON
% Absorption ( Y radiation) - 85%

Thickness 25.0 ± 1 mg/cm^ single crystal (100 plane) Peak

1

2

S (cm/s)

0.0000 ± 0.0001

(cm/s)

0.1726 ± 0.0001

r (cm/s) 0.0304 ± 0.0002

0.0308 ± 0.0002

Peak Area (counts) Height (counts) Base line (counts)

1 (2.687 ± U.U4/ CI QQQQ 4- Q.OOOO ± n c\r\n\ U.UU/

(2.19456 ± 0.005)

X 10^ X 10^ X 10^ 2 (2.768 ± U.U4; n c\c\n\ U.UU/)

X 10^ X 10^

Unprocessed data: 000000 185997 190807 189n? 19187R i J 1 u / u 18fifi4? 186686 i uuuuu

1 0 c 1 m looiyi 1000/10 1891 n

185753 186400 183291 185975 186520 184786 183915 180072 179562 182995 180623 179407 177123 173075 174157 172302 168264 162990 158375 153363 143202 137297 126193 114312 097781 090890 073297 061825 057296 058878 063861 070921 089636 102944 113602 127503 136850 144325 153755 159287 162577 167681 171 llfi 1 / i 1 ID 1717^0 i / to / 0 1777AQ i / /

177059 182134 101034 179461 181638 183761 1^4177 iO ODHO iOOHDi 100 J J

181701 186389 lOd/ ou 185731 187497 186049 iO't J JO iOD i't't 184291 184080 10 J 01/ 185205 182964 186028 182666 184621 181908 182042 182061 181927 181661 179842 176659 173915 172750 173972 170675 167063 161391 158778 151596 148028 136861 125277 116570 106843 089450 077905 064804 057807 055160 058619 068371 080458 093502 108667 122823 133804 142083 149065 158080 163265 165875 168543 171242 173599 175033 177722 176354 181707 181117 185265 182719 185656 185603 186113 186194 185562 185783 185786 185549 187370 188074 186808 190216 188192 192002 189848 190959 189255 191692 186963 187241 191423 187365 190103 190544 190650 189289 189857 192230 191437 191669 188937 190265 193064 190705 190663 190524 187944 191607 190787 191118 189108 189663 190713 191060 191569 193100 193253 191511 192120 191219 114977 100000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 42
APPENDIX D PHYSICAL CONSTANTS AND CONVERSION

FACTORS FOR IRON-57 MOSSBAUER SPECTROSCOPY

Nuclear Parameters

Excited State of 57.Fe Energy, E^ - 14.37 KeV, 0.864 A [38]

Half life, T^^2 = 9.8 x lO^^s [39]

Internal conversion coefficient, a = 9.2 ± 0.5 [40,4l]

Spin, I = 3/2" [41]

Magnetic moment, [i = -0.0154 nm [39]

Ground State of -^'Fe Spin, I = 1/2" [39]

Magnetic moment, ^ = +0.09024 t 0.00007 nm [4l]

Mossbauer Parameters

Cross section, = I.9I t 0.014 x 10~"^^cm^ [42]

Natural line width, = 4.655 x 10"^ eV [39]

= 0.009699 cm/s

Quadrupole moment, = +O.285 x 10'-24 2 cm^ [393

7.457 X

10"^-^ ergs.

1.126 X 10^ hertz

1.781 X 10"^^ kcal

3.755 X 10"^ cm"-^ Iron Atomic Parameters

Ground state configuration:
x-ray lines: = 6.4 keV, 1.936 A [43] = 7.06 keV, 1.75 A [43]

Mass adsorption coefficient, -n/p (l4„4keV) = 63.5 cmVg [13,45]

X-ray scattering cross section, a^(Fe^ l4 .4keV) = 4xl0"24cm2/atom [44]

Mossbauer Iron-57 Standard Reference Material Parameters

o Quadrupole splitting, AE^ = 8.284 ± 0.0095 x 10~° eV

= 0.1726 t 0.0002 cm/s

= 8.284 + 0.015 X 10"^^ ergs.

= 2.003 ± 0.023 X

10'^ hertz

= 1.979 t 0.036 X 10"^° kcal

= 6.682 + 0.077 X

10"'^ cm"-^ Percent effect, e = 17^

Temperature dependence of the quadrupole splitting,

(Q^) = 10-5cm,s-l,° K"^[30]

Temperature dependence of the chemical shift, 6^^ =

3 X 10-5cm,s-l,°K"^ [30]

Gamma attenuation = 85^

For -^'Fe 1 cm/s = only : 4.798 X 6.242 X 4.136 X 2.613 X 1.240 X

10"' eV

10^^ erg

10-^5 hertz

10^2 kcal

10-4 cm"'''

44
APPENDIX E ATTENUATION AND LINE BROADENING FOR ^'^FE ABSORBERS

The required thickness of the standard reference absorber,

and for all Mossbauer absorbers. Is determined by the gamma-ray

attenuation and the line broadening which limits the resolution.

The attenuation of the l4.4 keV radiation can be calculated

from the mass absorption coefficient, and the absorber area density, t^ (g/cm^), using the equation:

1 = 1 e"^^m^p

o ^ while for compounds:

U t = E LL t ^m p ^ ^m^ p^

The subscript referring to the elements forming the compound.

The mass absorption coefficients, \i , for l4.4 keV radla- m

tion plotted as a function of element [13] are shown in Figure 7. The line broadening can be calculated by the method of

Margulles and Ehrman [33] for the correction of Mossbauer line

width for source and absorber thickness, the result of which is

shown in Figure 7. The width can be found from the effective

absorber thickness T^ = f ' t , obtained from the Debye-Waller

a a p-^ factor, f ' of the absorber, and the absorber thickness in

2 g/cm of natural abundance iron. Figure 8 is a plot of the

broadening of the transmitted line for a source having a uniform distribution of cobalt-57 atoms on a non-ferrous matrix.

The emission and absorption spectra are assumed to be Lorentzlan. It is to be understood that this graph is to be used

as a guide. If highly reproducible results are destired,

mathematical computation should be used.

45
Figure Attenuation coefficients for l4.4 keV gamma

radiation as a function of element.

46
EFFECTIVE ABSORBER THICKNESS

Figure 8. Plot of effective source thickness. Adapted

from Margulies and Ehrman [35].

f = recollless fraction of source or absorber

where subscript l^a, l=s represents

absorber and source respectively,

t = thickness of absorber in mg/cm^.

P

s = Mossbauer cross section of -^^

' Fe cm /atom.

Ng = number of ^Tpe atoms in the source per cm-^. t = thickness of source in cm.

s a = experimental full width at half maximum.

= effective absorber thickness (mg/cm^).

T = source thickness.

47

Announcement of New Publications on Standard Reference Materials

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Dear Sir: Please add my name to the announcement list of new

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Publication 260 - Standard Reference Materials.

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