The Limits of EPMA Accuracy

[Probeman]

Using the new plot option of relative percent variance (i.e., accuracy) in Probe for EPMA from the Output | Plot Standard and Unknown XY plots menu dialog:

https://smf.probesoftware.com/index.php?topic=40.msg14388#msg14388

we can quickly evaluate our secondary standard accuracy. Here for Mg Ka in MgAl2O4 using MgO as a primary standard in the FIGMAS mount from Will Nachlas:



All within 1% relative accuracy. But since we're plotting relative percent accuracy, we can plot more than a single compound, here Ti Ka in SrTiO3 and RbTiOPO4 using TiO2 as a primary standard:



And here for Fe ka in a multitude of compounds using Fe metal as the primary standard for the sulfides, and magnetite as a primary standard for the oxides, silicates and glasses:



Note that only the natural chromite is significantly outside the 1% variance accuracy limits.

[John Donovan]

In order to utilize the accuracy checks shown in the above plots, one must run their secondary standards as standard samples. Therefore, some of you have asked: how do I run my standards more than once?

Well first, to re-run ones standard samples a second time, just check the "Acquire Standard samples (again)" checkbox.  Even if you don't have an unknown sample selected, the standards will run a second time.

To run your standard even more replicates, just create a random unknown sample to run along with your standards and check the Re-Standardization Interval checkbox and enter a short interval (in hours) as seen here:



Say every hour or so. That's easy, right?

[Probeman]

With the new plotting feature in the Output | Output Standard and Unknown XY Plots menu dialog, we can plot relative accuracy for multiple elements:



We can see generally ~1% or better relative accuracy for Si, Mg and Fe. In addition we can plot the absolute wt% differences from the published values of the glasses here for Fe Ka:



Most of these Fe analyses are off by only a few hundred PPM!

[John Donovan]

In case anyone missed this post over the July 4th weekend, I wanted to call attention to this post:

https://smf.probesoftware.com/index.php?topic=8.msg14405#msg14405

For best EPMA accuracy, please set your defaults in the [software] section of your Probewin.ini file for the following items to these values:

[software]
DeadtimeCorrectionType=4    ; 1=traditional, 2=high precision formula, 3=Super Precision, 4=Logarithmic, 5=Exponential
MACTypeFlag=6               ; default MAC file (1 = LINEMU, 2 = CITZMU, 3 = McMaster, 4 = MAC30, 5 = MACJTA, 6 = FFAST
DefaultZAFType=11           ; default zaf algorithm 1=armprz, 2=pdrzaf, ... 9=papfull, 10=papsimp, 11=DAM

[John Donovan]

Andrew and I presented our poster yesterday at M&M 2026: "Breaking the EPMA1% Accuracy Barrier".

I've attached it below (login to see attachments). I am happy to discuss details with all, as some of the material is quite unintuitive. Feel free to call or email me.

[Probeman]

When testing instrument accuracy you will want to utilize standards that you are very confident they are the composition they claim to be.  That is generally not the case for natural minerals. 

Some natural hematite and magnetite (and pyrite) standards may be pure and stoichiometric enough, but maybe not.

That is why my accuracy testing was generally performed with high purity synthetic minerals such as MgO, Al2O3, MgAl2O4, SiO2, SrTiO3, TiO2, YIG, Fe2SiO4 and Mg2SiO4 (and a natural magnetite and pyrite that have been checked for purity and stoichiometry).

https://smf.probesoftware.com/index.php?topic=1831.msg14108#msg14108

https://smf.probesoftware.com/index.php?topic=1831.msg14131#msg14131

What one would NOT want to do is to attempt to analyze Mg, Al or Si Ka in oxides or silicates using the pure metal because of the large peak shift between the metal and the oxide.

This Ka peak shift decreases as the atomic number increases, and is quite small by the time one reaches Fe. But depending on the quality of the LiF crystal, a peak shift in Fe Ka can be detected when performing high precision quant:

https://smf.probesoftware.com/index.php?topic=1423.msg14418#msg14418

Thus, it is best practice use Fe metal as a primary standard for Fe in alloys and sulfides, and utilize an oxide primary standard for oxides and silicates.

[Probeman]

What one would NOT want to do is to attempt to analyze Mg, Al or Si Ka in oxides or silicates using the pure metal because of the large peak shift between the metal and the oxide.

