What do I mean by "Non Physical EPMA"?
Well, basically any time the user is attempting to measure the same element with multiple spectrometers and/or EDS we have the potential for a non physical situation where the matrix may not be calculated with perfect rigor due to the same element being included in the matrix correction more than once.
Obviously, one should attempt to eliminate the potential for duplicate elements in the matrix correction physics by utilizing either the "disable quant" option for the duplicate elements for the unknown samples! as described here:
http://probesoftware.com/smf/index.php?topic=155.msg646#msg646or instead simply utilize the "aggregate intensity" feature as described here:
http://probesoftware.com/smf/index.php?topic=29.msg387#msg387With the caveat that the aggregate intensity feature can only aggregate intensities that are from the same element and x-ray, though they can have different Bragg analyzing crystals utilized.
However, there are situations where the presence of duplicate elements are necessary for improved precision, but the user wants to examine the statistics for each duplicate elements without aggregation. In these cases we might want to know what the effect of the duplicate elements in the matrix correction is exactly...
Let's start by looking at a Ti in quartz analysis where Ti was measured on all 5 spectrometers for maximum geometric efficiency as seen here for the TiO2 standard:
St 922 Set 1 TiO2 (elemental) (#22), Results in Elemental Weight Percents
ELEM: Ti Ti Ti Ti Ti Si O
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC SPEC
BGDS: LIN LIN LIN LIN LIN
TIME: 100.00 100.00 100.00 100.00 100.00
BEAM: 199.60 199.60 199.60 199.60 199.60
ELEM: Ti Ti Ti Ti Ti Si O SUM
XRAY: (ka) (ka) (ka) (ka) (ka) () ()
6 57.2174 57.3757 57.3689 57.5892 57.4592 .00000 40.0000 327.010
7 57.3874 57.3667 57.3167 57.4705 57.3516 .00000 40.0000 326.893
8 57.4199 57.2974 57.3111 57.3568 57.3109 .00000 40.0000 326.696
9 57.3539 57.3642 57.3707 57.2694 57.3508 .00000 40.0000 326.709
10 57.4238 57.3985 57.4350 57.1164 57.3299 .00000 40.0000 326.704
AVER: 57.3605 57.3605 57.3605 57.3605 57.3605 .000 40.000 326.802
SDEV: .08484 .03780 .05021 .18185 .05770 .000 .000 .14250
SERR: .03794 .01690 .02246 .08133 .02581 .00000 .00000
%RSD: .14791 .06589 .08754 .31703 .10060 .00000 .00000
PUBL: 59.9900 59.9900 59.9900 59.9900 59.9900 n.a. 40.0000 99.9900
%VAR: (-4.38) (-4.38) (-4.38) (-4.38) (-4.38) --- .00
DIFF: (-2.63) (-2.63) (-2.63) (-2.63) (-2.63) --- .00000
STDS: 922 922 922 922 922 0 0
STKF: .5621 .5621 .5621 .5621 .5621 .0000 .0000
STCT: 667.34 1600.07 1901.70 531.93 828.32 .00 .00
UNKF: .5621 .5621 .5621 .5621 .5621 .0000 .0000
UNCT: 667.34 1600.07 1901.70 531.93 828.32 .00 .00
UNBG: 2.12 5.17 7.04 1.70 3.41 .00 .00
ZCOR: 1.0204 1.0204 1.0204 1.0204 1.0204 .0000 .0000
KRAW: 1.00000 1.00000 1.00000 1.00000 1.00000 .00000 .00000
So, besides the fact that the total is obviously over 100%, we do observe that the "measured" Ti concentrations are off significantly, even though the standard k-factor is calculated correctly for Ti ka in TiO2 at 20 keV (0.5621) for each duplicate Ti element. Why is this? Because the ZAFCOR (Phi-RhoZ in this case) is *incorrect* due to the incorrect ratio of Ti to O in the specified matrix (because we added in Ti 5 times and oxygen only once!).
