Non Physical EPMA Situations

[Probeman]

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#msg646

or instead simply utilize the "aggregate intensity" feature as described here:

http://probesoftware.com/smf/index.php?topic=29.msg387#msg387

With 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.

[John Donovan]

This is an old topic but relevant for this post on using duplicate elements with different x-ray lines where the matrix correction will be affected by duplication of a major element quantification. 

Note that in this situation, where the element is duplicated but where the x-ray lines are different, we *cannot* utilize the "aggregate mode" feature in Probe for EPMA (as described in the previous post), because the photons are not the same energy.

And as above, if both duplicate elements are enabled for quantification, and the element is present in a significant concentration (in this example Fe Ka and Fe La in olivine), the totals will be will be excessively high and the matrix correction incorrectly calculated. But if either of the Fe channels are disabled for quantification (using the Disable Quant checkbox in the Elements/Cations dialog), the software should be able to correctly calculate the matrix correction.

That also means that the standard k-factor has to be calculated appropriately and there was a small bug (as Ben Buse and Gareth Seward independently pointed out to me) preventing that, which is now fixed (Gareth had previously sent me a similar example of W La and W Ma measured at the same time).

So here are the results of an olivine analysis with both Fe Ka and Fe La acquired, first with Fe Ka enabled and Fe La disabled:

Un   14 fayalite
TakeOff = 40.0  KiloVolt = 10.0  Beam Current = 200.  Beam Size =    1
(Magnification (analytical) =  20000),        Beam Mode = Analog  Spot
(Magnification (default) =     1000, Magnification (imaging) =    100)
Image Shift (X,Y):                                         .00,    .00
Number of Data Lines:  17             Number of 'Good' Data Lines:  17
First/Last Date-Time: 10/17/2017 06:56:23 PM to 10/17/2017 07:20:40 PM
WARNING- Using Exponential Off-Peak correction for Mg kb
WARNING- Quantitation is Disabled For Fe la, Spectro 1

Average Total Oxygen:       31.370     Average Total Weight%:  100.288
Average Calculated Oxygen:  31.370     Average Atomic Number:   18.697
Average Excess Oxygen:        .000     Average Atomic Weight:   29.166
Average ZAF Iteration:        2.00     Average Quant Iterate:     2.00

Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
WARNING- Duplicate analyzed elements are present in the sample matrix!!
Use Aggregate Intensity option or Disable Quant feature for accurate matrix correction.

Un   14 fayalite, Results in Elemental Weight Percents
 
ELEM:       Fe      Ca      Fe      Mn      Si      Mg       O
TYPE:     ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    CALC
BGDS:      LIN     LIN     LIN     LIN     LIN     EXP
TIME:      ---   10.00   10.00   10.00   10.00   10.00     ---
BEAM:      ---  199.06  199.06  199.06  199.06  199.06     ---

ELEM:     Fe-D      Ca      Fe      Mn      Si      Mg       O   SUM 
XRAY:     (la)    (ka)    (ka)    (ka)    (ka)    (kb)      ()
   672     ---    .109  52.006   3.080  13.502    .439  31.512 100.648
   673     ---    .105  52.374   3.107  13.477   -.403  31.041  99.700
   674     ---    .104  52.017   3.033  13.573   -.005  31.289 100.010
   675     ---    .105  52.100   3.008  13.524   -.503  30.922  99.156
   676     ---    .098  52.318   2.975  13.568    .223  31.501 100.684
   677     ---    .107  52.144   2.993  13.796    .139  31.663 100.842
   678     ---    .111  51.947   3.031  13.696    .577  31.795 101.159
   679     ---    .106  52.395   3.008  13.576    .128  31.482 100.695
   680     ---    .104  52.090   3.021  13.586    .023  31.339 100.162
   681     ---    .102  52.088   2.963  13.390    .539  31.437 100.520
   682     ---    .105  52.398   3.069  13.363   -.245  31.012  99.701
   683     ---    .114  52.227   3.033  13.678    .648  31.902 101.603
   684     ---    .094  52.309   2.975  13.731    .051  31.568 100.727
   685     ---    .110  51.914   3.079  13.539    .450  31.535 100.627
   686     ---    .111  52.122   3.024  13.342   -.482  30.742  98.859
   687     ---    .103  52.071   2.935  13.648    .338  31.586 100.681
   688     ---    .113  51.739   3.014  13.446   -.156  30.964  99.120

