NRLXRF, A FORTRAN PROGRAM 

FOR X-RAY FLUORESCENCE ANALYSIS: 

USERS' GUIDE 

L. S. BIRKS, J. V. GILFRICH AND J. W. CRISS 

X-RAY OPTICS BRANCH 

MATERIAL SCIENCES DIVISION

JULY 1977 

NAVAL RESEARCH LABORATORY 

WASHINGTON, D.C. 

"APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED." 
ABSTRACT 

The Naval Research Laboratory computer program for quantitative 

x-ray fluorescence analysis (NRLXRF) is designed to optimize the 

data reduction scheme for relating measured x-ray intensities to 

the chemical composition of a wide variety of sample types. The 

mathematics are versatile and large masses of data can be 

manipulated. The UsersÌ Guide introduces the potential user to 

the program by specifying the input requirements and format for 

three alternative methods of using the program: 

1. To analyze unknown bulk samples using multicomponent 

standards; 

2. To predict effects of particle size and chemical 

composition on the x-ray intensity emitted by thin samples 

such as particulate pollution collected on filters; and 

3. To predict the relative x-ray intensity for bulk samples. 

Annotated example runs of each of these options are given 

to assist the user in becoming familiar with the program. 

i 
CONTENTS 

ABSTRACT i 

INTRODUCTION 2 

BACKGROUND 3 

A NOTE ON INCIDENT SPECTRA 4 

INSTALLING THE PROGRAM 4 

EXAMPLES SHOWING THREE OPTIONS 

Option 1: Calculate Composition for Bulk Unknowns 5 

Option 2: Predict Effects of Particle Size and 

Chemical Composition for Thin Samples 12 

Option 3: Predict Relative X-Ray 

Intensities for Bulk Samples 13 

CONCLUSION 15 

ii
NRLXRF, A Fortran Program 

for X-Ray Fluorescence Analysis:

Users' Guide

INTRODUCTION 

The Naval Research Laboratory (NRL) computer program for 

quantitative x-ray fluorescence analysis employs both fundamentalparameter equations and influence-coefficient equations in order to 

optimize the matrix corrections for multicomponent samples. In its 

present form it requires a large computer such as the Digital 

Equipment Corporation PDP-10 but is very efficient and generally costs 

between $0.10 and $5.00 per sample for analysis (depending, of course, 

on how computer costs are charged). As a more concrete estimate of 

costs, all of the examples illustrated in this Users' Guide cost $3.00 

(total) to run in the interactive time-sharing mode on the NRL PDP-10 

computer. 

The program is extremely versatile in several respects: 

- It treats both homogeneous and heterogeneous samples. 

- Up to 20 components and 50 standards can be considered 

simultaneously. 

- Components can be either elements or compounds. 

- Particle size effects can be treated in bulk powders or thin 

pollution samples. 

- Corrections for background and counting rate (dead time) are 

made automatically. 

- Either pure elements or intermediate standards or a 

combination of both can be used to analyze the data. 

- The amount of a component may be fixed in an unknown (as for 

fluxes, binders, diluents, dopants, internal standards, minor 

elements not measured, etc.). 

- Either batch processing or time sharing may be used. 

- Other capabilities are mentioned in the Reference Manual. 

In this UsersÌ Guide, three different kinds of problems are 

described and illustrated by examples. These are: 

Option 1. For bulk samples, analyze an unknown using whatever 

pure elements and intermediate standards are available. 

Option 2. For thin samples such as for pollution analysis, 

predict effects of particle sizes and composition (requires assumed 

particle sizes, etc.). 

Option 3. For bulk samples, predict the relative x-ray 

intensities for any assumed composition.

2 
BACKGROUND 

The matrix effects of interelement absorption and secondary 

fluorescence (enhancement) have been recognized in x-ray 

analysis for many years. Many approaches for their correction 

in quantitative analysis have been proposed and used with 

varying success. The most common approach has been the use of 

equations in which empirical coefficients representing 

interelement effects are determined from a set of intermediate 

standards and then used in equations for analyzing unknown 

compositions. The limitations of this empirical equation 

approach include the fact that different standards must be used 

for each different type of sample, i.e. alloys of similar 

composition must be used to establish the empirical coefficients 

for alloys, powders of similar composition and particle size 

must be used to establish the coefficients for powders, etc. 

