A UNITED STATES DEPARTMENT OF COMMERCE

PUBLICATION NBS TECHNICAL NOTE 796

FRAME:

An On-Line Correction Procedure

for Quantitative

Electron Probe Microanalysis

QC

100

.U5753

W.7^

c.Z

U.S.

EPARTMENT

OF

COMMERCE

National

Bureau

of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

the Institute for Computer Sciences and Technology, and the Office for Information Programs. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

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with 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. The Institute consists of a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Nuclear

Sciences 2 — Applied Radiation ° — Quantum Electronics 3 — Electromagnetics 3 — Time

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THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effec- tiveness in the conduct of their programs through the selection, acquisition, and effective

utilization of automatic data processing equipment; and serves as the principal focus within

the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer languages. The Center consists of the following offices and divisions: Information Processing Standards — Computer Information — Computer Services —

Systems Development — Information Processing Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and

accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the development of the National Standard Reference Data System and

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

3 Part of the Center for Radiation Research.

3 Located at Boulder, Colorado 80302.

« Part of the Center for Building Technology.
FRAME: An On -Line Correction Procedure

for Quantitative Electron Probe Microanalysis

Nationai Bureau o." £ : APR 2 9 1974 H. Yakowitz

Metallurgy Division

and

R. L. Myklebust and K. F. J. Heinrich

Analytical Chemistry Division

Institute for Materials Research

National Bureau of Standards Washington, D.C. 20234

^r°?v

'V«of*V

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued October 1973
National Bureau of Standards Technical Note 796

Nat. Bur. Stand. (U.S.), Tech. Note 796, 51 pages (Oct. 1973) CODEN: NBTNAE

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.46:796). Price 80 cents.
TABLE OF CONTENTS

PAGE

Abstract 1 Introduction 2 Evolution of the Program FRAME 2 Fundamentals of FRAME 4 Structure of the Program Versions FRAME2 to FRAME4 . . 9 Limitations of FRAME 10

Comparison of Results from FRAME with COR2 12

Example Showing On-line Analysis using FRAME 13

Conclusions 13

LIST OF TABLES

TABLE NO.

la. Comparison of NBS programs for quantitative

microprobe analysis 15

lb. Comparison of NBS programs for quantitative

microprobe analysis . 15

Ic. Comparison of NBS programs for quantitative

microprobe analysis 16

II. Analysis of alloys: SRM's 481 and 482

(Au-Ag and Cu-Au) 17

III. Analysis of a silicate: Diopside 65 - Jadeite 35 18

IV. Analysis of the silicates: Johnstown Hypersthene and Diopside 65 - Jadeite 35, using

FRAME4 19

V. Input-output for FRAME4 — analysis of

Diopside 65 - Jadeite 35 21

VI. Results of analysis of SRM 483 containing

0.0322 Si - 0.968 Fe 22

111
PAGE

LIST OF FIGURES

FIGURE NO.

1. Flow sheet showing operations carried out by

FRAME program 2 3

2. Analytical fit to backscatter factor R .... 24

3a. Results of analysis on alloy data quoted by

Poole [19] as computed by COR using the

Heinrich-Yakowitz f(x) expression [11] . . 25

3b. Comparison of FRAME2 and COR for the alloy

data shown by Figure 3a 26

IV
FRAME: An On-Line Correction Procedure for

Quantitative Electron Probe Microanalysis

Harvey Yakowitz , Robert L. Myklebust,

and Kurt F. J. Heinrich

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

A procedure using a mini -computer for on-line correction

of x-ray data from electron microprobe analysis has been

developed. This program, called FRAME, allows mass fractions

to be computed on-line by the ZAF approach. Besides x-ray

intensities, the only input data required are the atomic

numbers of the elements present, the analytical line being

used, and the operating voltage. Other required parameters

such as atomic weights and x-ray mass attenuation coefficients

are stored or calculated by the program. FRAME is in FORTRAN

IV, and requires about 4K of computer core. Results from FRAME

are very close to those of C0R2 ,' which is considered to be

the most accurate program available for quantitative electron

probe microanalysis.

Key Words: Electron probe; mini-computer; on-line correction;

quantitative microanalysis.
Introduction

The relative characteristic x-ray intensities measured

with electron probe microanalyzers can be converted into

concentrations of emitting elements, either by theoretical

procedures, or by empirical calibration.

The theoretical procedures use generalized, though

empirically adjusted expressions for the intensities of x-ray

emission and absorption. They do not require, in principle,

the use of any standards except elements, but they involve

extensive calculation [1-3]. The empirical procedures, though

simpler in calculation [4-5], usually require composite standards which may not be available in practice.

Electron probe microanalysis frequently consists of a sequence of measurements at various points on the specimen

surface. In such case, it is useful to obtain the corrected

results of the analysis at any point before deciding on the

next step. Therefore, an on-line calculation procedure is

desirable. However, such calculations were, in the past,

available only for empirical data evaluation procedures [6].

This communication describes a correction procedure

incorporated into a program (FRAME) which renders possible

the on-line calculation with a minicomputer of concentrations

(mass fractions) by the traditional ZAF approach [7].

Evolution of the Program FRAME

The program MULTI8, developed by us and recently published [8], evaluates the experimental x-ray intensity lines

by the theoretical method. MULTI8 can be used in a batch

mode on a time-shared computer; it is similar to several

programs now in use for such purposes in other laboratories.

This program has the following limitations:

i Figures in brackets indicate the literature references at

the end of this paper.
a. It omits the correction for fluorescence due to the

continuum, and the integration over the range of energies of

the electrons decelerating within the specimen in the calculation of generated primary x-ray intensities.

b. It requires, as part of the input, the mass absorption coefficients for all lines and elements and decisions

concerning the applicability of fluorescence corrections for

each line and element present.

c. The ZAF procedure requires the input of relative

x-ray intensities corrected for detector dead-time and background. As MULTI8 does not contain provisions for these cor- rections, they must be performed externally before input.

A program such as MULTI8 would therefore be inadequate

for on-line use, and its accuracy may be less than optimal

under certain operating conditions. As it is more basic to

obtain an accurate procedure than to apply it on-line, for

the next step we developed a program, COR [3], which avoids,

insofar as possible, all simplifications, and incorporates

all correction steps known to us, including the correction

for continuum fluorescence. Our aim was to obtain a benchmark,

against which other programs could be compared. In effect,

diverse correction formulae can be tested by substituting

them into C0R2 , and the effects of simplifications, omissions,

and empirical fits to partial correction steps can thus be

evaluated

The correct-ion for the continuum fluorescence requires

a fairly large computation. It was found expedient in the

development of C0R2 to calculate internally all x-ray mass absorption coefficients required for this correction; it was also necessary to divide the wavelength of the continuum range

into regions confined by the absorption edges of the elements

present in the specimen. Once these provisions were included,

it was relatively simple to also determine internally which
corrections for fluorescence due to characteristic lines would

apply in each case. We added an auxiliary sub -program to

correct for background and dead-time, and we thus arrived at

a rigorous procedure which requires a minimum of input —

except for a table of constants which are kept in memory —

and which is quite easy to handle in practical applications.

Therefore, C0R2 , which was conceived primarily as a research

tool, has proven to be very satisfactory for routine data

calculation in the batch mode and is used extensively for

this purpose at the National Bureau of Standards and in

several other laboratories.

In the program FRAME, which is described here, we have

incorporated into a simple model based upon MULTI8 the decision making and the internal calculation of parameters

which were first developed for C0R2 . In this manner, we have

obtained a program simple enough to be used on-line in a small computer. We have also included procedures to correct

the observed x-ray intensities for dead-time and background,

so that the scaler readings can be directly used as input.

As to the simplifications contained in MULT 18, and also used

in FRAME, we have concluded that they will not observably

degrade the accuracy of the procedure if certain working con- ditions are adopted. The working rules concerning the choice

of lines and operating voltage are discussed at the end of the

paper. A comparison of important features of the three programs mentioned above is found in Table I.

Fundamentals of FRAME (See Figure 1)

We have adapted from MULTI8, essentially without change,

the multiplicative correction factors for absorption of

primary radiation, of the atomic number effects, and of

fluorescence due to characteristic lines (ZAF procedure).

The program thus operates on the assumption that the relationship between concentration and background dead-time
corrected intensity ratios can be expressed by

C = k • k

z

• kA• k

p (1)

where C is the mass fraction of the element being measured

k is the x-ray intensity ratio obtained from the

microprobe corrected for background and dead-time

k y is the atomic number correction

k. is the absorption correction, and

k- is the characteristic fluorescence correction.

t As in MULTI8, there is no provision for fluorescence due

to the continuum. The significant changes with respect to

MULTI8 are as follows.

1. As an input, FRAME can use x-ray photon counts collected in fixed time periods on scalers . A background

correction is performed by subtracting background counts,

which must also be accumulated in scalers, from the line

intensities. The operator must determine from where the

background readings are to be collected. In the present

version, the background readings are made on the standards,

and FRAME distinguishes background from standard line readings

by the intensities of the observed radiation.

