NBS

PUBLICATIONS

U.S. DEPARTMENT OF COMMERC!

National Bureau of Standards

NAT'L INST. OF STAND & TECH

AlllDS Tfl331fi

NBS Technical Note 1213

NBSGSC—A FORTRAN

Program for Quantitative

X-ray Fluorescence Analysis

G. Y. Tao. R A. Mia, and R. M. Rousseau

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'l ocated at Boulder, f O, >Aiih some elcmenis at Gaithersburg, MD.
NBS Technical Note 1213

JJATIONAL BUBEAU QV STANDARDS UEaaHY

no, 1^1^

NBSGSC—A FORTRAN

Program for Quantitative

X-ray Fluorescence Analysis

G. Y. Tao R. M. Rousseau P A. Bella

National Bureau of Standards Geological Survey of Canada

Gaithersburg, MD 20899 Ottawa, Canada

April 1985

Tk

U.S. Dq^rtment of Commove

Malcolm Baldrige, Secretary National Bureau of Standards

Ernest Ambler, Director
National Bureau of Standards U.S. Government Printing Office, For sale by the Superintendent

Technical Note 1213 Washington: 1985 of Documents,

Natl. Bur. Stand. (U.S.), U.S. Government Printing Office, Tech. Note 1213, Washington, DC 20402

119 pages (Apr. 1985)

CODEN: NBTNAE
NBSGSC - A FORTRAN Program

For Quantitative X-Ray Fluorescence Analysis

G. Y. Tao* and P. A. Pella

Center for Analytical Chemistry

National Bureau of Standards

Gaithersburg, Maryland 20899 U.S.A.

and

R. M. Rousseau

Geological Survey of Canada

Ottawa, Canada

ABSTRACT

A FORTRAN program (NBSGSC) was developed for performing quantitative

analysis of bulk specimens by x-ray fluorescence spectrometry. This program

corrects for x-ray absorption/enhancement phenomena using the comprehensive

alpha coefficient algorithm proposed by Lachance (COLA). NBSGSC is a revision of the program ALPHA and CARECAL originally developed- by R.M.

Rousseau of the Geological Survey of Canada. Part one of the program (CALCO)

performs the calculation of theoretical alpha coefficients, and part two

(CALCOMP) computes the composition of the analyte specimens. The analysis of

alloys, pressed minerals, and fused specimens can currently be treated by the

program. In addition to using measured x-ray tube spectral distributions,

spectra from seven commonly used x-ray tube targets could also be calculated

with an NBS algorithm included in the program. NBSGSC is written in FORTRAN

IV for a Digital Equipment Corporation (DEC PDP-11/23) minicomputer using

RL02 firm disks and an RSX 11M operating system.

Key words: Alpha coefficients; comprehensive algorithm; fundamental

parameters; interelement corrections; program; quantitative analysis; x-ray.

Guest Researcher from Shanghai Institute of Ceramics, Academia Sinica, The

People's Republic of China.

ill
TABLE OF CONTENTS

Page

ABSTRACT iii

INTRODUCTION 1

PROGRAM STRUCTURE 5

OPERATING PROCEDURE 9

REFERENCES 15

APPENDIX 1 : LISTING OF CALCO AND CALCOMP PROGRAMS 17

APPENDIX 2: DESCRIPTION OF SYMBOLS AND PERMANENT DATAFILES .... 51

APPENDIX 3: EXAMPLES FOR ALLOY, OXIDE, AND FUSED SAMPLES 61

APPENDIX 4: LISTING OF PROGRAMS FOR CREATING AND READING

PERMANENT DATAFILES 109

IV
I. INTRODUCTION

NBSGSC was developed in response to a need in the X-ray spectrometry

community for a generally available fundamental parameter program for

correction of interelement (matrix) effects in quantitative X-ray fluore- scence spectrometry. This program was designed for X-ray analysis of samples

where direct X-ray tube excitation is employed. Although there are fundamental parameter programs available through commercial suppliers, they are essentially proprietary documents. Probably the best known fundamental

parameter program generally available to the user is the Naval Research

Laboratories' NRLXRF (1). This program, however, requires extensive computer

capabilities and is not subject to general modification by the user. NBSGSC

was written to run on present-day minicomputers such as a DEC PDF 11/23

system. Because the entire source program information is well-documented in

this publication, any modification by the user should be possible for

particular applications. However, the authors specifically decline responsibility for any error arising from modifications made and/or improper use of

these algorithms.

Another impetus for developing NBSGSC was the opportunity to evaluate a recent comprehensive algorithm proposed by Lachance (2) which we call COLA.

This algorithm uses a theoretical alpha coefficient approach to the correction of matrix effects unlike most other fundamental parameter programs. In

addition, we also desired to test a new NBS algorithm (3) for calculation of

X-ray tube spectral distributions required in fundamental parameter methods

when the source of excitation of a specimen is an X-ray tube.

To test the COLA algorithm, we obtained a computer program developed by

R. M. Rousseau of the Geological Survey of Canada (GSC). This program was extensively modified at NBS and ultimately evolved into what we will now refer to as the NBSGSC program.

The modifications are summarized as follows:

(1) Instead of calculating a-coeff icients for alloys (element system),

minerals (oxide system) and fused disc specimens in separate programs, these

options were combined into a single program.

(2) Two options now exist for X-ray tube spectral distributions. Either

measured X-ray spectral distributions from the literature or distributions

calculated from the NBS algorithm for seven commonly used X-ray tubes at any

voltage can be employed.

^Disclaimer - In order to adequately describe materials and experimental

procedures, it was occasionally necessary to identify commercial products by

manufacturer's name or label. In no instance does such identification imply

endorsement by the National Bureau of Standards nor does it imply that the

particular products or equipment is necessarily the best available for that

purpose.
(3) Most of the fundamental parameters required for calculating alpha

coefficients such as mass absorption coefficients, fluorescence yields, jump

ratio, analyte line wavelength, absorption edge wavelength, are either

computed or stored in the program to minimize data input by the user.

(4) For calculating mass absorption coefficients, either the algorithm

of Heinrich or the necessary table values from Thinh and Leroux can be

selected. The table values for Thinh and Leroux are stored in a permanent

datafile.

(5) When analyzing specimens, known concentrations of any unanalyzed

elements can now be entered at fixed concentrations.

(6) A dead-time correction has been incorporated in the program.

(7) Four types of calibration curves can be selected for system

calibration.

(8) One of three sample preparation conditions can be chosen when fusing

specimens to allow greater flexibility in sample-to-flux ratios used in

various laboratories.

(9) If the results of analysis are to be compared with previously known

or "true" values for the analyte specimens, the program will output absolute

and relative errors.

An evaluation of the COLA algorithm has been performed and is the subject of

a publication iU) where results were intercompared with those obtained with

NRLXRF for typical alloys, and minerals both in the pressed powder and fused

disc form. The general form of the COLA expression is:

C^ = R^(1 + Za{jCj + Z I a{jj^CjC^) (1)

J J X

where C^ is the analyte weight fraction, and C^ j^ are the corresponding

weight fraction of elements j and k, respectively. ' R^^ is the analyte X-ray

intensity relative to the pure analyte. The coefficient a^^ quantifies the

effect of element j on i and is equal to

°'2 Cm

arj = ai ^ (2)

UagCl-C^)

where Cj^ = Cj + Cj^ +

The concept of "crossed" coefficients introduced by Claisse-Quintin (5) is

retained where a^4|^ is defined as follows:

•^ijk

CjCk

Ci — - (UaijCj+dii^C^)

^i

(3)
Both ar. and a^^j. are primed to indicate that the coefficients represent

variables which in practice, however, are treated as changing predictably

within relatively narrow limits. The three constants a-| , a2» and ao in

equation 2 are calculated from hypothetical binary samples. For example, in

alloy systems, a^ is the value of the coefficient near the C^^ = 1.0 limit (in

practice computed at C^ = 0.999; G^ = 0.001). The value for a2 is the range

within which a^^ will vary when the concentration of the analyte decreases to

the C^ = 0.0 limit (in practice computed from two binaries C^ = 0.001, 0.999;

C^ = 0.999; 0.001). The a^ coefficient expresses the rate with which ol[a is

made to vary hyperbolically within the two stated limits. In practice, it is

generally computed from three binaries where C^^ =0.001, 0.5, 0.999; C^ = 0.999, 0.5, 0.001. Since a^ can take on positive, zero, or negative values,

a^^ can be computed for the entire composition range from C^ = 1.0 to 0.0.

The ol[^\, coefficients are included to compensate for the fact that the total

interelement correction cannot be strictly represented by a sum of binary

matrix effects. A value for a^-jj^ calculated from equation 3 (C^ = 0.30, C^ = 0.35, C|^ = 0.35) where the binary a^^ and a^,^ are calculated at the C^ = 0.30, C^ j^ = 0.70 level can generally be used to represent the entire ol^a^

array.

For the multi-element assay of alloys, all the coefficients in equation 1 are calculated. For such specimens as cements, a^ is nearly equal to zero,

so that a^i in equation 2 can be simplified to

a^'j = ai + a2 Cjn . (4)

Note that a^^ here is equivalent to that coefficient in the Claisse-Quintin

model and equation 2 now reduces to the Claisse-Quintin expression. Hypothetical binary standards where C^^ = 0.2 and 0.8, and C^ = 0.8 and 0.2 are generally used to calculate a^^ values.

For fused specimens, another simplification in equation 2 can be made

because the concentration of the flux is by far the major constituent and can

be held relatively constant. In this case ao, a^, and ot^^j^ are approximately

zero, so that a^^ reduces to aj^^ in the conventional Lachance-Traill (6)

expression. Hypothetical binary standards are used to calculate a^^ values

where C^ equals the mid-range of the concentrations in the analyte.

We propose that NBSGSC is suitable for routine analysis of alloys, and

minerals both as powders, and as fused specimens. Once the theoretical alpha

coefficients are calculated and saved in a data file, the user can employ

them at any time along with measured X-ray intensity data on standards and

unknowns to obtain concentrations. Theoretical alpha coefficients only provide the general relationship of matrix influences on the analyte, and user- defined real standards are used to rescale it for matching experimental reality. Therefore, appropriate standards are very important for obtaining good

results as is the case with other fundamental parameter methods [1,7]. Since

NBSGSC is generally written in Standard FORTRAN IV, it should be readily

adaptable to most minicomputers in laboratories which use X-ray fluorescence

spectrometry.
To achieve optimum analytical results, it should be recognized by the user that accurate net x-ray intensities need to be measured. Corrections to

measured x-ray intensities for background, blanks, x-ray line overlaps,

detector dead-time, and spectral artifacts such as sum and escape peaks,

should always be carefully considered.
TI. PROGRAM STRUCTURE

NBSGSC is divided into two separate programs (CALCO and CALCOMP*) where

each program consists of a main program and a series of subprograms linked to

the main program as shown in Figures 1 and 2. The list of symbols and permanent data files used in programs CALCO ' and CALCOMP are presented in

appendix 2.

In CALCO, a subroutine TUBDAT along with subroutines CTNLIN, CHALIN,

INFTGT and datafile TGTWR.DAT are used mainly to perform the calculation of

the X-ray tube spectral distribution. This requires input of the X-ray tube

target, voltage, take-off angle, Be window thickness, and the ending wave- length of the continuum. The spectral distribution calculation is based on

an NBS algorithm proposed by Pella and Feng [3], which utilized experimental

electron microprobe data obtained under various conditions. The calculation

of the X-ray intensities for both the continuum and characteristic lines (KA,

KB, LAI, LBl ) from the X-ray tube are performed in CTNLIN and CHALIN respectively, and intensities for the other characteristic lines (LB2, LB3, LB4,

LG1 = LY1 , LG2 = LY2, LG3 = LY3, LL) are obtained from the intensity ratios

of the lines to the LAI line tabulated in the literature [8].

There are two real functions, named MAC and MACFUN, each of which could

be chosen for computing mass absorption coefficients. When using the function MAC, the mass absorption coefficients are calculated from the algorithm

of Heinrich [9] using the general relation

U = CX (5)

where A is the wavelength in angstroms and the coefficient C is calculated by

a least-squares fit. Parameters required in the function MACFUN using the

general equation of Thinh and Leroux [10], that is,

y = C E^jj X (6)

where E^^ is the absorption edge energy (keV), however, are all stored in the

direct-access datafile MACPRM.DAT. MACFUN requires more time to calculate

mass absorption coefficients than the function MAC.

The wavelengths of analyte lines (KA, KB or LAI, LBl or LB2), the

corresponding wavelengths of the absorption edges (for K or LII or LIII

shell) and the corresponding X-ray fluorescent yields (for K or LII or LIII

shell) are computed in Subroutines CHAWV, ABSEDG, and YIELD, respectively, by

means of empirical fits. The jump ratio values for the K or LIII shell, however, are stored in Subroutine JUMRAT. The atomic fraction of an analyte in an oxide compound is calculated in the Subroutine AFIOX.

^Disclaimer - CALCOMP is an acronym for calculation of composition and is not

intended to refer to the commercial company by the same name.
FIGURE 1 . STRUCTURE OF PROGRAM CALCO

S

U

B

R

U

T

IN

E

A

T

N

U

M

-^ SUBROUTINE

CHAWV

SUBROUTINE

ABSEDG

^-^ SUBROUTINE

YIELD

SUBROUTINE

JUMRAT

SUBROUTINE

AFIOX

J.

SUBROUTINE

SBATWT

MAIN PROGRAM CALCO

SUBROUTINE

ALPHA

TTA

<r SUBROUTINE

TUBDAT

SUBROUTINE

APAFD

SUBROUTINE

BDCOEF

REAL FUNCTION

MAC OR MACFUN

f

DATAFILE

MACPRM.DAT

SUBROUTINE

CTNLIN

SUBROUTINE

CHALIN

SUBROUTINE

INFTGT

DATAFILE

TGTWR.DAT
FIGURE 2. STRUCTURE OF PROGRAM CALCOMP

SUBROUTINE

DATA IN ^ >- MAIN PROGRAM SUBROUTINE

CALCOMP GETERR

SUBROUTINE

CALRI

SUBROUTINE ^ SUBROUTINE

SVLSF2 SLE
Subroutine ALPHA, along with subroutines BDCOEF and APAFD, completes the

major calculation of alpha coefficients, which are a-], a2, ao, and o.[i^

for an element system, a^ , a2» and a{-j|^ for an oxide system, or a^ for a fused disc system. Calculated alpha coefficients can be saved in a sequential-access datafile created by the main program CALCO if desired. Frequently

used common subroutines, ATNUM and SBATWT provide the atomic number and

atomic weight, respectively, when the chemical symbol of an element is given.

In CALCOMP, input data are required for alpha coefficients, intensities

and concentrations of standards, and intensities of unknowns using the subroutine DATAIN. After relative intensities of the standards are calculated,

subroutine CALRI calls subroutines SVLSF2 and SLE to obtain a least-square

fit for the calibration curve (R| versus I?), and then from this calibration

curve relative intensities for unknowns are computed and sent back to the

main program CALCOMP where iterations proceed to obtain the final concentrations of unknowns. Subroutine GETERR is used, if desired, to compare the

observed results with other previously known values for the unknowns. The

options for selecting different analysis systems, entering known concentrations of unanalyzed elements as fixed concentrations, dead time correction,

different calibration curves, and for using different standards such as multi-element or pure element standards are also provided in the program

CALCOMP.
III. OPERATING PROCEDURE

A menu procedure for operating the programs CALGO and GALGOMP is followed

where the user answers a question, selecting the appropriate answer among the ones provided, and enters the required data. This is illustrated by the

flowcharts in Figures 3 and 4. Examples of the menus are shown in appendix

3. For ensuring proper execution of the program, the following additional

comments are made to the user.

For CALGO (refer to figure 3)

(1) In step 2, if an oxide system is selected for analysis, and the user wishes to add LOI (loss of ignition) as an analyte, a^Qj is computed assuming

the hypothetical compound GO^ as an approximation to GO2 plus H2O. (See

example in Appendix 3.3A). If the fused disc system is selected, a^Ql ^^ automatically calculated at the 25/S level and stored by the program.

(2) The maximum number of analytes the program can handle in step 2 is

12. But in a fused disc analysis the actual number is 12 plus 1 because LOI

is already taken into account.

(3) It is recommended that names of the analytes are entered in the

order of increasing atomic number in step 4. For an element system, each

name occupies three spaces. The first two for the chemical symbol of the

analyte, the third one as a blank space such as FE# or V## where # represents

a blank space. For an oxide or fused disc system, a special format for the name is required to automatically calculate the atomic fraction of the element in its oxide. In this case, each name occupies six spaces. The first

two for the chemical symbol of analyte, the third one for number of analyte

atoms in the corresponding oxide, the fourth one for the chemical symbol of

oxygen, the fifth one for the number of oxygen atoms in the oxide, and the

sixth one as a blank space for example MG101#P#205#FE203# etc.

(4) If the user selects measured X-ray tube spectral data in step 12,

then a datafile should be created by EDT before running the program. The data

should be in the following order:

1Wavelengths of the continuum from the short wavelength limit to

the ending wavelength in intervals of 0.02 A.

2. The integral intensities of the continuum for each wavelength

interval.

3. The wavelengths of the X-ray tube characteristic lines in order

of KA, KB, LAI, LB1 , LB2, LB3, LB4, LG1 , LG2, LG3, and LL.

4. The intensities of the X-ray tube characteristic lines in the same order as 3 above.

Table 1 gives an example of a datafile named SDXT75.W45, containing

measured spectral data for the tungsten target at 45 kV published in 1975

[11]. The total number of wavelength intervals (maximum number = 300) of the

continuum for the measured spectrum is also entered in step 17.
FIC3URE 3. FLOWCHART FOR PROGRAM CALCO

10

11

12

Step No.

1 START CALCO

i

2 Select Analysis System(1) Element

(2) Oxide

(3) Fused Disc

Input Number of Analytes

Input Name of Analytes

I.

Select an Algorithm for Calc. Mass. Abs. Coef.

(1) Leroux Algorithm

(2) Heinrich Algorithm

Input Datafile Name of

Calc. Alpha Coef.

*If Step 2-3

If Step 2-1 or 2

Input Mean Cone, of Analytes

in Sample for Fused Disc

Input incidence and Emergence Angles

Select Analyte Line Number:

(1) Ka, (2) KB, (3) Lol,

(t) LB1, (5) LB2

Y or N

Select X-ray Tube Spectrum

you want to Use: (1) NBS algorithm and (2) Measured

END

N

Print Out Calc. Coef.

If step 11-Y

If Step 11=

Select fused disc condition:

(1), (2). or (3)

If Step 2-3

If Step 2= 1 or 2

-

Print out /'ray Tube Spectrum Data

>

If Step 13-Y

Ik

If step 13-N

^

1 I Input Ending Wavelength for X-ray tube spectrum '

1 Input Total Number of Wave-- length Intervals of Continui

for Measured Spectrum

'^ Input Datafile Name of Measured Spectrum

If Step 12-2

Input Voltage, Take'-off

If Step

12=1

AnfJJ.B of X-r

3K

i.iiuuw iiiiuKiicsa ay Tube

3

Input Name of X-ray

Tube Target

Y or N

Do you want to print out

the spectrum data?

Step No.

22

21

20

19

18

17

16

15

1«»

13

*Thi8 means If option 3 is selected in Step 2, etc.

10
FIGURE t. FLOWCHART FOR PROGRAM CALCOMP

Step

No.

Print out results

for each unk.

~-,^,__^ fixed

T

cone? ^_^,----*

1 Input number of all constituents, number of analytes and number of unk.

Input number of analytes

and n'jmber of unk.

*. Input names of constituents

\ 1 <

23

Select Alpha Coef. Input:

(1) By DatafUe

(2) By Keyboard

(1)

(2) 19

Input Dataflle Name of Alpha Coef.

Key^in Alpha Coef. on Keyboard

Select the type of Standard

you U3e: (1) pure std. and

(2) multielement std.

(1)

(2)

Input Pure Int. for each

analyte

13 Input nimber of std.

16

15

Select calibration curve ^

Type (1), (2), (3). or (H) W

Print out the contents for Step 22

Input dead time

TK—

Input Int. of Unk.

Input Int. or Cone,

of Unk.

If Step 3^T

-Sj Input I.D. of Unk. ^

Input Int. of Std.

Input Cone, of Std.

TT

Input I.D. of Std,

Tf^

Step

No.

28

29

30

32

If Step

3-N

Input Cone, of Unk.

Tabulating Results and Absolute and Relative Errors

11
Table 1. The Contents of Datafile SDXT75.W45 as an Example of Measured

X«ray Tube Spectral Data

.27,. 29,. 31,. 33,. 35,. 37,. 39,. 41,. 43,. 45,. 47,. 49,. 51,. 53

.55, .57, .59, .61, .63, .65, .67, .69, .71, .73,. 75, .77, .79, .81

.83,. 85,. 87,. 89,. 91,. 93,. 95,. 97,. 99, 1.01, 1.03, 1.05, 1.07

1. 09, 1.11»1. 13, 1.15, 1.17, 1.19, 1.21, 1.23, 1.25, 1.27,1. 29

1.31,1.33,1.35,1.37,1.39,1.41,1.43,1.45,1.47,1.49,1.51

1.53,1.55,1.57,1.59,1.61,1.63,1.65,1.67,1.69,1.71,1.73

1.75,1.77,1.79,1.81,1.83,1.85,1.87,1.89,1.91,1.93,1.95

1.97,1.99,2.01,2.03,2.05,2.07,2.09,2.11,2.13,2.15

2.17,2.19,2.21,2.23,2.25,2.27,2.29,2.31,2.33,2.35,2.37

2.39,2.41,2.43,2.45,2.47,2.49,2.51,2.53,2.55,2.57,2.59

0.0,4.4,13.1,20.9,27.7,32.7,35.7,37.8,39.0,39.3,39.2,38.8,38.2

37.4,36.6,35.7,34.8,34.0,33.1,32.2,31.4,30.4,29.6,28.8

28.0,27.2,26.3,25.6,24.8,24.0,23.4,22.6,21.9,21.2,20.6

20.0,19.4,19.1,18.9,18.9,19.3,19.6,19.0,18.4,18.0,17.4

17.0,17.6,21.1,21.4,20.8,20.2,19.7,19.1,18.5,18.0,17.5,17.0

16.5,16.0,15.5,15.0,14.6,14.1,13.7,13.3,12.9,12.5,12.2

11.8,11.4,11.1,10.8,10.4,10.2,9.8,9.6,9.3,9.0,8.7,8.4,8.2

7.9,7.7,7.4,7.2,7.0,6.7,6.5,6.2,6.0,5.8,5.6,5.4,5.2,5.0

4.8,4.7,4.5,4.4,4.2,4.0,3.8,3.7,3.6,3.5,3.3,3.2,3.1,3.0

2.8,2.7,2.6,2.5,2.4,2.3,2.2

0.0,0.0,1.4776,1.2818,1.2454,1.2627,1.3016,1.0986,1.0686

1.062, 1.6782, 0.0, 0.0, 535., 331. 5, 153., 50., 50., 61., 9. 25

6.95,18.2

12
(5) If the NBS algorithm is selected for calculating the X-ray tube

spectral distribution in step 12, one of the following seven X-ray targets

can be chosen: So, Cr, Mo, Rh, Ag, W, or Au.

(6) When the Cr target X-ray tube is used where Cr and Mn are among the

analytes, an aluminum filter, 0.081 g/cm thick is employed and the primary

spectrum is corrected by the absorption of the filter for these two analytes

automatically in the program.

For program CALCOMP (refer to figure 4).

(1) If you answer 'Y' in step 3. that means known concentrations of

unanalyzed elements could be entered as fixed concentrations, and 'NUMBER OF

ALL CONSTITUENTS' in step 4 means the sum of the number of analytes and

unanalyzed elements. In step 18 when asked for the input of intensities or concentrations of unknowns, the fixed concentrations (weight fraction) should

be entered for unanalyzed elements while intensities are entered for the

analytes.