Computers are usually used even with empirical equations for 

systems of more than three components but generally small 

dedicated computers suffice. 

The less common approach to correct for matrix effects 

relies on the fundamental parameters such as absorption 

coefficients, fluorescent yields, jump ratios, and incident 

spectral distributions. This approach has the important 

advantage that the standards need not be similar in composition 

to the unknowns; they may be pure elements or one known compound 

for each element of interest, or one multi-component standard. 

It is less necessary to use a different set of standards to 

analyze some new type of sample, and any number of components 

can be handled with equal facility. The present program is 

configured for large computers partly because it is relatively 

easy to convert from one large computer to another. With 

extensive revision it probably could run on some minicomputers 

equipped with floppy-disk storage. (Additional cost per sample 

to use the more versatile fundamental parameter program compared 

to using regression equations are negligible in terms of overall 

analytical costs.) 

At NRL we have devoted considerable effort to developing, 

improving, and simplifying a combination approach which uses the 

fundamental parameters plus whatever standards the analyst cares 

to supply. The estimate of composition of the unknown is 

obtained by iteration loops in which hypothetical standards are 

generated internally and adjusted to agree with the real 

standards. For highest accuracy, at least one multicomponent 

standard similar to the unknown is required. 

3 
The present version of the program contains many built-in 

capabilities which are deliberately concealed from the user 

unless he requests them explicitly. It has been prepared so 

that an inexperienced user can carry out the most-wanted options 

readily without worrying about details that are of no interest 

to him. By this means he can become familiar with, and 

confident in the use of, the method in the most painless 

fashion. We believe that once a user has tried the program he 

will find it far more convenient and accurate than less 

sophisticated approaches. 

A NOTE ON INCIDENT SPECTRA 

The program as issued in 1977, contains in data files the 

accurate spectral distributions for specific x-ray tubes (Cr 

target-Philips FAQ 60/1; Rh target-Machlett SEG 50H; W targetPhilips FAAQ 60/3.5) operated at 45 kV. If appropriate to the 

analytical conditions used, one of these spectra may be called 

for by specifying CR45C, RH45C or W45C as illustrated in some of 

the examples following. The use of targets other than those 

three elements and/or voltages other than 45 kV is facilitated 

by the capability in the program to calculate spectra for any 

target element at any operating voltage and for specific 

geometrical considerations (x-ray take-off angle and Be window 

thickness). While these calculated spectra are good 

approximations, their use is most dependable for the case where 

at least one multicomponent standard similar to the unknowns is 

used to mitigate the uncertainties in the fundamental parameters 

(including the primary spectrum) used in the calculation. If a 

multicomponent standard is not available, the accuracy will 

suffer due to these uncertainties. 

The user may call for any monochromatic primary radiation 

(fluorescer emission or effective primary wavelength) by 

specifying the element line designation, e.g. MO KA, the desired 

wavelength, e.g. 0.711 ≈, or the energy, e.g. 17.4 keV. In 

addition, the analyst may add any other spectra to the data file 

by using procedures described in the Reference Manual. 

INSTALLING THE PROGRAM 

The other documentation supplied with this program includes 

suggestions for its installation on the user's computer. It is 

presumed that the x-ray analyst will have initial help from 

someone versed in computer usage who will instruct him on how to 

call for the program on time sharing or how to supply data for 

batch processing.

4 
EXAMPLES SHOWING THREE OPTIONS 

When the program is called for in an interactive mode it 

will identify itself and then type a symbol (in the 

illustrations, a small star) at the beginning of a line 

indicating it is ready to receive information. The user may 

first type RESET followed by # OPTION 1 (or whatever heading he 

wishes), followed by another blank line. He is then ready to 

start entering data. The type of data entered and the form in 

which it should be entered is shown in the annotated examples 

below. It should be noted that the user must leave a blank line 

after each set of data so that the program will know that the 

set of data is complete. 

If the program is used in batch mode, keyword cards, data 

cards, and blank cards for separating sets of data replace the 

direct interaction via teletype. There should be one card for 

each star shown in the examples but the cards should not contain 

the stars. 

It is suggested that the user repeat the illustrations as 

shown and then repeat again with data from his own samples to 

become familiar with the procedure. 