2. A correction for counter coincidence (dead-time),

according to the equation of Ruark and Brammer [9] is applied

to the observed count rates for specimens and standards. A

method for determining the dead- time constant, t, has been

described elsewhere [10]. The relative x-ray intensity

ratio, k, is calculated for each measurement by dividing

the corrected intensity from the specimen by that of the

standard.
3. The energies of the K, L, and M absorption edges are calculated by means of fits based on Moseley's law. The

energies of the Ka , La, and Ma lines are also calculated

in the same way. One of these three lines is almost always

chosen as the analytical line. If conditions unfavorable

for analysis result from choice of line by the operator, a warning is printed by the program. The operator can then use another line or readjust the operating voltage, depending on

the nature of the difficulty.

4. The correction for absorption in the specimen of

primary x-rays is carried out with use of the absorption cor- rection factor f proposed by Heinrich and Yakowitz [11]:

1/f = 1 + 3 X 10" 6 (E 1,65-E 1,65

)x + 4.5 X

10" 13 - p

v o qJ A

rT, 1.65 „ 1.65.2 2 ro -> •CE -E

q

) X (2)

where X

= V csc ^ J an d ^. is the x-ray emergence angle;

E and E are the operating voltage and critical

o q

f & & excitation potential for the line of interest,

in kilovolts . The absorption correction is

k. = f /f* (3) A p p

* J

(Here, and in what follows, terms with an asterisk refer to

the unknown, and terms without superscript refer to the

standard.

)

The mass attenuation coefficients are calculated as proposed by Heinrich [12]. To reduce requirements for storage,

least squares fits were made to the logarithm of the coefficient

C and the exponent n in the general relation:

The exponent "-13" in the third term of equation (2) is cor- rect. This value was erroneously given as "-14" in reference

[11].

6
y = CA

in which X is the wavelength in angstroms.

A comparison of the calculated values with those given

by Heinrich [12] showed agreement within a few percent. To

avoid uncertainties which arise where lines close to edges

are used, a warning is printed if the analytical line falls

within 100 eV of an absorption edge of another element

present in the specimen.

5. The correction for atomic number used in FRAME is:

R* S

k

z = C—) C—

)

(4) L R S*

The electron backscattering correction factors, R and

R* , are those obtained by Duncumb and Reed from Monte Carlo

calculations [13], fitted by us with respect to the over- voltage, U, and the mean atomic number, Z, as follows:

R = R

1

- R

2 In (R3

Z" + 25) (5)

where R = 8.73 X 10" 3 U

3

- 0.1669U 2 + 0.9662U - 0.4523

R

2 = 2.703 X 10" 3 U

3

- 5.182 X 10~ 2 U

2 + 0.302U - 0.1836

R

3 = (0.887U 3

- 3.44U 2 + 9.33U - 6.43)/U 3

U = E /E , Z = Z C.Z., C = weight fraction of element i.

o' q' l l ' l &

If U > 10, then U is set equal to 10.

Figure 2 shows the values given by Duncumb and Reed

and the curves predicted by equation (5) . The value of R

*

n

is obtained from R* = I C.R.. (6)

k.-l ± X

i
Equation (5) is simpler than the fifth-order fit in

voltage and atomic number [14] used in MULTI8 and C0R2 , and

gives very similar results

.

The term S in equation (4) is an average stopping power

according to a form of Bethe's equation [15]. The stopping

power calculation is identical to that in MULTI8, except that

the mean electron energy is obtained, as previously proposed

by Thomas [16], as follows:

E -E

E = o q

This approximation is sufficiently accurate except at extreme

overvoltage values which should be avoided for accurate analysis

[17]. The atomic weights, required for the stopping power calculation, are stored in the program.

As in MULTI8, the characteristic fluorescence correction

is performed with the aid of Reed's equation [18]. MULTI8 and

C0R2 require the input of fluorescent yields; in C0R2 these

are stored in the permanent data file. In FRAME we use the

fluorescence yields for K and L shells which are calculated

by means of empirical fits . No fluorescence correction is

carried out if fluorescence is excited by M lines. We assume

that the absorption jump ratio is 0.88 for the K edge and 0.75

for the L_, edge.

FRAME contains the following provisions which decide

whether fluorescence correction is required. Call E- the

energy of the exciting line (K- or L-line) , E K and E

y the

critical excitation potentials for the excited K- and L-lines.

If < (E

£ -E

K

) < 5 then the K-line is indirectly

excited

.

If < (E„-E

T ) <_ 3.5, then the L-line is indirectly

excited

.
If fluorescent excitation occurs, the program prints

a message to this effect. Then, it calculates the new mass attenuation coefficients required for Reed's equation [18]

and performs the necessary calculation for the fluorescence

effect

This automatic selection of corrections for fluorescent

excitation where necessary eliminates the need for the operator to decide if such corrections must be applied.

As mentioned previously [2], the iteration procedure used

in MULTI8 and C0R2 — and again in FRAME — converges very

rapidly. For this reason, we stop the iteration after three

cycles in order to reduce the time of computation. The

resulting errors are smaller than the errors of measurement.

Structure of the Program Versions FRAME 2 to FRAME4

The version of FRAME which is reproduced in Appendix I is called FRAME3. The list of symbols used in FRAME3 is in

Appendix II. This version is adapted for on-line processing

3 of microprobe data on an EMR-6135 computer. FRAME2 is a computationally identical version for batch-processing on UNIVAC 1108; FRAME4 is adapted to a telephone- transmittal

time-share system. The statement lists of FRAME2 and FRAME4

are available on request. The sectors for input and output

will require modifications for use on other computers. These

adaptations should be easy to carry out. Areas of the program

specific to our set-up are identified by comment statements

in the appended program list

FRAME3 can be considered a model for on-line application.

The first part (2.8K) of this version (with subroutines CFCAL

and MAC) performs all preliminary calculations which are

3 Identification of any specific instrument does not imply

recommendation or endorsement by the National Bureau of

Standards, nor does it imply that the material or equipment

identified is necessarily the best available for the purpose.
independent of the composition of the specimen and standard,

and do not, therefore, require x-ray intensity data. The

second part (with subroutine QUDAT , 1 . 5K) uses the measured

x-ray intensities from standards and unknowns to compute

intensity ratios, which then are converted to concentrations,

by means of the correction factors obtained in CFCAL. For

a particular case — which may extend over several points

to be analyzed — the first part is calculated only once,

while the second part is executed every time a measurement is

being performed. The interaction of the main program with

the subprograms can be observed on the flow-diagram in

Figure 1.

Limitations of FRAME

As mentioned above, the limitations of available memory

have required several simplifications, (e.g., omission of the

correction for fluorescence due to the continuum). These

simplifications will not cause significant increase in the

error of the. analyses, as long as the following operational

conditions are maintained:

1. The overvoltage6 (E /E ) should not be smaller than 1.5 ^ o' q

J

2. The primary x-ray absorption factor, f , should not

be smaller than 0.75.

3. If an x-ray line falls within 100 eV on the high

energy side of an absorption edge, or 30 eV on the

low energy side of any element present, then this

line should not be used because of the uncertainties

concerning mass absorption coefficients near the edge.

The restrictions imposed by these conditions are not

serious or specific to FRAME, since working outside these

specifications is unwise, even when a more detailed computer

program is used. FRAME3 produces a printed warning when an analysis is computed with disregard of the above rules. In

10
the case of £ , the warning criterion is applied to the

absorption factor of the standard. For further control of

conditions, the values of f for the specimen are printed

in the output of FRAME.

In our version of FRAME, it is assumed that the x-ray

emergence angle is equal to 52.5°. The value of this angle

can be changed by a single statement, and even a change to

different angles for each spectrometer could be introduced

without much effort.

The number of elements in the specimen is presently

limited, in our versions, to six. Since the program is primarily intended for on-line use, it is assumed that the six

intensities are read simultaneously. However, the number of

x-ray lines which can be read simultaneously in an instrument

cannot exceed that of the spectrometers, unless part of the

information is provided by an energy-dispersive spectrometer.

Since this limitation may be significant in the analysis of

minerals, we consider introducing, in a later version, modifications which would permit the reading of x-ray intensities

in two steps in time, so that spectrometers could be realigned

to read more than one line per analysis.

We have also assumed that all measurements for a case were performed at the same operating voltage. If a two-step

read-out is considered, this criterion will be modified so that, if desired, some lines can be read at a lower voltage

than the rest. This experimental procedure is, however,

awkard and is not used frequently. Therefore, the limitation

to a single operating voltage is not stringent.

All versions of FRAME permit the determination of one element by difference. The use of stoichiometric relations

to determine the concentration of one element is provided in

FRAME4 and can easily be incorporated into other versions.

11
At present, it is not possible to replace the mass absorption coefficients calculated in the program by others

provided externally. Such a feature will be incorporated

later, as well as an option to assume that the concentration

of certain elements is known. We also plan to indicate at

a later date, modifications to obtain atomic fractions rather

than weight fractions. The number of iterations, which

presently is limited to three, could be changed by a simple

statement. However, as indicated by the data presented in

Tables II and III, computation beyond three iterations does

not provide any significant improvement in accuracy.

Comparison of Results from FRAME with C0R2

We have compared the FRAME and COR correction programs,

using the measurements on 228 binary alloys listed by Poole

[19], as well as 16 analyses on the binary alloys Au-Ag and

Au-Cu designated NBS Standard Reference Materials 481 and 482,

respectively, [20]. The analyses listed by Poole were performed in several laboratories from all over the world, and

they cover a variety of systems and experimental conditions.