AVER:      ---    .106  52.133   3.021  13.555    .104  31.370 100.288
SDEV:      ---    .005    .185    .045    .129    .370    .328    .759
SERR:      ---    .001    .045    .011    .031    .090    .080
%RSD:      ---    4.88     .35    1.51     .95  357.09    1.05
STDS:      ---     804    1010     818     803     803     ---

STKF:      ---   .3188   .4636  1.0000   .1546   .2591     ---
STCT:      ---  326.01   63.05  117.44    9.34    2.50     ---

UNKF:      ---   .0011   .4644   .0266   .1207   .0007     ---
UNCT:      ---    1.09   63.15    3.12    7.29     .01     ---
UNBG:      ---    1.96     .75     .27     .15     .74     ---

ZCOR:      ---   .9927  1.1226  1.1365  1.1232  1.3948     ---
KRAW:      ---   .0033  1.0016   .0266   .7805   .0029     ---
PKBG:      ---    1.56   84.95   12.74   50.06    1.01     ---

And now the same unknown sample but with Fe Ka disabled and Fe La enabled:

Un   14 fayalite
TakeOff = 40.0  KiloVolt = 10.0  Beam Current = 200.  Beam Size =    1
(Magnification (analytical) =  20000),        Beam Mode = Analog  Spot
(Magnification (default) =     1000, Magnification (imaging) =    100)
Image Shift (X,Y):                                         .00,    .00
Number of Data Lines:  17             Number of 'Good' Data Lines:  17
First/Last Date-Time: 10/17/2017 06:56:23 PM to 10/17/2017 07:20:40 PM
WARNING- Using Exponential Off-Peak correction for Mg kb
WARNING- Quantitation is Disabled For Fe ka, Spectro 4

Average Total Oxygen:       31.391     Average Total Weight%:  100.195
Average Calculated Oxygen:  31.391     Average Atomic Number:   18.679
Average Excess Oxygen:        .000     Average Atomic Weight:   29.135
Average ZAF Iteration:        4.00     Average Quant Iterate:     2.00

Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
WARNING- Duplicate analyzed elements are present in the sample matrix!!
Use Aggregate Intensity option or Disable Quant feature for accurate matrix correction.

Un   14 fayalite, Results in Elemental Weight Percents
 
ELEM:       Fe      Ca      Fe      Mn      Si      Mg       O
TYPE:     ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    CALC
BGDS:      LIN     LIN     LIN     LIN     LIN     EXP
TIME:    10.00   10.00     ---   10.00   10.00   10.00     ---
BEAM:   199.06  199.06     ---  199.06  199.06  199.06     ---

ELEM:       Fe      Ca    Fe-D      Mn      Si      Mg       O   SUM 
XRAY:     (la)    (ka)    (ka)    (ka)    (ka)    (kb)      ()
   672  51.705    .109     ---   3.081  13.565    .431  31.494 100.386
   673  50.470    .105     ---   3.111  13.536   -.396  30.569  97.395
   674  52.043    .104     ---   3.033  13.638   -.005  31.370 100.184
   675  51.706    .105     ---   3.009  13.588   -.494  30.888  98.802
   676  52.860    .098     ---   2.975  13.634    .220  31.729 101.515
   677  51.718    .107     ---   2.994  13.861    .137  31.614 100.430
   678  53.218    .111     ---   3.029  13.764    .568  32.230 102.921
   679  51.936    .106     ---   3.010  13.640    .126  31.422 100.239
   680  51.064    .104     ---   3.024  13.648    .022  31.116  98.978
   681  51.495    .102     ---   2.965  13.452    .529  31.333  99.877
   682  50.468    .105     ---   3.073  13.422   -.240  30.531  97.359
   683  52.069    .114     ---   3.034  13.742    .637  31.923 101.519
   684  52.480    .094     ---   2.975  13.797    .050  31.692 101.088
   685  50.881    .110     ---   3.082  13.601    .442  31.305  99.421
   686  52.649    .111     ---   3.023  13.407   -.474  30.973  99.691
   687  52.236    .103     ---   2.935  13.714    .332  31.705 101.024
   688  54.239    .113     ---   3.010  13.517   -.153  31.761 102.487