Option 1: The first option to be illustrated is that which 

calculates the composition of a bulk unknown using measured xray intensities and whatever standards are furnished. This is 

the option which will be most useful for analysts concerned with 

alloy specimens or other bulk samples. Note that each line must 

be measured in some standard but that a single multicomponent 

standard may suffice. The program will utilize whatever 

standards or reference samples are supplied. 

The first example of Option I illustrates a simple type of 

input for a bulk steel sample. 

5 

"OPTION 1" or any other label 

may be input if desired. Must 

be preceded by "#" to indicate 

a remark so that the computer 

will not act on it.

* RESET 

* #OPTION 1 
6 

"LINES" identifies the first 

group of input as the x-ray lines 

of interest. After the first 

x-ray line one puts the analysis 

conditions for that line: incidence 

angle is 57∫ , take off angle is 

40∫ , and the primary spectrum is 

from a W tube, at 45 kV (from the 

data file). Subsequent lines need 

no conditions unless they change. 

A blank line (after the star) indicates 

that the first input group is ended. 

* LINES 

* 1 FE KA 57 40 W45C 

* 2 NI KA 

* 3 CR KA 

* 

* COMPOSITION SRM1171 

* FE 68.3 

* NI 11.2 

* CR 17.4 

* MN 1.80 

COMPOSITION in percent and name of 

the one multicomponent standard 

are entered. The name of this 

standard is "SRM1171". (The 

computer only recognizes first 

eight characters of sample name; 

samples must be distinguished from 

one another within these eight 

characters.) 

INTENSITIES are given for the standard, 

In this example, raw intensities are 

entered in the following sequence; 

Line number. Total counts (signal 

plus background), Time in seconds 

 (signal plus background), Total counts 

 (background), Time in seconds 

 (background), and Dead Time in microseconds. Line 4 is given in counts 

per second, already corrected for 

background and dead-time. 

INTENSITIES for the unknown sample 

(named "STEEL") are entered in the 

 same format. 

* INTENSITIES SRM1171 

* 1 265900 20 340 20 2.2 

* 2 146271 100 28 10 2.2 

* 3 124266 20 281 20 2,2 

* 4 512.33 1 0 1 0 

* 

* INTENSITIES STEEL 

* 1 243676 20 356 20 2.2 

* 2 89613 100 28 10 2.2 

* 3 149572 20 281 20 2.2 

* 4 600 1 0 1 0 

* 

* ANALYZE STEEL Computer instructed to "ANALYZE 

 STEEL"
The second example of Option I is a minor variation on the 

first. In this case, the analytical conditions are specified 

for all the measurements by using the keyword "CONDITIONS", at 

any point in the input sequence. Here, the incident spectrum is 

to be calculated. Note that the conditions can be input 

following the designation of each line, negating the requirement 

for the "CONDITIONS" keyword, also permitting different 

conditions to be used for different lines (see first example of 

Option 3).

7 

COMPONENT AMOUNT 

FE 66.57 

NI 6.86 

CR 21.77 

MN 2.13 

(TOTAL) 97.32

Computer prints out the composition 

of "STEEL" in percent. 

Operator can call for additional 

 digits (usually they are not 

 significant) by using procedures 

 described in the Reference Manual.

Incidence angle is 57∫ , take-off 

angle is 40∫ , and the primary 

spectrum is calculated for a Wtarget tube operated at 45 kV, 

having a 26∫ x-ray take off angle 

and a 1 mm Be window (should be 

equivalent to measured spectrum 

used in preceding example). 

LINES, COMPOSITION of standard and 

INTENSITIES of standard and unknown 

are entered as before. 

* RESET 

* CONDITIONS 57 40 W 45 26 1 

* LINES 

* 1 FE KA 

* 2 NI KA 

* 3 CR KA 

* 4 MN KA 

* 

* COMPOSITION SRM1171 

* FE 68.3 

* NI 11.2 

* CR 17.4 

* MN 1.80 

* 

* INTENSITIES SRM1171 

* 1 265900 20 340 20 2.2 

* 2 146271 100 28 10 2.2 

* 3 124266 20 281 20 2.2 

* 4 512.33 1 0 1 0 

* 
A third example illustrates the use of pure element 

standards along with a multicomponent standard. 

* RESET 

8 

* INTENSITIES STEEL 

* 1 243676 20 356 20 2.2 

* 2 89613 100 38 10 2.2 

* 3 149572 20 340 20 2.2 

* 4 600 1 0 1 0 

* 

* ANALYZE STEEL Computer told to ÏANALYZE STEELÓ. 