A comparison of the results by FRAME with those by C0R2

for the Poole-Thomas compilation is shown in Figure 3. We

note that the disagreement between COR2 and FRAME is small

compared with the errors shown in the diagram for C0R2 . We

also note that larger discrepancies occur when the operating

conditions are outside the suggested boundaries.

Analyses performed at NBS are presented in Tables II,

III, and IV. The results show that FRAME is suitable for a wide variety of analytical studies. They also show, in the case of the two minerals analyzed, that the method of determining the background level was not critically important.

An example of the input and output for the analysis of

the Diopside 65 - Jadeite 35 is shown in Table V. All required

input statements follow a colon or question mark. The program

12
version is FRAME 4 . Table V shows that the concentrations

obtained by calculating oxygen by difference or by stoichiometric relations are the same. The FRAME4 routine was run on a time-shared computer with background dead-time

corrected relative intensity ratios (k-values) already calculated. The k-values shown are referred to pure element

standards as calculated from the mineral standards listed in

Table IV.

Example Showing On-line Analysis using FRAME

An iron-silicon alloy containing 3.22% Si and 96.81 Fe,

designated SRM-483, was analyzed. This material is certified

to be homogeneous with respect to iron and silicon [21]. Five

individual analyses were carried out. The results, as printed

on a teletype display during analysis, are shown in Table VI.

The average silicon content is 3.341, and the average iron

content is 96.21.

Conclus ions

The FRAME program is entirely suitable for on-line or off-line use to reduce data from the electron probe microanalyzer to concentrations of the elements present. FRAME

employs the analytical ZAF approach, but only occupies about

4K of computer memory. The FRAME program should be readily

adaptable to most mini-computers for use in many microprobe

laboratories

Comparisons have shown that FRAME give virtually the same results as the much larger batch-type program, COR,

provided that fluorescence effects due to the continuum can

be safely neglected. All of the data discussed in this paper,

including those reported by Poole, fall into this category.

The input requirements for FRAME are virtually the same,

13
however (see Table I). Results on two minerals, Johnstown

Hypersthene and Diopside 65 - Jadeite 35, give results close

to the chemical analysis (Tables III, IV and V). Furthermore,

the results were only slightly affected by the method of

determining background level or by using FRAME to calculate

the results obtaining the oxygen content by difference or by

stoichiometric relations.

14
Table la. Comparison of NBS programs for quantitative

microprobe analysis

C0R2 MULT 1

FRAME3

MECHANICAL ASPECTS

Memory

Intended mode

of operation

Input

50 K

Batch

Cards and

magnetic tape

4 K

Time-share

Teletype

4 K

Time-share

or dedicated

Teletype

or on-line

Output Line printer Teletype Teletype

Table lb. Comparison of NBS programs for quantitative

microprobe analysis

No. of elements

Atomic numbers

Atomic weights

Operating

voltage

Line

Crit. excit.

potential

Fluorescence

yield

u/p

Fluorescence - decisions

Valences

X-ray

intensities

COR2

INPUT

MULT 1

Yes Yes

Yes Yes Data file Yes

Yes Yes

Yes No Data file Yes

Data file Yes

Calculated

Made internally

Yes (if used)

Raw or k-values

Yes

Yes

Yes (if used)

k-values only

FRAME

Yes

Yes Stored

Yes

Yes Calculated

Calculated

Calculated

Made internally

Yes (if used)

Raw or k-values

15
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<NI O O O

(Nl -3- vO 00 O O CD O

•* Ol CO ^O to o o o N "*vO CO o o o o

o o o o

00 tO CN1 ^O

LO CTi CTl CTl t-» CTi CTl CTl Nl/)tOH

tO "3" (NO LO

00 vO CTl OO

CTi CTl CTi CTl rH tO LO t-^

CD O CD O

^t" (Nl (Nl t^

\0 00 CO CO

r-~ LO to i—

o o o o

tO (Nl ^t- LO O O O CD

(Nl -^- \0 CO O CD CD CD O O O O

t^ CTl 00 CI sOCOCON 1/1 H N Cv

CNlCTiCTiCTl I^CTlCTiCTi OHHH M KILO [n N W MH CNl^vDOO

o o o o CD O O CD

LO vo O (Nl HMHH

O O O O

O0 \D "* (Nl O CD O CD

^t CO O ^t

CTi CTl CTl CTl N W tOH

O CD O O

LO 00 LO tO

CTi CTi CTl CTi

r~- LO to i—

o o o o

2 W i—

Pi

CO s *

pel U

Ph +-> U M V)>No

1—1 W rH

T—

S* cd m

^PL, +J o U i-i

t/i H

m . >, w

rH 03

03 CD

Pi g < r*

03 H

Ml

PI

03

rH

COPh o

CO

03 ,—

4-> > rH^

o *— >

t-- CTl CO CT) i£) CO 00 N IOHCON LOOOLOtO

CNlCTiCTiCTl f~- CTi CTl CTi Or-I i—I i—I CTl CTl CTi CTl CNltOLOr-- NultO H CNl-^-OCO NLO MH

O O O O

I-- CTi CO CTl

(Nl CTi CTl CTl (ni to lo r~~

CD O O O

t—I (Nl CTl rH O \0 LO N

(Nl tO LO IN- o o o o

O CD CD CD O O CD O

COOCTiCO v£> tO CTl CO

I-- O CTl CTl OHHH MOMH CN1 ^ \D CO o o o o o o o o

^^-vOr-H OtOi—l^t" \Q COCO O) ^t L/l LO to

C~- LO tO t—I (Nl^)-^D0O

o o o o

oooo oooo

CD O O O

LO LO LO LO

(Nl (Nl (Nl (Nl

O O CD O

00 (Nl t—I CN1 00 CTi CTi CTl

IN- LO tO t—

CD O O CD

LO CTl i—I t3-

"3- (Nl tO LO

f-- LO tO rH OOOO

LO LO LO LO

(Nl (Nl (Nl (Nl

PIo

•HP

crj rHCD

4->

rHO

<4H

PIO

•H

+-> 03 •H>

CO

rH rQ

03

PI

pq

13 CO

Pi PI 03 -H

8 3 S 3

S S S S i i i i 3 3 3 3

< << <

a a a a

i i i i DO 00 bO 50 < < < <

a a a a asaa

3 3 3 3

u u u u

17

3 3 3 3

< < < <
Table III. Analysis of a silicate: Diopside 65 - Jadeite 35

(done with oxygen by s toichiometry using FRAME4)

10 kV = E

Na Mg Al Si Ca

V .0281 .0593 .0363 0.236 0.111

c

+ - Iteration I .0392 .0730 .0439 0.270 .121

c

- Iteration II .0384 .0718 .0433 0.268 .121

c

- Iteration III .0384 .0718 .0433 .268 0.121

c

- Chemical

Analysis .0398 .073 .0467 0.266 .120

f

p

.69 .77 .81 .86 .97

*k - measured intensity ratio corrected for background and

dead-time effects

C - mass fraction
Table IV. Analysis of the silicates: Johnstown Hypersthene

and Diopside 65 - Jadeite 35, using FRAME4

Chemical analysis of minerals used

Mineral Na Mg_ Al Si^ Ca Ti Fe

NaCl 0.393

sio

2 Fayalite -- Diopside«2%Ti0

2 -- Garnet 110752

Diopside 65 - Jadeite 35 0.039

Johnstown

Hypersthene

--

0.467

-- -- 0.137 -- -- 525

110 -- 0.254 181 012 -- 043 0.120 0.188 129

5 002 088

073 0.0467 0.266 120 -- --

164 0.002 0.251 0099 0013 .121

Standards used:

NaCl for Na in diopside 65 - Jadeite 35 Si0

2 for Si in both

Fayalite for Fe in Johnstown Hypersthene

Diopside*2ITi0 2 for Mg, Ca, Ti, in Johnstown Hypersthene

Garnet 110752 for Mg, Al, Ca, in Diopside 65 - Jadeite 35

Al.O, used as BKG specimen for Fe , Si, Mg, Ca, Ti i MgO used as BKG specimen for Na, Al, Ca I

Off-peak (above and below used for all elements Scheme II

19
Table IV. Continued

Analysis of Johnstown Hypersthene*

E = 15 kV

Mg_ Si Ca Ti Fe

k * - SI 0.114 0.202 Oil 0008 104 m

k * - S2 m

0.117 0.202 010 0007 104

C

+CALC " S1

C CALC " S2

0.165

0.169

0.260

0.260

.0110 .0110

.0009 .0008

.121 .121

r

_ Chemical

Analysis 0.164 0.251 .0099 .0013 .121

Analysis of Diopside 65 - Jadeite 35

E = 10 kV

o Na Mg_ Al Si_ Ca

k * - SI 0.0281 0.0593 0.0363 0.236 0.111

k

* - S2 0.0275 0.0595 0.0363 0.236 0.111 m

C

+ - SI 0.0384 0.0716 0.0433 0.268 0.121

C

+ . LC

- S2 0.0375 0.0718 0.0433 0.268 0.121

_ Chemical 0.0398 0.073 0.0467 0.266 0.120

Analysis

**Analysis carried out calculating oxygen by stoichiometry was exactly the same as that carried out calculating oxygen by

difference

51 - Background taken on Al-O, or MgO

52 - Background taken off-peak

k *- Measured intensity ratio corrected for background and

dead-time effects.

