Correcting for Particle Geometry Effects

[John Donovan]

We've been discussing modeling SF effects for inclusions in a matrix, but what if we have actual particles deposited on a substrate that we wish to characterize that are smaller than the beam interaction volume (e.g., 1 um or smaller)?

In these cases we are often interested in determining the actual composition of the particle (which is deposited or dispersed on a low Z substrate to minimize fluorescence from the substrate). Therefore, a carbon planchet works best, but sometimes a Si wafer can work unless you are trying to analyze a silicate mineral or glass particle!

Clearly if the emitted x-rays are similar in energy, the geometric effects tend to cancel each other out, but one can get surprised, so it is a good idea if you see a low total (because some electrons are falling outside the particle onto the planchet surface), to go ahead and model with a particle geometry correction which in CalcZAF is available from the Analytical menu (in Probe for EPMA this particle correction dialog is accessed from the Calculation Options dialog from the Analyze! window) as seen here:



For example, this olivine particle composition run with the typical EPMA flat smooth surface assumption, yields these results:

OLIVINE PARTICLE-JTA-1.0UM.DAT, Sample 1

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Mg Ka     273  34.554   .2176 10.5798  1.5616   .9952  1.0220  1.5882
   Fe Ka     263  54.809   .5083 18.6926   .9960  1.0000  1.0827  1.0783
   Mn Ka     275  54.406   .4993 18.0833   .9971  1.0000  1.0929  1.0897
   Si Ka     273  19.960   .1150 10.5798  1.6933  1.0000  1.0254  1.7363

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Mg Ka  1.0329   .9895   .7727   .4948   20.00  1.3050 15.3257
   Fe Ka  1.1320   .9564   .9695   .9734   20.00  7.1120  2.8121
   Mn Ka  1.1421   .9569   .9662   .9690   20.00  6.5390  3.0586
   Si Ka  1.0522   .9745   .8345   .4928   20.00  1.8390 10.8755

SAMPLE: 1, ITERATIONS: 5, Z-BAR: 12.05048

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Mg ka  1.8295   .9957  1.0088  1.8378  1.0108   .9981   .4223  1.3050 15.3257 399.740
   Fe ka   .9954  1.0000  1.1570  1.1517  1.2463   .9283   .9739  7.1120  2.8121 12.6621
   Mn ka   .9989  1.0000  1.1760  1.1747  1.2651   .9296   .9672  6.5390  3.0586 15.6175
   Si ka  1.7097   .9998  1.0127  1.7310  1.0299   .9833   .4881  1.8390 10.8755 328.303

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
   Mg ka  .14956  .03254   5.980   9.917  24.979   4.655   20.00               
   Fe ka  .03540  .01799   2.072   2.666   3.767    .702   20.00
   Mn ka  .00026  .00013    .015    .020    .028    .005   20.00
   Si ka  .19673  .02262   3.915   8.375  14.151   2.637   20.00
   O                        .000    .000    .000    .000
   O                        .000    .000    .000    .000
   O                       8.995   -----  57.075  10.637
   TOTAL:                 20.978  20.978 100.000  18.637


And although the total is only around 21%, the atomic/formula ratios of the elements are off by some 10% from olivine stoichiometry. Here is the same intensity data but treated using the particle corrections shown in the dialog above:

OLIVINE PARTICLE-JTA-1.0UM.DAT, Sample 1

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Mg Ka     273  34.554   .2178 10.5798  1.5595   .9952  1.0220  1.5861
   Fe Ka     263  54.809   .5083 18.6926   .9960  1.0000  1.0827  1.0783
   Mn Ka     275  54.406   .4993 18.0833   .9971  1.0000  1.0929  1.0897
   Si Ka     273  19.960   .1151 10.5798  1.6909  1.0000  1.0254  1.7338

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Mg Ka  1.0329   .9895   .7735   .4960   20.00  1.3050 15.3257
   Fe Ka  1.1320   .9564   .9695   .9734   20.00  7.1120  2.8121
   Mn Ka  1.1421   .9569   .9662   .9690   20.00  6.5390  3.0586
   Si Ka  1.0522   .9745   .8350   .4938   20.00  1.8390 10.8755

SAMPLE: 1, ITERATIONS: 3, Z-BAR: 12.54346

E-RANGE:  10.8350, INTE-STEP:  110
Particle or thin film corrections utilized were Square Pyramid (curved top and curved sides or sphere)

Particle parameters were a particle diameter of 1 microns, a particle density of 3 gm/cm^3, a thickness factor of 1, and a numerical integration step size of 0.00001 microns.