(2) In steps 5 or 7, each name occupies eight spaces and the name has no defined function meaning, so that TliHHHHHtViHHHHHHtFEiHHHHHt or LOI#####MGO###«SI02####P205###/^ are all correct (see example in appendix

3).

(3) If the alpha coefficients in step 8 are entered via '2-KEYBOARD'

,

the order to key in alpha coefficients is as follows:

1

.

The coefficients for the analytes are entered in the same order

as the input names of the analytes in steps 6 or 7.

2. For each analyte, the order of entering coefficients is a^ , a2,

ao, and cx^4|^, as listed in the tabulation of alpha coefficients

where blank spaces should be replaced by zero.

In appendix 3.1 A is an example of the tabulation of alpha coefficients

for the CR-FE-NI system. An example of how these data are keyed in appears

in appendix 3. IB.

(4) Calculated relative intensities of standards in step 22 are computed

using the COLA algorithm:

s °'2*^m

and intensities corresponding to the pure analyte element are computed from

multi-element standards using the equation: I^^ ^qq = l|/R?

(5) In step 24, four choices of calibration curves may be selected by

the user and are:

13
1. straight line: Y = A0+A1*X

2. quadratic line: Y = A0+A1 *X+A2*X*X

3. straight line oonstrained to zero intercept: Y = A1*X

4. quadratic line constrained to zero intercept: Y = A1*X+A2*X*X

In many cases, calibration curve 4 seems to partially compensate for

inaccuracies in fundamental parameters used in the calculation of theoretical

alpha coefficients especially over a wide range of analyte composition, and

better results have been observed. However, when the concentrations of the

unknowns are out of the range of the standards, it is suggested that the

other calibration curves listed above be used to check for consistency in the

results. The extrapolation provided by the quadratic line can sometimes give

large errors.

When only one multielement standard is available, calibration curve 3 is

the only option used by CALCOMP. At least two multielement standards are required for calibration curve 1 or M, while three are required for

calibration curve 2.

(6) In the final printout of the results for each unknown, 'R' is the

relative intensity 'C is the concentration in weight percent, and 'L' is the

number of iterations,

(7) The convergence criterion to be met for all analytes in the program

is 0.01 /&. If the number of iterations exceeds 10 and convergence is still

not reached, the program will pause and print out the warning message "NO. OF

ITERATION >10'. One could still print out the results at this stage by keying in the command 'RESUME', at which point the results of the last iteration

are printed out, and the program automatically begins to process the next

unknown sample. In practice, convergence is usually obtained in three to ssven iterations.

The examples given in appendix 3 illustrate the program input and output

structures for running the different analysis schemes. For more efficient

operation^ especially for routine applications, it is recommended that a com- mand file be created by the user which will contain the answers to the menu

questions and all required input data in the format specified in CALCO and

CALCOMP, prior to execution of the program. Use of a command file in this

way is especially advantageous when few changes in input data need to be made

as different specimens are analyzed.

14
IV. REFERENCES

[I] J. W. Criss, L. S. Birks, and J. V. Gilfrich, Anal. Chem. 50, 33

(1978).

[2] G. R. Lachance, Internat. Conf. on Ind. Inorg. Elemental Anal., Metz,

France, June 3, 1981

13] P. A. Pella, L. Y. Feng, and J. A. Small, "An Analytical Algorithm for

Calulation of Spectral Distrbutions of X-ray Tubes for Quantitative

X-ray Fluorescence Analysis", Accepted for publication in the January

1985 issue of X-ray Spectrometry.

[M] P. A. Pella, G. Y. Tao, and G. R. Lachance, "Intercomparison of

Fundamental Parameter Interelement Correction Methods - Part 2",

submitted to X-ray Spectrometry for publication.

[5] F. Claisse and M. Quintin, Can. Spectrosc, 12, 129 (1967).

[6] G. R. Lachance and R. J. Traill, Can. Spectrosc, y\_, 43 (1966).

[7] R. M. Rousseau, X-ray Spectrometry, j_3, 121 (1984).

[8] M. A. Blokhin, The Physics of X-rays, 2nd revised edition, Moscow,

1957, AEC Translation 4502, p. 401-403.

[9] K, F. J. Heinrich, The Electron Microprobe, John Wiley, New York, 1966,

p. 296.

[10] T. P. Thinh and J. Leroux, X-ray Spectrometry 8, 85 (1979).

[II] D. B. Brown, J. V. Gilfrich, and M. C. Peckerar, J. Appl. Phys. 46,

4537 (1975).

15

Appendix 1: Listing of CALCO and CALCOMP Programs

PROGRAM CALCO

C

C THIS IS A REVISION OF VERSION 1 OF A FUNDAMENTAL PARAMETER

C CCMPUTER PROGRAM FOR CORRECTICN OF INTERELEMENT EFFECTS FCR

C QUANTITATIVE X-RAY SPECTROMETRY. TOE ORIGINAL PROGRAM WAS

C WRITTEN BY R.M.ROUSSEAU OF THE GEOLOGICAL SURVEY OF CANADA

C (GSC) AND CONTAINS TOE PROGRAMS ALPHA AND CARECAL WHICH WERE

C EXTENSIVELY MODIFIED AT NBS. THE NBSGSC PROGRAM CONTAINS THE

C COMPREHENSIVE LACHANCE ALGORITHM (COLA) FOR CORRECTION OF INTERC ELEMENT EFFECTS.

C CALCO IS A REVISION OF ALPHA FOR CALCULATING TOEORETICAL ALPHA

C COEFFICIENTS, AND CALCCMP IS A REVISION OF CARECAL FOR CALCULAC TING CONCENTRATIONS IN ANALYTE SPECIMENS.

C

C OVERLAY STRUCTURE OF CALCO : C MAIN PROGRAM CALCO

C SUBROUTINE ALPHA,APAFD,ATNUM,CHAWV,ABSEDG

C JUMRAT, YIELD, AFIOX,BDCOEF,TUBDAT

C CTNLIN,INFTGT,CHALIN,SBA'IWT

C REAL FUNCTICN MAC,MACFUN

C CATAFILE TGIVIR.DAT,MACPRM.CAT

C

* C AirPHORS: G.Y. TAO AND P.A. PELLA CATE: 04-SEP-1984

C CENTER FOR ANALYTICAL CHEMISTOY, NATIONAL BUREAU OF STANDARDS

C GAITHERSBURG MD 20899 U.S.A.

C AND R.M.ROUSSEAU

C GEOLOGICAL SURVEY OF CANADA, OTTAWA, CANADA KTA-0E8

C

C * GUEST RESEARCHER FROM SHANGHAI INSTITUTE OF CERAMICS,

C ACADEMIA SINICA, THE PEOPLE'S REPUBLIC OF CHINA

C

DIMENSION IELE(12) ,NE(12) ,N0(12) ,A1(12,12) ,A2(12,12)

,

+ A3 (12,12) ,AIJK(12,12,12) ,IDATE(5) ,ITIME(4) ,NA^FIL(5)

COMMON K15,K1,N,IELE,NE,N0

COMMON /C0ESUB/A1,A2,A3,AIJK

CALL DATE(IDATE)

CALL TIME(ITIME)

WRITE ( 6 , 90 ) IDATE , ITIME

WRITE(6,100)

READ(5,*)K1

WRITE(6,105)

READ(5,*)N

IF(K1.EQ.1)WRITE(6,110)

IF(K1.EQ.1)READ(5,120) (lELE(I) ,I=1,N)

IF(K1.NE.1)WRITE(6,130)

IF(K1.NE.1)READ(5,140) (lELE(I) ,NE(I) ,N0(I) ,I=1,N)

WRITE (6, 145)

READ(5,*)K15

WRITE(6,150)

READ(5,160)KK1

IF(KK1.EQ.«N MGOTO 10

WRITE (6, 170)

READ ( 6, 180) NAME IL

10 CALL ALPHA

IF(KK1.EQ.'N ')GOTO 20

CALL ASSIGN ( 3, NAME IL, 10)

IF(K1.EQ.3)A1(1,3)=0.0

IF(K1.EQ.3)WRITE(3,*,ERR=15)A1(1,3) ,(A1(I,2) ,I=1,N) , (A1(I,1)

,

+ (A2(I,J),J=1,N),I=1,N)

IF(K1.EQ.1)WRITE(3,*,ERR=15) ((A1(I,J) ,J=1,N) , (A2(I,J) ,J=1,N)

,

+ (A3(I,J) ,J=1,N) , ((AIJK(I,J,K) ,K=1,N) ,J=1,N) ,I=1,N)

IF(K1.EQ.2)WRITE(3,*,ERR=15) ( (A1(I,J) ,J=1,N) , (A2(I,J) ,J=1,N)

,

+ ((AIJK(I,J,K) ,K=1,N) ,J=1,N) ,I=1,N)

17
15 CALL CLCSeO)

20 CALL DATC(IDATO)

CALL TIME(ITIME)

WRITC (6, 95) IDATE, ITIME

STOP

90 FORMAT (///IX/ DATE I • ,5A2,6X,'TIME: •,4A2/)

95 FORMKr(lHl,//lX,'DATE: ' ,5A2,6X,'TIME: •,4A2/)

100 FOBMATdX, 'WHICH SYSTEM DO YOU WISH TO ANALYZE: V3X,

> •l-ELEMEMT SYSTEM 2-OXIDE SYSTM 3-FUSED DISK SYSTEM ? • ,$)

105 FORMAT(lX,'IMPl/r NUMBER OP AMALYTES: ' ,$)

110 PORMAT(lX/INPt;r NAMES OF ANALYTES (XXS): * ,$)

120 P0RMAT(12(A2,1X))

130 FORMAT(lX,'INPlfr NAMES OF ANALYTES (XXNONS) : V)

140 FORMAT(12(A2,IlrlX,Il,lX))

145 FORMAT (IX, 'WHAT MASS ABS. COEF. ALGORIIW DO YOU WANT

•fTO USE :'/3X,'l-LER0UX ALGGRITW1 2-HEINRICH ALGORITHM ? ' ,$)

150 FORMAT (IX, '00 YOU WANT TO CREATE A CATAFILE FOR SAVING CALCULATE

+D ALPHA COEFFICIENTS (Y/N)? ' ,$)

160 FORMAT (Al)

170 FORMATdX/INPirr DATAFILE NAME OF ALPHA COEFFICIENTS (XXXXXX. XXX)

+: •»$)

180 FORMAT (5A2)

EM)

18
SUBROUTINE ALPHA

C

C THIS SUBBCXJTINE CALCULATES ALPHA COEFFICIENTS FOR

C INTERELEMEMT EFFECT CORRECTICN USED IN COLA EQUATION

C FOR ELEMENT, OXIDE, OR FUSED DISK SYSTEMS.

C

C NBS 04-SEP-1984

C

REAL MAC,MU

DIMENSION XIOT(2,300) ,XINT1(2,11) ,IELE(12) ,NE(12) ,N0(12) , + CL(12,4),ISR(12),IZ(12),A1(12,12),

+ A2(12rl2) ,A3(12,12) ,AIJK(12,12,12) ,UC0(12) ,UC(12,12) ,C(5,3)

,

-»- IE(12) ,G(5) ,ALFA(12) ,CAM(12) ,SWDB(12) ,SWDB1(12)

COMMON K15,K1,N,IELE,NE,N0,KK2,CAM,IZ,ITP,ITS corwcw /'njBEi/xiMr,xiNri,ND

COMMON /TUBE2/IDrUBE,V0LT

CO^WCN /BDSUB/TP,TS,C,CL,IE,UC,UC0,N5

COMMON /C0ESUB/A1,A2,A3,AIJK

DATA C/. 001,. 5,. 999,. 3,. 3,. 999,. 5,. 001,. 7,. 35, 4*0.0,. 35/

IF{K1.NE.3)G0T0 4 WRITE (6,950)

DO 2 1=1,

WRITE(6,960)I,IELE(I) ,NE(I) ,NO(I)

READ (5,*) CAM (I)

2 CONTINUE

GOTO 5

4 IF(K1.EQ.1)G0T0 5 C(l,l)=.2

C(2,l)=.8

C(l,2)=.8

C(2,2)=.2

5 WRITE (6, 1000)

READ(5,*)ITP,ITS

TP=1.0/SIN(FLOAT(ITP)*. 0174533)

TS=1.0/SIN(FLOAT( ITS)*. 0174533)

WRITE(6,1010)

DO 10 1=1,

WRITE(6,1020)I,IELE(I)

READ(5,*)ISR(I)

CALL ATNUM(IELE(I),IZ(I))

CALL CHAWV(CL{I,1),IELE(I),ISR(I))

CALL ABSEDG(CL(I,2),IELE(I),ISR(I))

CALL YIELD(Y,IELE(I),ISR(I))

CALL JUMRAT(RJM,IELE(I),ISR(I))

CL(I,3)=Y*RJM

CL(I,4)=1.0

IF(K1.NE.1)CALL AFI0X(CL(I,4) ,IELE(i) ,NE(I) ,NO(I)

)

IE(I)=IELE(I)

10 CONTINUE

C

WRITE (6, 1022)

READ(5,1024)KK2

CALL TUBCAT

IF(K1.EQ.3)CALL APAFD

IF(K1.EQ.3) RETURN

DO 170 11=1,

IF(K1.EQ.1.AND.KK2.EQ.'Y •) WRITE (6, 1030) IDTUBE,VOLT,ITP, ITS, + IELE(II),IZ(II)

IF(K1.EQ.2.AND.KK2.EQ.'Y ')WRITE(6, 1040) IDTUBE,VOLT,ITP, ITS, + IELE(II),NE(II),NO(II),IZ(II)

IF(KK2.EQ.'Y •)WRITE(6,1050) (IZ(I) ,I=1,N)

IF(K1.EQ.1.AND.KK2.EQ.'Y ') WRITE (6, 1060) (lELE(I) ,I=1,N)

IF(K1.EQ.2.AND.KK2.EQ.'Y ') WRITE (6, 1070) (lELE(I) ,NE(I) ,NO(I)

,

19
+ I=1,N)

DO 15 J=l,4

Z=CL(1,J)

CL(1,J)=CL(II,J)

CL(II,J)=Z

15 CONTINUE

NAM»IE(1)

IE(1)»IE(II)

IE(II)«=NAM

DO 20 1=1,

N

A1(II,I)=0.0

A2(II,I)=0.0

A3(II,I)=0.0

DO 20 J=1,N

AIJK{II,I,J)=0.0

20 CONTINUE

C

ICAS=1

N2=N

30 IF(ICAS.EQ.2)N2=N-1

DO 110 M=2,N2

DO 35 J=l,4

Z=CL(2,J)

CL(2,J)=CL(M,J)

CL(M,J)=Z

35 CONTINUE

NAM=IE(2)

IE(2)=IE(M)

IE(M)=NAM

M1=M+1

IF(ICAS.EQ.1)M1=N

DO 100 NW=M1,N

IF(ICAS.EQ.1)G0T0 40

DO 38 J=l,4

Z=CL(3,J)

CL{3,J)=CL(MM,J)

CL(MM,J)=Z

38 CONTINUE

NAM»IE(3)

IE(3)»IE(MM)

IE(^^l)=NAM

40 CONTINUE

C

IF(ICAS.EQ.1)N5=2

IF(ICAS.EQ.2)N5=3

DO 50 J=1,N5

IF(K15.EQ.1)UC0(J)='MU('0 •,CL(J,1))

IF(K15.EQ.2)UCO(J)=MAC('0 ' ,CL(J,1))

DO 50 K=1,N5

IF(K15.EQ.1)UC(J,K)=MU(IE(J),CL(K,1))

IF(K15.EQ.2)UC(JrK)=MAC(IE(J),CL(K,l))

50 CONTINUE

11=1

12=4

IF(ICAS.EQ.2)I1=5

IF(ICAS.EQ.2)I2=5

DO 90 1=11,12

SW1=0.0

SWDB1(1)=0.0

KK5=1

IF(IDTUBE.EQ.'CR'.AND.IE(1).EQ.'CR')KK5»2

IF(IDTUBE.EQ.'CR'.AND.IE(1).EQ.'MN»)KK5«2

K12=0

DO 60 K=1,ND

20
IF(XINT(1,K).GT.CL(1,2))G0T0 70

CALL BDC0EF(SW,SWEB,SWL0I,I,XINT(1,K) ,XINT(2,K) ,K1,KK5,K15,K12)

SW1=SW1+SW

SWDB1(1)=SWDB1(1)+SWDB(1)

60 CONTINUE

70 DO 80 K«l,ll

IF(XINTl(l,K).EQ.0.0)GOTO 80

IF(XINri(l,K).GT.CL(l,2))G0TO 80

CALL BDC0EF(SW,SWDB,SWL0I,I,XINT1(1,K),XINT1(2,K),K1,KK5, + K15,K12)

SW1=SW1+SW

SWDBl ( 1

) =SWDB1 ( 1 ) +SWDB ( 1

)

80 CONTINUE

C

G(I)»(SW1/SWCB1(1)-1.0)/C(I,2)

90 CONTINUE

C

IF(ICAS.EQ.1)GOTO 100

AIJK{II,MM,M)=(G(5)*C(5,2)-ALFA(M)*C(5r2)-ALFA(MM)*C{5,3))

+ /(C(5,2)*C(5,3))

DO 95 J=l,4

Z=CL(MM,J)

CL(Wi,J)»CL{3,J)

CL(3,J)=Z

95 CONTINUE

NAM»IE{MM)

IE(MM)»IE(3)

IE(3)»NAM

100 CONTINUE

C

IF(ICAS.EQ.2)G0T0 110

IF(K1.EQ.1)A1{II,M)=<3(3)

IF(K1.EQ.2)A1(II,M) = (G(1)*C(2,2)-G(2)*C(1,2))/(C(2,2)-

+ C(l,2))

IF(K1.EQ.1)A2(II,M)=G(1)-G(3)

IF(K1.EQ.2)A2(II,M)=(G(2)-G(1))/(C(2,2)-C(1,2))

IF(K1.EQ.1)A3(II,M)=(G(1)-G{2))/(G(2)-G(3))-1.0

IF(K1.EQ.2)A3{II,M)=0.0

ALFA{M)=G(4)

110 CONTINUE

IF(ICAS.EQ.2)G0T0 120

IF(N.EQ.2)G0T0 120

DO 118 1=3,

11=1-1

DO 115 J»l,4

Z=CL(I1,J)

CL(I1,J)=CL(I,J)

CL(I,J)=Z

115 CONTINUE

NAM»IE(I1)

IE(I1)»IE(I)

IE(I)=NAM

118 CONTINUE

ICAS-ICAS+1

GOTO 30

C

120 IF(II.EQ.1)G0T0 150

DO 140 J-2,II

JJ«J-1

2=A1(II,JJ)

A1(II,JJ)»A1(II,J)

A1(II,J)=Z

Z-A2(II,JJ)

A2(II,JJ)»A2(II,J)

21
A2(II,J)=Z

Z=A3(II,JJ)

A3(II,JJ)=A3(II,J)

A3(II,J)=Z

DO 130 1=2,11

11=1-1

Z=AIJK(II,I1,J)

AIJK(II,I1,J)=AIJK(II,I,J)

AIJK(II,I,J)=Z

130 CONTINUE

DO 140 1=2,

Z=AIJK(II,I,JJ)

AIJK(II,I,JJ)=AIJK(II,I,J)

AIJK(II,I,J)=Z

140 CONTINUE

150 CONTINUE

C

IF(KJ<2.EQ.'N ')GOTO 170

WRITE(6,1080)(A1(II,J),J=1,N)

WRITE(6,1090) (A2(II,J) ,J=1,N)

IF(K1.EQ.1)WRITE(6,1100) (A3(II,J) ,J=1,N)

IF(K1.EQ.1)WRITE(6,1110)IZ(1) ,IELE(1) ,AIJK(II,1,1)

IF(K1.EQ.2)WRITE(6, 1120) IZ(1),IELE(1),NE(1),N0(1),AIJK(II, 1,1)

DO 160 J=2,N

NA=J-1

IF(K1.EQ.1)WRITE(6,1130)IZ(J),IELE(J),(AIJK(II,J,K),K=1,NA)

IF(K1.EQ.2)WRITE(6,1140)IZ(J),IELE(J),NE(J),NO(J), + (AIJK(II,J,K),K=1,NA)

150 CONTINUE

C

N2=N-1

IF(N2.LT.3)GOTO 170

DO 168 1=3, N2

11=1-1

DO 165 J=l,4

Z=CL(I1,J)

CL(I1,J)=CL(I,J)

CL(I,J)=Z

165 CONTINUE

NAM=IE(I1)

IE(I1)=IE{I)

IE(I)=NAM

168 CONTINUE

170 CONTINUE

190 RETURN

950 FORMATdX,' INPUT MEAN CONCENTRATIONS (WEIGHT FRACTION) OF ANALYT

+ES IN THE SPECIMENS TO BE ANALYZED: '

)

960 F0RMAT(3X,'I=',I2,4X,A2,I1,1H0,I1,4X,$)

1000 FORMAT (IX, 'FOR SAMPLE GEOMETRY, INPUT INCIDENCE & EMERGENCE ANGL

+ES (DEGREE-XX): ' ,$)

1010 FORMATdX,' INPUT THE CHARACTERISTIC LINE NUMBER YOU WISH TO MEAS

+URE (1-KA, 2-KB, 3-LAl, 4-LBl, 5-LB2);')

1020 FORMATdX, 'Is', 12, 4X,A2,4X,$)

1022 FORMATdX, 'DO YOU WANT TO PRIOT OUT CALCULATED ALPHA COEFFICIENT

+S(Y/N): ",$)

1024 FORMAT (Al)

1030 F0RMAT(1H1,//,41X," BASIC ALPHA COEFFICIENTS FOR USE IN COLA

+EQUATICNV/58X, ' (ELEMENTAL SYSTEM) ' ,////, + 55X,' TARGET: • ,A2,2X,F5.1,' KV' ,/, + 55X,'GE0METOY: ',12, ',',12,' DEGREES',///,

+ 58X,' ANALYTE: ' ,A2,1X,' (',12,' )

' ,//)

1040 FORMAT (1H1,//,41X,' HYBRID ALPHA COEFFICIENTS FOR USE IN COLA

+ EQUATIONV/58X,' (OXIDE SYSTEM)',////,

+ 55X,' TARGET: ' ,A2,2X,F5.1,' KV' ,/,

22
«• 55X, 'GEOMETRY: M2,',M2,' DEGREES',///,

». 56X,' ANALYTE: ' ,A2,I1,'0' ,I1,1X,' (' ,12, ') ' ,//)

1050 F0RMAT(16X,16(5X,I2,1X),/)

1060 FORMAT(/17X,16(4X,A2,2X),/)

1070 F0RMAT(/18X,16(2X,A2,I1,'0',I1,1X),/)

1080 F0RMAT(/11X,'A1',4X,12F8.3)

1090 FORMAT (/11X,'A2',4X,12F8. 3)

1100 F0RMAT(/11X,'A3',4X,12F8.3)

1110 FORMAT (/5X, 'AUK ' ,I2,1X,A2,1X,F8.3,1X)

1120 FORMAT (/2X,'AIJK ' ,I2,1X,A2,I1,'0' ,I1,1X,F8.3,1X)

1130 P0RMAT(/11X,I2,1X,A2,1X,12F8.3)

1140 F0RMAT(/8X,I2,1X,A2,I1,'0',I1,1X,12F8.3)

END

23
SUBROUTINE APAFD

C

C THIS SUBROUTINE PERFORMS MOST OF THE CALCULATION FOR

C OBTAINING THE ALPHA COEFFICIENTS USED IN FUSED DISC

C SYSTEM.