C - Mass fraction

20
Table V. Input-output for FRAME4 —

analysis of Diopside 65 - Jadeite 35

(a) Analysis with oxygen calculated by difference

ATOMIC NUMBER AND LINE FOR EACH: 11 1 12 1 13 1 14 1 20 8 WARNING -• THE LINE OF 1

1

IS CLOSE TO AN EDGE OF 1 1 ELEMENT 1 1 IS EXCITED BY ELEMENT 12 ELEMENT 1 1 IS EXCITED BY ELEMENT 13 ELEMENT 1 1 IS EXCITED BY ELEMENT 14 ELEMENT 1 1 IS EXCITED BY ELEMENT 20

ELEMENT 12 IS EXCITED BY ELEMENT 1 3 ELEMENT 12 IS EXCITED BY ELEMENT 14 ELEMENT 12 IS EXCITED BY ELEMENT 20

ELEMENT 13 IS EXCITED BY ELEMENT 14 ELEMENT 13 IS EXCITED BY ELEMENT 20

ELEMENT 1 4 IS EXCITED BY ELEMENT 20

VALENCES

STANDARDS DATA? NO

K-VALUES: .0281 .0593

AT. NO. K-VALUE

.0363 .2364 .111

CONCENTRATION F(X)

1 1 < 12.

13. 14. 20.

.0281

.0593

• 0363

.2364

• 1 1 10

• 0000

TOTAL C =1 .0000

0384 • 6867

0718 .7690

0433 .8121

2685 .8555

1207 .9670

4573 1 .0000

(b) Analysis with oxygen calculated stoichiometrically

ATOMIC NU ^BEf* AN!) 1 _INt: FOR EA(:h: 11112 1 13 1 1 4 1 20 8 WARNING - THE LINE OF 1 1 IS CLOSE TO AN EDGE OF 1 1 ELEMENT 1 1 IS EXCITED BY ELEMENT 12 ELEMENT 1 1 IS EXCITED BY ELEMENT 13 ELEMENT 1 1 IS EXCITED BY ELEMENT 14 ELEMENT 1 1 IS EXCITED BY ELEMENT 20

ELEMENT 12 IS EXCITED BY ELEMENT 13 ELEMENT 12 IS EXCITED BY ELEMENT 14 ELEMENT 12 IS EXCITED BY ELEMENT 20

ELEMENT 13 IS EXCITED BY ELEMENT 14 ELEMENT 13 IS EXCITED BY ELEMENT 20

ELEMENT 1 4 IS EXCITED BY ELEMENT 20

VALENCES: 1 2 3 4 2 2 STANDARDS DATA? NO K-VALUES: .0281 .0593

AT. NO. K-VALUE

.0363 .2364 .111

CONCENTRATION F<X)

1 1 . 12.

13. 14.

20.

8. TOTAL C =

• 0281

.0593

.0363

• 2364

.1110

0.0000

• 9957

0384 • 6871

0718 .7693

0433 .8123

2685 .8557

1207 .9671

4531 1 .0000

21
Table VI. Results of analysis of SRM 483

containing 0.0322 Si - 0.968 Fe

Analysis performed "on-line" at NBS

FRAME3 1118HRS 187 DAY, 1973

ELECTRON PROBE ANALYSIS 15.0 KV

ELEMENT 14 IS EXCITED BY ELEMENT 26

2-LINE Z-ABSORBER MASS ABS. COEFF.

14 14 330.0

14 26 2495.8

26 14 113*8

26 26 70.9

AT. NO. K- VALUE CONC FC.CHI)

14 .0237 • 0337 .5544

26 .9532 .9595 .9834

TOTAL C = .9932

14 .0233 .0332 . 5543

26 .9583 .9640 .98 34

TOTAL C = .9972

14 • 0238 .0339 .5544

26 .9530 .9593 .98 34

TOTAL C = .9932

14 .0234 .0333 .5543

26 .9578 .9635 .98 34

TOTAL C = • 99 68

14 • 0236 .0337 .5544

26 .9552 .9612 .9834

TOTAL C = .9949

22
FRAME

INPUT OUTPUT MAIN

PROGRAM SUBROUTINES

PREPARATION

No. of elements

E , At. No

o j , and line for each.

PRINT all warnings

and headings

MEASUREMENT

OF STANDARDS

(NSW=0)

NSW COUNTS

TIME

MEASUREMENT

OF SPECIMENS

(NSW=1)

NSW COUNTS

TIME

PRINT RESULTS

COMMON BLOCK

[STORE | -

_l_ STORE -*

I

SUBROUTINE CFCAL

Compute all nec- essary factors

for the cor- rections .

SUBROUTINE MAC

to compute

mass absorp. coeff

SUBROUTINE QUDAT

Dead-time correction.

Average peaks and back- grounds for each standard

SUBROUTINE QUDAT

Dead-time correction.

Compute intensity

ratios

Compute concentrations:

Atomic Number,

Absorption and Fluorescence Corrections.

Figure 1. Flow sheet showing operations carried out

by FRAME program.

2 3
• •H o

-P3

rH a"

•H >,

rH XI O

CO T3

0)

OS -H o

+Jum

f-l o

+->

bO

Pi •H

t3

Pio

P.

to

f-i !hOU

OS

t/5

n +-) 3 V o

in t3 £ & cti o . •* U

rt i—

Oil -Q LO OJ U o P*

4-> t3

w

4-> S

•H OS < m OS T3 P-c rH Pi rt aJ o X

•H

X +->

+-> £

>s 3 I—I 1—

u • rf Pi o

PI 3 V < Q S y 'jopd-i jsuDOS^ODg

f-i 3

bO •H

PL,

24
o

c

<v3

cr

<v

Poole -Thomas Data COR Results

f(x) = H:Y

True Percentage -COR Percentage

f>0.7

fS0.7

D Inconsistent Data

55

50

45

40

35

30

25

20

15

10

<-7.0-70 -6.0 -5.0 -4 -3.0 -2.0 -1.0 +1.0 +2.0 +3.0 +4.0 +5.0 +6.0 +7.0>7O

Absolute Difference (Percent)

Figure 3a. Results of analysis on alloy data quoted

by Poole [19] as computed by COR using the

Heinrich-Yakowitz £(x) expression [11].

25
no

105

100

95

90

85

80

75

70

65

60

55

50

45-

40

35

30-

25-

20-

15-

10

5

i I r T "1 I r

Pooie- Thomas Data FRAME 2- COR

f > 0.7 Hf<07

J I L I I L

<70-7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 +1.0 +2.0 +3.0 +4.0 +5.0 +6.0 +7.0>70 Absolute Difference (Percent)

Figure 3b. Comparison of FRAME2 and COR for the alloy

data shown by Figure 3a.

26
References

[1] Heinrich, K. F. J., Editor, "Quantitative Electron Probe

Microanalysis," NBS Special Publication 298, U.S.

Government Printing Office, Washington, D. C. (1968).

[2] Heinrich, K. F. J., Anal. Chem. 44, 350 (1972).

[3] Henoc, J., Heinrich, K. F. J., and Myklebust, R. L .

,

"A Rigorous Correction Procedure for Quantitative

Electron Probe Microanalysis (COR 2)," U.S.' Natl.

Bur. Stds . Technical Note 769, U.S. Government

Printing Office, Washington, D. C. (1973).

[4] Ziebold, T. 0. and Ogilvie, R. E., Anal. Chem. 36, 322

(1964) .

[5] Bence, A. E. and Albee, A. L., J. Geology 76_, 382 (1968).

[6] Chodos, A. A. and Albee, A. L., Proc. Sixth Natl. Conf.

on Electron Probe Analysis, Pittsburgh, Pa., p. 15A

(1971) .

[7] Philibert, J. and Tixier, R. in "Quantitative Electron

Probe Microanalysis," Heinrich, K. F. J., Editor,

NBS Special Publication 298, p. 13, U.S. Government

Printing Office, Washington, D. C. (1968).

[8] Heinrich, K. F. J., Myklebust, R. L., Yakowitz, H., and

Rasberry, S. D., "A Simple Correction Procedure for

Quantitative Electron Probe Microanalysis," U.S. Natl.

Bur. Stds. Technical Note 719, U.S. Government Printing

Office, Washington, D. C. (1972).

[9] Ruark, A. and Brammer, F. E., Phys . Rev. 52_, 322 (1937).

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

,

in Advances in X-Ray Analysis , Vol. 9, Mallett, G. R.,

Fay, M. J., and Mueller, W. M., Editors, p. 208,

Plenum Press, New York (1966).

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

Proc. Seventh Natl. Conf. on Electron Probe Microanalysis, San Francisco, CA, paper no. 3, 6 pp. (1972).

[12] Heinrich, K. F. J., in The Electron Microprobe , McKinley,

T. D., Heinrich, K. F. J., and Wittry, D. B., Editors,

p. 296, John Wiley § Sons, Inc., New York (1966).

27
[13] Duncumb , P. and Reed, S. J. B., in "Quantitative Electron

Probe Microanalysis," Heinrich, K. F. J., Editor,

NBS Special Publication 298, p. 133, U.S. Government

Printing Office, Washington, D. C. (1968).

[14] Heinrich, K. F. J., in "Present State of the Classical

Theory of Quantitative Electron Probe Microanalysis,"

NBS Technical Note 521, p. 5, U.S. Government Printing

Office, Washington, D. C. (1970).

[15] Heinrich, K. F. J., Anal. Chem. 44_, 350 (1972).