AVER:   51.955    .106     ---   3.021  13.619    .102  31.391 100.195
SDEV:    .976    .005     ---    .046    .130    .364    .462   1.542
SERR:     .237    .001     ---    .011    .032    .088    .112
%RSD:     1.88    4.87     ---    1.54     .95  356.91    1.47
STDS:     9994     804     ---     818     803     803     ---

STKF:    .2674   .3190     ---  1.0000   .1554   .2546     ---
STCT:     1.68  326.01     ---  117.44    9.34    2.50     ---

UNKF:    .3147   .0011     ---   .0266   .1213   .0007     ---
UNCT:     1.98    1.09     ---    3.12    7.29     .01     ---
UNBG:      .24    1.96     ---     .27     .15     .74     ---

ZCOR:   1.6508   .9930     ---  1.1368  1.1231  1.3943     ---
KRAW:   1.1772   .0033     ---   .0266   .7805   .0029     ---
PKBG:     9.39    1.56     ---   12.74   50.06    1.01     ---

Even though the statistics on the Fe La channel are significantly lower than the Fe Ka channel, I am impressed with how well the two Fe measurements agree with each other.  And even more impressive is the deadtime correction on Ben's instrument, because he ran these quite "hot" at 200 nA (and 10 keV)...

Thank-you Ben (and Gareth) for sharing your data with us.
john

[John Donovan]

Even though the statistics on the Fe La channel are significantly lower than the Fe Ka channel, I am impressed with how well the two Fe measurements agree with each other. 

Ben Buse tells me that I should not be too impressed with his Fe La data because the unknown sample is the Fe std that was assigned to it.  Doh!

But it would be interesting if someone did such a measurement comparing Fe Ln or Ll with Fe Ka on olivines and "toggled" Fe channels on/off to see how well the quantification performs.  As Ben reminded me, Xavier Llovet has done some nice work on Fe alloys showing the problem with using Fe La lines for quantification.
john

[John Donovan]

We recently released an update to Probe for EPMA (and CalcImage and CalcZAF) that contains extensive modifications to the calculation of std k-factors when duplicate elements are being acquired and analyzed. This is version 12.0.3.

http://probesoftware.com/smf/index.php?topic=40.msg6422#msg6422

This is in regards to the "non-physical situation" of a major element being acquired and analyzed on more than one spectrometer.  In these situations, the matrix correction will be incorrect due to the totals being significantly over 100% (unless the duplicate elements all utilize the same x-ray line and the Probe for EPMA "aggregate" feature is turned on).  However, sometimes it is useful for research purposes to acquire duplicate elements with different x-rays lines for comparisons. In this case, one simply needs to utilize the "disable quant" feature for those duplicate elements that cannot be aggregated because they utilize different x-ray lines (or keVs).

I'm planning on acquiring some real sample data next week on some actual standards, but in the meantime I decided to create a simulation run and check that the calculated std-kfactors (and matrix corrections) on some standards look appropriate.  Yes, it's a "circular" test, but if I compare the results from the Standard app (which uses the new "normal sample " std kfac calculation code- since there are no duplicate elements in the Standard database), with the k-factors and matrix corrections from Probe for EPMA (which is using the new duplicate element std kfac calculation code), I can see if the two codes produce the same results and at least know we are internally consistent.   

So the simulation run has the following setup:

sp1 PET Au Ma
sp2 LIF Au La
sp3 PET Ag La
sp4 PET Ag La
sp5 LIF Cu ka

But first here are the calculated std kfacs and matrix corrections for one of the NIST Au-Cu-Ag standards at 15 keV and using Au La using the Standard app:

St  680 Au80-Cu20 alloy
TakeOff = 40.0  KiloVolt = 15.0  Density = 15.450  Type = alloy

ELEM:       Au      Cu
XRAY:      la      ka
ELWT:   80.150  19.830
KFAC:    .7375   .2514
ZCOR:   1.0868   .7889
AT% :   56.597  43.403

Now here is the simulation run in the same standard using the above spectrometer setup when all elements are enabled (the Ag channels are being aggregated because they are using the same x-ray line):