C

C NBS 04-SEP-84

C

REAL MAC,MU

DIMENSION CAM (12) ,UC0(12) ,UCF(12) ,SWDB1(12) ,XINT(2,300)

,

+ XINT1(2,11) ,UC(12,12) ,IELE(12) ,NE(12) ,N0(12) ; + C(5,3) ,CL(12,4) ,IE(12) ,A1(12,12) ,A2(12,12)

DIMENSION SWDB(12) ,IZ(12)

COMMON Kl 5 , Kl , N , lELE , NE , NO , KK2 , CAM ,11, ITP, ITS

COMMON /C0ESUB/A1,A2

COMMON /TUBE1/XINT,XINT1,ND

COMMON /TUBE2/IDTUBE,V0LT

COMMON /BDSUB/TP,TS,C,CL,IE,UC,UC0,N5,UCF,CA,CB,F,CL0I

COMMON /WFRA/WLI,WB,WO,WF

DATA CL0I/.25/

N5=N

WRITE(6,190)

READ(5,*)K12

GL=0.

WRITE(6,180)

180 FORMAT (• GRAMS OF SAMPLE :',$)

READ ( 5

, * ) GS

WRITE(6,182)

182 FORMATC GRAMS OF LI2B407:',$)

READ(5,*)GF

IF(K12.EQ.l) GO TO 4

IF{K12.EQ.2) WRITE(6,184)

184 FORMATC GRAMS OF LIF:',$)

IF(K12.EQ.3) WRITE(6,186)

186 FORMATC GRAMS OF LIB02:',$)

READ(5,*)GL

4 CONTINUE

TWT=GF+GL

F=GS/{TWT+GS)

GO TO (6,7,8) ,K12

6 WLI=.0821

WB=.2557

WF=0.

WO=.6623

GO TO 9

7 WLI=(GF*.0821+GL*.2675)/TWT

WB=GF*.2557/TWT

WO=GF*.6623/TWT

WF=GL*.7325/TWT

GO TO 9

8 WLI=(GF*.0821+GL*.1395)/TWT

WB= (GF* . 2557+GL* . 2173 ) /TWT

WO=(GF*.6623+GL*.6432)/TWT

WF=0.

9 CONTINUE

IF(KK2.NE.'Y MGOTO 5 WRITE(6,192)IDTUBE,VOLT,ITP,ITS, ( IZ ( I )

, 1=1 ,N)

WRITE (6,194) (lELE(I) ,NE(I) ,NO(I) ,I=1,N)

WRITE(6,196) (CAM(I) ,I=1,N)

WRITE (6, 198)

5 DO 100 1=1,

24
CA=CAM(I)

CB=1.0-CA

DO 10 J=l,4

Z=CL(1,J)

CL(1,J)=CL(I,J)

CL(I,J)=Z

10 CONTINUE

NAM=IE(1)

IE(1)=IE(I)

IE(I)=NAM

C

DO 20 J=1,N

IF(K15.EQ.2) GO TO 15

C K15 EQUALS 1 UCO(J)=MU('0 ^CLCJ^D)

UCF(J)=WLI*MU{'LI' ,CL(J,1) ) +WB*

1 MU('B • ,CL(J,1))+W0*UC0(J)+WF*MU('F '^CLCJ^l))

GO TO 18

C K15 EQUALS 2

15 UCO{J)=MAC('0 •,CL(J,1))

UCF(J)=WLI*MAC('LI' ,CL(J,1) ) +WB*

IMACCB ' ,CL(J,1))+W0*UC0(J)+WF*MAC( 'F •,CL(J,1))

18 CONTINUE

SWDB1(J)=0.0

DO 20 K=1,N

IF{K15.EQ.1)UC(J,K)=MU(IE(J) ,CL(K,1) ) IF(K15.EQ.2)UC(J,K)=MAC(IE(J) ,CL(K,1))

20 CONTINUE

SW1=0.0

SWLOI1=0.0

KK5=1

IFdDTUBE.EQ.'CR' .AND. IE (1) . EQ. ' CR' ) KK5 = 2

IFdDTUBE.EQ. 'CR' .AND.IE(l) . EQ. ' MN ' ) KK5 = 2

DO 40 K=1,ND

IF(XINT(1,K) .GT.CL(1,2))G0T0 50

CALL BDC0EF(SW,SWDB,SWL0I,1,XINT(1,K) ,XINT(2,K) ,K1 , KK5, K15 , K12)

SW1=SW1+SW

SWL0I1=SWL0I1+SWL0I

DO 30 J=2,N

SWDB1(J)=SWDB1(J)+SWDB(J)

30 CONTINUE

40 CONTINUE

50 DO 70 K=l,ll

IF(XINT1(1,K) .EQ.0.0)GOTO 70

IF(XINT1 (1,K) .GT.CL(1,2) )GOTO 70

CALL BDC0EF(SW,SWDB,SWL0I,1,XINT1(1,K) ,XINT1{2,K) ,K1,KK5,

+ K15,K12)

SW1=SW1+SW

SWLOI 1=SWL0I 1+SWLOI

DO 60 J=2,N

SWDB1(J)=SWDB1(J)+SWDB(J)

60 CONTINUE

70 CONTINUE

C

A2(I,1)=0.0

DO 80 J=2,N

RA=CA*SWDB1 (J ) /SWl

A2(I,J)=(CA/RA-1.0)/CB

80 CONTINUE

A1(I,1)=(SW1*(1.0-F*CLOI)/SWLOI1-1.0)/CLOI

A1(I,2)=0.0

25
IFd.EQ.DGOTO 100

DO 90 J=2,I

JJ=J-1

Z=A2(I,JJ)

A2(I,JJ)=A2(I,J)

A2(I,J)=Z

90 CONTINUE

100 CONTINUE

C

IF(KK2.NE.'Y ') RETURN

DO 110 1=1,

WRITE (6, 200) IZ( I) ,IELE(I) ,NE (I ) ,N0 (I ) , Al (I , 1) , { A2 (I , J) , J=l ,N)

110 CONTINUE

IF(K12.EQ.1)WRITE(6,210)GS,GF

IF(K12.EQ.2)WRITE(6,220)GS,GF,GL

IF(K12.EQ.3)WRITE(6,230)GS,GF,GL

RETURN

190 FORMAT (IX, 'WHAT FLUX CONDITIONS DO YOU WISH :'/ + 3X,'1-SAMPLE + LI2B407',/

+ 3X,'2-SAMPLE + LI2B407 + LIF',/

+ 3X,'3-SAMPLE + LI2B407 + LIB02 ? ',$)

192 FORMAT (1H1,//36X,' MODIFIED ALPHA COEFFICIENTS FOR USE IN COLA EQ

+UATION'//57X,' (FUSED DISK SYSTEM)',////,

+ 55X,' TARGET: ' ,A2, 2X, F5. 1 ,

' KV ,/ + 55X, 'GEOMETRY: ',12, ',',12,' DEGREES',///,

+ 58X, 'MATRIX CONSTITUENTS ' //18X, 12 (6X, 12)

)

194 FORMAT (/15X,'L0I' , 3X, 12 ( 1X,A2, 1 1, IHO, 1 1, 2X)

)

196 FORMAT (/IX, 'MEAN CONC ,2X,' 25.00 ' , 12 (2PF6. 2, 2X) ) 198 FORMAT (/3X,'ANALYTE')

200 F0RMAT(/2X,I2,2X,A2,I1,1H0,I1,13F8.3)

210 FORMAT (/// IX,'* FUSED DISK :',F6.4,'G SAMPLE +',F6.4,'G LI2B407')

220 FORMAT (///' * FUSED DISK :',F6.4,'G SAMPLE +',F6.4,'G LI2B407 +',

+F6.4,'G LIF')

230 FORMAT (/// IX,'* FUSED DISK :',F6.4,'G SAMPLE +',F6.4,'G LI2B407',

+F6.4,'LIB02')

END

26
SUBROUTINE ATNUM(INAM,I2)

C

C THIS SUBROUTINE PROVIDES TOE ATOMIC NUMBER WHEN A

C CORRESPONDING ELEMEOT NAME IS GIVEN.

C

C NBS 04-SEP-1984

C

DIMENSION ID (94)

DATA ID/'H '/BE'/LI'^'BE'/B ','0 '^'N '/O '/F ', 1 *NE','NA'/HG%'AL\«SI%'P ' ,'S ' , 'CL' ,

' AR' , 'K '/CA',

1 "SC'TI'/V •/CR'/MN'/FE'/CO'/NI'/CU'^'ZN^'GA',

1 'GE'/ASS'SE'/BR'^'KR'/RB'/SR'/Y ',

1 «ZR\'NB'/MO'/TC'/RU'/RH','PD','AG'/CD','IN'/SN*,

1 *SB%''TE','I '/XE'/CS'/BA'/LA'/CE'r'PR'/ND'/PM',

1 •SM','EU','GD','TB','Dy','HO','ER','TM'/YB','LU','HF',

1 JTA'/W '/RE'/OS'/IR^'PT^'AU'r'HC'lL'/PB'/BI',

1 'PO'/AT'/RN'/FR'/RA'/AC'/TH'/PA'/U '/NP'/PU'/

DO 10 1=1,94

IF(INAM.EQ.ID(I)) GO TO 20

10 CONTINUE

WRITE(6,100)INAM

STOP

20 IZ=I

100 F0RMAT(/1X,' ERROR: ',A2,' IS NOT A CORRECT ELEMENT NAME AMONG 1 +H-94 PU.')

RETURN

END

SUBROUTINE CHAWV(WV,IELE, ISR)

C

C THIS SUBROUTINE PROVIDES CHARACTERISTIC LINE

C WAVELENGTHS (KA,KB,LA1,LB1,LB2) BY MEANS OF AN

C EMPIRICAL FIT. TOIS FIT IS NOT RECOMMENDED FOR

C LINES BELOW 1 KEV.

C

C NBS 04-SEP-1984

C

DIMENSION D1(5),D2{5),D3{5)

DATA Dl/-. 0199726, -.060101, -.123941, -.00322523, -.197431/

DATA 02/2.22412,2.52781,3.29533,2.48613,4.01718/

DATA D3/-5 . 1774 , -5 . 6437 , -9 . 75836 , -8 . 37742 , -1 1 . 3323/

CALL ATNUM(IELE,IZ)

ZI=IZ

ZL=ALOG{ZI)

WV=12 . 398/EXP (Dl ( ISR) *ZL*ZL+D2 ( ISR) *ZL+D3 ( ISR)

)

RETURN

END

27
SUBROUTINE ABSEDG (WV, lELE, ISR)

C

C THIS SUBROUTINE CALCULATES THE WAVELE^^GTH OF AN ABSORPTION

C EDGE FROM THE CHARACTERISTIC LINE V^VELENGTH.

C THIS EMPIRICAL FIT IS NOT RECOMMENDED BELOW 1 KEV.

C

C NBS 04=SEP-1984

C

DIMENSIC»I C1(3),C2(3),C3(3)

DATA CI/-. 0397931,-. 0865397,-^2283427/

DATA C2/2« 423000, 3. 323153, 4. 311724/

DATA C3/5, 509104, 10. 25054, 12.00253/

CALL ATNUMCIELE,IZ)

ZI»IZ

ZL=ALOG(ZI)

IF(ISR.EQ.1,0R.ISR.EQ.2)W^EXP(C1(1)*ZL*ZL+C2(1)*ZL-C3(1))

IF(ISR.EQ.3.0R.ISR.EQ.5)WV=EXP(C1(3)*ZL*ZL+C2{3)*ZL-C3(3))

IF(ISR.EQ.4)WV=EXP(C1(2)*ZL*ZL+C2(2)*ZL-C3(2))

W=12.398/WV

RETURN

END

SUBROUTINE JUMRAT (JUMP, lELE, ISR)

C

C THIS SUBROUTINE PROVIDES JUMP RATIOS (1-1/R)

C FOR K OR L III ABSORPTION EDGES.

C FROM REFERENCE: E.P.BERTIN, 'PRINCIPLES & PRACTICE OF

C X-RAY SPECTROMETRIC ANALYSIS' SECOND

C EDITION, 1975. P977-979

C

C NBS 04-SEP-1984

C

DIMENSION JKC94),X(94)

REAL JK,JL,JUMP

DATA JK/3*1.0, .970, o965, .959, .953, .948, .943, .937, .932, .927, + .921,. 916, .911,. 903,. 895,. 899,. 887,. 890,. 883,. 883,. 886, + .886, .884, .878, .881, .873, .874, .868, .865, .862, .861, .855, + .857, .858,. 854,. 858, .854,. 852,. 860,. 856,. 853,. 852,. 847, + .856,. 848,. 846,. 840,. 845,. 843,. 839,. 838,. 835,. 832,. 828, + .835,. 830,. 828,. 833,. 831,. 827,. 824,. 827,. 819,. 818,. 812, + .818,. 813,. 807,. 808,. 816,. 801,. 805,. 791,. 803,. 807,. 805, + .797,. 801 ^.795,. 791,. 788, 2*0.0,. 788, 3*0.0,. 772, 0.0, + .773, 0.0,. 779/

DATA JL/27*0.0, .639, .652, .824, .824, .825, .795, .782, .782^ .760, + ,763,. 744,. 752,. 748,. 735,. 728,. 722,. 708,. 731,. 706, + .690,. 692,. 693,. 673,. 660,. 664,. 650,. 653,. 649,. 648, + .632,, 635,. 629,. 624,. 630,. 627,. 633,. 630,. 631,. 636,. 650, + .659,. 637,. 611,. 618,. 586,. 615,. 618,. 626,. 605,. 581, + .620,. 590,. 583,. 600,. 591,. 572, 2*0.0,. 573, 3*0.0,. 581, + 0.0, ,562,0.0, .556/

CALL ATNUM(IELE,IZ)

IF ( ISR. EQ. 1 . OR. ISR. EQ. 2) JUMP^K ( IZ)

IF(ISR.EQ.3.0R.ISR,EQ,4.0R.ISR.EQ.5)JUMP=JL(IZ)

RETURN

END

28
SUBROUTINE YIELD (Y,IELE,ISR)

C

C TOE SUBROUTINE PROVIDES X-RAY FLUORESCENT YIELDS FOR K,

C L II OR L III SERIES LINES BY MEANS OF EMPIRICAL FITS.

C

C NBS 04-SEP-1984

C

CALL ATNUM(IELE,IZ)

ZI=IZ

ZLs=ALOG(ZI)

IF(ISR.EQ.3.0R.ISR.EQ.5)GOTO 10

IF(ISR.EQ.4)G0T0 20

CM1=(.015+.0327*ZI-6.4E-7*ZI**3)**4

Y=QM1/(1.0+OM1)

RETURN

10 0M1=(-.901+.0466*ZI-4.961E-4*ZI*ZI+2.296E-6*ZI**3)**4

Y=GM1/(1.0+QM1)

RETURN

20 OM1»(.491-.010*ZI+2.55E-4*ZI*ZI-9.20E-7*ZI**3)**4

Y=OM1/(1.0+OM1)

RETURN

END

SUBROUTINE AFIOX(A£OX,IELE,NE,NO)

C

C raiS SUBROUTINE CALCULATES TOE ATOMIC FRACTION OF TOE

C ANALYTE IN A DEFINED OXIDE.

C

C NBS 04-SEP-1984

C

CALL SBATWTCO ' ,AWO)

CALL SBA'IWT(IELE,AWE)

AFOX=AWE*FLQAT (NE)

AFOX=APOX/(APOX+WO*FLQAT(NO)

)

RETURN

END

29
SUBROUTINE BDCOE F ( SW , SWDB , SWLO I , I , WVl , WV2 , Kl , KK5 , Kl 5 , Kl 2

)

C

C THIS SUBROUTINE CALCULATES BETA AND DELTA COEFFICIENTS

C IN MODIFIED VERSION OF SHERMAN'S EQUATION AT A CERTAIN

C WAVELENGTH AND CORRESPONDING X-RAY TUBE SPECTRAL INTENSITY.

C

C NBS 31-OCT-1984

C

REAL MAC.MU

DIMENSION C(5,3) rCL(12,4) ,U(12) ,BETA(12) ,DELTA(12) ,UC(12,12) , + IE (12) ,UC0(12) ,UCF(12) , SWDB (12)

COMMON /BDSUB/TP,TS,C,CL, IE, UC, UC0,N5, UCF,CA, CB,F,CLOI

COMMON/WFRA/WLI,WB,WO,WF

IF(K15.EQ.2) GO TO 4 C K15 EQUALS 1 UO=MU('0 ',WV1)

UF=WLI*MU('LI' ,WI1)+WB*MU('B ' ,WV1 )+ WO*UO+WF*MU (' ',WV1)

GO TO 6

4 CONTINUE

C K15 EQUALS 2

UO=MAC('0 '^WVl)

UF=WLI*MAC('LI' ,WV1)+WB*MAC('B ' ,WV1 )+WO*UO+WF*MAC (

' F ',WV1)

6 CONTINUE

DO 10 J=1,N5

IF(K15.EQ.1)U(J)=MU(IE(J) ,WV1)

IF(K15.EQ.2)U(J)=MAC(IE(J) ,WV1)

10 CONTINUE

C

C CALCULATION OF BETA COEFFICIENTS

C 0.081 G/CM2 AL FILTER IS USED FOR ANALYTES CR & MN

C WHEN CR TARGET OF X-RAY TUBE IS EMPLOYED.

C

IF(KK5.EQ.2.AND.K15.EQ.1)WV2=WV2*EXP(-.081*MU('AL' ,WV1))

IF(KK5.EQ.2.AND.K15.EQ.2)WV2=WV2*EXP(-.081*MAC('AL' ,WV1))

DEN=CL ( 1 , 4

) * ( U ( 1) *TP+UC (1,1) *TS ) + ( 1 . 0-C L { 1 , 4 )) * ( UO*TP+UCO ( 1) *TS

)

W=U(1)*WV2/DEN

IF(KK5.EQ.2.AND.K15.EQ.1)WV2=WV2/EXP(-.081*MU('AL' ,WV1))

IF(KK5.EQ.2.AND.K15.EQ.2)WV2=WV2/EXP(-.081*MAC('AL' ,WV1))

IF (Kl . EQ. 3) PHIF= (UF*TP+UCF ( 1

) *TS ) /DEN-1 . IF(K1.NE.3)SBETA=0.0

N2 = 2

IF(K1.EQ.3)N2=1

DO 20 J=N2,N5

BETA(J)=(CL(J,4)*(U(J)*TP+UC(J,1)*TS)+(1.0-CL(J,4))*(UO*TP+

+ UC0(1)*TS) ) /DEN-1.

I F ( Kl . NE . 3 ) SBETA=SBETA+C ( I , J

) * BETA ( J

)

20 CONTINUE

C

C CALCULATION OF DELTA COEFFICIENTS

C

IF ( K 1 . NE . 3 ) SDE LTA=0 . DO 60 J=1,N5

IF(WV1.GT.CL(J,2) .0R.CL(J,1) .GT.CL (1 , 2) ) GOTO 40

IF(K1.EQ.3)G0T0 32

UE=0.0

UEI=0.0

UEJ=0.0

DO 30 L=1,N5

UE=UE+(CL(L,4)*U(L)+(1.0-CL(L,4))*UO)*C(I,L)*TP

UEI=UEI+(CL(L,4)*UC(L,1)+(1.0-CL(L,4))*UCO(1))*C(I,L)*TS

UEJ=UEJ+(CL(L,4)*UC(L,J)+(1.0-CL(L,4))*UCO(J))*C(I,L)

30
30 CONTINUE

GOTO 34

32 UE=((CL(1,4)*U(1)+(1.0-CL(1,4))*UO)*CA+(CL(J,4)*U(J)+(1.0-

+ CL(J,4))*U0)*CB)*TP

UE=F*UE+ (1 . 0-F) *UF*TP

UEI=((CL(1,4)*UC(1,1)+(1.0-CL(1,4))*UCO(1))*CA+(CL(J,4)*

+ UC(J,1)+(1.0-CL(J,4))*UCO(1))*CB)*TS

UEI=F*UEI+(1.0-F)*UCF(1)*TS

UEJ=(CL(1,4)*UC(1,J)+(1.0-CL(1,4))*UCO(J))*CA+(CL(J,4)*

+ UC(J,J)+(1.0-CL(J,4))*UCO(J))*CB

UEJ=F*UE J+ ( 1 . 0-F) *UCF ( J

34 T1=.5*CL(J,3)*CL(J,4)*UC(1,J)*U(J)/U(1)

T2= ( ALOG (1 . 0+UE/UE J) ) /UE

T3=(AL0G (1. 0+UEI/UEJ) ) /UEI

DELTA(J)=T1*(T2+T3)

GOTO 50

40 DELTA(J)=0.0

50 IF ( Kl . NE . 3) SDELTA=SDELTA+C ( I , J) *DELTA( J

60 CONTINUE

IF(K1.EQ.3)G0T0 70

SWDB ( 1

) =W* ( 1 . 0+SDELTA) / ( 1 . 0+SBETA)

RETURN

70 SW=W/(1.0+(1.0-F)*PHIF)

CF=(1.0-F)/(1.0-F*CLOI)

SWLOI=W/ ( 1 . 0+CF*PHIF)

DO 80 J=2,N5

SWDB(J)=W*(1.0+F*CB*DELTA(J))/(1.0+F*CB*BETA(J)+(1.0-F)*PHIF)

80 CONTINUE

RETURN

END

31
SUBROl/riNE TUBmT

C

C THIS SUBROUTINE PROVIDES TOE X-RAY TUBE SPECTRAL DISTRIBUTION

C NEEDED FOR QikLCULATING ALPHA COEFFICIENTS BY USING EITOER THE

C NBS ALGORITHM (M MEASURED DATA FROM THE LITERATURE.