[16] Thomas, P. M., AERE Report 4593, U. K. Atomic Energy

Authority (1964). Also see reference [12].

[17] Heinrich, K. F. J. and Yakowitz , H., Mikrochim. Acta

1970 , p. 123.

[18] Reed, S. J. B., Brit. J. Appl . Phys . 16_, 913 (1965).

[19] Poole, D. M. , in "Quantitative Electron Probe Microanalysis," Heinrich, K. F. J., Editor, NBS Special

Publication 298, p. 93, U.S. Government Printing

Office, Washington, D. C. (1968).

[20] Heinrich, K. F. J., Myklebust, R. L., and Rasberry, S. D.

"Preparation and Evaluation of SRM's 481 and 482

Gold-Silver and Gold-Copper. Alloys for Microanalysis,"

NBS Special Publication 260-28, U.S. Government

Printing Office, Washington, D. C. (1971).

[21] Yakowitz, H., Fiori, C. E., and Michaelis, R. E.,

"Homogeneity Characterization of Fe-3Si Alloy," NBS

Special Publication 260-22, U. S. Government Printing

Office, Washington, D. C. (1971).

28
APPENDIX I

Listing of FRAME3 in FORTRAN IV

29
C FRAME3

C ON-LINE PROGRAM FOR QUANTITATIVE ELECTRON PROBE w ICROANALYSIS

.

C FORTRAN IV MAY 22, 1973

C THE INPUT AND OUTPUT WILL NEED TO BE MODIFIED TO FIT THE COMPUTER

C BEING USED.

C NOTE - ALL STATEMENTS PRECEDED BY AN * RESULT FROM SYSTEM ROUTINES

C ON THE ANALYTICAL CHEMISTRY DIVISIONS COMPUTER FOR DATA ACQUISITION

C AND CONTROL.

SUBROUTINE CFCAL(TAB)

C THIS ROUTINE IS LOADED FIRST TOGETHER WITH MAC. READ THE INITIAL

C INPUT PARAMETERS AND COMPUTE ALL NECESSARY CONSTANTS.

INTEGER MESSUO) rPST

* INTEGER TAB»CRLF

REAL JI

* LOGICAL SETSW

DIMENSION Z(6),EC(9»6),EL(3r6)»LI(6),EQ(6)»E<6),AC(6»6) »FAC(6,6) »H 1(6),FC(6)»R(6,6),S(6»6)»U(6) ,KEY(6»6) »C1 (Q) ,C2 (9) ,C3 (9)

2 ,P(6)»Rl(6)»0M(6),A(6)»X(6)»AN(92)rY(6)

* DIMENSION ISPC(4) ,IFDB(3)

DIMENSION MHD(5) fIZ(6T

DIMENSION XL (6) »XXK(6> t BK ( 6) , PK ( 6) » PB (6)

DIMENSION IBUFC50) rSC(7)

COMMON/ENER/ELrEC

C0MM0N/ST0RE/N,N1»LI»S,R»AC»H»KEY»FAC,E0»EQ,P,0M,R1,X»Y,A,FC, Z,SC,

1SETSW»IBUF»PST,NFSW,NFLAG»XL»XXK,BK,PK,PB»C0SEC

* COMMON/ESTOR/IDUM

EQUIVALENCE(MESSd) .CRLF)

DATA AN/1. 008, 4. 003 ,6. 94, 9. 013 ,10. 82 ,12. 01 1,14. 007 ,16., 19. ,20. 18,

1 22. 99 , 24. 31 , 26. 98 » 28. 09 , 30. 97 , 32. 06 , 35. 45 * 39. 95 » 39. 1»40. 08 ,44. 96

247.9, 50. 94, 52. » 54. 94 » 55.85 , 58.93 » 58.71 » 63.54 , 65.37 , 69. 72 #72. 59,

371. 92 t 78. 96 » 79. 91 , 83. 8 » 85. 47 , 87. 62 '88. 91 ."l. 22, 92. 91 ,P5. 94, 99.

4101H1, 102. 9,106. 4,107. 9, 112. 4, 114. 8, 118. 7,121.8,127.6, 126. 9, 131. 3,

5132H9, 137. 3 ,138.9, 140. 1,140. 9, 144. 2, 145., 150.4, 152. ,157.2 ,158.9,

6162.5,164.9,167.3,168.9,173. ,175. »178.5 »1«0. 95, 183. 85 ,186. 2 ,190.2,

7192. 2, 195. 1,196. 97, 200*6,204. 4, 207.2,209.' 210., 210., 222., 223. ,226.

8,227. ,232., 231., 238./

DATA CI/-. 0397931, -.0339160, -.0865397, -.2283427, 1.251 788,

1.8349031, .4422173,. 251 4096, .2729506/

DATA C2/2. 4230 00, 2. 825262, 3. 323153, 4.31 1724, -7. 837999,

1-4. 149247, -.9792409, .9319132 ,. 6889060/

DATA C3/5. 5091 04, 9. 035256, 10. 25054, 12. 00253, -11. 58026,

1-3. 3380 1 6, 3. 153478, 8. 035bl 2 '7.424300/

C THE FOLLOWING CONSTANTS ARE NEEDED BY OUR COMPUTER TO PRINT OUT THE

C RESULTS ON A TELETYPE.

* DATA ISPC/2*$41503, 2*541101/

* DATA IADTTY/5176145/

* DATA IFDB(2)/0/

* DATA IPRI/10/

* DATA CRLF/S41101/

C THE FOLLOWING STATEMENTS APPLY TO OUR COMPUTER AMD ARE EQUIVALENT TO

C READING THE INPUT DATA.

C THIS SECTION READS AND DECODES A BUFFER CONTAINING THE INPUT

C PARAMETERS - EO (KILOVOLTS) , LI (LINE- 1=K, 2=L, 3=M, 0= NOT ANALYZED),

C N(NUMBER OF ELEMENTS), IZUTOMIC NUMBER).

30
* CALL RESTOR(TAB)

* I = KBCDBN(IEXTR(5»16f TBUF(B) )

)

EO=I/10.

* LK1) = IEXTR(13rl6»IBUF(12) ) * LK2) = IEXTRdOr 12»IBUF(12))

* LK3) = IEXTR(7.9»IBUF(12))

* Lldt) = IEXTRU»6»TBUF(12>)

* LK5) = IEXTR(lr3rIBUF(12) ) * LK6) = IEXTR(13» lb, IBUF(ID)

* N = lEXTR(.lrt»IBUF(ll))

* IZ(1)= KBCDBN(IEXTR(9rl6»lBUF(14) )

)

* IZ(2)= KBCDBN(IEXTR(1»R»IRUF(14) )

)

* IZ(3)= KBCDBN(IEXTR(9»16»IBUF(13) )

)

* IZU) = KBCDBN(IEXTR(l»8rIRUF(13)))

* IZ(5)= KBCDBN(IEXTR(9rl6»IBUF(16) )

)

* IZ(6)= KBCDBN(IEXTR(l»8rIBUF(16) )

)

DO 10 I = l»6

10 Z(I)=FLOAT(IZ(I)>

COSEC=1.2605

N1=N

IF(LKN) .EQ.O) N1=N-1

C OPEN THE BUFFERS FOR STORING TELETYPE OUTPUT.

* CALL ALU(LUTY.IADTTY)

* CALL OPEN(LUTY»IFDB)

* IF(IFDB(2) .LE.O) CALL ERROR ( 721 » TAB)

* NW = 4

C RIOS IS THE SYSTFM I/O ROUTINE USED HERE FOR SPOOLING TELFTYPE OUTPUT,

C EVERYTHING IS PRINTED ON THE TELETYPE WHEN THIS FILE IS CLOSED

C (STATEMENT 777). SCHENT IS THE SCHEDULED PROGRAM ENTRY FROM PIOS.

C IS REPRESTNTS STATUS RETURNED FR-OM RIOS.

* CALL RIOS2(0»0»IPRIr$l»LUTY»IADTTYr IS»NW»ISPC)

* 1 SCHENT

* IF(IS.LE.O) GO TO S

C GET THE TIME OF YEAR.

* CALL GDB(MHD)

MHD U) =VHD U ) +MHD < 5

)

NYEAR=1973

C PRINT TITLE AND HATE.

ENCODE(72r200(+»MESS(2) .NO MHDU) »MHD(3) rNYEAR

200<* FORMATC FRAME3 'fl^r'HRS '»I3,» DAY» ».ia)

* NW=18

* CALL RI0S2(0»0»IPRIr$9rLUTY»IADTTYfIS»NWrMESS)

* 9 SCHENT

* IF(IS.LE.O) GO TO 8 MESS(2)=CRLF

C PRINT KILOVOLTAGF.

ENCODE(72r2001»MESS(3) »NC) EO

2001 FORMAT( 'ELECTRON PROBE ANALYSIS' , IX ,F<+. 1 1 • KV •) MESS(19)=CRLF

* NW=19

* CALL RIOS2(0»0rIPRIr$2»LUTY»IADTTY»IS»NW»WE!sS)

31
* 2 SCHENT

* IF(IS.LE.O) GO TO 8

C COMPUTE ALL ABSORPTION EDGES AND X-RAY LINES.