St  680 Set   1 Au80-Cu20 alloy
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 30.0  Beam Size =    0

St  680 Set   1 Au80-Cu20 alloy, Results in Elemental Weight Percents
 
ELEM:       Au      Au      Ag      Ag      Cu   SUM 
XRAY:     (ma)    (la)    (la)    (la)    (ka)
    10  78.179  77.070    .000    .000  19.374 174.622
    11  78.203  76.902   -.070    .000  19.490 174.525
    12  78.292  76.904    .009    .000  19.528 174.732

AVER:   78.225  76.959   -.021    .000  19.464 174.627
SDEV:     .059    .096    .043    .000    .080    .104
SERR:     .034    .056    .025    .000    .046
%RSD:      .08     .13 -208.64   .0000     .41

PUBL:   80.150  80.150    n.a.    n.a.  19.830  99.980
%VAR:    -2.40   -3.98     ---     ---   -1.85
DIFF:   -1.925  -3.191     ---     ---   -.366
STDS:      579     579     547       0     529

STKF:   1.0000  1.0000   .9911   .0000   .9974
UNKF:    .7568   .7340  -.0001   .0000   .2537
ZCOR:   1.0336  1.0485  1.4029   .0000   .7671
KRAW:    .7568   .7340  -.0001   .0000   .2544

As we can see, the totals are very high because we've added in the Au measurement twice. The matrix correction (ZCOR) is also quite wrong for the same reason). Now let's disable the Au Ma line and look at the Au La line:

St  680 Set   1 Au80-Cu20 alloy
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 30.0  Beam Size =    0

St  680 Set   1 Au80-Cu20 alloy, Results in Elemental Weight Percents
 
ELEM:     Au-D      Au      Ag      Ag      Cu   SUM 
XRAY:     (ma)    (la)    (la)    (la)    (ka)
    10     ---  79.938    .000    .000  19.933  99.870
    11     ---  79.781   -.069    .000  20.055  99.768
    12     ---  79.790    .008    .000  20.097  99.895

AVER:      ---  79.836   -.020    .000  20.028  99.845
SDEV:      ---    .088    .042    .000    .085    .068
SERR:      ---    .051    .024    .000    .049
%RSD:      ---     .11 -208.64   .0000     .42

PUBL:     n.a.  80.150    n.a.    n.a.  19.830  99.980
%VAR:      ---    -.39     ---     ---    1.00
DIFF:      ---   -.314     ---     ---    .198
STDS:      ---     579     547       0     529

STKF:      ---  1.0000   .9911   .0000   .9974
STCT:      ---  330.79  664.67     .00  333.53

UNKF:      ---   .7340  -.0001   .0000   .2537
ZCOR:      ---  1.0877  1.3686   .0000   .7894

KRAW:      ---   .7340  -.0001   .0000   .2544

As one can see the Au La matrix corrections (ZCOR) in both Standard and PFE, now agree with each other.  We can now disable quant for Au La and enable Au Ma, but first the results from the Standard app for the Au Ma line at 15 keV:

St  680 Au80-Cu20 alloy
TakeOff = 40.0  KiloVolt = 15.0  Density = 15.450  Type = alloy

ELEM:       Au      Cu
XRAY:      ma      ka
ELWT:   80.150  19.830
KFAC:    .7550   .2514
ZCOR:   1.0616   .7889

Now for the results from Probe for EPMA using the Au Ma line:

St  680 Set   1 Au80-Cu20 alloy
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 30.0  Beam Size =    0

St  680 Set   1 Au80-Cu20 alloy, Results in Elemental Weight Percents
 
ELEM:       Au    Au-D      Ag      Ag      Cu   SUM 
XRAY:     (ma)    (la)    (la)    (la)    (ka)
    10  80.314     ---    .000    .000  19.928 100.242
    11  80.344     ---   -.069    .000  20.048 100.324
    12  80.435     ---    .008    .000  20.088 100.532

AVER:   80.364     ---   -.020    .000  20.022 100.366
SDEV:     .063     ---    .042    .000    .083    .150
SERR:     .037     ---    .024    .000    .048
%RSD:      .08     --- -208.64   .0000     .42