C

C NBS 04-SEP-1984

C

DIMENSION XINT(2,300) ,IDLINE(4) ,DATTGT(2,11) ,DFSP(6)

+ XINri(2,ll)

COMMON K15

COMMON /TUBE1/XINT,XINT1,ND

COMMON /TUBE2/IDTUBE,V0LT,T0FAGL,WINTHI

DATA IDLINE/'KA','KB',"LA','LBV

WRITE (6, 100)

READ(5,*)K11

WRITE(6,105)

READ(5,125)KK11

WRITE(6,140)

READ(5,125)IDTUBE

WRITE(6,150)

READ ( 5 , * ) VOLT , TOFAGL,WINTOI

IF(K11.EQ.1)G0T0 10

WRITE(6,110)

READ(5,120)DFSP

WRITE(6,130)

READ(5,*)ND

OPEN (UNIT=3 ,NAME=DFSP,TYPE=' OLD*

READ(3,*,ERR=5) ( (XINT(I,J) ,J=1,ND) ,1=1,2) , ( (XINTl {I,J) ,J=1,11) , + 1=1,2)

5 CLOSE (UNIT=3)

GOTO 50

10 WRITE(6,160)

READ (5,*) EDGE

WVMIN=12.398/VOLT

ND=IFIX( (EDGE-WVMIN)/.02)+l

WV=WVMIN

XINT(1,1)=WVMIN

XINT(2,1)=0.0

DO 20 1=2, ND

WV=WV+.02

XINT(1,I)=WV

CALL CTNLIN(XINT(2,I),WV)

20 CONTINUE

CALL INFTGT(K12,IDLINE,DATTGT,IDTUBE)

DO 25 1=1,11

XINT1(1,I)=0.0

XINT1(2,I)=0.0

25 CONTINUE

DO 30 1=1,4

IF(IDLINE(I).EQ.' •)GOTO30

XINri(l,I)=DATTGT(l,I)

CALL CHALIN(CINT,DATTGT(1,I),IDLINE(I))

IF(IDLINE{I) .EQ.'LA')RLA=CINT

XINT1(2,I)=CINT*50.0

30 CONTINUE

IF(K12.EQ.1)GOTO 50

DO 40 1=5,11

IF(K12.EQ.2.AND.I.GT.8)GOTO 50

XIMri(l,I)=DATTGT(l,I)

CINT=RLA*DATTGT ( 2 , I) XINT1(2,I)=CINT*50.0

40 CONTINUE

32
50 IF(KK11.EQ.'N MGOTO 60

IF(K11.EQ.1)WRITE(6,180)

IF(K11.EQ.2)WRITE(6,190)

WRITE(6,200)IDTUBE,VOLT,TOFAGL,WINTHI,(XINT(1,I),XINT(2,I)

+ ,I=1,ND)

WRITE(6,210)((XINT1(I,J),J=1,11),I=1,2)

WRITE (6, 220)

60 RETURN

100 FORMAT (• WHICH X-RAY TUBE SPECTRAL DISTRIBUTION DO YOU PREFER:' + /3X, • 1-CALCULATED SPECTRUM FROM NBS ALGORITW ; 2-MEASURED SPE

+CTRUM ? ' ,$)

105 F0RMAT(1X,'D0 YOU WANT TO PRINT OUT THE SPECTRAL DISTRIBUTI(»I(Y/

+N) ? ',$)

110 FORMAT (' INPUT THE DATAFILE NAME OF X-RAY TUBE SPECTRUM (XXXXXX.X

+XX) : •,$)

120 FORMAT (6A4)

125 FORMAT (A2)

130 FORMATdX,' INPUT TOTAL NUMBER OF WAVELENGTH INTERVALS FOR CONTIN

+UUM (MAX.=300) : ' ,$)

140 FORMATdX,' INPUT NAME OF X-RAY TUBE TARGET (XX) :

' ,$)

150 FORMAT (• INPUT VOLTAGE (KV) , TAKE-OFF ANGLE OF X-RAY FROM TUBE TA

+RGET (DEGREE) , AND'/' WINDOW THICKNESS (ftl) OF X-RAY TUBE : ' ,$)

160 FORMATdX,' INPUT THE ENDING WAVELENGTH OF X-RAY TUBE SPECTOUM(AN

4GSTR0M) ! •,$)

180 FORMAT (1H1,////36X,' CALCULATED X-RAY TUBE SPECTRAL DISTRIBUTION

+ ' ,/47X, ' USING NBS ALGORITW

)

190 FORMAT (1H1,////,37X, 'MEASURED X-RAY TUBE SPECTRAL DISTRIBUTION + •) 200 FORMAT(//34X,' X-RAY TUBE TARGET: •,A2,4X,'KV: ',F5.1,4X,/, + 27X, 'TAKE-OFF ANGLE(DEGREE) :

' ,F4.1,4X,'BE WINDOW THICKNESS(^W)

:

+ ',F5.3,///,3X,'LAMDA(A)',5X,'I*.02A',4X,'LAMDA(A)',5X,

+ • I* .02A' ,4X, • LAMDA(A) ' , 5X, ,

' I*.02A' ,4X, ' LAMDA(A) ' , 5X, ' I*.02A'

,

+ 4X,'LAMDA(A)',5X,'I*.02A',//(1X,5(F9.4,2X,E12.4)))

210 FORMAT(///6X,'KA',10X,'KB',10X,'LA1',9X,'LB1',9X,'LB2',

+ 9X,'LB3',9X,'LB4',9X,'LG1',9X,'LG2',9X/LG3',9X/LL',//

+ 11(F10.4,2X)/11E12.4)

220 FORMAT (///)

END

33
SUBROUTINE CTNLIN{HINT,WV)

C

C THIS SUBROUTINE CALCULATES THE CONTINUUM INTENSITY OP THE X-RAY

C TUBE SPECmUM AT A GIVEN lAVELENGlH USING THE NBS ALGORITHM.

C (UNIT: PHOTONS/VE/STRD)

C

C NBS 04-SEP-1984

C

REAL MACMU

COWCN K15

COMMON /TUBE2/IDTUBE,VOLT,T0FAGL,WINTOI

WVMIN=12.398A0LT

TB=.185*WINTHI

R=.0174533*T0FAGL

CALL ATNUM(IDTUBE,IZ)

Z=FL0AT(IZ)

IF(K15.EQ,1)PSE=MU(IDTUBE,WV)*(WVMIN**(-1.65)-WV**(-1.65))/

+ SIN(R)

IF(K15.EQ. 2) PSE=MAC( IDTUBE,WV) * (WVMIN** (-1 .65) -WV** (-1 .65) )/ + SIN(R)

F=1.0+PSE*{1.0+(1.0+2.56E-3*Z**2)**(-1))/(1.0+2.56E3*WVMIN

+ *Z**(-2))/(.25*PSE+1.0E4)

HINT=2. 72E-6*Z* (WV/WVMIN-1 .0) *WV** (-2) *F** (-2) * + EXP(-.35*TB*WV**2.86)

RETURN

END

SUBROUTINE INFTGT (Kl , IDLINE,CATTGT, IDTUBE)

C

C THE SUBROUTINE PROVIDES THE DATA NEEDED

C FOR CALCULATING CHARACTERISTIC LINE INTENSITY

C OF AN X-RAY TUBE SPECTRUM.

C

C NBS 04-SEP-1984

C

DIMENSION IDLINE(4),IDrGT(7),CATrGT(2,ll)

DATA IDTGT/'SC','CR','MO','RH','AG*,'W ','AUV

Kl=2

IFdDTUBE.EQ.'SC* .OR. IDTUBE. EQ.'CR' .OR. IDTUBE. EQ.'M0')K1=1

IF(K1.EQ.1)IDLINE(3)»' ' IF(K1.EQ.1)IDLINE(4)=' • IF ( IDTUBE. EQ.'W ' .OR. IDTUBE. EQ.'AU') Kl=3

IF(K1.EQ.3)IDLINE(1)=' ' IF(K1.EQ.3)IDLINE(2)=' ' DO 10 1=1,7

IF(IDTUBE.EQ.IDTGT(I))G0TO 20

10 CONTINUE

WRITE (6, 100)

STOP

20 11=1

N1=2*I1-1

N2=N1+1

0PEN(UNIT=3,NAME='TGTWR.DAT' ,TYPE='OLD' ,ACCESS=' DIRECT'

+ MAXRBC=14,REC0RDSIZE»11)

READ(3'N1) (DATTGT(1,J) ,J=1,11)

READ(3'N2) (DATTGT(2,J) ,J=1,11)

CLOSE {UNIT=3)

RETURN

100 F0RMAT(/1X,'ERRER: THE NAME OF X-RAY TUBE TARGET YOU INPUT IS NO

+T CORRECT !'/3X,'IT SHOULD BE ONE OF THE SEVEN TARGETS: SC, CR, MO

+, RH, AG, W & AU.')

END

34
SUBRO/riNE CHALIN (ClirT,VN, IDLINE)

C

C TOIS SUBROUTINE CALCULATES TOE CHARACTERISTIC LINE INTENSITY

C OF AN X-RAY TUBE SPECTOUM USING THE NBS ALGORITHM.

C (UNIT: PHOTONS/E/STRD)

C

C NBS 24-JUL-1984

C

COMMON K15

CCMMON /'njBE2/IDTUBE,V0LT,T0FAGL,WINTOI

CALL ATOUM(IDTUBE,IZ)

Z=FLQAT(IZ)

IF(IDLINE.EQ.'KA')FZ»3.22E6/(9.76E4+Z**4)-.39

IF(IDLINE.EQ.'KB')FZ=5.13E5/(2.05E5+Z**4)-.014

IF(IDLINE.EQ.'LA')FZ«2.02E7/(2.65E6+Z**4)+.21

IF(IDLINE.EQ.'LB')FZ=1.76E7/(6.05E6+Z**4)-.09

U=WV*V0LT/12.398

R=EXP(-.5*((U-1.0)/(1.17*U+3.20))**2)

RATI0=R*FZ* (U*AL0G (U) /(U-1.0) -1.0)

CALL CTNLIN(HINT,WV)

CIMr=RATIO*HINr

RETURN

END

SUBROUTINE SBATWT(NAME,ATWT)

C

C TOIS SUBROUTINE PROVIDES TOE ATOMIC WEIGHT WHEN A

C CORRESPONDING ELEMENT NAME IS GIVEN.

C

C NBS 04-SEP-1984

C

DIMENSION AW (94)

DATA AW/1.00797,4.0026,6.939,9.0122,10.811,12.01115,14.0067,

1 15.9994,18.9984,20.183,22.9898,24.312,26.9815,28.086,30.9738,

1 32.064,35.453,39.948,39.102,40.08,44.956,47.90,50.942,51.996,

1 54.938,55.847,58.933,58.71,63.54,65.37,69.72,72.59,74.922,78.96,

1 79.909,83.80,85.47,87.62,88.905,91.22,92.906,95.94,98.0,101.07,

1 102.905,106.4,107.870,112.40,114.82,118.69,121.75,127.60,

1 126.904,131.30,132.905,137.34,138.91,140.12,140.907,144.24,147.0,

1 150.35,151.96,157.25,158.924,162.50,164.930,167.26,168.934,

1 173.04,174.97,178.49,180.948,183.85,186.2,190.2,192.2,195.09,

1 196.967,200.59,204.37,207.19,208.980,210.0,210.0,222.0,223.0,

1 226.0,227.0,232.038,231.0,238.04,237.0,242.0/

CALL ATOUM(NAME,IZ)

ATWr=AW(IZ)

RETURN

END

35
REAL FUNCTION MAC(INAM,WV)

C

C THIS SUBROOTINE GENERATES MASS ABSORPTION COEFFICIENTS

C AT A GIVEM VAVELENGTH FCR VARIOUS ELEMENTS ACCORDING

C TO HEINRICH.

C

C NBS 04-SEP-84

C

DIMENSION Cl(9) ,C2(9) ,C3(9) ,EC(9) ,CN(4) ,R(10)

DIMENSION D1(4),D2(4);D3(4)

D^TA CI/-. 0397931, -.0339160, -.0865397, -.2283427, 1.251788, + .8349031,. 4422173,. 2514096,. 2729506/

DATA 02/2.423000,2.825262,3.323153,4.311724,-7.837999, + -4. 149247, -.9792409,. 9319132,. 6889060/

DATA C3/5. 509104, 9. 035256, 10. 25054, 12. 00253, -11. 58026, + -3.338016,3.153478,8.035612,7.424300/

DATA CN(3),CN(4)/2.6,2.22/

DATA R/1. 0,1. 0,1. 17, 1.63, 1.0, 1.16, 1.4, 1.621, 1.783, 1.0/

DATA D1/-.2322294, -.2544711, .2562163, 1.359165/

DATA 02/4.070053,4.769245,1.15119,-9.492116/

DATA D3/-6. 220746, -10. 37878, -5. 684848, 18. 64081/

CALL ATNUM(INAM,IZ)

E=12.398/VIV

ZI=IZ

ZE^ALOG(ZI)

DO 10 1=1,9

EC(I)=EXP(C1(I)*ZL*ZL4C2(I)*ZL-C3(I))

10 CONTINUE

CN(1)=EXP(-.0045522*ZL*ZL-.0068535*ZL+1. 070181)

CN(2)=2.73

IF(IZ.LT.42)GOTO 20

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

20 CONTINUE

DO 40 M=l,10

IF(M.EQ.10)GOTO 30

IF(E.LT.EC(M))GOTO 40

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

C=EXP (Dl (MI) *ZL*ZL+D2 (MI) *ZL+D3 (MI) ) /R(M)

MAC=C*WV**CN(MI)

RETURN

40 CONTINUE

END

36
REAL Ell^C^ION MU(INAM,WV)

C

C THIS SUBROlfTINE GENERATES MASS ABSORPTION COEFFICIENTS AT

C A GIVEN WAVELENGTH FOR VARIOUS ELEMENTS ACCORDING TO

C LEROUX ALGORITm (1979 VERSION)

C

C ^BS 04-SEP-1984

C

IMPLICIT INTEGER (I, J)

IMPLICIT REAL (A-H,K-Z)

CALL ATNUM(INAM,IZ)

E=12.3981/WV

0PEN(UNIT=3,NAME»'MACPRM.I:AT' ,TYPE»'0LD' , ACCESS- 'DIRECT'

1 MAXREC=94,REC0RDSIZE=24)

READO'IZ) C,K,NKrEP,CKl,NCKl,Ll,NLl,L2,NL2,L3,NL3,Ml,M41,

1 M2,^f12,M3r^M3,M4,NM4,MS,^t15,Nl,^>ll

CLOSE (UNIT=3)

IF(E.GT.K) GO TO 30

IF(E.GT.U) GO TO 40

IF(E.GT.L2) GO TO 50

IF(E.GT.L3) GO TO 60

IF(E.GT.Ml) GO TO 70

IF(E.GT.M2) GO TO 80

IF(E.GT.M3) GO TO 90

IF(E.GT.M4) GO TO 100

IF(E.GT.M5) GO TO 110

IF{E.LT.N1) GO TO 120

MU=C*N1*WV**NN1

GO TO 150

30 IF(IZ.GT.57) GO TO 120

IF(E.LT.EP) GO TO 35

MU=C*K*WV**NK

GO TO 150

35 MU=CK1*WV**NCK1

GO TO 150

40 MU=C*L1*WV**NL1

GO TO 150

50 MU«C*L2*WV**NL2

GO TO 150

60 MU=C*L3*WV**NL3

GO TO 150

70 MU=C*M1*WV**NM1

GO TO 150

80 MU=C*M2*WV**NM2

GO TO 150

90 MU«C*M3*WV**NM3

GO TO 150

100 MU»C*M4*WV**^W4

GO TO 150

110 MU»C*M5*WV**W5

GO TO 150

120 MU"0.

150 RETURN

END

37
PROGRAM CALCOMP

C

C THIS IS A REVISION OF VERSION 1 OF A FUNDAMENTAL PARAMETER

C COMPUTER PR0GRW1 FOR CCBRECTION OF INTERELEMEWT EFFECTS FC»

C QUANTITATIVE X-RAY SPACTRCMETRY. TOE ORIGINAL PROGRAM WAS

C WRITTEN BY R.M.ROUSSEAU OF THE GEOLOGICAL SURVEY OF CANADA

C (GSC) AND CONTAINS THE PROGRATIS ALPHA AND CARECAL WHICH WERE

C EXTENSIVELY MODIFIED AT NBS. THE NBSGSC PROGRAM CONTAINS THE

C COMPREHENSIVE LACHANCE ALGORITHM (COLA) FOR CORRECTION OF INTERC ELEMENT EFFECTS.

C CALCO IS A REVISION OF ALPHA FOR CALCULATING TOEORETICAL ALPHA

C COEFFICIENTS, AND CALCCMP IS A REVISION OF CARECAL FOR CALCULAC TING COJCENTRATIC^IS IN ANALYTE SPECIMENS.

C

C OVERLAY STRUCTURE OF CALCOMP : C MAIN PROGRAM CALCOMP

C SUBROUTINE DATAIN,CALRI,GETERR,SVLSF2,SLE

C

* C AUTHORS: G.Y. TAO AND P.A. PELLA EATEs 07-SEP-1984

C CENTER FOR ANALYTICAL CHEMISTRY, NATIONAL BUREAU OF STANDARDS

C GAITHERSBURG MD 20899 U.S.A.

C AND R.M.ROUSSEAU

r. GEOLOGICAL SURVEY OF CANADA, OTTAWA, CANADA KlA-OES

C

C * GUEST RESEARCHER FROM SHANGHAI INSTITUTE OF CERAMICS,

C ACADEMIA SINICA, THE PEOPLE'S REPUBLIC OF CHINA

C

REAL IP(13),IX(20,13),IS(20,13)

DIMENSION IDATE(5) ,ITIME(4) ,A1(13,13) ,A2(12,12) ,A3(12,12)

+ AIJK(12,12,12),CS(20,13),CIM(13),SCI(13),CX(20,13),

+ TOT(20) ,CX1(20,13),RX(20,13),RX1(20,12)

DOUBLE PRECISION NQA(13) ,N0A1(13) ,NS(20) ,NX(20)

COMMON K1,N6,N,M,M1,K2,KK1,KK6

COMMON /DATSUB/CS,IS,IX,NS,IP

COftlCN /C0ESUB/A1,A2,A3,AIJK

COMMON /CALSUB/RX,RX1

COrWCN /GETSUB/NOA,NQA1,NX,CX,TOT

DATA KK6/'N '/

CALL DATE(IDATE)

CALL TIME(ITIME)

WRITE ( 6 , 500 ) IDATE, ITIME

WRITE{6,510)

READ(5,*)K1

CALL DATAIN

N2=N6-1

WRITE (6, 520)

READ(5,530)KK7

IF(KK7.EQ.'Y ' )WTRITE(6,540)

IF(KK7.EQ.'Y •)READ(5,*)D

I>=D*1.0E-6

IF(K2.EQ.2)GOT0 45

DO 40 1=1,

IF(KK1.EQ.'Y •)J7=0

DO 40 J=1,N6

DO 10 18=1,

IF(NQA(J).EQ.NQA1(I8))G0T0 20

10 CONTINUE

GOTO 30

20 IF(KK1.EQ.'Y •)J7=J7+1

IF(KK7.EQ.'Y •) IP(J)=IP(J)/(1.0-D*IP(J)

IF(KK7.EQ.'Y • ) IX(I,J)=IX(I,J)/(1.0-D*IX(I,J)

RX(I,J)=IX(I,J)/IP(J)

IF(KK1.EQ.'Y ')RX1(I,J7)=RX(I,J)

38
GOTO 40

30 RX(I,J)»IX(I,J)

40 CONTINUE

GOTO 55

45 IF(KK7.EQ.'N ^GOTO 50

DO 46 1=1,Ml

DO 46 J=1,N6

DO 46 18=1,

IF(NQA(J).EQ.NQA1(I8))IS(I,J)=IS(I,J)/(1.0-D*IS(I,J))

46 CONTINUE

DO 48 1=1,

DO 48 J=1,N6

DO 48 18=1,

IF(N0A(J).EQ.NQM(I8))IX(I,J)=IX(I,J)/(1.0-D*IX(I,J))

48 CONTINUE

50 CALL CALRI

55 WRITE(6,545)

DO 200 L=1,M

IF(KK1.EQ.'Y •)WRITE(6,550)NX(L),(NCA1(I),RX1(L,I),I=1,N)

IF(KK1.EQ.'N ')WRITE(6,550)NX(L),(NQA(I),RX(L,I),I=1,N)

DO 60 1=1, N6

CIM(I)=0.0

IF(RX(L,I) .LT.0.0)RX(L,I)=0.0

CX(L,I)=RX(L,I)

60 CONTINUE

Ll=l

65 DO 130 1=1, N6

IF(KK1.EQ.'N MGOTO 90

DO 70 18=1,

IF(NCIA(I).EQ.N0A1(I8))G0T0 90

70 CONTINUE

GOTO 130

90 SCI (I) =0.0

IF(ABS(CX(L,I)-CIM(I)).LE.0.0001)GOTO 130

CM=0.0

DO 100 19=1, N6

CM=CM4CX(L,I9)

100 CONTINUE

CM=CM-CX(L,I)

DO 110 J=1,N6

IF(K1.EQ.3)SCI(I)=SCI(I)+CX(L,J)*A1(I,J)

IF(K1.EQ.2)SCI(I)=SCI(I)-K:X(L,J)*(A1(I,J)+A2(I,J)*CM)

IF(Kl.EQ.l)SCI(I)=SCI(I)+CX(L,J)*(Al(I,J)+A2(I,J)*aV

+ (1.0+A3(I,J)*(1.0-CM)))

110 CONTINUE

IF(K1.EQ.3)G0T0 125

DO 120 J=1,N2

KK=J+1

DO 120 K=KK,N6

SCI(I)=SCI(I)+AIJK(I,K,J)*CX(L,J)*CX(L,K)

120 CONTINUE

125 CIM(I)=CX(L,I)

CX(L,I)=RX(L,I)*(1.0+SCI(I))

130 CONTINUE

DO 160 1=1, N6

IF(KK1.EQ.'N MGOTO 150

DO 140 18-1,

IF(NQA(I).EQ.NQA1(I8))G0T0 150

140 CONTINUE

GOTO 160

150 IF(ABS(CX(L,I)-CIM(I)).LE.0.0001)GOTO 160

GOTO 170

160 CONTINUE

GOTO 180

39
170 IF(L1.LE.10)L1=L1+1

IF(L1.LE.10)GOTO 65

IF(Ll.C?r.lO)PAUSE'NO. OF ITERATION > 10'

180 TOT(L)=0.0

DO 190 19=1, N6

CX1(L,I9)=CX(L,I9)*100.0

CX{L,I9)=AINT(1.0E4*CX(L,I9)+.5)/100.0

TOT(L) =TOT(L) +CX(L, 19)

190 CONTINUE

WRITE(6,560)L1,(NOA(I),CX1(L,I),I=1,N6)

WRITE (6, 570) TOT (L)

200 CONTINUE

WRITE(6,572) (NCIA(I) ,I=1,N6)

DO 210 L=1,M

WRITE(6,574)NX(L),T0T(L),(CX1(L,I),I=1,N6)

210 CONTINUE

Vv'RITE(6,580)

READ(5,530)KK5

IF(KK5.EQ.'Y •)CALL GETERR

IF(M1.EQ.1.0R.K2.EQ.1)GOTO 220

WRITE (6, 590)

READ(5,530)KK6

IF(KK6.EQ.'Y MGOTO 50

220 WRITE(6,600)

STOP

500 FORMAT (///IX, 'DATE: • ,5A2,6X, 'TIME: ' ,4A2/)

510 F0RMAT(1X,'WHAT TYPE OF UNKNOWNS DO YOU WISH TO ANALYZE :'/ + 3X, • 1-ELEMENT SYSTEM 2-OXIDE SYSTEM 3-FUSED DISK SYSTEM ? + '.$)

520 F0RMAT(1X,'D0 YOU WANT TO CORRECT INTENSITIES FOR DEAD TIME (Y/N

+) ? ',$)

530 FORMAT (Al)

540 FORMATdX,' INPUT THE DEAD TIME IN MICROSECONDS :

' ,$)

545 FORMAT (/• RESULTS OF LAST ITERATICN '/)

550 F0RMAT(/1X/SMP.N0.=' ,A8,2X,'R=' ,6(A8,F8.5,1X)/21X,6(A8,F8.5,

+ IX))

560 F0RMAT(13X,'L=M2,2X,'C=',6(A8,F7.3,1H%,1X)/21X,6(A8,F7.3,

+ 1H%,1X)/21X,A8,F7.3,1H%)

570 FORMAT (19X,'TOTAL=',F7. 2, 1H%/)

572 FORMAT (//45X,' TABULATION OF RESULTS (%)'//

+ 1X,'SMP.N0. TOTAL •,13A8)

574 F0RMAT(/1X,A8,1X,F7.2,13(F7.3,1X))

580 F0RMAT(///1X,'D0 YOU WISH TO COMPARE THESE RESULTS WITH OTHER P

+REVIOUSLY KNOWN VALUES FOR THESE SPECIMENS (Y/N) ? ' ,$)

590 FORMAT (//IX,' DO YOU WANT TO TRY ANOTHER TYPE OF CALIBRATION CURV

+E (Y/N) ? ',$)

600 FORMAT (///)

END

40
SUBROUTINE CATAIN

C

C MOST OF THE INPUT CATA REQUIRED EXDR CALCULATING CONCANTRATICWS

C IS HANDLED BY THIS SUBROUTINE.