DO 20 I=lrN

ZL=ALOG(Z(I) ) DO 30 M=l»9

30 EC(MrI)=EXP(Cl(M)*ZL*ZL+C2(M)*ZL-C3(M)

)

EL(1»I)=EXP(-.0188608*ZL*ZL+2.218585*ZL-5.170825)

EL (2» I >=EXP(-.l 23941 l*ZL*ZL+3.295325*ZL-9. 758363)

EL(3»I)=EXP(-.4755497*ZL*ZL+6.8466l8*ZL-20.08326)

NZ=Z(I>

A(I)=AN(NZ)

L=LI(I)

IF(L.EQ.O) GO TO 20

LS=L*L

EO(I)=EC(LS»I)

E(I)=EL(L#I)

U(I)=EO/EQ(I>

Y(I)=U(I)

IF(U(I).GT.10.) U(I)=10.

C PRINT WARNING IF THE OVERVOLTAGE IS LESS THAN 1.5.

IF(U(I) .GE.1.5) GO TO 20

ENCODE(72r2006»MESS(2) »NC) IZ(I)

2006 FORMAT ('WARNING - THE OVERVOLTAGE OF ELEMENT 'rI2»' IS BELOW 1.5»)

* NW=27

* CALL RIOS2(0»0fIPRI»S80O»LUTY»IADTTYrIS»NWrMESS)

* 800 SCHENT

* IF(IS.LE.O) GO TO 8 20 CONTINUE

DO 50 I=1»N1

L=LI(I)

DO 40 J=1.N

C GET MASS ABSORPTION COEFFICIENTS.

CALL MAC(I»L»JrZ»ABCO)

DO 600 M=l»9

IF(EC(M,J) .LE.EL(Lrl)-.l) GO TO 600

IF(EC(M»J) ,GE.EL(L»D+.03) GO TO 600

C PRINT WARNING IF X-RAY LINE FALLS TOO NEAR AM ABSORPTION EDGE.

ENCODE ( 72 r 2005 t MESS (2) »NC) IZd) »IZ(J)

2005 FORMAT( 'WARNIMG - THE LINE OF 'fI2»» IS CLOSE TO AN EDGE OF «fI2)

* NW=26

* CALL RIOS2(0»n,IPRI,$900rLUTY»IADTTYrIS»NW»MESS)

* 900 SCHENT

* IF(IS.LE.O) GO TO 8 GO TO 40

600 CONTINUE

40 AC(J»I)=ABCO

50 CONTINUE

C COMPUTE BACKSCATTER COEFFICIENTS AND STOPPING POWERS.

DO 200 I=1»N1

Al=8.73E-3*U(I)**3-.1669*U(I)**2+.9662*U(I)+.4523

B=2.703E-3*U(I)**3-5.182E-2*U(I)**2+.302*U(I)-.1836

32
0=.887-3.44/U(I)+9.33/U(I)**2-6.43/U(T>**3

DO 100 J=1»N

JI=9.76*Z(J)+S8.5*Z(J)**(-.19)

R(JrI)=Al-B*AL0G(Q*Z(J)+25.)

100 S(J»I)=2.*Z(J)/(A(J)*(E0+EQ(I) ) )*AL0G(583.*(E0+EQ(I) )/JI)

C COMPUTE ABSORPTION CORRECTION.

C PRINT WARNING IF CORRECTION IS TOO LARGE.

H(I)=3.0E-6*(FO**1.65-EQ(I)**1.65)

FC(I)=1.+H(I)*AC(I»I)*COSEC+H(I)**2*(AC(I»I)*COSEC)**2*.05

RFC=1./FC(I)

IFtRFC.GT.O^-S) GO TO 3 ENCODE ( 72. 200? r MESS (2) »NC) IZ(I) »RFC

2002 FORMAT( 'WARNING - THE F(X) OF ELEMENT »»I2»« IS'rF'S.S)

* NW=21

* CALL RIOS2(0»0>IPRI»$<+rLUTY»IADTTYrISrNWrMESS)

* <+ SCHENT

* IF(IS.LE.O) GO TO 8

3 CONTINUE

C DETERMINE IF THERE IS A CHARACTERISTIC FLUORESCENCE CORRECTION.

L=LI(I)

GO TO (280»290»295) »L 280 C0=5.

KK=0

GO TO 31+0 290 C0=3.5

KK = 1 GO TO 340

295 C0=3.5

KK=2

31+0 DO 300 J=1»N

IF(J.EQ.I) GO TO 300

K=l

309 IF(EL(K»J)-EQ(I) ) 330»330»310

310 IF(EL(K»J)-EQ(D-CO) 320r320r329

320 KEY(I»J)=K+2*KK

C PRINT THE FLUORESCENCE CORRECTIONS FOUND.

ENCODE (72»2003»MESS(2)»NC)IZ(I) »IZ(J)

2003 FORMAT( • ELEMENT »»I2»« IS EXCITED BY ELEMENT »»I2)

* NW=19

* CALL RI0S2(0»0rIPRI»$5»LUTY»IADTTYfIS»NW»MESS)

* 5 SCHENT

* IF(IS.LE.O) GO TO 8 KS=K*K

X(J)=EO/EC(KS»J)

DO 325 M=1»N

IF(EL(Kf J)-E(M) ) 325f335»325

325 CONTINUE

DO 11 II=1*N

C GET ANY ADDITIONAL MASS ABSORPTION COEFFICIENTS REQUIRED.

CALL MAC(J»K»II»Z»ABCO)

FAC(II»J)=ABCO

11 CONTINUE

GO TO 330

335 DO 336 II=1»N

33
336 FAC(IItJ)=AC(II»J)

GO TO 330

329 IF(K.EQ.2) GO TO 330

K=2

GO TO 309

330 CONTINUE

300 CONTINUE

C SELECT PARAMETERS FOR CHARACTERISTIC FLUORESCENCE CORRECTION.

DO 199 J=1»N

IF(KEY(I»J) .EQ.O) GO TO 199

P(J)=1.

R1(J)=.88

K=KEY(I»J)

GO TO (110»120»110r120»110#120) »K 110 0M(J)=EXP(2.373*AL0G(Z<J) ) -8.902)

IF(K.EQ.l) GO TO 199

IF(K.EQ.5) GO TO 198

P(J)=.21

R1(J)=.75

GO TO 199

120 0M(J)=EXP(2.916*ALOG(Z(J) ) -13.91)

IF(K.EQ.6) GO TO 198

IF(K.EQ.2) P(J)=1.2

IF(K.EQ.I) R1(J)=.75

GO TO 199

198 P(J)=.02

R1(J)=.5

199 CONTINUE

200 CONTINUE

C PRINT TABLE OF MASS ABSORPTION COEFFICIENTS.

ENCODE(72r708»MESS(2) 'NO

708 F0RMAT( »Z-LINE» »5X» •Z-ABSORBER* »5X» 'MASS ABS. COEFF.M

* NW=22

* CALL RIOS2(0»0»IPRI»$12»LUTY»IADTTY,IS»NWfMESS)

* 12 SCHENT

* IF(IS.LE.O) GO TO 8

* NW=19

DO 500 I=1»N1

DO 100 J=1»N

ENCODE ( 72 » 710 r MESS (2) 'NO IZ ( I ) » IZ ( J) » AC ( J. I

)

710 F0RMAT(2X'I2»llX»I2'12XfF7.1)

* CALL RIOS2(0»0»IPRI»$13»LUTY»IADTTY,IS'NW'MESS)

* 13 SCHENT

* IF(IS.LE.O) GO TO 8 100 CONTINUE

500 CONTINUE

* NW=1

* CALL RIOS2(0»0»IPRI'$7,LUTY#IADTTY»IS»NW»CRLF)

* 7 SCHENT

* IF(IS.LE.O) GO TO 8

C PRINT HEADINGS.

ENCODE<72»707,MESS(2> »NO

707 FORMATCAT. NO. ' »5X» 'K-VALUE' »5X» 'CONC • »8Xr 'F(CHI ) • ) * NW=22

* CALL RI0S2(0r0»IPRI»$6rLUTY»IADTTY»IS»NW»MESS)

* 6 SCHENT

34
C CLOSE PRINT FILE. THE FOLLOWING STATEMENTS APPLY TO OUR COMPUTER.

* 777 CALL CLOSE(LUTYrlFDB)

* CALL ERROR (333»TAB)

NFSW=0

C SAVE ALL PARAMETERS NEEDED IN QUDAT.

* 666 CALL SAVE(TAB)

RETURN

8 CONTINUE

END

SUBROUTINE MAC

(

JrL» I ' Zr ABCO)

C LOAD WITH CFCAL. THIS SUBROUTINE COMPUTES A MASS ABSORPTION

C COEFFICIENT FOR ALL NECESSARY LIMES AND ABSORBERS.