PUBL:   80.150    n.a.    n.a.    n.a.  19.830  99.980
%VAR:      .27     ---     ---     ---     .97
DIFF:     .214     ---     ---     ---    .192
STDS:      579     ---     547       0     529

STKF:   1.0000     ---   .9911   .0000   .9974
UNKF:    .7568     ---  -.0001   .0000   .2537
ZCOR:   1.0619     ---  1.3690   .0000   .7891
KRAW:    .7568     ---  -.0001   .0000   .2544

Again, nice agreement between to two different std kfac codes.   Of course we don't have to utilize the pure elements as the primary standards, so here is the same sample but using another NIST alloy (Au60Ag40) as the primary standard for Au:

St  680 Set   1 Au80-Cu20 alloy
TakeOff = 40.0  KiloVolt = 15.0  Beam Current = 30.0  Beam Size =    0

St  680 Set   1 Au80-Cu20 alloy, Results in Elemental Weight Percents
 
ELEM:       Au    Au-D      Ag      Ag      Cu   SUM 
XRAY:     (ma)    (la)    (la)    (la)    (ka)
    10  80.324     ---    .000    .000  19.928 100.252
    11  80.355     ---   -.069    .000  20.048 100.334
    12  80.446     ---    .008    .000  20.088 100.542

AVER:   80.375     ---   -.020    .000  20.021 100.376
SDEV:     .063     ---    .042    .000    .083    .150
SERR:     .037     ---    .024    .000    .048
%RSD:      .08     --- -208.64   .0000     .42

PUBL:   80.150    n.a.    n.a.    n.a.  19.830  99.980
%VAR:      .28     ---     ---     ---     .97
DIFF:     .225     ---     ---     ---    .191
STDS:      681     ---     547       0     529

STKF:    .5344     ---   .9911   .0000   .9974
UNKF:    .7569     ---  -.0001   .0000   .2537
ZCOR:   1.0619     ---  1.3690   .0000   .7891
KRAW:   1.4162     ---  -.0001   .0000   .2544

All this shows of course is that the two std kfac codes agree with each other, but using completely different methods...  but internal consistency is a good starting point.  I hope to have some real data next week to share.
john

PS I've attached the MDB file below if anyone wants to try some calculations of their own.

[John Donovan]

Just as a brief follow up to the above post. I wanted to mention that I fixed a minor display issue last night that is related to the situation where one has duplicate elements with different x-ray lines and/or different keVs.   But it was an interesting bug because it didn't affect any quantitative results, just the Assign MAN Standards dialog plot. So...

In the case where we have duplicate elements with different x-ray lines or keVs, because we are loading in the concentration of each element one at a time for the std kfactor calculation, if the standard does not contain the element in question, the simply code skipped that std kfactor calculation.  After all, why would one ever want to calculate the standard k-factor for an element that is not in the standard? It would be zero or very close to zero. So can you guess?

That's right!  It's when that standard is utilized as a standard for the MAN background correction. Remember, a primary standard needs to have a known (major) concentration of the element in question, but an MAN standard needs to have a *zero* concentration of the element in question!  After all, it's determining the *background* at the on-peak position, so the element in question must *not* be present in the standards utilized for the MAN bgd calibration for that emission line. 

However, the MAN background intensity still needs to be corrected for continuum absorption for each emission line for each MAN standard.  And even if the element concentration is zero in an MAN standard (and it had better be!), one still needs to calculate the absorption correction for that emission line in that standard!  For samples with no duplicate elements or samples with duplicate elements that have the same x-ray (or keVs), the "normal" std kfactor code worked just fine as all elements are calculated at once. But for the one element at a time calculation (for samples with duplicate elements and different x-ray lines or keVs), we now calculate standard k-factors for all elements in the standard even if the element concentration is zero.

This bug didn't affect any quant analyses because when the MAN bgd calculation is actually applied to a sample analysis, the code utilizes the absorption correction term for the sample (unknown or standard), that is currently being analyzed. It only affected the MAN plot display in the Assign MAN Standards, and only if the sample contained duplicate elements with different x-rays lines and/or keVs.

I thought this was actually a very funny but cute illustration of the difference between normal (primary) standards and MAN standards. Or maybe I'm just a little bit weird with my sense of humor!   
john