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Mg ka  7.9954   .9990  1.0045  8.0236  1.0034  1.0011   .0967  1.3050 15.3257 2040.46
   Fe ka  6.3427  1.0000  1.1514  7.3028  1.2379   .9301   .1529  7.1120  2.8121 60.2582
   Mn ka  6.5215  1.0000  1.1704  7.6325  1.2564   .9315   .1482  6.5390  3.0586 74.2905
   Si ka  8.0531  1.0000  1.0085  8.1211  1.0225   .9863   .1037  1.8390 10.8755 1561.62

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL NORMEL% NORMOX%
   Mg ka  .14956  .03258  26.142  43.352  23.434   4.373   20.00 26.2125 43.4681         
   Fe ka  .03540  .01799  13.140  16.905   5.126    .957   20.00 13.1754 16.9501
   Mn ka  .00026  .00013    .099    .128    .039    .007   20.00 .099347 .128281
   Si ka  .19673  .02265  18.392  39.348  14.267   2.663   20.00 18.4418 39.4535
   O                        .000    .000    .000    .000
   O                        .000    .000    .000    .000
   O                      41.958   -----  57.134  10.663         42.0711
   TOTAL:                 99.732  99.732 100.000  18.663         100.000 100.000


Not only is the total now much closer to 100%, but the atomic/formula ratios are closer to the expected olivine geometry.

But what about compositions where the emitted x-rays are *not* similar in energy? Let's take a "textbook" case from the John Armstrong's Lehigh course: CaF2 or fluorite. The data file used for these calculations is attached below. Let's start first with the bulk CaF2 measurement just as a "sanity check":

CaF2 bulk

SAMPLE: 1, ITERATIONS: 10, Z-BAR: 14.647

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ca ka  1.0043  1.0000  1.0059  1.0102  1.0467   .9610   .9343  4.0390  4.9517 153.733
   F  ka  4.6091   .9998   .9822  4.5261   .9497  1.0342   .1379   .6870 29.1121 6821.05

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL               
   Ca ka  .50810  .50810  51.327   -----  33.335   8.000   20.00             
   F  ka  .10750  .10750  48.655   -----  66.665  15.999   20.00
   TOTAL:                 99.983   ----- 100.000  23.999


These intensities are relative to the CaF2 standard, so we expect a reasonable measurement and we obtain a 100% total as expected (make sure the particle correction is *off* for these bulk intensities!).

Now, let's take an relatively easy case, but still with visible particle geometry effects, starting with the 10 um particle and again using bulk CaF2 (std #831) as the primary standard).

According to the lab notes, this is rectangular particle so we will use the following parameters for the 10 um particle and assume fluorite has a density of 3.1 (remember, density is important in EPMA whenever we are dealing with interaction volumes larger than our specimen).

First the 10 um particle *without*any particle corrections:

CaF2 10 um particle- use Rectangular Prism model

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Ca Ka     831  51.200   .5068 14.6320  1.0043  1.0000  1.0059  1.0102
    F Ka     831  48.800   .1080 14.6320  4.6000   .9998   .9822  4.5173

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Ca Ka  1.0468   .9609   .9383   .9343   20.00  4.0390  4.9517
    F Ka   .9498  1.0341   .6357   .1382   20.00   .6870 29.1121

SAMPLE: 2, ITERATIONS: 10, Z-BAR: 14.36482

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ca ka  1.0045  1.0000  1.0063  1.0109  1.0492   .9591   .9340  4.0390  4.9517 162.053
   F  ka  4.3985   .9998   .9830  4.3229   .9522  1.0323   .1445   .6870 29.1121 6870.21

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL                       
   Ca ka 1.00190  .50779  51.332   -----  31.094   8.000   20.00             
   F  ka 1.15460  .12473  53.919   -----  68.906  17.728   20.00
   TOTAL:                105.252   ----- 100.000  25.728


Note the high total due to over correcting F ka. Next the 10 um particle *with* the rectangular particle correction:



CaF2 10 um particle- use Rectangular Prism model

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Ca Ka     831  51.200   .5069 14.6320  1.0043  1.0000  1.0059  1.0102
    F Ka     831  48.800   .1082 14.6320  4.5945   .9998   .9822  4.5119

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Ca Ka  1.0468   .9609   .9384   .9344   20.00  4.0390  4.9517
    F Ka   .9498  1.0341   .6374   .1387   20.00   .6870 29.1121

SAMPLE: 2, ITERATIONS: 9, Z-BAR: 14.67521

E-RANGE:  11.1924, INTE-STEP:  113
Particle or thin film corrections utilized were Rectangular Prism (flat top and flat sides or cube)

Particle parameters were a particle diameter of 10 microns, a particle density of 3.1 gm/cm^3, a thickness factor of 1, and a numerical integration step size of 0.00001 microns.