COMPONENT AMOUNT 

FE 66.63 

NI 6.86 

CR 21.80 

MN 2.13 

(TOTAL) 97.42 

Results appear remarkably similar 

to the previous set, indicating 

the adequacy of a calculated 

spectrum when a multi-component 

standard similar to the unknown 

is used. 

LINES and conditions are input 

Before. 

* LINES 

* 1 FE KA 57 40 W45C 

* 2 NI KA 

* 3 CR KA 

* 4 MN KA 

* 

COMPOSITION and INTENSITIES for 

the standards are given. Each 

standard is identified by a 

name. IRON is the Fe standard, 

etc. COMPOSITION is in weight 

percent. 

* COMPOSITION IRON 

* FE 100 

* INTENSITIES IRON 

* 1 490524 20 708 20 2.2 

* COMPOSITION NICKEL 

* NI 100 

* 

* INTENSITIES NICKEL 

* 2 2626800 100 336 10 2.2 

* COMPOSITION CHROMIUM 

* CR 100 

* 
A fourth example of Option 1 deals with the homogeneous 

sample which results from the fusion of a geological, 

mineralogical or similar type of material (which may be 

heterogeneous before fusion) using any of the borate materials. 

The flux is conventionally added to the sample in a known amount 

and is an example of the use of a "fixed" component. The 

example shown here illustrates sample components which are not 

independent elements (viz. they are compounds). 

9 

As illustrated in previous 

examples, pure standards are 

not required. It is recommended 

that they be used to provide 

fixed end points in the calibration. * COMPOSITION MANGANESE 

* MN 100 

*

* INTENSITIES MANGANESE 

* 4 255080 10 3443 100 2.2 

* 

* INTENSITIES CHROMIUM 

* 3 504406 20 818 20 2.2 

* 

COMPOSITION in weight percent 

is given for the multicomponent 

standard (named ÏSRM1171Ó). 

* COMPOSITION SRM1171 

* FE 68.3 

* NI l1.2 

* CR 17.4 

* MN 1.80 

* 

* INTENSITIES SRM1171 

* 1 265900 20 340 20 2.2 

* 2 146271 100 28 10 2.2 

* 3 124266 20 281 20 2.2 

* 4 600 1 0 1 0 

* 

INTENSITIES for the multicomponent 

standard are given. 

* INTENSITIES STEEL 

* 1 243676 20 356 20 2.2 

* 2 89613 100 38 10 2.2 

* 3 149572 20 340 20 2.2 

* 4 600 1 0 1 0 

* 

INTENSITIES for the unknown 

 (named ÏSTEELÓ) are given. 

COMPONENT AMOUNT 

FE 66.57 

NI 6.85 

CR 21.81 

MN 2.13 

(TOTAL) 97.37 

Computer instructed to "ANALYZE 

STEEL". 

Again the results are very similar 

 to the previous two examples. 

* ANALYZE STEEL 
10 

LINES as before. 

Here, incidence angle is 60∫

and take-off angle is 80∫ , the 

primary radiation is a Cr tube 

at 30 kV, having 26∫ take-off 

angle and 0.3 mm Be window. 

Components of the sample are 

compounds which must be defined. 

First compound is SiO2, its 

density is 2.64 g/cm3 and its 

definition is given in atomic 

proportions (AT) rather than 

weight (WT) proportions. 

Other components of the sample are

TiO2 and Fe2O3. 

* RESET 

* LINES 

* 1 SI KA 60 80 CR 30 26 .3 

* 2 TI KA 

* 3 FE KA 

* 

* DEFINE SIO2 2.64 AT 

* SI 1 

* O 2 

* 

* DEFINE FE2O3 5.1 AT 

* FE 2 

* O 3 

* 

The COMPOSITION of sample (named 

"PELLET") is unknown except for 

 75% ÏBORATEÓ.

* DEFINE BORATE 1.4 AT 

* LI 2 

* B 4 

* O 7 

* 

The flux (named "BORATE") is 

Lithium Tetraborate. 

* INTENSITIES PELLET 

* 1 .083 0 

* 2 .0065 0 

* 3 .092 0 

* 

* COMPOSITION PELLET 

* S1O2 ? 

* TIO2 ? 