C

C NBS 05-SEP-1984

C

REAL IP(13),IX(20,13),IS(20,13)

DIMENSION Al(13,13) ,A2(12,12) ,A3(12,12) ,AIJK(12,12,12)

,

+ NAMFIL(5),CS(20,13)

DOUBLE PRBCISICN N0A(13) ,NCIA1(13) ,NS(20) ,NX(20)

COMMON K1,N6,N,M,M1,K2,KK1

co^^lCN /datsub/cs,is,ix,ns,ip

COMMON /C0ESUB/A1,A2,A3,AIJK

COrtlON /GETSUB/N0A,N0A1,NX

WRITE(6,500)

READ(5,510)KK1

IF{KK1.EQ.'Y •)WRITE(6,520)

IF(KK1.EQ.'Y ')READ(5,*)N6,N,M

IF(KK1.EQ.'N •) WRITE (6, 530)

IF(KK1.EQ.'N •)READ(5,*)N,M

IF(KK1.EQ.'N ')N6=N

IF(KK1.EQ.'Y •)WRITE(6,540)

IF(KK1.EQ.'Y •)READ(5,550) (NQA(I) ,I=1,N6)

WRITE(6,560)

READ(5,550) (NOAl(I) ,I=1,N)

IF(KK1.EQ.'Y •)GOTO 20

DO 10 1=1, N6

N0A(I)=NQA1(I)

10 CONTINUE

20 WRITE (6, 570)

READ(5,*)K4

IF(K4.EQ.1)G0T0 30

WRITE (6, 580)

IF(K1.EQ.1)READ(5,*) ((A1(I,J) ,J=1,N6) , (A2(I,J) ,J=1,N6), + (A3(I,J),J=1,N6) ,((AIJK(I,J,K) ,K=1,N6) ,J=1,N6) ,I=1,N6)

IF(K1.EQ.2)READ{5,*)(A1(I,J) ,J=1,N6)

,

(A2(I,J) ,J=1,N6)

,

+ ((AIJK(I,J,K) ,K=1,N6) ,J=1,N6) ,I=1,N6)

IF(K1.EQ.3)READ(5,*) ( (A1(I,J) ,J=1,N6) ,I=1,N6)

GOTO 50

30 WRITE(6,590)

READ(5,600)NAMFIL

CALL ASSIGN(3,NAMFIL,10)

IF{K1.EQ.1)READ(3,*,ERR=40)

(A1(I,J) ,J=1,N6)

,

(A2(I,J) ,J=1,N6)

,

+ (A3(I,J) ,J=1,N6) , ((AIJK(I,J,K) ,K=1,N6) ,J=1,N6) ,I=1,N6)

IF(K1.EQ.2)READ(3,*,ERR=40)

(A1(I,J) ,J=1,N6) , (A2(I,J) ,J=1,N6)

,

+ ((AIJK(I,J,K) ,K=1,N6) ,J=1,N6) ,I=1,N6)

IF(K1.EQ.3)READ(3,*,ERR=40)((A1(I,J),J=1,N6),I=1,N6)

40 CALL CLOSE (3)

50 WRITE (6, 610)

READ(5,*)K2

IF(K2.EQ.2)WRITE(6,620)

IF(K2.EQ.2)READ(5,*)M1

IF(K2.EQ.2)GOTO 70

IF(KK1.EQ.'Y ')WRITE(6,630)

IF(KK1.EQ.'N •)WRITE(6,635)

DO 60 1=1, N6

DO 55 18=1,

IF(NCIA(I).EQ.N0A1(I8))G0T0 57

55 CONTINUE

GOTO 60

57 WRITE(6,640)NQA(I)

READ(5,*)IP(I)

41
60 CC»JTINUE

GOTO 100

70 WRITE (6, 650)

DO 80 1=1, Ml

WRITE (6, 660)

I

READ(5,670)NS(I)

80 CONTINUE

WRITE (6, 680)

DO 90 1=1,Ml

WRITE(6,690)I,NS(I)

READ(5,*) (CS(I,J) ,J=1,N6)

90 CONTINUE

IF(KK1.EQ.'Y •) WRITE (6, 695)

IF(KK1.EQ.'N •)WRITE(6,697)

DO 96 1=1, Ml

WRITE(6,690)I,NS(I)

READ(5,*) (IS(I,J) ,J=1,N6)

96 CONTINUE

100 WRITE(6,700)

DO 110 1=1 ,M

WRITE (6, 660)

I

READ(5,670)NX{I)

110 CONTINUE

IF(KK1.EQ.'Y •)WRITE(6,710)

IF(KK1.EQ.'N •)WRITE(6,720)

DO 120 1=1,

M

WRITE(6,690)I,NX(I)

READ(5,*) (IX(I,J) ,J=1,N6)

120 CONTINUE

RETURN

500 FORMAT(1X,'DO YOU WANT TO INPUT KNOWN CONCENTRATIONS OF UNANALYZ

+ED ELEMENTS (Y/N)? ' ,$)

510 FORMAT (Al)

520 FORMATdX,' INPUT N6 (NUMBER OF ALL CONSTITUENTS), N (NUMBER OF ANA

+LYTES) AND* /3X,'M (NUMBER OF SPECIMENS TO BE ANALYZED) :',10X,$)

530 FORMATdX,' INPUT N (NUMBER OF ANALYTES) & M(NUMBER OF SPECIMENS T

+0 BE ANALYZED) : ' ,$)

540 FORMATC INPUT NAMES OF CONSTITUENTS (XXXXXXXX) (MAX. =8/LINE) :'/)

550 FORMAT (8A8)

560 FORMATdX, 'INPin- NAMES OF ANALYTES (XXXXXXXX) (MAX.=8/LINE) : •/)

570 FORMATC DO YOU WANT TO INPl/T ALPHA COEFFICIENTS BY: 1-DATAFILE

+ 2-KEYBOARD ? ' ,$)

580 FORMATdX, 'TYPE IN THE ALPHA COEFFICIENTS :'/)

590 FORMATC X,'INPin' DATAFILE NAME OF ALPHA COEFFICIENTS (XXXXXX. XXX) + : ',$)

600 FORMAT (5A2)

610 FORMATC WHAT TYPE OF STANDARDS ARE AVAILABLE: 1-PURE STANDARDS

+ 2-MULTIELEMEWr STANDARDS ? ' ,$)

620 FORMAT(lX,'INPl/r Ml (NUMBER OF STANDARDS)' :

' ,$)

630 FORMATdX, 'INPl/r NET PURE INTENSITIES FOR EACH ANALYTE FOLLOWED

+BY A PERIOD AND'/3X,' ENTER 0.0 FOR EACH UNANALYZED ELEMENT:'/)

635 F0RMAT(1X,' INPUT NET PURE INTENSITIES FOR EACH ANALYTE FOLLOWED

+BY A PERIOD :•/)

640 FORMAT(2X,A2,4X,$)

650 FORMATdX, 'INPirr I.D. OF STANDARDS «=8 CHARACTERS) : V)

660 F0RMAT(2X,'I=',I2,4X,$)

670 FORMAT (A8)

680 FORMATC INPUT CONCENTRATIONS (WEIGHT FRACTION) OF STANDARDS :'/)

690 FORMAT(2X,'I=',I2,4X,A8,2X,$)

695 FORMATdX, 'INPin* NET INTENSITIES FOLLOWED BY A PERIOD FOR THE AN

+ALYTE ELEMENTS IN STANDARDS AND' /3X,' ENTER 0.0 FOR EACH UNANALYZED

+ ELEMENT:'/)

697 FORMATdX, 'INPUT NET INTENSITIES FOLLOWED BY A PERIOD FOR TOE AN

+ALYTE ELEMENTS IN STANDARDS :')

42
700 FORMAT(lX,'INPl/r I.D. OF SPECIMENS TO BE ANALYZED : '/)

710 FORMAT(lX,'INPLrr NET INTENSITIES FOR ANALYTES IN SPECIMENS AND'/

+3X,' ENTER CONCENTFiATIONS (WEIGHT FRACTION) FOR UNANALYZED ELEMENTS:

+• /)

720 FORMAT {' INPUT NET INTENSITIES OF SPECIMENS TO BE ANALYZED : '/)

END

43
suBRarriNE calri c

C TOIS SUBROUTINE CALCULATES RELATIVE INTENSITIES OF ANALYTE

C SPECIMENS USING MULTIELEMENT STANDARD (S) AND THE COLA

C EQUATION.

C

C NBS 05-SEP-1984

C

REAL IP1(20,13) ,IS(20,13) ,IP11(20,13) ,IPP(12) ,IP(13) ,IX(20,13)

DIMENSION SCI(13) ,CS(20,13) ,A1(13,13) ,A2(12,12) ,A3(12,12)

,

+ AIJK(12,12,12) ,RS(20,13) ,RS1(20,12) ,RX(20,13) ,RX1(20,12)

DOUBLE PRECISION NQA(13) ,NQA1(13) ,NS(20)

,

+ X(20) ,Y(20) ,S(3) ,A(12,3) ,AA(11,3)

COrtlON K1,N6,N,M,M1,K2,KK1,KK6

COMMON /DATSUB/CS,IS,IX,NS

COWCN /C0ESUB/A1,A2,A3,AIJK

COMMON /LSFSUB/X,Y

COWCN /CALSUB/RX,RX1

COMMON /GETSUB/NQA,NQA1

EC3UIVALENCE (X(l) ,IP11(1,1)) , (Y(l) ,IP11(1,3)) , (A{1,1) ,IP11(1,5)) + ,(AA{1,1),IP11(1,9)),(IP1,RX),(RS1,RX1)

IF(KK6.EQ.'Y MGOTO 210

N2=N6-1

DO 90 L=1,M1

IF(KK1,EQ.'Y •)J7=0

DO 90 1=1, N6

IF(KK1.EQ.'N MGOTO 30

DO 10 18=1,

N

IF(N0A(I).EQ.NQA1(I8))G0T0 20

10 CONTINUE

GOTO 90

20 J7=J7-t-l 30 SCI(I)=0.0

CM=0.0

DO 40 19=1, N6

CM=CJ1+CS(L,I9)

40 CONTINUE

CM=CM-CS(L,I)

DO 50 J=1,N6

IF(K1.EQ.3)SCI(I)=SCI(I)-K:S(L,J)*A1(I,J)

IF(K1.EQ.2)SCI(I)=SCI(I)+CS(L,J)*(A1(I,J)+A2(I,J)*CM)

IF(Kl.EQ.l)SCI(I)=SCI(I)+CS(L,J)*(Al(I,J)+A2(I,J)*aV + (1.0+A3(I,J)*(1.0-CM)))

50 CONTINUE

IF(K1.EQ.3)G0T0 70

DO 60 J=1,N2

KK»J+1

DO 60 K>KK,N6

SCI{I)=SCI(I)+AIJK(I,K,J)*CS(L,J)*CS(L,K)

60 CONTINUE

70 RS(L,I)=CS(L,I)/(1.0+SCI(I))

IF(RS(L,I).EQ.0.0)GOTD 80

IPl(L,I)aIS(L,I)/RS(L,I)

80 IF(KK1.EQ.'Y •)RS1(L,J7)-RS(L,I)

IF(KK1.EQ.'Y •)IP11(L,J7)»IP1(L,I)

90 CONTINUE

IF(KK6.EQ.«Y MCXDTO 160

WRI'n:(6,500)

READ(5,510)KK3

IF(KK3.EQ.'N •)GOT0 160

IF(KK1.EQ.'Y ') WRITE (6, 520) (NQAl(J) ,J=1,N)

IF(KK1.EQ.'N ')WRITE(6,520) (NOlA(J) ,J-1,N)

DO 100 1=1,Ml

44
IF(KK1.EQ.'Y •)WRITE(6,530)NS(I),(RS1U,J),J=1,N)

IF(KK1.EQ.'N •)WRITE(6,530)hB(I),(RS(I,J),J=l,N)

100 CONTINUE

IF(KK1.EQ.'Y •)J7=0

DO 140 1=1, N6

M11=M1

DO 110 18=1,

IF(NOA(I).EQ.NOM(I8))G0T0 120

110 CONTINUE

GOTO 140

120 IF(KK1.EQ.'Y •)J7=J7+1

IP(I)=0.0

DO 130 L»1,M1

IF(CS(L,I) .EQ.0.0)K11»1

IF(CS(L,I) .EQ.0.0)M11=M11-1

IF(CS(L,I).EQ.0.0)GOTO 130

IP(I)=IP(I)+IP1(L,I)

130 CONTINUE

IF(K11.NE.1)IP(I)=IP(I)/FLQAT(M1)

IF(K11.EQ.1)IP(I)=IP(I)/FL0AT(M11)

IF(K11.EQ.1)K11=2

IF(KK1.EQ.'Y •)IPP(J7)=IP(I)

140 CONTINUE

IF(KK1.EQ.'Y •)WRITE(6,540) {NCAl(J) ,J=1,N)

IF(KK1.EQ.'N •) WRITE (6, 540) (NOA(J) ,J=1,N)

DO 150 1=1, Ml

IF(KK1.EQ.'Y •)WRITE(6,550)NS(I),(IP11(I,J),J=1,N)

IF(KK1.EQ.'N •)WRITE(6,550)NS(I) ,(IP1(I,J) ,J=1,N)

150 CONTINUE

IF(KK1.EQ.'Y •) WRITE (6, 555) (IPP(J) ,J=1,N)

IF(KK1.EQ.'N •)WRITE(6,555) (IP(J) ,J=1,N)

160 IF(M1.NE.1)G0T0 210

WRITE (6, 557)

K3=3

GOTO 215

210 WRITE(6,560)

READ(5,*)K3

215 IF(K3.EQ.1.0R.K3.EQ.3)N9=1

IF(K3.EQ.2.0R.K3.EQ.4)N9=2

WRITE(6,570)

READ(5,510)KK4

IF(KK1.EQ.'Y )J7=0

DO 270 L=1,N6

IF(KK1.EQ.'N MGOTO 240

DO 220 18=1,

IF(NCA(L).EQ.NOA1(I8))GOTO 230

220 CONTINUE

GOTO 270

230 J7-J7+1

240 DO 250 1=1, Ml

X(I)«IS(I,L)

Y(I)»RS(I,L)

250 CONTINUE

CALL SVLSF2(S,K3,N9,M1)

DO 260 1-1,3

A(L,I)»S{I)

IF(KK1.EQ.'Y •)AA(J7,I)=A(L,I)

260 CONTINUE

270 CONTINUE

DO 320 L»1,M

IF(KK1.EQ.'Y •)J7=0

DO 320 1=1,N6

IF(KK1.EQ.'N •)GOTO 300

DO 280 I8<>1,N

45
IF(N0A(I).EQ.NQA1{I8))G0T0 290

280 CONTINUE

GOTO 310

290 J7=J7+1

300 IF(IX(L,I).EQ.0.0)IX(L,I)=1.0E-20

RX(L,I)=A(I,1)+A(I,2)*IX(L,I)+A(I,3)*IX(L,I)*IX(L,I)

IFIKKI.EQ.'Y •)RX1(L,J7)^RX(L,I)

GOTO 320

310 IF(KKl.EQ.'y ')RX(L,I)=IX(L,I)

320 CONTINUE

IF(KK4.EQ.'N •)RETURN

WRITE(6,580)

DO 330 1=1, r.I IF(KK1.EQ.'¥ '|WRITE(6,590)NCIA1(I),(AA(I,J),J=1,3)

I?(KK1.EQ.'N ')WRITE(6,59Q)NQA(I) ,(A(I,J) ,J=1,3)

330 CONTINUE

RETURN

500 FORMAT (IX, 'DO YOU WANT TO PRINT OUT CALCULATED RELATIVE INTENSIT

+IES OF STANDARDS &V2X,' CALCULATED PURE INTENSITIES FROM STANDARD

+S (Y/N) ? ',$)

510 FORMAT (Al)

520 FORMAT (/IX,' CALCULATED RELATIVE INTENSITIES OF STANDARDS :

' ,/ + 19X,12ax,A8))

530 FORMATax/STDoKO.=',A8,2X,12(F8.5,lX))

540 FORMAT(/lX,'a»,LCULATED PURE INTENSITIES FROM STANDARDS : ' ,/ + 19X,12(1X,A8|)

550 FORMAT{lX,'S'ro.NO.=' ,A8,2X, 12F9.0)

555 FORMAT (/IX/ AVERAGE VALUES' ,4X,12F9.0)

557 FORMAT (/IX/ BECAUSE GtiLY ONE STANDARD IS AVAILABLE, THE ONLY CHO

+ICE FOR LSF CALIBRATION CURVE IS: Y=A1*X.')

560 FORMAT (/IX, 'WHAT TYPE OF LSF CURVES DO YOU WANT TO USE FOR CALIB

+RATION :' /3X,'(1) Y=A0+A1*X (2) Y=A0+A1*X+A2*X*X'

+ /3X,'{3) Y=A1*X (4) Y=A1«'X+A2*X*X ? ' ,$)

570 FORMATC DO YOU WANT TO PRINT OUT LSF COEFFICIENTS (Y/N) : ' ,$)

580 FORMAT (/15X,'TABULATICN OF CALCULATED LSF COEFFICIENTS',/

+ 19X,' (X=MEAS.INT. ; Y=CALC.REL. INT.) ' //)

590 FORMAT(lX,A8,2X,'A0=',E12.5,2X,'Al=',E12.5,2X,'A2=',E12.5)

END

46
SUBROUTINE GETERR

C

C THIS SUBROirriNE COMPARES RESULTS FROM COLA WITH OTHER

C PREVIOUSLY KNOMN VALUES.

C

C NBS 05-SEP-1984

C

DIMENSION acr(20,13) ,CX(20,13) ,TOTT(20) ,EA(13) ,ER(13)

,

+ DIF(20,13),Dira(20,13),TOT(20)

DOUBLE PRECISION NX(20) ,N0A(13) ,N0A1(13)

C0N4GN Kl,N6,N,M,Ml,K2,KKlrKK6

COMMON /GETSUB/NQA,NQA1,NX,CX,T0T

IF(KK6.EQ.'Y ')GOT0 45

WRITE (6, 500)

DO 10 1=1 ,M

WRITE(6,505)NX(I)

READ(5r*) (CXT(I,J) ,J=1,N6)

10 CONTINUE

20 DO 40 L=1,M

TOTr(L)=0.0

DO 30 1=1, N6

CXT(L,I)=AINT(1.0E4*CXT(L,I)+.5)/100.0

TOTT(L) =TOTr(L)+CXT(L, I) 30 CONTINUE

40 CONTINUE

45 DO 80 I=1,N6

EA(I)=0.0

ER(I)=0.0

IF(KK1.EQ.'N ')GOTO 60

DO 50 18=1,

N

IF(NCIA(I).EQ.N0A1(I8))G0T0 60

50 CONTINUE

GOTO 80

60 DO 70 L=1,M

DIF(L,I)=CX(L,I)-CXT(L,I)

IF(CXT(L,I) .EQ.O.O)Dire(L,I)=0.0

IF(CXT(L,I).EQ.0.0)GOTO 70

Dira(L,I)=100.0*DIF(L,I)/CXT(L,I)

EA(I)=EA(I)+ABS(DIF(L,I))

ER(I)=ER(I)+100.0*ABS(DIF(L,I))/CXT(L,I)

70 CONTINUE

EA(I)=EA(I)/FLOAT(M)

ER(I)=ER(I)/FLOAT(M)

80 CONTINUE

WRITE(6,510) (NOA(I) ,I=1,N6)

DO 90 L=1,M

WRITE(6,520)NX(L),T0TT(L),(CXT(L,I),I=1,N6)

WRITE(6,530)TOT(L) ,(CX(L,I) ,I=1,N6)

WRITE(6,540) (DIF(L,I) ,I=1,N6)

WRITE(6,550) (DIFR(L,I) ,I=1,N6)

90 CONTINUE

WRITE(6,560) (EA(I) ,I=1,N6)

WRITE(6,570) (ER(I) ,I«1,N6)

RETURN

500 FORMATdX,' ENTER KNOWN CONCENTRATIONS OF SPECIMENS :'/)

505 F0RMAT(1X,'SMP.N0.=',A8,2X,$)

510 FORMAT(//45X, 'TABULATION OF RESULTS (%)'// + IX/SMP.NO. TOTAL M3A8)

520 F0RMAT(/1X,A8,1X,F7.2,13(F7.2,1X))

530 FORMAT(10X,F7.2,13(F7.2,1X))

540 F0RMAT(9X,'ABS.ERR.M3{F7.2,1X))

550 F0RMAT(9X,'REL.ERR.M3(F7.2,1X))

560 P0RMAT(//5X,'AVG.ABS.ERR.M3(n.2,lX))

570 F0RMAT(5X,'AVG.REL.ERR.M3(F7.2,1X))

END

47
SUBROl/riNE SVLSF2(S,K1,N9,N)

C

C THE SUBROUTINE PERFORMS A LEAST-SQUARES FIT FOR

C SINGLE VARIABLE.

C

C NBS 24-MAY~1984

C

DIMENSION S(3) ,X(20) ,Y(20) ,A(3,4) ,T(5)

DOUBLE PRBCISICN S,A,X,Y,T1,T2,T,S1,S2,S3,V,U,P1

COMMON /LSFSUB/X,Y

N10=N9+1

Nll=N9+2

N12=N9*2+1

IF(K1.EQ.1.0R.K1.EQ.2)G0T0 15

T1=0.0

IF(K1.EQ.4)T2=0.0

S1=0.0

IF(K1.EQ.4)S2=0.0

IF(K1.EQ.4)S3=0.0

DO 10 1=1,

N

IF(X(I) .EQ.0.0)X(I)=1.0E-20

T1^1+X(I)*Y(I)

IF(K1.EQ.4)T2=T2+X(I)*X(I)*Y(I)

S1=S1+X(I)*X(I)

IF(K1.EQ.4)S2=S2+X{I)**3

IF(K1.EQ.4)S3=S3+X(I)**4

10 CONTINUE

IF(K1.EQ.3)S(1)=0.0

IF(K1.EQ.3)S(2)=T1/S1

IF(K1.EQ.3)S(3)=0.0

IF(K1.EQ.3)G0TO 70

N10=N10-1

N11=N11-1

A(1,1)=S1

A(1,2)=S2

A(1,3)=T1

A(2,1)=S2

A(2,2)=S3

A(2,3)=T2

GOTO 55

15 DO 30 1=1, N12

V=0.0

U=0.0

DO 20 J=1,N

IF(X(J) .EQ.0.0)X(J)=1.0E-20

P1=X(J)**(I-1)

U=U+P1

IF(I.GT.N10)GOTO 20

V=V+Y(J)*P1

20 CONTINUE

T(I)=U

IF(I.GT.N10)GOTO 30

A(I,N11)=V

30 CONTINUE

LL=0

DO 50 1=1, NIO

DO 40 J=1,N10

A(I,J)=T(J+LL)

40 CONTINUE

LL=LL+1

50 CONTINUE

55 CALL SLE{S,A,N10)

IF(K1.EQ.1)S(3)=0.0

48
IF(K1.EQ.4)G0T0 60

GOTO 70

60 N10=N10+1

N11=N11+1

S(3)=S(2)

S(2)=S(1)

S(1)=0.0

70 RETURN

END

SUBROUTINE SLE(S,A,N)

C

C THIS SUBROl/riNE IS USED TO SOLVE

C SIMULTANEOUS LINEAR EQUATIONS

C

C NBS 22-MAY-1984

C

INTEGER P,Q,0

DIMENSION A(3,4),S(4),0(3)

DOUBLE PRECISION A,E,S,R

N1=N+1

DO 220 1=1,

N

P=I

0=1

E=A(I,1)

DO 120 J=I,N

DO 100 K=1,N

IF(ABS(A(J,K)).LE.ABS(E))GOTO 100

E=A(J,K)

Q=K

P=J

100 CONTINUE

120 CONTINUE

IF{ABS(E).GT.1.0E-30)GOTO 140

C THE LARGEST ELEMENT IS EQUAL TO ZERO

VvKITE(6,260)

STOP

C TO CHANGE P-TH RCW WITH I-TH ROW

140 DO 160 K=1,N1

S(K)=A(I,K)

A(I,K)=A(P,K)

A(P,K)=S(K)

160 CONTINUE

C TO ZERO OUT Q-TH COLUMN

DO 200 J=1,N

IF(J.EQ.I)GOTO 200

IF(A(J,Q).EQ.0.0)GOTO 200

R=A(J,Q)/A(I,Q)

DO 180 K=1,N1

A(J,K)=A(J,K)-A(I,K)*R

180 CONTINUE

200 CONTINUE

0(I)=Q

220 CONTINUE

DO 240 1=1,

N

Q=0(I)

S(Q)=A(I,N1)/A(I,Q)

240 CONTINUE

RETURN

260 FORMAT (/IX,' NO UNIQUE SOLUTION')

END

49

Appendix 2: Description of Symisois and Permanent Datafiies

2.1 List of Symbols and Variables in CALCO

(1) Main Program CALCO

Variable Names

Aid, J)

A2(I,J)

A3(I,J)

AIJK(I,J,K)

IDATE(5)

lELE(I)

ITIME(M)

K1

K15

KK1

N

NAMFIL(5)

NE(I)

NO(I)

Common Symbols

«1

«2

«ijk

ALFA(I) «i

C(5,3) Ci

CAM(I)

CL(I,4) A,-

Remarks

Coefficient of element J on element I Coefficient of element J on element I Coefficient of element J on element I Cross coefficient of elements J and K on element I Date from computer's real-time clock

Chemical symbol of analyte I Time from computer's real-time clock

Optional switch for analyzing: (1) element or

(2) oxide or (3) fused disc system

Optional switch for choosing: (1) Leroux or

(2) Heinrich algorithm for calculating mass absorption coefficients

Optional switch for creating datafile for

saving calculated alpha coefficients

Number of analytes

Datafile name for saving alpha coefficients

Number of the element atoms in the defined

oxide formula for analyte I

Number of oxygen atoms in the defined oxide

formula for analyte I

(2) Additional Variables in ALPHA

^i' ^i.ab'

(o.Ml-t/T,.