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ca ka   .9987  1.0000  1.0058  1.0045  1.0464   .9612   .9396  4.0390  4.9517 152.004
   F  ka  3.9033   .9998   .9821  3.8326   .9494  1.0344   .1633   .6870 29.1121 6774.41

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL NORMEL% NORMOX%
   Ca ka 1.00190  .50781  51.011   -----  33.563   8.000   20.00 51.5928   ----- 
   F  ka 1.15460  .12488  47.861   -----  66.437  15.835   20.00 48.4072   -----
   TOTAL:                 98.872   ----- 100.000  23.835         100.000   -----


As we can see, the total is much better, almost 99%, so a decent job. More importantly the Ca:F atomic ratio went from 31:69 without the particle correction, to 33:66 with the particle correction, the latter which is what we should expect from CaF2.

Here is the next example, a 5 um CaF2 particle also calculated with a square pyramid geometry:



CaF2 5 um particle- use Square Pyramid model

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Ca Ka     831  51.200   .5069 14.6320  1.0043  1.0000  1.0059  1.0102
    F Ka     831  48.800   .1082 14.6320  4.5945   .9998   .9822  4.5119

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Ca Ka  1.0468   .9609   .9384   .9344   20.00  4.0390  4.9517
    F Ka   .9498  1.0341   .6374   .1387   20.00   .6870 29.1121

SAMPLE: 3, ITERATIONS: 8, Z-BAR: 14.64268

E-RANGE:  11.1911, INTE-STEP:  113
Particle or thin film corrections utilized were Square Pyramid (curved top and curved sides or sphere)

Particle parameters were a particle diameter of 5 microns, a particle density of 3.1 gm/cm^3, a thickness factor of 1, and a numerical integration step size of 0.00001 microns.

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ca ka  1.7920  1.0000  1.0059  1.8025  1.0468   .9609   .5236  4.0390  4.9517 138.020
   F  ka  4.7739   .9998   .9822  4.6879   .9497  1.0342   .1335   .6870 29.1121 6119.71

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL NORMEL% NORMOX%
   Ca ka  .50400  .25545  46.045   -----  33.300   8.000   20.00 51.2971   -----
   F  ka  .86220  .09325  43.717   -----  66.700  16.024   20.00 48.7029   -----
   TOTAL:                 89.762   ----- 100.000  24.024         100.000   -----


The total isn't so great (~90%), but the stoichiometry is excellent and therefore the "normalized" elemental % values (Ca = 51.29 and F = 48.7) are excellent as seen in the NORMEL %" column.

[Probeman]

As stated in the Thin Film/Particle Correction dialog, smaller particles and/or higher beam energies, may require a smaller integration step size.

Let's examine the 0.5 um CaF2 particle, here without any particle correction:

CaF2 0.5 um particle- use Square Pyramid model

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Ca Ka     831  51.200   .5068 14.6320  1.0043  1.0000  1.0059  1.0102
    F Ka     831  48.800   .1080 14.6320  4.6000   .9998   .9822  4.5173

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Ca Ka  1.0468   .9609   .9383   .9343   20.00  4.0390  4.9517
    F Ka   .9498  1.0341   .6357   .1382   20.00   .6870 29.1121

SAMPLE: 6, ITERATIONS: 13, Z-BAR: 12.17671

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ca ka  1.0064  1.0000  1.0105  1.0170  1.0682   .9460   .9323  4.0390  4.9517 14.7444
   F  ka  2.8483   .9999   .9896  2.8182   .9716  1.0184   .2232   .6870 29.1121 401.961

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL                       
   Ca ka  .05310  .02691   2.737   -----  16.141   8.000   20.00
   F  ka  .22140  .02392   6.740   -----  83.859  41.564   20.00
   TOTAL:                  9.478   ----- 100.000  49.564


Note that the atomic ratios are far from stoichiometry for CaF2. Now we specify the geometric mode (square pyramid), the particle size (0.5 um), the density (3.1) and the default integration step size (0.000010):

