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ecltnicat <v2cte 284

AN OUTLINE FOR COOPERATIVE ACTION ON THE DETERMINATION

OF X-RAY MASS ATTENUATION COEFFICIENTS IN THE WAVELENGTH

RANGE FROM 0.5 TO 100 A (25 to 0.12 keV)

KURT F. J. HEINRICH

E

DEPARTMENT OF COMMERCE

IAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards is a principal focal point in the Federal Government for assur- ing maximum application of the physical and engineering sciences to the advancement of technology

in industry and commerce. Its responsibilities include development and maintenance of the national

standards of measurement, and the provisions of means for making measurements consistent with

those standards; determination of physical constants and properties of materials; development of methods for testing materials, mechanisms, and structures, and making such tests as may be necessary, particularly for government agencies; cooperation in the establishment of standard practices

for incorporation in codes and specifications: advisory service to government agencies on scientific and technical problems; invention and development of devices to serve special needs of the Govern- ment; assistance to industry, business, and consumers in the development and acceptance of commercial standards and simplified trade practice recommendations; administration of programs in cooperation with United States business groups and standards organizations for the development

of international standards of practice; and maintenance of a clearinghouse for the collection and

dissemination of scientific, technical, and engineering information. The scope of the Bureau's

activities is suggested in the following listing of its three Institutes and their organizational units. Institute for Basic Standards. Applied Mathematics. Electricity. Metrology. Mechanics. Heat. Atomic Physics. Physical Chemistry. Laboratory Astrophysics.* Radiation Physics. Radio Standards

Laboratory:* Radio Standards Physics; Radio Standards Engineering. Office of Standard Reference

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* Located at Boulder, Colorado, 80301.

'* Located at 5285 Port Royal Road, Springfield, Virginia, 22171.
NATIONAL BUREAU OF STANDARDS

Technical Note 284

ISSUED FEBRUARY 21, 1966

AN OUTLINE FOR COOPERATIVE ACTION ON THE DETERMINATION

OF X-RAY MASS ATTENUATION COEFFICIENTS IN THE WAVELENGTH

RANGE FROM 0.5 TO 100 A (25 to 0.12 keV)

Kurt F. J. Heinrich

Spectrochemical Analysis Section

Analytical Chemistry Division

Institute for Materials Research

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, Government Printing Office

Washington, D.C., 20402 - Price 15 cents
PREFACE

Investigators in x-ray spectrometry., as well as in other

related fields, are becoming increasingly aware of the urgent

need for a revision of available information concerning x-ray

mass attenuation coefficients. It is the purpose of this

report to show the extent to which progress In x-ray

fluorescence spectrometry and electron probe microanalysis

depends upon reliable attenuation coefficients. A list of

the limited sources of information presently available is

included, and the necessity for further work in this area is

indicated.

As a consequence of the unsatisfactory situation, an

increasing number of laboratories is presently involved in

the measurement of x-ray mass absorption coefficients, and

others are planning such activities in the near future.

There is, however, a need for a coordinating group which

will promote the exchange of information concerning such

research, assist in the selection of techniques when requested

to do so, suggest areas in which measurement is most

urgently needed, and obtain by interpolation procedures the

mass absorption coefficients for those elements and wavelength regions for which experimental data are not available.

Discussions of these problems with prominent

investigators in the field, in this country as well as abroad,

have indicated that our group here at the National Bureau of

Standards would be appropriate for coordinating this work.

It is therefore hoped that those readers who are involved in

such measurements or plan to perform them, will assist us in

this cooperative task to the benefit of all concerned.