)

G(5)

ICAS

Coefficient a^. when C^ = 0.3, Cj = 0.7

Concentration of hypothetical standards used

to calculate alpha coefficients in element or oxide systems

Mean concentration of analyte I in sample for

fused disc system

Calculated wavelength of analyte line and

its corresponding absorption edge., and

product of fluorescent yield and jump ratio

and atomic fraction of element I in its oxide

Expression (Cj^/R^-1 )/Cj

Switch for calculating a^^ or o,^.^

51
IDTUBE

IE(I)

ISR(I)

IIP *1 ITS ^2

IZ(I) Z K12

KK2

KK5

MAC UiCx)

MU Ui(X)

N5,NAM

RJM 1-1/Y

SW,SW1, SWDB

SWDB1 ,SWLOI

TP CSC f^

TS CSC f2

UC(I,J) Ui(Xj)

UCO(J) Uo(^j)

VOLT

XINT(2, 300)

XINT1(2 ,11)

y (0

z

Chemical symbol of x-ray tube target

Intermediate variable

Analyte line number d'K^^, 2-Kg, S-L^^^^ , '^"^61'

5-Lg2)

X-ray incidence angle

X-ray emergence angle

Atomic number of analyte I Optional switch used for different fused disk

conditions: (1) Sample* LI2BM07; (2)

sample+ LI2B407+ LIF; (3) sample+LiB02.

Optional switch for printing out calculated

alpha coefficients

Switch for using AL filter when analyzing Cr

and Mn with Cr X-ray tube

Real function for calculating mass absorption

coefficients with Heinrich algorithm

Real function for calculating mass absorption

coefficients with Leroux algorithm

Intermediate Variables

Jump Ratio

Intermediate Variables

Intermediate Variables

Cosecant of incident angle ^.^ Cosecant of emergence angle ^2

Mass absorption coefficient of element I at

wavelength \s

Mass absorption coefficient of oxygen at

wavelength, \s

Voltage (KV) used in X-ray tube

Wavelength and intensity of X-ray tube

continuum

Wavelength and intensity of X-ray tube

characteristic lines

X-ray fluorescent yield

Intermediate variable

(3) Additional Variables in APAFD

CA

CB

Concentration C^^ used for fused disc system

Concentration C^ used for fused disc system

52
CLOI

F

RA

UCF(J)

W

WV1

WV2

CI NT

DATTGT(2,11)

'DFSP(6)

EDGE

IDLINE(4)

K11

KK11

ND

RLA

R

Loss of Ignition treated as a concentration

Ratio of sample to fused disk weight

Calculated relative intensity

Mass absorption coefficient of flux at

wavelength A

(4) Additional Variables in BDCOEF

BETA(I) eij(Xk)

CF

DELTA(I) «ij(^k)

DEN,PHIF,SBETA

SDELTA,T1,T2,,T3

U(I) yi(Ak)

UE,UEI,UEJ

UF UF^^k)

UO uo^^k)

^k

Io(^k)AX

Intermediate variables

Ratio of flux to fused disk weight

Intermediate variables

Intermediate variables

Intermediate variables

Mass absorption coefficient of element I at

wavelength \^

Intermediate variables

Mass absorption coefficient of flux at

wavelength A]^ Mass absorption coefficient of oxygen at

wavelength \^

Intermediate variable

Wavelength of primary spectrum

Integral intensity of primary spectrum at

wavelength A|^

(5) Additional Variables in TUBDAT

Calculated intensity of characteristic line

emitted from X-ray tube with NBS algorithm

Wavelength and intensity ratio of each

L-series characteristic line to that of L^i

line

Dataflle name of x**ray tube spectrum

Ending wavelength of primary spectrum

Symbols of characteristic lines K^^, Kg, L^, L^ Optional swtich for choosing: (1) calculated

or (2) measured primary spectrum

Optional switch for printing out data of

primary spectrum used

Number of wavelength intervals (.02A) between

wavelengths WVMIN and EDGE

Calculated intensity of L^^ line emitted from

x**ray tube

53
TOFAGL

WINTHI

WV

WVMIN

F

HINT

PSE,TB

R

Z

FZ,R,U

RATIO

IDTGT(7)

C1(9), C2(9),

C3(9)

CN(il) Hi

D1(^),D2(14),D3(^)

E

ED(9)

INAM

MI

<|> Take-off angle in x-ray tube

Window thickness of x-ray tube

X A given x-ray wavelength

^min Short wavelength limit of x-ray tube at a given voltage

(6) Additional Variables in CTNLIN

Intermediate variable

IqAX Integral intensity of primary spectrum

Intermediate Variables

CSC (}) Cosecant of take-off angle in x'^ray tube

Conversion of IZ from integer to real mode

(7) Additional Variables in CHALIN

Intermediate Variables

Calculated ratio of intensity of

characteristic line to that of the

corresponding continuum from x-ray tube

(8) Additional Variables in INFTGT

Chemical symbols of seven commonly used X'^ray

tube targets

(9) Additional Variables in MAC

Coefficient in the expresion:

Pi(X) = Ci * X"i

Coefficients for computing the absorption edge

energies

The value of n in the above expression

Coefficients for computing the necessary value

of C

Energy of the wavelength WV

Eab Energy of each absorption edge

Chemical symbol of a given element

Number for selecting the proper coefficient

for computing C

54
M_ MI M_^ MI

1 1 6.3

2 2 7 3

3 2 8 3

M 2 9 3

5 3 10 4

R(10) Energy Jump for each edge ZI

Conversion of IZ from integer to real mode

ZL LN(Z) Logarithm of ZI

(10) Additional Variables in MACFUN

C Coefficient in the expression:

yi(X) = CiEi,ab ^"^

CK1 Coefficient in the expression:

yi(X) = Cik X"i

EP Energy edge

K,L1,L2,L3 Energy of each absorption edge

Ml ,M2,M3,M4, ,M5, Energy of each absorption edge

Nl

NCK1 ,NK,NL1 ,NL2, The value of n in the above expression

NL3

NM1 ,NM2,NM3,NM4, The value of n in the above expression

NM5,NN1

(11) Additional Variables in AFIOX

AFOX Atomic fraction of a given element in its

oxide

AWE Atomic weight of a given element

AWO Atomic weight of oxygen

(12) Additional Variables in ABSEDG

CI (4),C2(4),C3('4) Coefficients for computing the absorption edge

energies

WV Xab Wavelength of absorption edge

(13) Additional Variables in CHAWV

D1 (6),D2(6),D3(6) Coefficients for computing the characteristic

line wavelength

WV Wavelength of characteristic line

55
WV Wavelength of characteristic line

(U) Additional Variables in JUMRAT

JKO'I) Jump ratios for the absorption edge K

JL(94) Jump ratios for absorption edge L

JUMP 1-1 /Y Jump ratio at a given absorption edge

(15) Additional Variables in Yield

0M1 Intermediate variable

Y 0) X-ray fluorescence yield

(16) Additional Variable in ATNUM

ID(9M) Chemical symbols of the element (1*^94)

(17) Additional Variables in SBATWT

AW(9^) Atomic weight of the elements (1-94)

ATWT Atomic weight of a given element

NAME Chemical symbol of a given element

56
Aid, J) ai

A2(I,J) a2

A3(I,J)

""S AIJKd.J.K) o'ijk

CS(M1,I)

s

CX(M,I)

X

CX1(M,I)

X

Ci

2.2 List of Symbols and Variables in CALCOMP

( 1 ) Main Program

Variable Names Common Symbols Remarks

Coefficient of element J on elanent I Coefficient of element J on elanent I Coefficient of elanent J on elaiient I Cross coefficient of elements J and K on element I CIM(I) Intermediate concentration during interation

process

CM Concentration Cm = 1-Cj^ = Z Cj

Concentration of standard

Concentration calculated or fixed for

unknown

Concentration calculated or fixed for

unknown

D Dead time

IDATE(5) Date from computer's real-time clock

IP(I) li Intensity of pure elanent I

s IS(M1,I) Ij^ Intensity of standard

ITIME(4) Time from computer's real'^time clock

X

IX(M,I) Ij^ Intensity of unknown

K1 Optional switch for analyzing (1) element or

(2) oxide, or (3) fused disk system

K2 Optional switch for using (1) pure or

(2) multielement standard

KK5 Optional switch for obtaining error message

KK6 Optional switch for trying another type of

calibration

KK7 Optional switch for dead time correction

M Number of unknown (s)

Ml Number of standard(s)

N Number of analytes

N6 Number of all constituents

57
RX(M,I)

X

Hi

RX1 (M,I)

X

SCKI)

TOT(M)

NOA(I) Chemical symbols of constituents

NOAI(I) Chemical symbols of analytes

NS(I) Identification of standar(l(s)

NX(I) Identification of unknownCs)

Calculated relative intensity of unknown

Calculated relative intensity of unknown

Sum of terms afj Cj and afji^ Cj C^. Sum of concentrations calculated for unknown

(2) Additional Variables in DATAIN

KM Optional switch for inputting coefficients by

(1) datafile or (2) key-in on keyboard

KK1 Optional switch for using fixed concentrations"

NAMFIL(5) Datafile name of ALPHA coefficients

(3) Additional Variables in CALRI

A(I,3) Calibration coefficient obtained with least

squares fitting of R^ versus I^

i i AA(I,3) Calibration coefficient obtained with least

squares fitting of R^ versus I^

i i IP1(M1,I) Calculated pure intensity from standard

IP11(M1,I) Calculated pure intensity from standard

IP (I) Average of calculated pure intensity from

standards

IPP(I) Average of calculated pure intensity from

standards

KB Optional switch for choosing a certain type of

least squares fit for calibration:

(1) Y=A0+A1^fX; (2) Y=A0+A1 *X+A2*X*X;

(3) Y=A1*X; (4) Y=A1^fX+A2*X*X

KK3 Optional switch for printing out calculated

relative intensity of standard and pure

intensity calculated from standard

KK4 Optional switch for printing out calibration

coefficient

N9 Fitting exponent of least squares

s RS(M1,I) Ri Calculated relative intensity of standards

58
RS1(M1,I)

S(3)

X(20)

Y(20)

CXT(M,I)

DIF(M,I) A.R

DIFR(M,I) E.R

EA(I)

ER(I)

TOTT(M)

Calculated relative intensity of standards

Coefficients of least squares fit

Independent variables in least squares fit

Dependent variables in least squares fit

(4) Additional Variables in GETERR

True concentration of unknowns

Absolute error of calculated concentration for

unknowns

Relative error of calculated concentration for

unknowns

Average of absolute error of calculated

concentration for unknown

Average of relative error of calculated

concentration for unknown

Sum of true concentration for unknown

Program

CREMAC

RECREMAC

WRTTGT

REWRTTGT

2.3 Description of Permanent Datafiles

Function Remarks

Create the datafile of

MACPRM.DAT

Print out the

contents of the

dataf ile

MACPRM.DAT

Create the datafile of

TGTWR.DAT

Print out the

contents of the

datafile

TGTWR.DAT

Storing the parameters needed for computing

mass absorption coefficients with the Leroux

algorithm

For user to check if the contents of the

datafile MACPRM.DAT are correct

Storing the wavelengths and intensity ratios

of L-series lines to La line for seven types

of x-ray tube targets

For user to check if the contents of the

datafile TGTWR.DAT are correct

59
3.1 A is an example of the analysis of Cr-FE-NI ternary alloys where the

measured W target X-ray tube spectral data at 45 kV [11] were used. A datafile named SDXT75.W45 was created before running the program CALCO. The program CALCO printed out calculated alpha coefficients, and could be saved, if

desired, in a datafile if the answer to step 6 (figure 3) is 'Y'. An example

of how to input the calculated alpha coefficients is given in 3. IB where only

one multielement standard was employed.

3.2A is an example of the analysis of high temperature alloys using a CR

target X-ray tube spectral data at 45 kV calculated from the NBS algorit+un.

The calculated alpha coefficients were saved in the datafile called

ALL0Y2,C45. In 3. 23, unknowns were analyzed where Cr, Mn, Fe, Ni, Cu, and

Mo, were treated as the analytes, and C, Al, Si, V, Co, Nb are unanalyzed

elements whose concentrations were previously known and entered as fixed concentrations.

(3) Examples of the analysis of cement treated as an oxide system are

shown in 3.3A and 3.3.B, where among 12 constituents AL203, SI02, K20, CAO,

TI02, MN203. and FE203 were the analytes, and the rest were entered as known

constituents. In example 3.3B, two different calibration curves were used to

obtain the concentrations of the unknown samples.

(4) Example 3.4A and 3.4B, illustrate the analysis of rock samples as

fused disc specimens. In this system, the alpha coefficients are computed at

an average composition level for the analyte in the range of interest. Also,

a choice of three flux conditions can be selected by the user.

60
Appendix 3: Examples for Alloy, Oxide, and Fused Samples

3.1 A Alpha Coefficient Calculation for Cr-Fe-Ni Alloy System Using

Measured X-ray Tube Spectral Distribution from the Literature

SRUN CALCO

»TE: 02-OCT-84 TIME: 15:39:03

WHICH SYSTEM DO YOU WISH TO ANALYZE: 1-ELEMENT SYSTEM 2-OXIDE SYSTEM 3-FUSED DISK SYSTtW ? 1 INPirr NUMBER OF Ar4ALYTES: 3 INPUT NAMES OF ANALYTES (XXS) » CR FE NX WHAT MASS ABS. COEP. ALGORITHM DO YOU WAOT TO USE : 1-LEROUX ALCXMHTW 2-HEINRICH AITXIRITHM ? 2 DO YOU WANT TO CREATE A CATAFILE FOR SAVING CALCULATED ALPHA COEFFICIENTS (Y/N)? N

FOR SAMPLE GEOMETRY, INPOT INCIDENCE & MERGENCE ANGLES (DEGREE-XX) : 63,33

INPUT TOE CHARACTERISTIC LINE NUWER YOU WISH TO MEASURE (1-KA, 2-KB, 3-LAl, 4-LBl, 5-LB2)

1= 1 CR 1 I» 2 FE 1 1= 3 NI 1 DO YOU WANT TO PRINT OUT CALCULATED ALPHA COEFFICIENTS (Y/N) : Y WHICH X-RAY TUBE SPECTRAL DISTRIBUTION DO YGU PREFER: 1-CALCULATED SPECTRUM FROM NBS ALGORITW ; 2-MEASURED SPECTRUM ? 2 DO YOU WANT TO PRINT OITT TOE SPECTRAL DISTRIBUTION (Y/N) ? Y INPUT NAME OF X-RAY TUBE TARGET (XX) : W

INPUT VOLTAGE(KV) , TAKE-OFF ANGLE OF X-RAY FROM TUBE TARGET (DEGREE) , AND

WINDOW TOICKNESS(MM) OF X-RAY TUBE : 45.0,26.0,1.0

INPUT TOE DATAFILE NAME OF X-RAY TUBE SPECTRUM(XXXXXX.XXX) : SDXT75.W45

INPUT TOTAL NUMBER OF WAVELENGTO INTERVALS FOR CONTINUUM (MAX. =300) : 117

61
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62
BASIC ALPHA COEFFICIENTS FOR USE IN COLA EQUATION

(ELEMENTAL SYSTEM)

Al

A2

A3

AIJK 24 CR

26 FE

28 NX

24 26 28

CR FE NI

0.000 -0.107 0.025

0.000 -0.334 -0.328

0.000 0.696 0.261

0.000

0.000

0.000 0.384

TARGET: W 45.0 KV GEOMETRY: 63,33 DEGREES

ANALYTE: CR (24)

Al

A2

A3

AIJK 24 CR

26 FE

28 Nl

24 26 28

CR FE NI

2.197 0.000 -0.179

-0.197 0.000 -0.297

-0.756 0.000 0.588

0.000

0.000

-0.291 0.000

ANALYTE: FE (26)

ANALYTE: NI (28)

Al

A2

A3

AIJK 24 CR

26 FE

28 NI

24 26 28

CR FE NI

1.314 1.834 0.000

-0.178 -0.218 0.000

-0.689 -0.745 0.000

0.000

0.000

0.000 0.000

63
3. IB Calculated Compositions for Cr-Fe-Ni Alloys Using one Type Standard

$RUN CALCOMP

CATE: 02-OCT-84 TIME: 15:52:55

WHAT TYPE OF UNKNCWNS DO YOU WISH TO ANALYZE : 1-ELEMENT SYSTEM 2-OXIDE SYSTEM 3-FUSED DISK SYSTEM ? 1 DO YOU WANT TO INPITT KNOWN CONCENTRATIONS OF UNANALYZED ELEMENTS (Y/N)? N INPUT N(NUMBER OF ANALYTES) & M(NUMBER OF SPECIMENS TO BE ANALYZED) : 3,3

INPirr NAMES OF ANALYTES(XXXXXXXX) (MAX.=8/LINE) :

CR FE NI DO YOU WANT TO INPUT ALPHA COEFFICIENTS BY: 1-DATAFILE 2-KEYBOARD ? 2 TYPE IN THE ALPHA COEFFICIENTS :

0.0, -.107,. 025, 0.0, -.334, -.328, 0.0,. 696,. 261, 3*0. 0,3*0.0, 0.0,. 384, 0.0

2. 197, 0.0, -.179, -.197, 0.0, -.297, -.756, 0.0,. 588, 3*0. 0,3*0.0, -.291, 2*0.0

1.314, 1.834, 0.0, -.178, -.218, 0.0, -.689, -.745, 0.0, 3*0. 0,3*0.0,3*0.0 WHAT TYPE OF STANDARK ARE AVAILABLE: 1-PURE STANDARDS 2-MULTI ELEMENT STANDARDS ? 2 INPUT Ml (NUMBER OF STANDARDS) : 1 INPUT I.D. CF STANDARDS «=8 CHARACTERS) :

1= 1 5074 INPUT CONCENTRATIONS (WEIGHT FRACTION) OF STANDARDS :

1= 1 5074 .2525,. 6838,. 0498 INPUT NET INTENSITIES FOLLOWED BY A PERIOD FOR THE ANALYTE ELEMENTS IN STANDARDS : 1= i 5074 3258., 4522., 203.

INPirr I.D. CF SPECIMENS TO BE ANALYZED :

1= 1 5054

1= 2 5202

1= 3 5364 INPUT NET INTENSITIES OF SPECIMENS TO BE ANALYZED :

1= 1 5054 3348., 4^89.,^.

1= 2 5202 2784., 4480., 642.

1= 3 5364 3361. ,3179. ,1115. DO YOU WANT TO CORRECT INTENSITIES FOR DEAD TIME (Y/N) ? N DO YOU WANT TO PRINT OUT CALCULATED RELATIVE INTENSITIES OF STANDARDS & CALCULATED PURE INTENSITIES FROM STANDARDS (Y/N) ? Y

CALCULATED RELATIVE INTENSITIES OF STANDARDS : CR FE NI STO.NO.=5074 0.32018 0.45370 0.02079

CALCULATED PURE INTENSITIES FROM STANDARDS : CR FE NI STD.NO.=5074 10175. 9967. 9764.

AVERAGE VALUES 10175. 9967. 9764.

BECAUSE ONLY ONE STANDARD IS AVAILABLE, THE ONLY CHOICE FOR LSF CALIBRATION CURVE IS: Y=A1*X. DO YOU WANT TO PRINT OUT LSF COEFFICIENTS (Y/N) : Y

TABULATION OF CALCULATED LSF COEFFICIENTS

(X=MEAS.INT. ; Y=CALC.REL. INT.)