DIMENSION EC(9»6)»EL(3'6) »Z<6) » CN(4)» Dl <4) »D2(4) »D3(4) »R(10)

COMMON/ENER/EL>EC

DATA Dl/-. 2322294 t-. 2544711*. 2562163 »1.35<U65/

DATA D2/4. 070053 »4. 769245 » 1.15 119 » -9. 4921 16/

DATA D3/-6. 220746 r -10. 37878 » -5. 684848* 18. 64081/

DATA R/l.»l.»1.17»1.63»l.»1.16'1.4'1.62l»1.783»l./

DATA CN(3> »CN(4)/2.6»2.22/

ZL=ALOG(Z(I)

)

CN(1)=EXP(-.0045522*ZL*ZL-.0068535*ZL+1.070181)

CN(2)=2.73

IF(Z(I).LT.42.) GO TO 30

CN( 2) =EXP(-.1131595*ZL*ZL+.8368829*ZL-. 5459687)

30 CONTINUE

DO 50 M=l»10

IF(M.EQ.IO) GO TO 40

IF(EL(L»J).LT.EC(M»I).T GO TO 50

40 MI=M-M/3-M/4-M/7

C=EXP(Dl(MI)*ZL*ZL+D2tMI)*ZL+D3(MI) )/R(M)

ABC0=C*(12.398/EL(L»J> )**CN(MI)

RETURN

50 CONTINUE

END

SUBROUTINE QUDAT(NSW)

C THIS SUBROUTINE TAKES DATA FROM THE SCALERS* COMPUTES AN INTENSITY

C RATIO FOR EACH ELEMENT* AND THEN COMPUTES AND PRINTS THE

C CONCENTRATIONS OF EACH ELEMENT.

C THE OUTPUT IS PRINTED IN THE SAME MANNER AS IN CFCAL.

REAL L»K INTEGER MESSUO) »PST

* INTEGER TAB'CRLF

* LOGICAL SETSW

DIMENSION Z(6)»LI(6)»EQ(6)rAC(6r6) »FAC(6»6) »H(6)»FC(6)»R(6»6

1) 'S(6'6) »KEY(6»6) »P(6)»R1(6)»0M(6)»A(6)»X<6)»Y(6)»XK(6)'C(6) »FCS(6

2) »W(6) »XKF(6> »BK(6) »PK(6) »PB(6) »K(6) »L(6) »SF(6) »ISPC(4) *IFDB(3> »SC

35
3(7) .IBUF(50)

COMMON/STORE/N»NlfLI»S»RrAC»HfKEY»FAC»EO»EQrPrOM»RlrX»Y»A»FCfZ»SC>

1SETSW 1 1 BUF t PST » NFSW t NFLAG L t K t BK » PK » PB » C05EC

* COMMON/ESTOR/IDUM

EQUIVALENCE(MESSd) rCRLF)

* DATA ISPC/2*$41503»2*$i+1101/

* DATA IADTTY/$1761<+5/

* DATA IFDB(2)/0/

* DATA IPRI/10/

* DATA CRLF/S41101/

DATA SF/6*1./

DEADT(E)=E/(l.-E*3.E-6)

C READ IN COMPOUND STANDARD FACTORS AT THIS POlNTf OTHFRWISE THEY ARE

C ASSUMED EQUAL TO 1. (SF(6))

MI=N1+1

IF(NFSW.EQ.l) GO TO 1

C COLLECT AND STORE PEAK AND BACKGROUND DATA FOR EACH ELEMENT.

3 NFSW=1

NFLAG=0

DO 2 I=1»N1

L(I)=-1.

BK(I)=0.

PK(I)=0.

2 K(I)=-1.

1 IF(NFLAG.EQ.l) GO TO BOO

C FOR STANDARDS ONLY - IF THE TOTAL COUNTS IN A SCALER IS LESS THAN

C lOOOOr THE MEASUREMENT IS A BACKGROUND* IF IT IS GREATER THAN 10000

C IT IS A PEAK.

C ANY SCALER CONTAINING A ZERO IS NOT COUNTED.

DO 10 I=1»N1

IF(SC(I) .LT.l.) GO TO 10

IF(SC(I).GT. 10000.) GO TO 5 K(I)=K(I)+1.

3K ( I ) = ( BK ( I ) *K ( I ) +DEADT ( SC ( I ) /SC (Nl)*10.))/(K(I)+1.)

GO TO 10

5 L(I)=L(I)+1.

PK(I)=(PK(I)*L(I)+DEADT(SC(I)/SC(NI)*10.) )/(L<I)+i.)

10 CONTINUE

IF(NSW.EQ.l) GO TO 40

RETURN

40 NFLAG=1

C AFTER ALL STANDARDS HAVE BEEN READ* SUBTRACT THE AVERAGE BACKGROUND

C FROM THE AVERAGE PEAK FOR EACH ELEMENT.

DO 20 I=1»N1

20 PB(I)=PK(I)-BK(I)

RETURN

800 IF(NSW.EQ.l) GO TO 15

GO TO 3

C COMPUTE THE INTENSITY RATIO FOR EACH ELEMENT.

15 DO 30 I=lrNl

30 XK ( I ) = ( DEADT ( SC ( I ) /SC ( NI ) *1 .

) -BK ( I ) ) /PB ( I ) *SF ( I

)

36
C IF INTENSITY RATIOS ARE TO BE ENTERED DIRECTLY, THEY SHOULD BE READ

C HERE. TO OBTAIN INTENSITY RATIOS FROM KNOWN CONCENTRATIONS* READ

C CONCENTRATIONS HERE.

ES=0.

DO 500 I=1»N1

IF(XK<I) .LE.O.) XK(I>=0.

500 ES=ES+XK(I>

IF(LKN) .NE.O) GO TO 501

C(N)=1.-ES

ES=1.

501 DO 502 I=lrNl

502 C(I)=XK(I)/ES

C BEGIN ITERATION ^OR COMPUTING CONCENTRATIONS.

C TO OBTAIN INTENSITY RATIOS FROM KNOWN CONCENTRATIONS t CHANGE

C THE NEXT STATEMENT TO NM=3

DO 550 NM=1>3

DO 510 I=1»N1

SS=0.

RS=0.

AS=0.

DO 520 J=1»N

SS=SS+C(J)*S(J»I)

RS=RS+C(J)*R(J»I)

520 AS=AS+C(J)*AC(J»I)

FCS ( I ) =1 .+H( I ) *AS*COSEC+H ( I ) **2* ( AS*COSEC ) **2* . 05

W(I) = (R(I»I)*SS)/(5(I»D*RS)

C COMPUTE CHARACTERISTIC FLUORESCENCE CORRECTIONS.

XKF(I)=0.

DO 530 J=1»N

IF(KEY(I»J) .EO.O) GO TO 530

AT = 0. DO 528 II=1»N

528 AT=AT+C(II)*FflC(IIrJ)

XU=COSEC*AT/AS

V=(3.33E5/(E0**1.65-EQ(I)**1.65) )/AT

XUV=ALOG(l.+XU)/XU+ALOG(l.+V)/V

XKF(I)=XKF(I)+C( J)*P( J)*0M(J)/2.*RKJ)*( ( X ( J) -1 . ) / ( Y ( I

) -1 . ) ) **1 .67

1*A(I)/A(J)*FAC(I»J)/AT*XUV

530 CONTINUE

IF(XK(D) 511.511»510

510 EK=C(I)/W(I)*(1.+XKF<D)*FC(I)/FCS(I)

C TO ORTAIN INTENSITY RATIOS FROM KNOWN CONCENTRATIONS* INSERT THE

C TWO STATEMENTS -

C C(I)=^K

C GO TO 512

C COMPUTE CONCENTRATIONS BY ITERATION METHOD ACCORDING TO CRISS.

C<I) = (XK(I)*Cm*(l.-EK) )/<XK(I)*(C(I)-EK>+EK*(l.-C(I)>)

GO TO 512

511 C(I)=0.

512 CONTINUE

ES=0.

DO 5t0 I=lrNl

5t0 ES=ES+C(I)

IF(LKN) .NE.O) GO TO 5tl

37
C(N)=1.-ES

ES=1.

5i+l IF(NM.EQ.3) GO TO 550

DO 545 I = 1»N

545 C(I)=C(I)/ES

550 CONTINUE

C PRINT RESULTS.

* CALL ALU(LUTY.IADTTY)

* CALL OPEN(LUTY.IFDB)

* IF(IFDB<2> .LE.O) CALL ERROR (721 , TAB

)

* NW=4

* CALL RIOS2(0»0»IPRI»SIOO»LUTY»IADTTY»IS»NW»ISPC)

* 100 SCHENT

* IF(IS.LE.O) GO TO 650

* NW=22

DO 600 I=lrN

NZ=Z(I)

IF(Nl.EQ.N) GO TO 125

IF(I.EQ.N) GO TO 130

125 RFC=1./FCS(I)

ENCODE (72r 706 .MESS (2) »NC) NZ»XK ( I ) »C( I ) .R^C

706 FORMAT (2X» 12. 8X^6.4.^X^6.4.7X^6.4)

GO TO 140

130 ENCODE(72.707.MESS(2) »NC) NZ.C(I)

707 F0RMAT(2X»I2»10X. •N.A. » . 4X » F6. 4 IX

)

* NW=16

* 140 CALL RIOS2(0»n,IPRI,$110.LUTY»IADTTY.IS.NW.MESS)

* 110 SCHENT

* IF(IS.LE.O) GO TO 650

600 CONTINUE

MESS(2)=CRLF

ENCODE(72.708.MESS(3) »NC) ES

708 F0RMATQ3X. 'TOTAL C = '.F6.4.1X)

* NW=17

* CALL RIOS2(0.0, IPRI $120 LUTY » I ADTTY » IS. NW» MESS)

* 120 SCHENT

C CLOSE THE PRINT FILE AND PRINT OUT THE RESULTS.