Kurt F, J. Heinrich

11
TABLE OF CONTENTS

PAGE

1. INTRODUCTION . . . . • • . . 1

2. NEEDS FOR MASS ATTENUATION COEFFICIENT

TABLES o . o . . 2

2. SOURCES OF INFORMATION ...... „ . . 5

4. PRESENT SITUATION «... 8

5. NEED FOR COORDINATION 9

6. PLAN FOR OPERATION „ _ „ 10

7. FIGURE 1, TYPICAL PAGE FROM HEINRICH'S

TABLES „ . . . . 12

8. FIGURE 2. REGIONS IN WHICH X-RAY MASS

ABSORPTION COEFFICIENTS ARE WELL

DOCUMENTED (DARK BARS) . . . . . . . 13

in

AN OUTLINE FOR COOPERATIVE ACTION ON THE DETERM [NATION

OF X-RAY MASS ATTENUATION COEFFICIENTS IN THE WAVELENGTH

RANGE FROM 0.5 to 100A (25 to 0.12 keV)

Kurt F. J. Heinrich

ABSTRACT

Sources of information on x-ray mass attenuation

coefficients and the present status of data in this area are

reviewed. Many gaps are observed in the existing data and

some values derived by interpolation may be of questionable

accuracy. Because of the importance of accurate mass

attenuation coefficients, the extension and improvement of

these measurements is proposed together with a plan for

coordination of effort and exchange of information.

1. INTRODUCTION

In the first half of this century, an impressive amount

of work was performed on the experimental determination of

x-ray attenuation coefficients. The tables published by

Allen and re-published in the book X-Rays in Theory and

Experiment ^ by Compton and Allison, are representative of the

results achieved In this period. The amount of effort spent

in this endeavor can be appreciated if it is taken into

account that early workers in this field did not have at

their disposal the stable x-ray sources and sensitive x-ray

measuring devices which are now available. Practically all

of the early work was done by photographic registration of

x-rays or by measurements with ionization chambers.

Presently available instrumentation permits the

measurement of mass attenuation coefficients with much less

experimental effort and greater accuracy,, The stability of

x-ray sources has been improved considerably; and photon

counting techniques using scintillation and proportional,

detectors permit satisfactory measurements over a wide range

of intensities. As a greater sensitivity is achieved with

these detectors, it is now possible to measure attenuation

of secondary (fluorescent) radiation. The investigator has

at his disposal a very wide range of useful x-ray radiations

produced by secondary fluorescent targets external to the

vacuum enclosure of the primary x-ray generator. Meanwhile,

the amount of work on experimental determination of mass

attenuation coefficients has diminished considerably in the

last two decades. X-ray physics is not at present as

interesting a field for most theoretical physicists as it

was forty years ago; those working in the x-ray field are

now more concerned about fine structure in absorption and
emission spectra than in absolute values of mass

attenuation coefficients. As a result,, the present technical

capabilities of improving our knowledge of mass attenuation

coefficients have remained largely unused.

2. NEEDS FOR MASS ATTENUATION COEFFICIENT TABLES

Under the impact of the instrumental developments

mentioned above , x-ray spectrometry has developed into one

of the most important methods for instrumental analysis of

elementary composition. The two techniques employed most

frequently are x-ray fluorescence spectrometry and electron

probe microanalysis.

In x-ray fluorescence spectrometry, use is made of the

fact that the wavelengths of x-ray lines produced within a specimen irradiated by a polychromatic beam of primary xrays are characteristic of the elements present in the

specimen. As x-ray spectra contain fewer lines than emission

spectra in the visible range , the use of such spectra for

qualitative analysis is particularly attractive. The

intensity of observed lines is also uniquely related to the

composition of the emitting specimen. Since x-ray intensity

measurements of a precision of 0.1-0 o 2^ of total intensity

can be made fairly easily, quantitative x-ray fluorescence

emission analysis is often capable of a precision comparable

to that of conventional chemical analysis. In many

applications this technique is superior in simplicity, economy,

and speed, to other analytical procedures. Further advantages

are the non-destructive nature of x-ray spectrometry, and

the fact that the digital electronic signal output is

particularly useful for computer applications and for

automated systems.

One major limitation of this technique, however, lies

in the fact that the intensity of a particular emission line,

although primarily related to the concentration of the

element originating it, is also a function to a minor degree

of all other elements present in the specimen. The interelement effects thus observed make it necessary, for

quantitative analysis, to compare the x-ray intensities

obtained from an unknown specimen with those emitted by

standards of known composition close to that of the unknown.