CR A0= O.OOOOOE+00 Al= 0.98276E-04 A2= O.OOOOOE+00

FE A0= O.OOOOOE+00 Al= 0.10033E-03 A2= O.OOOOOE+00

NI A0= O.OOOOOE+00 Al= 0.10242E-03 A2= O.OOOOOE+00

RESULTS OF LAST ITERATION

64
3. IB Calculated Compositions for Cr-Fe-Ni Alloys Using one Type Standard

(Continued)

SMP.NO.=5054 R=CR 0.32903 FE 0.47045 NI 0.00061

L= 6 C=CR

'lVrAL= 25.576%

97.80%

FE 72.0fi7% NI 0.150%

SMP.NO.=5202 R=CR 0.273^0 FE 0.44948 NI 0.06575

L= 6 C=CR

TOTAL=

21.744%

99.59%

FE 62.906% NI 14.938%

SMP.NO.=5364 R=CR 0.33031 FE 0.31895 NI 0.11419

U= 6 C=CR

iurAL=

28.179%

99.40%

FE 47.279% NI 23.943%

TABULATION OF RESULTf^ (%)

EWP.NO. TOTAL CR FE NI

5054 97.80 25.576 72.067 0.150

5202 99.59 21.744 62.906 14.938

5364 99.40 28.179 47.279 23.943

DO YOU WISH TO COMPARE THESE RESULTS WITH OTHER PREVIOUSLY KNOWN VALUES FOR THESE SPECIMENS

ENTER KNOWN CONCENTRATIOC OF SPECIMENS : (Y/N)

SMP.NO.=5054

SMP.NO.=5202

91P.N0.=5364

.2577,. 7250,. 001

.21 30,. 6303,. 1480

.2784,. 4721,. 2357

TABULATION OF RESULTS (%)

SMP.NO. TOTAL CR

5054

FE

5202

5364

NI

98.42 25.77 72.50 0.15

97.80 25.58 72.07 0.15

ABS.ERR. -0.19 -0.43 0.00

REL. ERR. -0.74 -0.59 0.00

99.13 21.30 63.03 14.80

99.59 21.74 62.91 14.94 ABS.ERR. 0.44 -0.12 0.14

REL. ERR. 2.07 -0.19 0.95

98.62 27.84 47.21 23.57

99.40 28.18 47.28 23.94 ABS.ERR. 0.34 0.07 0.37

REL. ERR. 1.22 0.15 1.57

AV3.ABS.ERR. 0.32 0.21 0.17 AVG.REL.ERR. 1.34 0.31 0.84

65
3.2A Calculation of Coefficients for High Temperature Alloys

SRUN CALCO

DME: 02-OCT-84 TIME: 16:01:18

WHiai SYSTEM DO YOU WISH TO ANALYZE: l-ELEMENT SYSTEM 2-OXIDE SYSTEM 3-FUSED DISK SYSTEM ? 1 INPirr NUMBER OF ANALYTES: 12

INPirr NAMES OF ANALYTES (XXS) : C AL SI V CR MN FE CO NI CU NB MO

WHAT MASS ABS. COEF. ALGORITHM DO YOU WANT TO USE : 1-LEROUX ALGORITHM 2-HEINRICH ALGORITHM ? 2 DO YOU WANT TO CREATE A a\TAHLE FOR SAVING CALCULATED ALPHA COEFFICIENTS (Y/N)? Y INPUT DATAFILE NAME OF ALPHA COEFFICIENTS(XXXXXX.XXX) : ALL0Y2.C45

FOR SAMPLE GEOMETRY, INPUT INCIDENCE & EMERGENCE ANGLES (DBGREE-XX) : 55,35

INPirr THE CHARACTERISTIC LINE NUMBER YOU WISH TO MEASURE (1-KA, 2-KB, 3-LAl, 4-LBl, 5-LB2)

1

11

11

1

11

11

11 DO YOU WANT TO PRINT OUT CALCULATED ALPHA COEFFICIENTS (Y/N) : Y WHICH X-RAY TUBE SPECTRAL DISTRIBUTION DO YOU PREFER: 1-CALCULATED SPECTRUM FROM NBS ALGORITIW ; 2-MEASURED SPECTRUM ? 1 DO YOU WANT TO PRINT OUT TOE SPECTRAL DISTRIBUTION (Y/N) ? Y INPUT NAME OF X-RAY TUBE TARGET (XX) : CR

INPirr VOLTAGE (KV), TAKE-OFF ANGLE OF X-RAY FROM TUBE TARGET ( DEGREE) , AND

WINDOW THICKNESS{MM) OF X-RAY TUBE : 45. 0,26.0,. 45 INPUT TOE ENDING WAVELENGTH OF X-RAY TOBE SPECTRUM (ANGSTROM) : 2.99

1= 1 C

1= 2 AL

1= 3 SI 1= 4 V

1= 5 CR

1= 6 MN

1= 7 FE

1= 8 CO

1= 9 NI 1=10 CU

1=11 NB

1=12 MO

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79
3.2B Calculated Compositions of High Temperature Alloys. (Six Analytes Plus

Known Concentrations of Minor Elements)

$RUN CALXrOMP

DATE: 03-OCT-84 TIME: 08:19:00

WHAT TYPE OF UNKNOWNS DO YOU WISH TO ANALYZE : 1-ELEMENT SYSTEM 2-OXIDE SYSTEM 3-FUSED DISK SYSTEM ? 1 DO YOU WANT TO INPITT KNOWN CONCENTRATIONS OF UNANALYZED ELEMENTS (Y/N) ? Y

INPirr N*; (NUMBER OF ALL CONSTITUENTS), N (NUMBER OF ANALYTES) AND

M(NUMBER OF SPECIMENS TO BE ANALYZED) : 12,6,4

INPirr NAMES OF CONSTITUENTS (XXXXXXXX)(M^X.=8/LINE) :

C AL SI V CR MN FE CO

NI CU NB MO

INPUT NAMES OF ANALYTES (XXXXXXXX) (MAX. =8/LINE) :

CR MN FE NI CU MO DO YOU WANT TO INPUT ALPHA COEFFICIENTS BY: 1-DATAFILE 2-KEYBOARD ? 1 INPl/T DATAFILE NAME OF ALPHA COEFFICIENTS (XXXXXX. XXX) : ALLOY2.C45 WHAT TYPE OF STANDARDS ARE AVAILABLE: 1-PURE STANDARDS 2-MULTI ELEMENT STANDARDS ? 2 INPirr Ml (NUMBER OF STANDARDS) : 5

INPirr I.D. OF STANDARDS (<=8 CHARACTERS) :

1= 1 C1151

1= 2 C1153

1= 3 C1285

1= 4 C1288

1= 5 C1289

INPUT CONCENTRATIONS (WEIGHT FRACTION) OF STANDARDS :

1= 1 C1151 .0004, 0.0, .0038, .0004, .2270, .0250, .6536, .0003, .0729, .0042, 0.0,. 0080

1= 2 C1153 .0026, 0.0, .0107, .0010, .1669, .0050, .7096, .0013, .0377, .0023, 0.0, .0024

1= 3 C1285 .0006, .0012, .0036, .0015, .0000, .0033, .9633, .0004, .0117, .0037, 0.0, .0016

1= 4 C1288 .0006, 0.0, .0041, .0009, .1955, .0083, .4155, .0010, .2930, .0372, .0022, .0283

1= 5 C1289 .0001, 0.0, .0016, .0001, .1222, .0035, .8172, .0004, .0413, .0021, .0010, .0082

INPin" NCT INTENSITIES FOLLOWED BY A PERIOD FOR THE ANALYTE ELEMENTS IN STANDARDS AND

ENTER 0.0 FOR EACH UNANALYZED ELEMENT:

1= 1 C1151 4*0. 0,16511. ,141. ,11810. ,0.0, 2892. ,211. ,0.0, 1248.

1= 2 C1153 4*0. 0,13016. ,29. ,14027. ,0.0, 3486. ,119. ,0.0, 294.

1= 3 C1285 4*0. 0,917. ,19. ,24913. ,0.0, 417. ,163. ,0.0, 239.

1= 4 C1288 4*0. 0,12598. ,46., 8736. ,0.0, 14190. ,2211. ,0.0, 4016.

1= 5 C1289 4*0. 0,10265. ,19. ,17093. ,0.0, 1552. ,102. ,0.0, 1220. INPUT I.D. OF SPETIMENS TO BE ANALYZED :

1= 1 C1152

1= 2 C1154

1= 3 1286

1= 4 C1287

INPUT NET INTENSITIES FOR ANALYTES IN SPECIMENS AND

ENTER CONCENTRATIONS (WEICm FRACTION) FOR UNANALYZED ELEMENTS:

.0015, 0.0,. 0080,. 0003, 13579., 54., 13316.,. 0022, 4367., 60., 0.0, 640. .0009, 0.0,. 0050,. 0014, 14272., 82., 12448.,. 0038, 5250., 207., 0.0, 78. .0020,. 0011,. 0013,. 0001, 1659., 8., 24071.,. 0012, 1014., 23.,. 0001, 504. .0036, .0006, .0166, .0009,16245. ,87. ,9578. , .0031,9088. ,329. ,.0007,723. DO YOU WANT TO CORRECT INTENSITIES FOR DEAD TIME (Y/N) ? N DO YOU WAOT TO PRIOT OUT CALCULATED RELATIVE INTENSITIES OF STANDARDS i, CALCULATED PURE INTENSITIES FROM STANDARDS (Y/N) ? Y

CALCULATED RELATIVE lOTENSITIES OF STANDARDS : CR MN FE NI CU MO

Sro.N0.=C1151 0.28026 0.02344 0.43075 0.02597 0.00167 0.00908

1= 1 C1152

1= 2 C1154

1= 3 1286

1= 4 C1287

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82
3.3A Calculation of Coefficients for Cement Samples as an Example of an Oxide System

SRUN CALCO

rv\TE: 03-OCr-84 TIME: 14:12:05

WHICH SYSTEM DO YOU WISH TO ANALYZE: 1-ELEMENT SYSTEM 2-OXIDE SYSTEM 3-FUSED DISK SYSTEM ? 2

INPITT NUMBER OF ANALYTES: 12 INPUT NAMES OF ANALYTES (XXNONS)

C 103 NA201 MGlOl AL203 31102 P 205 S 103 K 201 CAlOl TI102 MN203 FE203 WHAT MASS ABS. COEF. ALGORITHM DO YOU WAtTT TO USE : 1-LEROUX ALGORITIIM 2-HEINRICM ALGORITHM ? 2 DO YOU WANT TO CREATE A DATAEILE FOR SAVING CALCULATED ALPHA COEFf ICIEKKJ (Y/N)? Y INPUT lyi^TAFILE NAME Of ALPHA COEFFICIEWIS(XXXXXX.XXX) : 0XCEMT.C/J5 FOR SAMPLE GEOMETRY, INPUT INCIDENCE & EMERGENCE ANGLES (DEGREE-XX) : 55,35

INPUl' THE CHARACTERISTIC LINE NUMBER YCU WISH TO MEASURE (1-KA, 2-KB, 3-LAl, 4-LBl, 5- LB2)

1= 1 C 1 1= 2 NA 1 1= 3 MG 1 1= 4 AL 1 1= 5 SI 1 1= 6 P 1 1= 7 S 1 1= 8 K 1 1= 9 CA 1 1=10 TI 1 1=11 MN 1 1=12 FE 1 DO YOU WANT TO PRINT OITF CALCULATED ALPHA COEFFICIENTS(Y/N) : Y WHICH X-RAY TUBE SPECTRAL DISTRIBUTION DO YOU PREFER: 1-CALCULATED SPECTRUM FROM NHS ALGORITHM ; 2-MEASURED SPECTRUM ? 1: DO YOU WANT TO PRINT OUT TOE SPECTRAL DISTRIBUTION (Y/N) ? Y INPUT NAME OF X-RAY TOBE TARGET (XX) : CR

INPUT VOLTAGE (KV) , TAKE-OFF ANGLE OF X-RAY FROM TUBE TARGET (DEGREE) , AND

WINDOW •miCKNESS(W) OF X-IWY TUBE : 45.0,26.0, .45 INPUT THE ENDING WAVELENGTH OF X-RAY TOBE SPECTRUM (ANGSTROM) : 2.9956

83
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3.3B Calculated Compositions of Cement Samples Using Different

Calibration Curves

$RUN CALCOMP

DATE: 03-OCT-84 TIME: 13:35:08

WHAT TYPE OF UNKNOWNS DO YOU WISH TO ANALYZE : 1-ELEMENT SYSTEM 2-OXIDE SYSTEM 1-FUSED DISK SYSTEM ? 2 DO YOU WANT TO INPITT KNOVN CONCENTRATIONS OF UNANALYZED ELEMENTS (Y/N)? Y

INPirr N6 (NUMBER OF ALL CONSTITUENTS), N (NUMBER OF ANALYTES) AND

M(NUMBER OF SPECIMENS TO BE ANALYZED) : 12,8,2

INPUT NAMES OF CONSTITUENTS (XXXXXXXX) (MAX. =8/LINE) :

LOI NA20 MGO AL203 SI02 P205 SOB K20

CAO TI02 MN203 FE203

INPUT NAMES OF ANALYTES (XXXXXXXX) (MAX. =8/LINE) :

AL203 SI02 503 K20 CAO TI02 MN203 FE203

DO YOU WANT TO INPUT ALPHA COEFFICIENTS BY: 1-DATAFILE 2-KEYBOARD ? 1 INPUT DATAFILE NAME OF ALPHA COEFFICIENTS(XXXXXX.XXX) : OXCEMT.C45 WHAT TYPE OF STANDARDS ARE AVAILABLE: 1-PURE STANDARDS 2-MULTI ELEMENT STANDARDS ? 2 INPUT Ml (NUMBER OF STANDARDS) : 7 INPUT I.D. OF STANDARDS (<=8 CHARACTERS) :

1= 1 r,33 1= 2 634

1= 3 635

1= 4 636

1= 5 637

1= 6 638

1= 7 639 INPUT CONCENTRATIONS (WEIGHT FRACTION) OF STANDARDS :

1= 1 633 .0075, .0064, .0104, .0378, .2188, .0024, .0220, .0017, .6450, .0024, .0004, .0420

1= 2 634 .0162, .0015, .0330, .0521, .2073, .0010, .0221, .0042, .6258, .0029, .0028, .0284

1= 3 635 .0324, .0007, .0123, .0629, .1841, .0017, .0707, .0045, .5983, .0032, .0009, .0261

1= 4 636 .0116, .0011, .0395, .0302, .2322, .0008, .0231, .0059, .6354, .0010, .0012, .0161 1= 5 637 .0169, .0015, .0067, .0328, .2307, .0024, .0238, .0025, .6604, .0021, .0006, .0180

1= 6 638 .0095, .0013, .0383, .0445, .2140, .0006, .0234, .0059, .6209, .0025, .0005, .0355

1= 7 639 .0100,. 0065,. 0126,. 0428,. 2161,. 0008,. 0248,. 0006,. 6576,. 0032,. 0008,. 0240

INPUT I.D. OF SPECIMENS TO BE ANALYZED :

1= 1 BLACK

1= 2 WHITE

INPUT NET INTENSITIES FOR ANALYTES IN SPECIMENS AND

ENTER CONCENTRATIONS (WEIGHT FRACTION) FOR UNANALYZED ELEMENTS:

1= 1 BLACK .0139, .0028, .0269, 3669. ,18475. ,.0029, 9174. ,65774. ,144509. ,7806. ,97. ,20489.

1= 2 WHITE .0201, .0004, .0262, 3134. ,20372. ,.0009, 9955. ,82080. ,134125. ,6881. ,318. ,33818.

DO YOU WANT TO CORRECT INTENSITIES FOR DEAD TIME (Y/N) ? N DO YOU WANT TO PRIhTT OUT CALCULATED RELATIVE INTENSITIES OF STANDARDS & CALCULATED PURE INTENSITIES FROM CTANDARDS (Y/N) ? Y

CALCULATED RELATIVE INTENSITIES OF STANDARDS :

97
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3.4A Calculation of Coefficients for Fused Rock Samples

$RUN CALCO

DATE: 03-OCT-84 TIME: 08:45:48

WHICH SYSTEM DO YOU WISH TO ANALYZE: 1-ELEMENT SYSTEM 2-OXIDE SYSTEM 3-FUSED DISK SYGTf>l ? 3 INPin- NUMBER Of' ANALYTES: 12

INPirr NAMES OF ANALYTES (XXNONS)

:

NA201 MGlOl AL203 SI 102 P 205 S 103 K 201 CAlOl TI102 CR203 MNlOl FE203 WHAT MASS ABS. COEF. ALCORITJW DO YOU WANT TO USE : 1-LEROUX ALGORITW 2-HEINRICH ALGORlTtW ? 2 DO YOU WANT TO CREATE A DATAFILE FOR SAVING CALCULATED ALPHA COEFFICIENTS (Y/N)? Y

INPin" EATAFILE NAME OF ALPHA COEFFICIENTS(XXXXXX.XXX) : FDROCK.C60

INPUT MEAN CONCENTRATIONS (WEIGHT FRACTION) OF ANALYTES IN THE SPECIMENS TO BE ANALYZED:

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.40 FOR SAMPLE GEOMETRY, INPUT INCIDENCE 6 &1ERGENCE ANGLES (DBGREE-XX) : 55,35

INPITT THE CHARACTERISTIC LINE NUMBER YOU WISH TO MEASURE (1-KA, 2-KB, 3-LAl, 4-LBl, 5-LB2)

1= 1 NA201

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1=12 FE203 FOR SAMPLE GEOMI

INPITT THE CHARA(

1= 1 NA 1 1= 2 MG 1 1= 3 AL 1 1= 4 SI 1 1= 5 P 1 1= 6 S 1 1= 7 K 1 I» 8 CA 1 I« 9 TI 1 1=10 CR 1 I»ll 144 1 I»12 FE 1 DO YOU WANT TO PRINT OUT CALCULATED ALPHA COEFFICIENTS (Y/N) : Y WHICH X-RAY TVBE SPECTRAL DISTRIBUTION DO YOU PREFER: 1-CALCUUTED SPECTRUM FROM NBS ALGORITW ; 2-MEASURED SPECTRUM ? 1 DO YOU WANT TO PRINT OUT THE SPECTRAL DISTRIBUTION (Y/N) ? Y

INPUT NAME OF X-RAY TUBE TARGET (XX) : CR INPUT VOLTAGE (KV), T7VKE-0FF ANGLE OF X-RAY FROM TUBE TARGET (DEGREE) , AND

WINDOW TOICKNESS(MM) OF X-RAY TUBE : 60.0,26.0, .45 INPUT -niE ENDING WAVELENGTH OF X-RAY TUBE SPECTRUM (ANGSTROM) : 2.99

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3. MB Calculated Compositions of Fused Rock Samples

SHUN CALCOMP

DATE: 03-OCT-84 TIME: 10:07:34

WHAT TYPE OF UNKNOWNS DO YOU WISH TO ANALYZE : , 1-ELEMENT SYSTEM 2-OXIDE SYSTEf^ 3-FUSED DISK SYSTEM ? 3 DO YOU WANT TO INPUT KNOWN CONCENTT^ATIONS Ot' UNANALYZED ELEMENTS (Y/N) ? Y

INPirr N6 (NUMBER OF ALL CONSTITUENTS), N (NUMBER OF ANALYTES) AND

M(NUMBER OF SPECIMENS TO BE ANALYZED) : 13,8,5

INPOT NAMES OF CONSTITUENTS (XXXXXXXX) (MAX. =8/LINE) :

LOI NA20 MGO AL203 SI02 P205 SOB K20

CAO TI02 CR203 mO FE203

INPtrr NAMES OF ANALYTES(XXXXXXXX)(MAX.=8/LINE) :

NA20 MCX) AL203 SI02 K20 CAO TI02 FE203

DO YOU WANT TO INPITT ALPHA COEFFICIENTS BY: 1-DATAFILE 2-KEYBOARD ? 1 INPirr CATAFILE NAME OF ALPHA COEFFICIENTS (XXXXXX. XXX) : FDROCK.CiO WHAT TYPE OF STANDARDS ARE AVAILABLE: 1-PURE STANDARDS 2-MULTI ELEMENT STANDARDS ? 2 INPirr Ml (NUMBER OF STANDARDS) : 10 INPOT I.D. OF STANDARDS (<=8 CHARACTERS) :

1= 1 SI02

I* 2 BCS-309

1= 3 BCS-367

1= 4 BR

1= 5 NBS-77

1= 6 NIM-D

1= 7 NIM-P

1= 8 NIM-S

1= 9 NS-1

1=10 SCH-1

INPUT CONCENTRATIONS (WEIGHT FRACTION) OF STANDARDS :

1= 1 SI02 3*0.0, .0005, .9972, .0001, .0010, .0002, .0003, .0001, 0.0, .0001, .0005

1= 2 BCS-309 .0008, .0034, .0017, .6110, .3410, 2*0.0, .0046, .0022, .0192, 0.0, .0003, .0151

1= 3 BCS-367 0.0, .0044, .0710, .2000, .3440, .0014, .0094, .0117, .3240, .0075, 0.0, .0116, .0111

1= 4 BR .0317, .0307, .1335, .1025, .3839, .0105, .0004, .0141, .1387, .0261, .0006, .0020, .1290

1= 5 NBS-77 .0021,. 0006,. 0050,. 5939,. 3238,. 0045, 0.0,. 0211,. 0026,. 0293, 2*0.0,. 0090

1= 6 NIM-D . 0070, . 0004, . 4351, .0030, .3896, 0.0,. 0002, .OCOl,. 0028, .0002, .0042, .0022, .1700

1= 7 NIM-P .0034, .0037, .2533, .0418, .5110, .0002, .0002, .0009, .0266, .0020, .0350, .0022, .1264

1= 8 NIM-S .0031, .0043, .0046, .1734, .6363, .0012, .0001, .1535, .0068, .0004, 0.0, .0001, .0140

1= 9 NS-1 .0081, .0989, .0065, .2130, .5337, .0028, .0001, .0651, .0173, .0106, 0.0, .0019, .0420

1=10 SCH-1 .0295, .0003, .0003, .0096, .0811 , .0012, .0001 , .0003, .0004, .0005,0.0, .0100, .8706

INPirr NET INTENSITIES FOLLOWED BY A PERIOD FOR TOE ANALYTE ELEMENTS IN STANDARDS AND

ENTER 0.0 FOR EACH UNANALYZED ELEMENT:

1= 1 SI02 0.0, 7. ,0.0, 15. ,14373. ,2*0. 0,166. ,42. ,194. ,2*0. 0,25.

1= 2 BCS-309 0.0, 4., 7., 6369., 4083., 2*0. 0,2626., 210., 24736., 2*0. 0,920.

1= 3 BCS-367 0.0, 12. ,297. ,2022. ,4503. ,2*0.0, 7404. ,28386. ,7515. ,2*0. 0,491.

1= 4 BR 0. 0,64. ,574. ,955. ,4988. ,2*0. 0,8719. ,12693. ,30193., 2*0. 0,6''i04. 1= 5 NBS-77 0.0, 5. ,17. ,6183. ,3945. ,2*0. 0,12571. ,159. ,37519. ,2*0. 0,505.

1= 6 NIM-D 0.0, 2., 1888., 21., 4776., 2*0. 0,44., 288., 290., 2*0. 0,10281.

1= 7 NIM-P 0.0, 9., 1112., 384., 6548., 2*0. 0,537., 2480., 2422., 2*0. 0,7080.

1= 8 NIM-S 0.0, 6. ,21. ,1776. ,8658. ,2*0. 0,86602. ,537. ,506. ,2*0. 0,739.

1= 9 NS-1 0.0, 219. ,27. ,2178. ,6966. ,2*0. 0,38381. ,1417. ,12295. ,2*0. 0,2305.

1=10 SCH-1 0.0, 2. ,4. ,84. ,968. ,2*0. 0,235. ,71. ,738. ,2*0. 0,41013.

INPirr I.D. OF SPECIMENS TO BE ANALYZED :

1= 1 BX-N

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107

Appendix 4: Listing of Programs for Creating and Reading Permanent Datafiles

PR0GRM1 CREMAC

C

C THIS PRCGRAM CREATES A CATAFILE NAMED 'MACFRM.DAT'

C FOR SAVI^G PARAMETERS NEEDED FOR CALCULATING MASS

C ABSORPTION COEFFICIENTS WITO LEROUX ALG0RITW1.

C (1979 VERSION)

C

C NBS 06-SEP-1984

C

IMPLICIT INTEGER (I, J)

IMPLICIT REAI^ (A-H,K-Z)

OPEN (UNIT=3,NAME='MACFRM.I:AT' ,TYPE='NEW' ,ACCESS=' DIRECT'

,

1 MAXREC=94,RBC0RDSIZE=24)

DO 50 1=1,94

WRITE (6, 100)

READ(5,*)C,K,NK,EP,CK1,NCK1,L1,NL1,L2,NL2,L3,NL3,

1 Ml,tWl,M2,NM2,M3,NM3,M4,NM4,M5,NM5,Nl,NNl

WRITE(3'I) C,K,NK,EP,CK1,NCK1,L1,NL1,L2,NL2,L3,NL3,M1,M^1,M2,

1 ^M2,M3,^W3,M4,^M4,M5r^M5,Nl,NNl

50 CONTINUE

CLOSE (UNIT=3)

100 FORMAT (• Z=',I3)

END

PROGRAM RDCREMAC

C V C THIS PROGRAM PRINTS OUT THE CONTENTS OF THE

C DATAFILE NAMED 'MWCPRM.DAT* . C

C NBS 06-SEP-1984

C

IMPLICIT INTEGER (I, J)

IMPLICIT REAL (A—H K—Z)

OPEN (UNIT=3,NAME='MACPRM.I:AT' ,TyPE*'OLD' ,ACCESS=' DIRECT'

,

1 MAXREC=94,REC0RDSIZE=24)

DO 10 1=1,94

READ(3'I) C,K,NK,EP,CK1,NCK1,L1,NL1,L2,NL2,L3,NL3,M1,M>11,

1 M2,^W2,M3,NM3,M4,NM4,M5,NM5,N1,I*I1

WRITE(6,100) C,K,NK,EP,CK1,NCK1,L1,NL1,L2,NL2,L3,NL3,M1,IW1,

1 M2,M«12,M3,NM3,M4,NM4,M5,NM5,N1,I»I1

10 CONTINUE

CLOSE (UNIT=3)

STOP

100 P0RMAT(/1X,12F9.4)

END

109
PWGRP^^ WRTTGT

C

C THIS PROGRAM WRITES A DIRECT mTAFILE CALLED

C • TGTWR.DAT' TO PROVIDE INFORMATION NEEDED FOR

C CALCULATING CHARACTERISTIC LINE INTENSITIES

C IN AN X-RAY TUBE SPECTOUM.