CaF2 0.5 um particle- use Square Pyramid model

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Ca Ka     831  51.200   .5069 14.6320  1.0043  1.0000  1.0059  1.0102
    F Ka     831  48.800   .1082 14.6320  4.5945   .9998   .9822  4.5119

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Ca Ka  1.0468   .9609   .9384   .9344   20.00  4.0390  4.9517
    F Ka   .9498  1.0341   .6374   .1387   20.00   .6870 29.1121

SAMPLE: 6, ITERATIONS: 3, Z-BAR: 14.66793

E-RANGE:  11.1921, INTE-STEP:  113
Particle or thin film corrections utilized were Square Pyramid (curved top and curved sides or sphere)

Particle parameters were a particle diameter of 0.5 microns, a particle density of 3.1 gm/cm^3, a thickness factor of 1, and a numerical integration step size of 0.00001 microns.

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ca ka 15.3581  1.0000  1.0058 15.4475  1.0465   .9611   .0611  4.0390  4.9517 124.051
   F  ka 16.6308  1.0000   .9821 16.3330   .9495  1.0344   .0383   .6870 29.1121 5522.26

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL NORMEL% NORMOX%
   Ca ka  .05310  .02691  41.575   -----  33.504   8.000   20.00 51.5266   -----                                       
   F  ka  .22140  .02395  39.111   -----  66.496  15.877   20.00 48.4734   -----
   TOTAL:                 80.686   ----- 100.000  23.877         100.000   -----


The atomic ratio is much closer to 33:66, but not exact. But what if we specify a smaller integration step size (0.0000010) as seen here:

CaF2 0.5 um particle- use Square Pyramid model

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Ca Ka     831  51.200   .5069 14.6320  1.0043  1.0000  1.0059  1.0102
    F Ka     831  48.800   .1082 14.6320  4.5945   .9998   .9822  4.5119

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Ca Ka  1.0468   .9609   .9384   .9344   20.00  4.0390  4.9517
    F Ka   .9498  1.0341   .6374   .1387   20.00   .6870 29.1121

SAMPLE: 6, ITERATIONS: 3, Z-BAR: 14.6523

E-RANGE:  11.1916, INTE-STEP:  1121
Particle or thin film corrections utilized were Square Pyramid (curved top and curved sides or sphere)

Particle parameters were a particle diameter of 0.5 microns, a particle density of 3.1 gm/cm^3, a thickness factor of 1, and a numerical integration step size of 0.000001 microns.

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ca ka 14.8145  1.0000  1.0058 14.9011  1.0466   .9610   .0633  4.0390  4.9517 120.003
   F  ka 16.1334  1.0000   .9822 15.8452   .9496  1.0343   .0395   .6870 29.1121 5328.93

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL NORMEL% NORMOX%
   Ca ka  .05310  .02691  40.105   -----  33.378   8.000   20.00 51.3845   -----
   F  ka  .22140  .02395  37.943   -----  66.622  15.968   20.00 48.6155   -----
   TOTAL:                 78.048   ----- 100.000  23.968         100.000   -----


Nailed it!   

[Probeman]

Paul Carpenter has pointed out to me that the new CalcZAF produces slightly different numbers from the previous version when the particle size is very small (0.5 um).  This is true and is due to recent improvements in the Reed fluorescence correction by myself, Zack Gainsforth and John Armstrong.  The new code works much better for situations with large fluorescence corrections such as bulk Co-Cu or Ni-Fe and also in particle and thin film geometries where the fluorescence correction becomes dominant.

See here for more details:

http://probesoftware.com/smf/index.php?topic=490.0

Taking the above CaF2 0.5 um particle example, we again obtain this result with no particle correction:

CaF2 0.5 um particle- use Square Pyramid model

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Ca Ka     831  51.200   .5068 14.6320  1.0043  1.0000  1.0059  1.0102
    F Ka     831  48.800   .1080 14.6320  4.6000   .9998   .9822  4.5172

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Ca Ka  1.0468   .9609   .9383   .9343   20.00  4.0390  4.9517
    F Ka   .9498  1.0341   .6357   .1382   20.00   .6870 29.1121

STDELEM        6       6
STDDENS     2.10    2.10
STDTHIC    200.0   200.0
STDSINT    311.1   311.1

SAMPLE: 6, ITERATIONS: 13, Z-BAR: 12.1767

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ca ka  1.0064  1.0000  1.0105  1.0170  1.0682   .9460   .9323  4.0390  4.9517 14.7444
   F  ka  2.8483   .9999   .9896  2.8182   .9716  1.0184   .2232   .6870 29.1121 401.961