When the specimens to be analyzed cover a wide range of

composition, and particularly with specimens containing more

than two components, a great number of well characterized

standards is thus necessary to cover the whole compositional

range under investigation.
Although several attempts have been made in the past to

overcome this difficulty by an analysis of the underlying

physical events, this was found to be too cumbersome a task.

Current practices are in general limited to the use of

matching standards , or semiempirical approaches, which, in

turn, also are based on the analysis of a great number of

specimens

At a recent discussion session at NBS sponsored by the

Spectrochemical Analysis Section of its Analytical Chemistry

Division and attended by some of the leading investigators in

x-ray fluorescence spectrometry, ways and means of improving

the technique of quantitative analysis were discussed. It

was the consensus of the participants that the current

semiempirical techniques, while more useful than a technique

of matching standards, still are cumbersome and imperfect.

The need for testing such a system by means of known

standards renders the results dependent upon the accuracy of

the chemical methods used in characterizing the standards.

Furthermore, the enhancement effects of fluorescent

excitation of one element by fluorescent radiation emitted by

another element in the specimen, are not well described by the

equation systems currently in use. It was also suggested that

in recent years calculation techniques by electronic computers

have advanced to a degree that would permit a quantitative

re-investigation of the theory of x-ray fluorescence

spectrometry on a computational basis not available previously,

The x-ray intensity observed on an irradiated specimen

depends to a great extent upon the absorption of the primary

radiation penetrating the specimen, and the absorption of

the secondary or fluorescent radiation on its way to the

specimen surface. What renders the calculation so tedious

is the fact that strong monochromatic x-ray sources are not

available at present, so that the absorption of the primary

polychromatic radiation must be integrated over a wide range

of wavelengths. It is also true that the success of such a- calculation depends upon the knowledge of the mass

attenuation coefficients for the radiation of all wavelengths

involved in the process. As x-ray techniques are extended

more and more to long wavelengths, the lack of knowledge of

attenuation coefficients in the soft range becomes more

serious. It was thus concluded at the aforementioned

session, that better knowledge of mass attenuation

coefficients is a prerequisite for successful theoretical

tre atmervG of quantitative x-ray fluorescence analysis.
The inter element' effects observable in x-ray

fluorescence are also present in electron probe microanalysis . However, empirical correction method's are even more

impractical in this technique, in view of the difficulty in

obtaining standard reference materials of composition close

to that of the sample and homogeneous on a microscopic scale.

The theoretical treatment of electron probe analysis,

although quite involved, is somewhat simplified by the fact

that the exciting electrons are monochromatic, i.e., all

electrons striking the specimen possess the same energy

within very narrow limits.

The corrections to be applied to the experimentally

obtained x-ray intensities in order to calculate the

composition of a specimen are the following:

a. The absorption correction , which corrects for

differences in the attenuation of characteristic radiation

within specimen and standard.

b. The fluorescence corrections , which correct

for indirect x-ray excitation (fluorescent radiation) produced

by characteristic and continuous radiation of energy higher

than that of the line under investigation.

c

The atomic number effect correction , which

corrects for differences in the efficiency of production of

characteristic x-ray photons, as a function of atomic

number of the specimen or standard.

Numerous attempts have been made to establish methods

for the corrections outlined above. Practical progress is,

however, very slow because of the difficulties in testing

experimentally the proposed procedures and in separating

correctly the effects of the three corrections. These

difficulties are due to the lack of adequate standard

materials to be used for critical tests, and to insufficient

knowledge of physical parameters, such as the x-ray mass

attenuation coefficients, x-ray excitation efficiencies and

fluorescence yields, and electron backscattering

coefficients.

While the atomic number effect is at present the most

controversial, in most cases the absorption correction is

of greatest magnitude. The exact value of this correction

depends primarily on the mass attenuation coefficients of

the specimen for the radiation under investigation. Hence,

satisfactory knowledge of the mass attenuation coefficients

of all elements within the wavelength region used in electron

probe microanalysis is required before performing correct

k
absorption corrections. Only after the absorption effects

have been corrected can the other corrections be tested.

Incidentally j mass attenuation coefficients enter into the

other corrections as well.