* FE2O3 ? 

* BORATE 75 

* 

* DEFINE TIO2 4.5 AT 

* TI 1 

* O 2 

* 

Use of zero for counting time 

 indicates that intensities of 

 the unknown are given as relative 

 x-ray intensity (RXI). RXI is 

 the intensity of a given line in a 

 multielement sample divided by the 

 intensity of the same line from a 

 pure sample of same element. No 

 data for standards need be input.
A fifth example of Option 1 calculates the composition of a 

bulk heterogeneous unknown using measured x-ray intensities and 

whatever standards are furnished. This option requires that the 

analyst have some knowledge, or can make some reasonable 

assumptions, of the degree of heterogeneity of the samples such 

as particle sizes and voids fractions. 

11 

*ANALYZE 

COMPONENT AMOUNT 

S1O2 23.42 

T1O2 0.21 

FE2O3 2.11 

BORATE 75.0000 (FIXED) 

(TOTAL) 100.74 

Computer is told to ANALYZE. 

Sample name is omitted. Last 

sample named (PELLET) will be 

treated. 

Computer prints out the composition 

of "PELLET" in terms of the 

components which were defined. 

Since no multicomponent standard 

was used, these results are purely 

Ïfundamental parameter.Ó 

After "ANALYZE" the results can 

be called for in terms of the 

ELEMENTS also. 

* ELEMENTS 

SI 10.9450 

TI 0.1237 

FE 1.4788 

O 62.8619 

LI 6.1547 

B 19.1781 

* RESET 

* LINES 

* 1 SI KA 60 80 .496 A 

* 2 TI KA 

* 3 FE KA 

* 

LINES as before. 

The primary radiation is defined 

by its wavelength. 

* DEFINE SIO2 

* SI 1 

* O 2 

* 

Since "RESET" was used 

components must be redefined. 

* DEFINE TIO2 4,5 AT 

* TI 1 

* O 2 

* 

* DEFINE FE2O3 5.1 AT

* FE 2 

* O 3 

* 
Option 2 is used for particulate samples deposited on a thin 

substrate at small mass-thickness (small enough so that it can 

be assumed the particles do not shadow each other); the program 

predicts the effects of particle size and chemical composition 

on the emitted x-ray intensity. This option is particularly 

applicable to environmental samples such as the particulate 

material collected out of air or water on filters or impactor 

stages. The analyst must estimate particulate sizes and 

chemical composition for the material which he expects to 

deposit on his collection substrate. 

12 

Parameters of importance in 

 describing heterogeneity need 

 to be given, including particle 

 sizes of compounds. Sample is 

 thick (100 g/cm2

), has 10% voids 

 (O.1) and void size is 10 μm. 

Unknown percentage of components 

 is listed as Ï?Ó, their particle 

 sizes are 30,5 and 20 μm, 

 respectively. 

INTENSITIES of the lines from 

 "RAWMIX" are given in RXI for 

 this example. Again, no 

 multicomponent standard is used. 

COMP RAWMIX PARTIC 100 .1 10

SIO2 ? 30 

TIO2 ? 5 

FE2O3 ? 20 

The computer prints out the 

results of the calculation. 

* INTENSITIES RAWMIX 

* 1 .23 0 

* 2 .017 0 

* 3 .31 0 

* 

* ANALYZE RAWMIX 

COMPONENT AMOUNT 

SIO2 59.72 

TIO2 2.52 

FE2O3 37.66 

(TOTAL) 99.89 

* RESET 

* # OPTION 2 

* LINES 

* 1 S KA 57 40 CR45C 

* 

LINES as before. This time the 

tabulated Cr tube is used. 
Option 3: The third option to be illustrated is that which 

predicts relative x-ray intensities for bulk samples of any 

assumed composition. This option is useful for establishing the 

intensity-versus-composition relation for a set of simulated 

standards, for examining the effect of filters placed in the 

primary x-ray beam, the effect of primary spectra, etc. 

The first example of Option 3 predicts the relative x-ray 

intensities for a bulk homogeneous sample. 

13 

* DEFINE N2H4SO4 1.796 AT 

* N 2 

* H 8 

* S 1 

* O 4 

* 

* COMP SULFATE SEPARATE 

* N2H8SO4 1.E-6 10 

* 

A particular material of interest 

is defined [(NH4)2SO4, ammonium 

sulfate]. 