* 650 CALL CLOSE(LUTY.IFDB)

* IF (IFDB(2) .LF.O) CALL ERROR (721 . TAB)

RETURN

END

38
APPENDIX II

List of Symbols Used in FRAME Program

39
Variables in FRAME

Subroutine CFCAL

Program Variable

Name

A(I)

Al

ABCO

AC (J, I)

AN ( I Z

)

B

BK(Ij

C1(M),C2(M) ,C3(M)

COSEC

CO

CRLF

E(Ij

EC (M, I)

EL(J,I)

Common Symbols

A.

3

l A

CSC1JJ

q,m

q,m

Remarks

Atomic weight of element I Intermediate step in computation of backscatter

Mass absorption coefficient

Mass absorption coefficient

for line of element I in element J

Atomic weight of element

whose atomic number is IZ

Intermediate step in computation of backscatter

Measured background of element I

Coefficients for computing

the absorption edge energies

Cosecant of the x-ray emer- gence angle

Variable used in determining

if there is a characteristic

fluorescence correction

Teletype carriage returnline feed

Energy of the measured line

of element I Energy of each absorption

edge of element I Energy of each line of

element I

40
Program Variable

Name Common Symbols Symbols Remarks

E

o E

q

B

i/£(x) , 1/f

' - P

EO E Operating kilovoltage

EQ(I) E^ Energy of the absorption

edge of the measured line

of element I FAC(J,I) y^ Absorption coefficients

needed in characteristic

fluorescence correction

FC(I) l/f(x), 1/f^ 1/f of the standard for

the^pure element I

H(I) Voltage dependent term in

expression v for f P IADTTY Address of our teletype

(do not use)

IBUF(50) Input buffer

IDUM Dummy storage location

IFDB(2) Variables needed for our

IPRI output (do not use)

IS Error condition of output

buffer (applicable to our

system)

ISPC(4) 4 rubouts and 2 carriage

return-line feeds on teletype

IZ(I) Z.. Atomic number of element I

J as an integer

JI J Mean ionization potential

in Bethe's equation

K Variables in test for charKK acteristic fluorescence

K5 correction

KEY(J,I) The value of this variable

defines which characteristic

fluorescence corrections

have been found

41
Program Variable

Name

L or LI (I)

Common Symbols

LS

MESS(40)

MHD(5)

N

Nl

NFSW

NW

NYEAR

NZ

OM ( I

)

P(I)

PB(I)

IK(I)

P(k,j)

Remarks

Code defining the x-ray

lines

1 = Ka-line, 2 = La-line,

3 = Ma-line, = element

not analyzed

L

2

Message array — used for

all output

Date (must be loaded from

your computer's clock if

you want it)

Number of elements in

specimen

Number of elements analyzed

NFSW=0 for the initialization of variables needed

during the measurement of

the standards

Number of characters to be

output to the output buffer

RI0S2

The year (1973)

Atomic number

Fluorescence yields of elements which excite secon- dary emission of other

elements

Parameter in Reed's equation

for L-*K and K->L fluorescence

Peak intensity - background

intensity for the standard

for element I Peak intensity for the

standard for element I

42
Program

N. Vari

a. me able

PST

Q

R(J,I)

R1(I)

Common Symbols

RFC

S(J,I)

SC(I)

v. r

J

f(x)

s

Remarks

Do not use Intermediate step in compu

tation of backscatter

Backscatter factors for

radiation I and element J

Jump ratio for characteristic fluorescence cor- rection

1/FC(I)

Stopping powers

Counts measured in scaler

I SETSW

TAB

ucn

X(I)

XL(I)

XXK(I)

Y(I)

Z(I)

ZL

E /E

o q

E /E

q

E /E

Z . J ln(Z.)

Do not use

Overvoltage of element I Overvoltage needed in

characteristic fluorescence

correction

Number of peak measurements

made on standard I Number of background mea- surements made for element

IOvervoltage of element I Atomic number of element I Natural log of atomic

number

43
Subroutine MAC

Program Variable

Name Common Symbols Remarks

C C. Coefficient in the expres

s ion

y B

= C

i

A

<>B

)ni

CN(4) n. The value of n in the

1 above expression

Dl_(4) ,D2(4) ,D3(4) Coefficients for computing

the necessary value of C.

MI Number for selecting the

proper coefficients for

computing C

M MI_

1 1

2 2 3 2 4 2 5 3 6 3

7 3

8 3

9 3 10 4

R(10) Energy jump for each edge

44
Subroutine QUDAT

Program Variable

Name Common Symbols Remarks

ft AS u. Absorption coefficient of

C(I)

EK

ES

FCS(I )

*A

* the specimen

AT y_ Absorption coefficient

needed in characteristic

fluorescence correction

C. Concentration of element I

k. Computed intensity ratio

^ for element I

EC. Sum of concentrations

J

ft ft l/£(x),l/f Absorption factor, fp

" of the specimen for

element I

K(I) Number of times the background is measured for

element I

L(I) Number of times the peak

is measured for element I NFLAG NFLAG=0 while standards are being measured and =1 while

the specimen is being

measured

NFSW NFSW=1 after the first mea- surement is made on a

s tandard

.

NSW Switch to change from

standards (NSW=0) to the

specimen (NSW=1_)

RFC £ (x)tf

p

* 1/FCS(I)

RS R* Backscatter from the

specimen

SF(I) Factors for compound

standards

45
Program Variable

Name Common Symbols Remarks

SS S* Stopping power for the

specimen

V (—'-*—T-T i

f-fO ( —*-) V term in characteristic

E ' -E u n fluorescence correction

o q ^B

W(I) RS*/SR* Atomic number factor

XK(I) k. Measured intensity ratio

XU

1 for element I XKF(I) Characteristic fluorescence factor for element

I —w csctjj u term in characteristic

U A fluorescence correction

XUV ln(l+u) ln(l+v)

: U. S. GOVERNMENT PRINTING OFFICE : 1973— 542-650/58

46
form NBS-114A d-711

U.S. Df.PT. OF COMM. BIBLIOGRAPHIC DATA

• SHEET

1. PUBLICATION OR REPORT NO. NBS TN-7962. Gov't Accession No.3. Recipient's Accession No.

4. TITLE AND SUBTITLE FRAME: An On-Line Correction Procedure for

Quantitative Electron Probe Microanalysis

5. Publication Date October 1973

6. Performing Organization Code

7.author(s) Harvey Yakowitz, Robert L. Myklebust,

and Kurt F. J. Heinrich

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. Project/Task/Work Unit No. NATIONAL BUREAU OF STANDARDS DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Same as No. 9.

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) A procedure u x-ray data from el

This program, call

on-line by the ZAF

input data require

the analytical lin

required parameter

coefficients are s FORTRAN IV, and re FRAME are very clo

most accurate prog

microanalysis

sing a mini-computer for on- ectron microprobe analysis h

ed FRAME, allows mass fracti

approach. Besides x-ray in

d are the atomic numbers of

e being used, and the operat

s such as atomic weights and

tored or calculated by the p quires about 4K of computer

se to those of C0R2 , which i ram available for quantitati

line correction of

as been developed.

ons to be computed

tensities, the only

the elements present,

ing voltage. Other

x-ray mass attenuation

rogram. FRAME is in core. Results from

s considered to be the

ve electron probe

''• KEY WORDS (Alphabetical order, separated by semicolons) Electron DTObe ' mini - COITTDLlt QT ' on-line correction; quantitative microanalysis.

18. AVAILABILITY STATEMENT

QUNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

51

22. Price

80 cents

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the world's literature and critically evaluated. Product Standards. Provide requirements for sizes, types, quality, and methods for testing various industrial products. , These standards are developed co- operatively with interested Government and industry groups and provide the basis for common understanding of product characteristics for both buyers and

sellers. Their use is voluntary. Technical Notes. This series consists of communications and reports ( covering both other-agency and

NBS-sponsored work) of limited or transitory interest. Federal Information Processing Standards

Publications. This series is the official publication within the Federal Government for information on

standards adopted and promulgated under the Public Law 89-306, and Bureau of the Budget Circular A-86

entitled. Standardization of Data Elements and Codes

in Data Systems. Consumer Information Series. Practical information, based on NBS research and experience, covering areas of interest to the consumer. Easily understandable language and illustrations provide useful background knowledge for shopping in today's tech- nological marketplace.

BIBLIOGRAPHIC SUBSCRIPTION SERVICES

The following current-awareness and literature-survey bibliographies are issued periodically by the Bureau

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Cryogenic Data Center Current Awareness Service (Publications and Reports of Interest in Cryogenics). A literature survey issued weekly. Annual subscription : Domestic, $20.00; foreign, $25.00.

Liquefied Natural Gas. A literature survey issued quarterly. Annual subscription: $20.00. Superconducting Devices and Materials. A literature survey issued quarterly. Annual subscription : $20.00. Send subscription orders and remittances for the preceding bibliographic services to the U.S. Department

of Commerce, National Technical Information Service, Springfield, Va. 22151. Electromagnetic Metrology Current Awareness Service (Abstracts of Selected Articles on Measurement

Techniques and Standards of Electromagnetic Quantities from D-C to Millimeter-Wave Frequencies). Issued monthly. Annual subscription: $100.00 (Special rates for multi-subscriptions). Send subscription order and

remittance to the Electromagnetic Metrology Information Center, Electromagnetics Division, National Bureau

of Standards, Boulder, Colo. 80302. Order NBS publications (except Bibliographic Subscription Services) from : Superintendent of Documents, Government Printing Office, Washington, D.C. 20402.
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