Microprobes are now being provided with x-ray

spectrometers for the soft x-ray wavelength range from 10

to 100 a. In this region,, attenuation coefficients are

virtually unknown. Hence , the need for the determination

of such data becomes even more pressing.

There are, obviously 3 other fields of science in which

a better knowledge of mass attenuation coefficients is

considered desirable, as for instance in the study of

radiation in the upper atmosphere and in space. X-ray

spectrometric analysis merely gives most striking

demonstration for the need to revise the current attenuation

data.

3. SOURCES OF INFORMATION

About 100 publications communicating the results of

experimental determination of mass attenuation can be found

in the literature. Most of these communications cover a

rather narrow range of wavelengths and absorbers , and while

there is a considerable overlap in the regions covered,

many elements have not been investigated at all. Several

attempts have therefore been made to provide the user of

mass absorption coefficients with tables in which the

available information is covered. In some cases data for

those regions which have not been covered experimentally

have been derived by interpolation between existing values.

Some of the tables most frequently employed by the x-ray

spectroscopist will be described in the following sections.

1. S. J. M. Allen, "Mean values of the mass absorption

coefficients of the elements." In A. H. Compton, and S. K.

Allison, X-Rays in Theory and Experiment, D. Van Nostrand

Co., New York, 1935. This compilation reflects the results

obtained in early research in the field, and is widely used.

Interpolation has been employed, and the tables do not

clearly distinguish between experimental data and those

obtained by interpolation. Several recent, and presumably

reliable, experimental results are at variance with Allen's

data; these time-honored tables should by now be considered

obsolete.

2. L. S. Birks, Electron Probe Microanalysis, Appendix

~3, Interscience Publishers, New York-London, 1963.

5
3. S. J. M. Allen, "Mass Absorption Coefficients for

X and Gamma Rays," Handbook of Chemistry and Physics, 43rd

Ed. (1961) 2718-2723. The Chemical Rubber Publishing Co.,

Cleveland, Ohio.

4. H. A. Liebhaf sky, et al. , X-Ray Absorption and

Emission in Analytical Chemistry, Appendix IV, J. Wiley,

New York, i960.

5. Philips Electronics Instruments, "Table of X-Ray

Mass Absorption Coefficients," Norelco Reporter 9 (1962),

May-June (Supplement).

6. K. Sagel, Tabellen zur Rontgen-Emissions- Und

Absorptions-Analyse, Springer Verlag, Berlin, Gottingen,

Heidelberg, 1959. The preceding tables are basically

modifications of Allen's data; particularly for longer

wavelength there are serious disagreements among these

references; all of them tend to disagree with recent

measurements.

7. E. Petrassi, Table of X-Ray Mass Absorption

Coefficients, in R. Theisen, Quantitative Electron

Microprobe Analysis, p. 32. Springer Verlag, Berlin,

Heidelberg, New York, 1965. The section of this table

corresponding to soft x-rays and low atomic number elements

has been constructed using some of the newest experimental

data available. The part concerning heavier elements,

however, is inconsistent and disagrees with some of the newer

measurements.

8. G. White Grodstein, X-Ray Attenuation Coefficients

from 10 kev to 100 Mev. National Bureau of Standards

Circular 583 (1957) (35 cents), and Supplement to Circular

583 (1959) (15 cents), available from U. S. Govt. Printing

Office, Washington, D. C. This work includes a lucid

discussion of the physics of mass absorption coefficients.

The wide range of energies considered precluded a detailed

documentation of the low energy range of special interest

to the x-ray spectroscopist

9. H. M. Stainer, X-Ray Mass Absorption Coefficients.

A Literature Survey. U. S. Bureau of Mines Information

Circular 8166 (1963). Available from U. S. Govt. Printing

Office, Washington, D. C. This excellent survey contains

all references to published data, experimental, calculated,

or compiled, up to the date of publication. The published

values as well as the corresponding references are included,

and the more important sources are characterized as to

technique of measurement, the nature of the absorber,
and estimate of errors. The wavelengths are indicated

in the scale used by each individual author.