COMPOSITION of the compound 

 (here named "SULFATE") is 

 identified as SEPARATE particles 

 at 10-6 g/cm2 mass per unit area 

 and 10 μm in size.

The computer then prints out the 

intensity XI for the defined sample

divided by the intensity XI0 for 

the same mass per unit area at zero

particle size (i.e. without 

absorption effects).

* PREDICT SULFATE 

 LINE XI/XI0 

1 S KA 0.782840 

* RESET 

* # OPTION 3 Identify # OPTION 3. 

LINES and measuring conditions 

introduced as for OPTION 1. 

LINES 

1 V KA 57 40 W45C 

2 CR KA 

3 FE KA 

4 W LA1 57 40 W45C NI .03 For the W LA1 calculation a Ni 

primary beam filter, 0.03 g/cm2

in thickness, is assumed. If a 

calculated spectrum were used, the

filter and its thickness would 

be listed after the complete 

specification for the tube (e.g. 

following the CR 30 26 .3 in the 

line for Si in the example on the 
The second example of Option 3 predicts relative x-ray 

intensities for bulk heterogeneous samples for any composition 

and defined heterogeneity. This example requires that 

parameters such as particle sizes and voids fractions be used to 

characterize the heterogeneity. 

14 

Next keyword indicates that 

 COMPOSITION of sample will be 

 given. ("STEEL" is a name 

 which identifies the sample.) 

Each line lists an element and 

 its concentration in percent 

Computer is told to PREDICT RXI 

 for the ÏSTEELÓ sample.

* COMPOSITION STEEL 

* V 3 

* CR 5 

* FE 73 

* W 19 

* 

* PREDICT STEEL 

 LINE RXI 

1 V KA 0.026741 

2 CR KA 0.051762 

3 FE KA 0.565698 

4 W LA1 0.14170 

Computer prints out the 

 calculated RXI for each LINE.

* RESET 

As in the previous example, 

the components of interest 

need to be defined.

* LINES 

* 1 SI KA 60 80 MN KA 

* 2 TI KA 

* 

LINES entered as before. 

Here, incidence angle is 60∫ , 

 take-off angle is 80∫ , and 

 primary radiation is Mn Kα. 

* DEFINE SIO2 2.64 AT 

* SI 1 

* O 2 

* 

* DEFINE TIO2 4.5 AT 

* TI 1 

* O 2 

* 

* DEFINE FE2O3 5.1 AT 

* FE 2 

* O 3 

* 
CONCLUSION

The purpose of this Users' Guide is to help get the x-ray 

analyst started and familiar with the common kinds of problems 

which the computer program can handle. Therefore the examples 

have been put in very simple form. However, the program has 

many additional capabilities which have not been illustrated in 

this UsersÌ Guide but which the analyst will find discussed in 

the Reference Manual which is a separate document. One of the 

most important of the additional capabilities is performing the 

multivariate error analysis of the data so the analyst can see 

just what limitations in final accuracy arise from the 

experimental x-ray measurements themselves as distinguished from 

the mathematical treatment of the data. Hopefully, the analyst 

will explore the Reference Manual after becoming experienced 

with the examples contained in this UsersÌ Guide. 

15 

* COMP RAWMIX PARTIC 100 .1 10

* SIO2 80 30 

* TIO2 3 5 

* FE2O3 17 20 

COMPosition of the sample to 

 be predicted is given. 

Name of the sample is 

"RAWMIX"; it is PARTICulate, 

infinitely thick (100 g/cm2), 

has 10% voids (.1) of 10 μm 

diameter. "RAWMIX" by weight 

is 80 parts Si02, 3 parts Ti02

and 17 parts Fe203; the particle 

sizes are 30, 5 and 20 μm 

respectively. 

* PREDICT RAWMIX 

 LINE RXI 

1 SI KA 0.247651 

2 TI KA 0.043261 

Computer prints out RXI for 

the two lines input at the 

start. (No Fe line was input 

so no RXI is predicted, but the 

Fe2O3, must be considered.) 

For comparison, calculation of 

RXI for a homogeneous sample 

of same composition can be made. 

* PREDICT RAWMIX HOMOGENEOUS 

 LINE RXI 

1 SI KA 0.194917 

2 TI KA 0.039748 

Computer prints out RXI for 

the homogeneous sample.