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL                             
   Ca ka  .05310  .02691   2.737   -----  16.141   8.000   20.00         
   F  ka  .22140  .02392   6.741   -----  83.859  41.565   20.00
   TOTAL:                  9.478   ----- 100.000  49.565

With the particle correction options seen here:



we obtain this result:

CaF2 0.5 um particle- use Square Pyramid model

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Ca Ka     831  51.200   .5069 14.6320  1.0043  1.0000  1.0059  1.0102
    F Ka     831  48.800   .1082 14.6320  4.5945   .9998   .9822  4.5118

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Ca Ka  1.0468   .9609   .9384   .9344   20.00  4.0390  4.9517
    F Ka   .9498  1.0341   .6374   .1387   20.00   .6870 29.1121

STDELEM        6       6
STDDENS     2.10    2.10
STDTHIC    200.0   200.0
STDSINT    311.1   311.1

SAMPLE: 6, ITERATIONS: 3, Z-BAR: 14.66375

E-RANGE:  11.1920, INTE-STEP:  113
Particle or thin film corrections utilized were Square Pyramid (curved top and curved sides or sphere)

Particle parameters were a particle diameter of 0.5 microns, a particle density of 3.18 gm/cm^3, a thickness factor of 1, and a numerical integration step size of 0.00001 microns.

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ca ka 15.3415  1.0000  1.0058 15.4309  1.0466   .9611   .0612  4.0390  4.9517 124.012
   F  ka 16.6378  1.0000   .9821 16.3400   .9495  1.0344   .0383   .6870 29.1121 5516.88

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL NORMEL% NORMOX%
   Ca ka  .05310  .02691  41.530   -----  33.471   8.000   20.00 51.4886   ----- 
   F  ka  .22140  .02395  39.129   -----  66.530  15.902   20.00 48.5114   ----- 
   TOTAL:                 80.659   ----- 100.000  23.902         100.000   -----


But note that if we increase the number of interation steps by changing this parameter seen here:



we obtain this similar result:

CaF2 0.5 um particle- use Square Pyramid model

STANDARD PARAMETERS:

 ELEMENT  STDNUM STDCONC STDKFAC   Z-BAR  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR
   Ca Ka     831  51.200   .5069 14.6320  1.0043  1.0000  1.0059  1.0102
    F Ka     831  48.800   .1082 14.6320  4.5945   .9998   .9822  4.5118

 ELEMENT STP-POW BKS-COR   F(x)e   F(x)s      Eo      Ec   Eo/Ec
   Ca Ka  1.0468   .9609   .9384   .9344   20.00  4.0390  4.9517
    F Ka   .9498  1.0341   .6374   .1387   20.00   .6870 29.1121

STDELEM        6       6
STDDENS     2.10    2.10
STDTHIC    200.0   200.0
STDSINT    311.1   311.1

SAMPLE: 6, ITERATIONS: 3, Z-BAR: 14.63986

E-RANGE:  11.1912, INTE-STEP:  1121
Particle or thin film corrections utilized were Square Pyramid (curved top and curved sides or sphere)

Particle parameters were a particle diameter of 0.5 microns, a particle density of 3.18 gm/cm^3, a thickness factor of 1, and a numerical integration step size of 0.000001 microns.

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ca ka 14.3957  1.0000  1.0059 14.4801  1.0468   .9609   .0652  4.0390  4.9517 116.877
   F  ka 15.7480  1.0000   .9822 15.4671   .9497  1.0342   .0405   .6870 29.1121 5179.92

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL NORMEL% NORMOX%
   Ca ka  .05310  .02691  38.971   -----  33.277   8.000   20.00 51.2714   -----                           
   F  ka  .22140  .02395  37.039   -----  66.723  16.041   20.00 48.7286   -----
   TOTAL:                 76.010   ----- 100.000  24.041         100.000   -----


The total is slightly lower (which merely means that the particle is somewhat smaller than 0.5 um!), but note that the stoichiometry has improved.

Note: one can actually "solve" for the particle size by adjusting the size (Particle Diameter) until the analysis total approaches 100%.  In practice there are so many variables that this is at best a rough estimate.  In any case, the particle geometry correction isn't affected all that much, so long as the total is between 80 and 120% depending on the physics details of course.