10. J. Leroux, "Method for finding mass absorption

coefficients by empirical equations and graphs/' Advances

in X-Ray Analysis, Vol. V (1961), 153-160. Plenum Press,

New York. Leroux proposes a self-consistent set of mass

absorption coefficients, obtained by interpolation from

experimental data, and using the exponential expression

\±/p = C. 7P in which ~h is the wavelength in angstroms,

and C and n are determined empirically. Leroux gives the

values for C and n for elementary absorbers and the

homologous region between absorption edges. The values of

C are assumed to vary in a regular fashion as a function of

the atomic number of the absorber. An analysis of recently

obtained experimental data shows that the equation used by

Leroux is a good approximation. Deviation from the

exponential equation found in older data seems chiefly due

to experimental error. For a given region between

homologous absorption edges, the values of C vary with the

atomic number of the absorber, being approximately

proportional to the third power of the atomic number.

Since, however, atomic cross-sections will vary more smoothly

than mass absorption coefficients, it is reasonable to expect

that the value of G.A.Z "" , in which A is the atomic weight

and Z the atomic number, should vary more smoothly than

C.Z-3. in practice, these two expressions will be almost

equivalent within the accuracy of known mass absorption

coefficients. Leroux did not, however, precede his

interpolation by a critical selection of experimental data,

so that his data still reflect the errors of Allen's tables.

11. K. F. J. Heinrich, "X-Ray Absorption Uncertainty,"

in T. D. McKinley, K. F. J. Heinrich, and D. B. Wittry,

The Electron Microprobe, Proc. of an Electron Probe Analysis

Symposium, Wiley & Sons, New York, 1966.

Experimental data through 1963 are tested for selfconsistency and proper technique, and a selected group of

data is used as the basis for interpolation, according to

the method of Leroux. From the coefficients and exponents

obtained by this procedure, the mass attenuation coefficients

of all elements except hydrogen and helium are calculated

for the K alpha, K beta, L alpha 1, L beta 1, M alpha, and

M beta lines of all elements, within the wavelength region

from 0.7 to 12 angstroms. Areas in which further work is

most urgently needed are pointed out. The data published

in the tables included in this work have been obtained

by a computer, and the calculation is carried out to a tenth

of a unit, regardless of the estimated accuracy. The tables

7
are believed to be more reliable than previously mentioned

sources. A typical page from a preprint of the table is

reproduced at the end of this report. Experimental data

obtained after the publication of the tables , in regions

not documented previously, show in general a satisfactory

agreement. However , in many areas, the data reproduced in

the tables have been derived from very meager and uncertain

experimental evidence. The graph attached at the end of

the report shows the wavelength and atomic number regions

within which data usable for extrapolation were found. It

can be seen from this graph that not too much can be

expected from an extrapolation starting with such a small

amount of experimental data.

Among recent publications not contained in Stainer '

bibliography or used in Heinrich's publication, the

following should be consulted:

12. G. D. Hughes and J. B. Woodhouse, "X-Ray Mass

Absorption Coefficients," Proc. 4th International Congress

on X-Ray Optics and Microanalysis, Or say, September I965

(to be published).

13. R. W. Carter and R. H. Rohrer, "The Determination

of Low Energy X-Ray Mass Absorption Coefficients," Final

Report on Research Contract At-(40-l)-2953j Emory

University, Atlanta, Georgia, 1964.

14. J. H. Hubbell and M. J. Berger, "Photon Attenuation

and Energy Transfer Coefficients. Tabulation and Discussion"

National Bureau of Standards, Unpublished report (I965).

15. B. A. Cooke, and E. A. Stewardson, "The

Absorption of X-Rays in the Range 7-I7S by Be, Mg, Al, Cu,

and Ag" Brit. J. Appl. Phys . , 15, 1315-1319.

4. PRESENT SITUATION

The urgent need for further data has recently induced

several laboratories to perform measurements of mass

attenuation coefficients. Some of these laboratories are

well qualified to undertake such work, some others, not

normally involved in this type of work, should be provided

with guide lines in order to avoid the production of data

of poor accuracy which could further increase the existing

confusion. Facilities for evaluating the uniformity of the

absorbers are not available in all of these laboratories.