C

C NBS 06-SEP-1984

C

DIMENSION DAT (14, 11)

OPEN (UNIT=3,NAME='TG*I\VR. DAT* ,TYPE='NEW' ,ACCESS=' DIRECT' , + MAXREC=14,REC0RDSIZE=11)

WRITE (6, 5)

5 FORMATdX,' INPUT D^TA BY KEYBOARD:'/)

DO 10 1=1,14

READ(5,*) (DAT(I,J) ,J=1,11)

WRITEO'I) (DAT(I,J) ,J=1,11)

10 CONTINUE

CLOSE ( UNIT=3)

END

PROGRAM RDWRTTGT

C

C THIS PROGRAM PRINTS OUT THE CONTENTS OF

C DATAFILE NAMED 'TGIV/R.DAT'

.

C

C NBS 06-SEP~1984

C

DIMENSION DAT (14, 11)

OPEN (UNIT=3,NAME='TGTVfR. EAT' ,TYPE='OLD' , ACCESS- 'DIRECT'

,

+ MAXRBC=14,REC0RDSIZE=11)

DO 20 1=1,14

READO'I) (DAT(I,J) ,J=1,11)

WRITE(6,100) (DAT(I,J) ,J=1,11)

20 CONTINUE

CLOSE (UNIT=3)

100 F0RMAT(/1X,11(F8.4,2X))

END

110
Contents of the permanent datafile called • MACPRM.DAT' for calculating

mass absorption coefficients using the expression of Thinh and Leroux. The

following tabulated values are in the same order as given in Table 1 of

reference 10.

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

1.0727 0.0246 3.0300 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

1.8894 0.0548 3.0300 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2.4604 0.1110 3.0300 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0000

3.0824 0.1880 3.0300 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

3.8531 0.2838 3.0940 1.7500 2.1900 2.7345 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

4.5355 0.4016 3.0660 2.1200 3.2600 2.7345 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

5.3268 0.5320 3.0410 2.5000 4.6100 2.7345 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

6.1058 0.6854 3.0190 3.0000 6.2500 2.7345 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

6.8419 0.8669 3.0000 3.5500 8.2000 2.7345 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

7.5844 1.0721 2.9830 4.4000 10.4900 2.7345 0.0633 2.8350 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

8.3105 1.3050 2.9670 6.4000 13.1400 2.7345 0.0894 2.8200 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

8.5946 1.5596 2.9530 6.2000 16.1600 2.7345 0.1177 2.8050 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

9.1309 1.8389 2.9400 5.9000 19.5700 2.7345 0.1487 2.7900 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 O.OnOO 0.0000 0.0000 0.0000

9.6522 2.1455 2.9270 6.7000 23.3900 2.7345 0.1893 2.7750 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

10.1931 2.4720 2.9160 7.5000 27.6300 2.7345 0.2292 2.7600 0.0000 0.0000 0.0000 0.0000

111
Values - Continued

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

10.7343 2.8224 2.9050 8.4000 32.3200 2.7345 0.2702 2.7450 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

11.2540 3.2029 2.8950 9.5000 37.4700 2.7345 0.3200 2.7300 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

11.7770 3.6074 2.8860 11.0900 43.0800 2.7345 0.3771 2.7300 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

12.2904 4.0381 2.8500 13.3000 49.1900 2.7345 0.4378 2.7300 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

12.5125 4.4928 2.8500 13.2000 55.8000 2.7345 0.5004 2.7300 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

12.7473 4.9664 2.8500 13.0000 62.9300 2.7345 0.5637 2.7300 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

12.9768 5.4651 2.8500 12.9500 70.5900 2.7345 0.6282 2.7300 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

13.2009 5.9892 2.8500 12.9000 78.7900 2.7345 0.6946 2.7300 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

13.4196 6.5390 2.8500 12.6000 87.5600 2.7345 0.7690 2.7300 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

13.6384 7.1120 2.8500 12.5000 96.8900 2.7345 0.8461 2.7300 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

13.8555 7.7089 2.8500 12.4000 106.8200 2.7345 0.9256 2.7300 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

14.0657 8.3328 2.8500 12.4000 117.3400 2.7345 1.0081 2.7300 0.8719 2.6144 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

14.2775 8.9789 2.8500 12.1000 128.4800 2.7345 1.0961 2.7300 0.9510 2.6144 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

14.4732 9.6586 2.8500 12.0000 140.2500 2.7345 1.1936 2.7300 1.0428 2.6144 1.0197 2.3554

0.1359 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

14.6620 10.3671 2.8500 12.0000 152.6500 2.7345 1.2977 2.7300 1.1423 2.6144 1.1154 2.3554

0.1581 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

14.8464 11.1031 2.8500 12.0000 165.7000 2.7345 1.4143 2.7300 1.2478 2.6144 1.2167 2.3554

112
Values - Continued

0.1800 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

15.0268 11.8667 2.8500 12.0000 179.4100 2.7345 1.5265 2.7300 1.3586 2.6144 1.3231 2.3554

0.2035 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

15.2038 12.6578 2.8500 0.0000 0.0000 0.0000 1.6539 2.7300 1.4762 2.6144 1.4358 2.3554

0.2315 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

15.3807 13.4737 2.8500 0.0000 0.0000 0.0000 1.7820 2.7300 1.5960 2.6144 1.5499 2.3554

0.2565 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

15.5452 14.3256 2.8500 0.0000 0.0000 0.0000 1.9210 2.7300 1.7272 2.6144 1.6749 2.3554

0.2850 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

15.7132 15.1997 2.8500 0.0000 0.0000 0.0000 2.0651 2.7300 1.8639 2.6144 1.8044 2.3554

0.3221 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

15.8756 16.1046 2.8500 0.0000 0.0000 0.0000 2.2163 2.7300 2.00'-)8 2.6144 1.9396 2.3554

0.3575 2.6000 0.0000 o.onoo n.nooo 0.0000 0.0000 o.oono o.ooon n.onon o.oooo o.ooon

16.0348 17.0384 2.8500 0.0000 0.0000 0.0000 2.3725 2.7300 2.1555 2.6144 2.0800 2.3554

0.3936 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

16.1942 17.9976 2.8500 0.0000 0.0000 0.0000 2.5316 2.7300 2.3067 2.6144 2.2223 2.3554

0.4303 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

16.3507 18.9856 2.8500 0.0000 0.0000 0.0000 2.6977 2.7300 2.4647 2.6144 2.3705 2.3554

0.4684 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

16.5071 19.9995 2.8500 0.0000 0.0000 0.0000 2.8655 2.7300 2.6251 2.6144 2.5202 2.3554

0.5046 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

16.6595 21.0440 2.8500 0.0000 0.0000 0.0000 3.0425 2.7300 2.7932 2.6144 2.6769 2.3554

0.5400 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

16.8097 22.1172 2.8500 0.0000 0.0000 0.0000 3.2240 2.7300 2.9669 2.6144 2.8379 2.3554

0.5850 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

16.9573 23.2199 2.8500 0.0000 0.0000 0.0000 3.4119 2.7300 3.1461 2.6144 3.0038 2.3554

0.6271 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

17.1037 24.3503 2.8500 0.0000 0.0000 0.0000 3.6043 2.7220 3.3303 2.6144 3.1733 2.3554

0.6699 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

17.2453 25.5140 2.8500 0.0000 0.0000 0.0000 3.8058 2.7140 3.5237 2.6144 3.3511 2.3554

0.7175 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

17.3824 26.7112 2.8500 0.0000 0.0000 0.0000 4.0180 2.7060 3.7270 2.6144 3.5375 2.3554

113
Values - Continued

0.7702 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

17.5165 27.9399 2.8500 0.0000 0.0000 0.0000 1.2375 2.6980 3.9380 2.61/14 3.7301 2.3551

0.8256 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

17.6481 29.2001 2.8500 0.0000 0.0000 0.0000 4.4647 2.6900 4.1561 2.6144 3.9288 2.3554

0.8838 2.6000 0.0000 O.OOOO 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

17.7775 30.4912 2.8500 0.0000 0.0000 0.0000 4. 6983 2.6820 4.3804 2.6144 4.1322 2.3554

0.9437 2.6000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

17.9048 31.8138 2.8500 0.0000 0.0000 0.0000 4.9392 2.6740 4.6120 2.6144 4.3414 2.3554

1.0060 2.6000 0.8697 2.4471 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

18.0291 33.1694 2.8500 0.0000 0.0000 0.0000 5.18B1 2.6660 4.8521 2.6144 4.5571 2.3554

1.0721 2.6000 0.9305 2.4471 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

18.1326 34.5614 2.8500 0.0000 0.0000 0.0000 5.4528 2.65R0 5.1037 2.6144 4.7822 2.3554

1.1400 2.6000 0.9990 2.4471 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

18.2062 35.9846 2.8500 0.0000 0.0000 0.0000 5.7143 2.6500 5.3594 2.6144 5.0119 2.3554

1.2171 2.6000 1.0650 2.4471 0.9976 2.4471 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

18.2781 37.4406 2.8500 0.0000 0.0000 0.0000 5.9888 2.6500 5.6236 2.6144 5.2470 2.3554

1.2928 2.6000 1.1367 2.4471 1.0622 2.4471 0.7961 2.4000 0.0000 0.0000 0.0000 0.0000

18.3506 38.9246 2.8500 0.0000 0.0000 0.0000 6.2663 2.6500 5.8906 2.6144 5.4827 2.3554

1.3613 2.6000 1.2044 2.4471 1.1234 2.4471 0.8485 2.4000 0.0000 0.0000 0.0000 0.0000

18.4209 40.4430 0.0000 0.0000 0.0000 0.0000 6.5488 2.6500 6.1642 2.6144 5.7234 2.3554

1.4346 2.6000 1.2728 2.4471 1.1854 2.4471 0.9013 2.4000 0.0000 0.0000 0.0000 0.0000

18.4913 41.9906 0.0000 0.0000 0.0000 0.0000 6.8348 2.6500 6.4404 2.6144 5.9643 2.3554

1.5110 2.6000 1.3374 2.4471 1.2422 2.4471 0.9511 2.4000 0.0000 0.0000 0.0000 0.0000

18.5613 43.5689 0.0000 0.0000 0.0000 0.0000 7.1260 2.6500 6.7215 2.6144 6.2079 2.3554

1.5753 2.6000 1.4028 2.4471 1.2974 2.4471 0.9999 2.4000 0.0000 0.0000 0.0000 0.0000

18.6282 45.1840 0.0000 0.0000 0.0000 0.0000 7.4279 2.6500 7.0128 2.6144 6.4593 2.3554

1.6540 2.5750 1.4714 2.4471 1.3569 2.4471 1.0515 2.4000 1.0269 2.2000 0.3300 2.4980

18.6932 46.8342 0.0000 0.0000 0.0000 0.0000 7.7368 2.6500 7.3118 2.6144 6.7162 2.3554

1.7228 2.5750 1.5407 2.4471 1.4198 2.4471 1.1060 2.4000 1.0802 2.2000 0.3457 2.4920

18.7564 48.5190 0.0000 0.0000 0.0000 0.0000 8.0520 2.6500 7.6171 2.6144 6.9769 2.3554

1.8000 2.5750 1.6139 2.4471 1.4806 2.4471 1.1606 2.4000 1.1309 2.2000 0.3602 2.4850

18.8179 50.2391 0.0000 0.0000 0.0000 0.0000 8.3756 2.6500 7.9303 2.6144 7.2428 2.3554

114
Values - Continued

1.8808 2.5750 1.6883 2.4471 1.5440 2.4471 1.2172 2.4000 1.1852 2.2000 0.3758 2.4790

18.8773 51.9957 0.0000 0.0000 0.0000 0.0000 8.7080 2.6500 8.2516 2.6144 7.5140 2.3554

1.9675 2.5750 1.7677 2.4471 1.6113 2.4471 1.2750 2.4000 1.2412 2.2000 0.3979 2.4720

18.9350 53.7885 0.0000 0.0000 0.0000 0.0000 9.0458 2.6500 8.5806 2.6144 7.7901 2.3554

2.0468 2.5750 1.8418 2.4471 1.6756 2.4471 1.3325 2.4000 1.2949 2.2000 0.4163 2.4660

18.9909 55.6177 0.0000 0.0000 0.0000 0.0000 9.3942 2.6500 0.9178 2.6144 8.0711 2.3554

2.1283 2.5750 1.9228 2.4471 1.7412 2.4471 1.3915 2.4000 1.3514 2.2000 0.4357 2.4600

19.0446 57.4855 0.0000 0.0000 0.0000 0.0000 9.7513 2.6500 9.2643 2.6)44 8.3579 2.3554

2.2065 2.5750 2.0058 2.4471 1.8118 2.4471 1.4533 2.4000 1.4093 2.2000 0.4491 2.4540

19.0969 59.3896 0.0000 0.0000 0.0000 0.0000 10.1157 2.6500 9.6169 2.6144 8.6480 2.3554

2.3068 2.5750 2.0898 2.4471 1.8845 2.4471 1.5146 2.4000 1.4677 2.2000 0.4717 2.4480

19.1472 61.3323 0.0000 0.0000 0.0000 0.0000 10.4864 2.6500 9.9782 2.6144 8.9436 2.3554

2.3981 2.5750 2.1730 2.4471 1.9498 2.4471 1.5763 2.4000 1.5278 2.2000 0.4872 2.4420

19.1957 63.3138 0.0000 0.0000 0.0000 0.0000 10.8704 2.6500 10.3486 2.6144 9.2441 2.3554

2.4912 2.5750 2.2635 2.4471 2.0236 2.4471 1.6394 2.4000 1.5885 2.2000 0.5062 2.4360

19.2376 65.3508 0.0000 0.0000 0.0000 0.0000 11.2707 2.6500 10.7394 2.6144 9.5607 2.3554

2.6009 2.5750 2.3654 2.4471 2.1076 2.4471 1.7164 2.4000 1.6617 2.2000 0.5381 2.4300

19.2812 67.4164 0.0000 0.0000 0.0000 0.0000 11.6815 2.6500 11.1361 2.6144 9.8811 2.3554

2.7080 2.5750 2.4687 2.4471 2.1940 2.4471 1.7932 2.4000 1.7351 2.2000 0.5655 2.4250

19.3223 69.5250 0.0000 0.0000 0.0000 0.0000 12.0998 2.6500 11.5440 2.6144 10.2068 2.3554

2.8196 2.5750 2.5749 2.4471 2.2810 2.4471 1.8716 2.4000 1.8092 2.2000 0.5950 2.4190

19.3611 71.6764 0.0000 0.0000 0.0000 0.0000 12.5267 2.6500 11.9587 2.6144 10.5353 2.3554

2.9317 2.5750 2.6818 2.4471 2.3673 2.4471 1.9489 2.4000 1.8829 2.2000 0.6250 2.4140

19.3979 73.8706 0.0000 0.0000 0.0000 0.0000 12.9680 2.6500 12.3850 2.6144 10.8709 2.3554

3.0485 2.5750 2.7922 2.4471 2.4572 2.4471 2.0308 2.4000 1.9601 2.2000 0.6543 2.4080

19.4320 76.1110 0.0000 0.0000 0.0000 0.0000 13.4185 2.6500 12.8241 2.6144 11.2152 2.3554

3.1737 2.5750 2.9087 2.4471 2.5507 2.4471 2.1161 2.4000 2.0404 2.2000 0.6901 2.4030

19.4643 78.3948 0.0000 0.0000 0.0000 0.0000 13.8799 2.6500 13.2726 2.6144 11.5637 2.3554

3.2960 2.5750 3.0265 2.4471 2.6454 2.4471 2.2019 2.4000 2.1216 2.2000 0.7220 2.3980

19.4943 80.7249 0.0000 0.0000 0.0000 0.0000 14.3528 2.6500 13.7336 2.6144 11.9187 2.3554

3.4249 2.5750 3.1478 2.4471 2.7430 2.4471 2.2911 2.4000 2.2057 2.2000 0.7588 2.3930

19.5219 83.1023 0.0000 0.0000 0.0000 0.0000 14.8393 2.6500 14.2087 2.6144 12.2839 2.3554

115
Values - Continued

3.5616 2.5750 3.2785 2.4471 2.8471 2.4471 2.3849 2.4000 2.2949 2.2000 0.8003 2.3880

19.5466 85.5304 0.0000 0.0000 0.0000 0.0000 15.3467 2.6500 14.6979 2.6144 12.6575 2.3554

3.7041 2.5750 3.4157 2.4471 2.9566 2.4471 2.4851 2.4000 2.3893 2.2000 0.8455 2.3830

19.5696 88.0045 0.0000 0.0000 0.0000 0.0000 15.8608 2.6500 15.2000 2.6144 13.0352 2.3554

3.8507 2.5750 3.5542 2.4471 3.0664 2.4471 2.5856 2.4000 2.4840 2.2000 0.8936 2.3780

19.5909 90.5259 0.0000 0.0000 0.0000 0.0000 16.3875 2.6500 15.7111 2.6144 13.4186 2.3554

3.9991 2.5750 3.6963 2.4471 3.1769 2.4471 2.6876 2.4000 2.5796 2.2000 0.9382 2.3730

19.6083 93.1050 0.0000 0.0000 0.0000 0.0000 16.9393 2.6500 16.2443 2.6144 13.8138 2.3554

4.1494 2.5750 3.8541 2.4471 3.3019 2.4471 2.7980 2.4000 2.6830 2.2000 0.9953 2.3680

19.6248 95.7299 0.0000 0.0000 0.0000 0.0000 17.4930 2.6500 16.7047 2.6144 14.2135 2.3554

4.3170 2.5750 4.0080 2.4471 3.4260 2.4471 2.9087 2.4000 2.7867 2.2000 1.0420 2.3640

19.6395 98.4040 0.0000 0.0000 0.0000 0.0000 18.0490 2.6500 17.3371 2.6144 14.6194 2.3554

4.4820 2.5750 4.1590 2.4471 3.5380 2.4471 3.0215 2.4000 2.8924 2.2000 1.0970 2.3590

19.6510 101.1370 0.0000 0.0000 0.0000 0.0000 18.6390 2.6500 17.9065 2.6144 15.0312 2.3554

4.6520 2.5750 4.3270 2.4471 3.6630 2.4471 3.1362 2.4000 2.9999 2.2000 1.1530 2.3550

19.6607 103.9219 0,0000 0.0000 0.0000 0.0000 19.2367 2.6500 18.4843 2.6144 15.4444 2.3554

4.8220 2.5750 4.4895 2.4471 3.7918 2.4471 3.2484 2.4000 3.1049 2.2000 1.2084 2.3500

19.6695 106.7553 0.0000 0.0000 0.0000 0.0000 19.8400 2.6500 19.0832 2.6144 15.8710 2.3554

5.0020 2.5750 4.6560 2.4471 3.9090 2.4471 3.3702 2.4000 3.2190 2.2000 1.2690 2.3460

19.6749 109.6509 0.0000 0.0000 0.0000 0.0000 20.4721 2.6500 19.6932 2.6144 16.3003 2.3554

5.1823 2.5750 4.8304 2.4471 4.0461 2.4471 3.4908 2.4000 3.3320 2.2000 1.3295 2.3410

19.6786 112.6014 0.0000 0.0000 0.0000 0.0000 21.1046 2.6500 20.3137 2.6144 16.7331 2.3554

5.3669 2.5750 5.0009 2.4471 4.1738 2.4471 3.6112 2.4000 3.4418 2.2000 1.3871 2.3370

19.6808 115.6061 0.0000 0.0000 0.0000 0.0000 21.7574 2.6500 20.9476 2.6144 17.1663 2.3554

5.5480 2.5750 5.1822 2.4471 4.3034 2.4471 3.7276 2.4000 3.5517 2.2000 1.4408 2.3330

19.6796 118.6780 0.0000 0.0000 0.0000 0.0000 22.4268 2.6500 21.6005 2.6144 17.6100 2.3554

5.7232 2.5750 5.3662 2.4471 4.4347 2.4471 3.8503 2.4000 3.6658 2.2000 1.5007 2.3280

19.6751 121.8180 0.0000 0.0000 0.0000 0.0000 23.0972 2.6500 22.2662 2.6144 18.0568 2.3554

5.9329 2.5750 5.5412 2.4471 4.5566 2.4471 3.9726 2.4000 3.7781 2.2000 1.5586 2.3240

116
Contents of the Permanent Datafile Called 'TGTWR.DAT'

3.0320

0.0000

2.2910

0.0000

0.7100

0.0000

0.6140

0.0000

0.5610

0.0000

0.0000

0.0000

0.0000

0.0000

2.7800

0.0000

2.0850

0.0000

0.6320

0.0000

0.5460

0.0000

0.4970

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

4.5970

1.0000

4.1540

1.0000

1.4760

1.0000

1.2770

1.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

4.3740

0.5400

3.9350

0.5270

1.2820

0.4660

1.0830

0.4580

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

4.1300

0.1150

3.7030

0.1880

1.2450

0.1790

1.0700

0.2060

0.0000

0.0000

O.OOfiO

0.0000

0.0000

0.0000

4.2530

0.1070

3.8340

0.0840

1.2630

0.0740

1.0680

0.0740

n.oooo

0.0000

0.0000

0.0000

0.0000

0.0000

4.2890

0.0700

3.0700

0.0520

1.3020

0.0470

1.1060

0.0470

o.nono

0.0000

0.0000

0.0000

0.0000

0.0000

3.9440

0.0680

3.5230

0.1070

1.0980

0.0810

0.9270

0.0990

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

1.0680

0.0130

0.9050

0.0100

0.0000

0.0000

0.0000

0.0000

0.0000

o.nooo

0.0000

0.0000

0.0000

0.0000_

1.0620

0.0180

0.8980

0.0200

o.nnoo

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

1.6780

0.0290

1.4600

0.0310

TilrU.S. GOVERNMENT PRINTING OFFICE: 1 9 8 5 k61 105 2008«f

117

NBS-IMA (REV. 2.80) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

PUBLICATION OR

REPORT NO.

NBS/TN-1213

2. Performing Organ. Report No. 3. Publication Date

April 1985

4. TITLE AND SUBTITLE

NBSGSC—A FORTRAN Program for Quantitative X-ray Fluorescence Analysis

5. AUTHOR(S)

G. Y. Tao, P. A. Pella, and R. M. Rousseau

6. PERFORMING ORGANIZATION C/f jo/'nt or other thcjn NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Same as in item 6 above.

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. 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 FORTRAN program (NBSGSC) was developed for performing quantitative

analysis of bulk specimens by x-ray fluorescence spectrometry. This program

corrects for x-ray absorption/enhancement phenomena using the comprehensive

alpha coefficient algorithm proposed by Lachance (COLA). NBSGSC is a revision of the program ALPHA and CARECAL originally developed by R.M.

Rousseau of the Geological Survey of Canada. Part one of the program (CALCO)

performs the calculation of theoretical alpha coefficients, and part two

(CALCOMP) computes the composition of the analyte specimens. The analysis of

alloys, pressed minerals, and fused specimens can currently be treated by the

program. In addition to using measured x-ray tube spectral distributions,

spectra from seven commonly used x-ray tube targets could also be calculated

with an NBS algorithm included in the program. NBSGSC is written in FORTRAN

IV for a Digital Equipment Corporation (DEC PDP-11/23) minicomputer using

RL02 firm disks and an RSX 11M operating system.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

alpha coefficients; comprehensive algorithm; fundamental parameters; interelement

corrections; program; quantitative analysis; x-ray

13. AVAILABILITY

[X] Unlimited

I I For Official Distribution. Do Not Release to NTIS

fXl Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

\2Z\ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

119

15. Price

USCOMM-DC 8043-P80





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