So again, we can use the disable quant or aggregate intensity feature to have the standard calculated correctly as seen here:
St 922 Set 1 TiO2 (elemental) (#22), Results in Elemental Weight Percents
ELEM: Ti Ti Ti Ti Ti Si O
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC SPEC
BGDS: LIN LIN LIN LIN LIN
TIME: 100.00 .00 .00 .00 .00
BEAM: 199.60 .00 .00 .00 .00
AGGR: 5
ELEM: Ti Ti Ti Ti Ti Si O SUM
XRAY: (ka) (ka) (ka) (ka) (ka) () ()
6 60.0175 .00000 .00000 .00000 .00000 .00000 40.0000 100.018
7 59.9893 .00000 .00000 .00000 .00000 .00000 40.0000 99.9893
8 59.9532 .00000 .00000 .00000 .00000 .00000 40.0000 99.9532
9 59.9829 .00000 .00000 .00000 .00000 .00000 40.0000 99.9829
10 60.0057 .00000 .00000 .00000 .00000 .00000 40.0000 100.006
AVER: 59.9897 .00000 .00000 .00000 .00000 .000 40.000 99.9897
SDEV: .02453 .00000 .00000 .00000 .00000 .000 .000 .02453
SERR: .01097 .00000 .00000 .00000 .00000 .00000 .00000
%RSD: .04088 .00000 .00000 .00000 .00000 .00000 .00000
PUBL: 59.9900 n.a. n.a. n.a. n.a. n.a. 40.0000 99.9900
%VAR: (.00) (.00) (.00) (.00) (.00) --- .00
DIFF: (.00) .00 .00 .00 .00 --- .00000
STDS: 922 0 0 0 0 0 0
STKF: .5621 0 0 0 0 .0000 .0000
STCT: 5529.37 .00 .00 .00 .00 .00 .00
UNKF: .5621 .0000 .0000 .0000 .0000 .0000 .0000
UNCT: 5529.37 .00 .00 .00 .00 .00 .00
UNBG: 19.44 .00 .00 .00 .00 .00 .00
ZCOR: 1.0672 .0000 .0000 .0000 .0000 .0000 .0000
And now we see that the ZAFCOR matrix correction for Ti ka in TiO2 is calculated correctly (1.0672).
But what about our unknown quartz samples? How much does it matter in that situation if we don't "aggregate"? Here is the quartz blank standard (1.42 PPM Ti) without the aggregate intensity feature:
Un 31 1920 sec on SiO2, Results in Elemental Weight Percents
ELEM: Ti Ti Ti Ti Ti Si O
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC CALC
BGDS: LIN LIN LIN LIN LIN
TIME: 1920.00 1920.00 1920.00 1920.00 1920.00
BEAM: 200.76 200.76 200.76 200.76 200.76
ELEM: Ti Ti Ti Ti Ti Si O SUM
XRAY: (ka) (ka) (ka) (ka) (ka) () ()
271 -.00003 .00039 .00003 -.00006 .00051 46.7430 53.2576 100.001
272 .00010 .00039 .00022 -.00036 -.00030 46.7430 53.2570 100.000
273 .00003 .00037 .00008 .00007 .00048 46.7430 53.2577 100.002
274 .00002 .00016 .00015 -.00005 .00009 46.7430 53.2572 100.001
275 -.00010 .00019 -.00002 .00016 .00009 46.7430 53.2572 100.001
AVER: .00000 .00030 .00009 -.00005 .00017 46.743 53.257 100.001
SDEV: .00007 .00011 .00010 .00020 .00034 .000 .000 .00067
SERR: .00003 .00005 .00004 .00009 .00015 .00000 .00012
%RSD: 4057.70 37.3350 103.073 -404.32 193.525 .00000 .00050
STDS: 922 922 922 922 922 0 0
STKF: .5621 .5621 .5621 .5621 .5621 .0000 .0000
STCT: 667.34 1600.07 1901.70 531.93 828.32 .00 .00
UNKF: .0000 .0000 .0000 .0000 .0000 .0000 .0000
UNCT: .00 .01 .00 .00 .00 .00 .00
UNBG: .99 2.63 3.41 .79 1.38 .00 .00
ZCOR: 1.1969 1.1969 1.1969 1.1969 1.1969 .0000 .0000
So now we see the standard k-factor is still calculated correctly, and the ZAFCOR matrix correction is also very close to the anticipated value.