The need is greatest in the region from 10 to 100 angstroms,

and it is in this region where the technical requirements

8
are most exacting. Furthermore, some of the data will only

be published in internal reports if at all. A considerable

fraction of the work under way is repetitious; while

confirmation of some data is desirable, it is unfortunate

that much of the work concentrates on the shorter wavelength

region and on absorbers such as copper, iron, and aluminum,

whose mass absorption coefficients are relatively well known

in the short wavelength region.

5. NEED FOR COORDINATION

Clearly, coordination of experimental work on mass

absorption coefficients would present considerable

advantages. A coordinating group for this type of work

would be in a position to inform interested persons

concerning the regions of wavelength and absorbers which are

fairly well established, and indicate regions in which

further work is most urgently needed. It could also provide

a means for communicating to interested persons the results

of investigations performed by others. Discussions with

prominent workers in the field show that in general there

is very little awareness of work going on in other

laboratories, and even of results of concluded work, some

of which is published in reports of very limited circulation,

Communication should also be established with respect

to techniques of mass absorption coefficient determination.

Some work is performed in an incidental manner by

laboratories in need of data in a certain region.

Precautions as to absorber conditions (especially uniformity

of thickness) and to conditions of measurement are not

always properly taken. Information on the detector

acceptance angle, needed to estimate the effect of smallangle coherent scattering on a given measurement, is often

omitted.

Finally, one group must undertake at periodic intervals

the task of performing the interpolations for data in

regions not covered experimentally, and of communicating

the results of these interpolations to the user.

In numerous conversations with persons working in this

field we have been assured that such a cooperative task is

considered desirable, and that our Spectrochemical Analysis

Group, National Bureau of Standards would be an appropriate

group for such coordination. We therefore propose the

following plan of operation.
6. PLAN FOR OPERATION

As a first step It is proposed that laboratories

working in this field give us information concerning the

areas which they are presently covering or intend to cover

in the near future, and briefly outline the techniques

they employ for testing the absorbers and performing their

measurements. We propose to prepare an outline of suggested

procedures for those laboratories which are interested in

such information. Information and inquiries should be

directed to Dr. Kurt F. J. Heinrich, Spectrochemical Analysis

Section 510. 02, National Bureau of Standards, Washington,

D. C. 20234,

It is also requested that the laboratories involved

give information concerning the results obtained, and give

an estimation of the accuracy of the data. We suggest that

copies of recent publications In the field, or data

originating from other sources be made available. We would

also appreciate being informed of other laboratories working

In this area.

With the aid of the data that were published since the

appearance of Heinrich 's tables, and of further information

that we expect to receive from these laboratories, a new

table of interpolations will be prepared and made available

to the users.

We wish to express our thanks to the following

participants in the discussions concerning quantitative

x-ray fluorescence analysis, which have greatly contributed

to our understanding of the problems in this field.

Mr. L., S. Birks, U. S. Naval Research Laboratories,

Washington, D. C,

Mr. E. J. Brooks, U. S. Naval Research Laboratories,

Washington, D. 0.

Mr. J. Criss, U. S. Naval Research Laboratories,

Washington, D. C.

Dr. A. H. Gillie son, Dept. of Mines and Technological

Surveys, Ottawa, Ontario, Canada

Dr. J. Leroux, Dept. of National Health and Welfare,

Ottawa, Ontario, Canada

10
Our thanks are also due to the many persons with whom

we have discussed the possibility of cooperation in this

field, especially to:

Dr. Y. Cauchois, Sorbonne, Paris

Dr. P. Duncumb, Tube Investments Research Laboratory,

Cambridge, England.

Dr, J. Philibert, IRS ID, Saint-Germain-en-Laye.

Drs. G. D. Hughes and J. B. Woodhouse, Metals Research

Ltd., Cambridge, England.

Prof. Harms Mails s a, Techn. Hochschule, Vienna, Austria.

Dr. Ugo Fano, NB3, Washington, D. C.

Dr. R. D. Deslattes, N33, Washington, D C.

Mr. J c H D Hubbell, NBS, Washington, D. C.

Profc B Henke, Pomona College, Pomona, California

11
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8
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