Un 31 1920 sec on SiO2, Results in Elemental Weight Percents
ELEM: Ti Ti Ti Ti Ti Si O
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC CALC
BGDS: LIN LIN LIN LIN LIN
TIME: 1920.00 .00 .00 .00 .00
BEAM: 200.76 .00 .00 .00 .00
AGGR: 5
ELEM: Ti Ti Ti Ti Ti Si O SUM
XRAY: (ka) (ka) (ka) (ka) (ka) () ()
271 .00019 .00000 .00000 .00000 .00000 46.7430 53.2571 100.000
272 .00012 .00000 .00000 .00000 .00000 46.7430 53.2571 100.000
273 .00022 .00000 .00000 .00000 .00000 46.7430 53.2571 100.000
274 .00011 .00000 .00000 .00000 .00000 46.7430 53.2571 100.000
275 .00007 .00000 .00000 .00000 .00000 46.7430 53.2570 100.000
AVER: .00014 .00000 .00000 .00000 .00000 46.743 53.257 100.000
SDEV: .00006 .00000 .00000 .00000 .00000 .000 .000 .00011
SERR: .00003 .00000 .00000 .00000 .00000 .00000 .00002
%RSD: 43.8974 .00000 .00000 .00000 .00000 .00000 .00008
STDS: 922 0 0 0 0 0 0
STKF: .5621 0 0 0 0 .0000 .0000
STCT: 5529.37 .00 .00 .00 .00 .00 .00
UNKF: .0000 .0000 .0000 .0000 .0000 .0000 .0000
UNCT: .01 .00 .00 .00 .00 .00 .00
UNBG: 9.21 .00 .00 .00 .00 .00 .00
ZCOR: 1.1969 .0000 .0000 .0000 .0000 .0000 .0000
What if we aggregate the Ti ka and Al ka intensities? As we can see the ZAFCOR matrix correction hasn't changed because the Ti is essentially at zero concentrations. Now what about a real world sample? Here is the Audetat SiO2 standard without aggregate intensities turned on:
Un 4 Rusk sample, Results in Elemental Weight Percents
SPEC: Si O
TYPE: DIFF CALC
AVER: 46.707 53.251
SDEV: .002 .000
ELEM: Ti Ti Al Al
BGDS: LIN LIN EXP EXP
TIME: 400.00 400.00 400.00 400.00
BEAM: 100.05 100.05 100.05 100.05
ELEM: Ti Ti Al Al SUM
XRAY: (ka) (ka) (ka) (ka)
114 .00446 .00524 .01576 .01530 100.000
115 .00409 .00526 .01537 .01563 100.000
116 .00536 .00507 .01569 .01509 100.000
117 .00640 .00588 .01592 .01510 100.000
118 .00561 .00620 .01482 .01554 100.000
119 .00558 .00523 .01502 .01564 100.000
120 .00487 .00548 .01637 .01539 100.000
121 .00604 .00602 .01555 .01504 100.000
122 .00639 .00672 .01702 .01557 100.000
123 .00508 .00504 .01536 .01566 100.000
124 .00771 .00698 .01616 .01589 100.000
125 .00465 .00539 .01597 .01579 100.000
126 .00375 .00532 .01637 .01561 100.000
127 .00400 .00466 .01628 .01609 100.000
128 .00427 .00542 .01588 .01568 100.000
129 .00341 .00399 .01341 .01221 100.000
130 .00429 .00576 .01578 .01586 100.000
131 .00279 .00653 .01617 .01583 100.000
132 .00653 .00568 .01671 .01595 100.000
133 .00485 .00656 .01604 .01564 100.000
134 .00511 .00642 .01531 .01574 100.000
135 .00606 .00626 .01572 .01549 100.000
136 .00556 .00537 .01525 .01528 100.000
137 .00499 .00533 .01583 .01512 100.000
138 .00536 .00520 .01604 .01527 100.000
139 .00496 .00712 .01634 .01567 100.000
140 .00635 .00653 .01580 .01568 100.000
141 .00320 .00680 .01495 .01534 100.000
142 .00457 .00535 .01436 .01447 100.000
AVER: .00504 .00575 .01570 .01540 100.000
SDEV: .00111 .00075 .00073 .00070 .00000
SERR: .00021 .00014 .00013 .00013
%RSD: 22.0325 12.9763 4.61999 4.55493
STDS: 22 22 374 374
STKF: .5616 .5616 .0626 .0626
STCT: 103.63 374.70 147.71 503.19
UNKF: .0000 .0000 .0001 .0001
UNCT: .01 .03 .27 .91
UNBG: .07 .25 1.15 3.89
ZCOR: 1.1969 1.1969 1.3538 1.3538
And here is the same Audetat sample again with the aggregate intensity feature turned on:
Un 4 Rusk sample, Results in Elemental Weight Percents
SPEC: Si O
TYPE: DIFF CALC
AVER: 46.725 53.254
SDEV: .001 .000
ELEM: Ti Ti Al Al
BGDS: LIN LIN EXP EXP
TIME: 400.00 .00 400.00 .00
BEAM: 100.05 .00 100.05 .00
AGGR: 2 2
ELEM: Ti Ti Al Al SUM
XRAY: (ka) (ka) (ka) (ka)
114 .00507 .00000 .01540 .00000 100.000
115 .00501 .00000 .01557 .00000 100.000
116 .00513 .00000 .01523 .00000 100.000
117 .00599 .00000 .01529 .00000 100.000
118 .00607 .00000 .01538 .00000 100.000
119 .00530 .00000 .01550 .00000 100.000
120 .00535 .00000 .01562 .00000 100.000
121 .00602 .00000 .01516 .00000 100.000
122 .00665 .00000 .01590 .00000 100.000
123 .00504 .00000 .01559 .00000 100.000
124 .00714 .00000 .01595 .00000 100.000
125 .00523 .00000 .01583 .00000 100.000
126 .00497 .00000 .01578 .00000 100.000
127 .00451 .00000 .01614 .00000 100.000
128 .00517 .00000 .01572 .00000 100.000
129 .00387 .00000 .01248 .00000 100.000
130 .00544 .00000 .01584 .00000 100.000
131 .00571 .00000 .01591 .00000 100.000
132 .00586 .00000 .01612 .00000 100.000
133 .00619 .00000 .01573 .00000 100.000
134 .00613 .00000 .01564 .00000 100.000
135 .00621 .00000 .01554 .00000 100.000
136 .00541 .00000 .01527 .00000 100.000
137 .00526 .00000 .01528 .00000 100.000
138 .00523 .00000 .01544 .00000 100.000
139 .00664 .00000 .01582 .00000 100.000
140 .00649 .00000 .01571 .00000 100.000
141 .00601 .00000 .01525 .00000 100.000
142 .00518 .00000 .01444 .00000 100.000
AVER: .00560 .00000 .01547 .00000 100.000
SDEV: .00070 .00000 .00067 .00000 .00000
SERR: .00013 .00000 .00012 .00000
%RSD: 12.5764 .00000 4.33292 .00000
STDS: 22 0 374 0
STKF: .5616 0 .0626 0
STCT: 478.33 .00 650.90 .00
UNKF: .0000 .0000 .0001 .0000
UNCT: .04 .00 1.19 .00
UNBG: .32 .00 5.04 .00
ZCOR: 1.1969 .0000 1.3537 .0000
Note that the Ti ka ZAFCOR did not change with 5 digits of precision, but the Al ka ZAFCOR changed from 1.3538 to 1.3537, so no significant change there.
The bottom line: duplicate elements can introduce systematic accuracy errors if the duplicate elements are not disabled for quant or utilizing the aggregate intensity feature, but it depends on the physics details including the concentrations and absorption correction magnitudes.