This Ka peak shift decreases as the atomic number increases, and is quite small by the time one reaches Fe. But depending on the quality of the LiF crystal, a peak shift in Fe Ka can be detected when performing high precision quant:

https://smf.probesoftware.com/index.php?topic=1423.msg14418#msg14418

Thus, it is best practice use Fe metal as a primary standard for Fe in alloys and sulfides, and utilize an oxide primary standard for oxides and silicates.

As mentioned in the previous post I have found it necessary for WDS to utilize a metal standard for alloys and sulfides, and utilize an oxide standard for oxides and silicates. Basically WDS has too much spectral resolution than it really needs for quantitative work!

We all know that there is some degree of peak shift with these metal vs oxide measurements, but how much of the effects in quantification accuracy are actually changes in peak position (peak shift) as opposed to changes in peak shape?

Recently I decided to see if I could determine that by first adjusting the peak position for the metal vs the oxide separately. Here are my metal peak positions for Si, Ti and Fe:

On and Off Peak Positions:
ELEM:    si ka   ti ka   fe ka
CRYST:    LTAP    LLIF     LIF
ONPEAK 27553.3 68316.3 48009.0
OFFSET 187.316 -24.867 106.402
HIPEAK 29450.3 69220.3 49037.0
LOPEAK 24731.3 67397.3 46923.0
HI-OFF 1897.00 904.000 1028.00
LO-OFF -2822.0 -919.00 -1086.0

and here are the peak positions for the oxides:

On and Off Peak Positions:
ELEM:    si ka   ti ka   fe ka
CRYST:    LTAP    LLIF     LIF
ONPEAK 27534.2 68327.5 48009.0
OFFSET 206.418 -36.070 106.402
HIPEAK 29431.9 69231.4 49037.1
LOPEAK 25211.9 67408.5 46922.5
HI-OFF 1897.67 903.891 1028.13
LO-OFF -2322.3 -919.05 -1086.5

Note that the peak position for Fe Ka is the same for the metal and the oxide.  That should be a clue as to what we see next...

When analyzing SiO2 using the pure metal as the primary standard we see this:

St  914 Set   2 SiO2 (elemental) (#14), Results in Elemental Weight Percents
 
ELEM:       Si      Ti      Fe       O
TYPE:     ANAL    ANAL    ANAL    SPEC
BGDS:      LIN     LIN     LIN
TIME:    60.00   60.00   60.00     ---
BEAM:    29.98   29.98   29.98     ---

ELEM:       Si      Ti      Fe       O   SUM  
   362  48.806    .002    .006  53.260 102.073
   363  48.820    .007   -.003  53.260 102.084
   364  48.785   -.001   -.001  53.260 102.044
   365  48.805   -.012   -.016  53.260 102.036
   366  48.849   -.004   -.017  53.260 102.088

AVER:   48.813   -.002   -.006  53.260 102.065
SDEV:     .024    .007    .010    .000    .024
SERR:     .011    .003    .004    .000
%RSD:      .05 -415.49 -159.41     .00

PUBL:   46.740    n.a.    n.a.  53.260 100.000
%VAR:     4.44     ---     ---     ---
DIFF:    2.073     ---     ---     ---
STDS:      514     522     526     ---

For TiO2 we see this:

St  922 Set   2 TiO2 (elemental) (#22), Results in Elemental Weight Percents
 
ELEM:       Si      Ti      Fe       O
TYPE:     ANAL    ANAL    ANAL    SPEC
BGDS:      LIN     LIN     LIN
TIME:    60.00   60.00   60.00     ---
BEAM:    29.98   29.98   29.98     ---

ELEM:       Si      Ti      Fe       O   SUM  
   367    .005  61.155    .009  40.000 101.169
   368    .003  61.229   -.025  40.000 101.207
   369    .003  61.123    .015  40.000 101.141
   370    .006  61.147   -.007  40.000 101.147
   371    .002  61.018   -.004  40.000 101.016

AVER:     .004  61.134   -.002  40.000 101.136
SDEV:     .002    .076    .015    .000    .072
SERR:     .001    .034    .007    .000
%RSD:    42.35     .12 -633.05     .00

PUBL:     .000  59.990    .000  40.000  99.990
%VAR:      .00    1.91     .00     ---
DIFF:     .000   1.144    .000     ---
STDS:      514     522     526     ---

and for Fe3O4 using Fe metal as a primary standard we see this:

St  895 Set   2 Magnetite (std #395), Results in Elemental Weight Percents
 
ELEM:       Si      Ti      Fe      Al       O
TYPE:     ANAL    ANAL    ANAL    SPEC    SPEC
BGDS:      LIN     LIN     LIN
TIME:    60.00   60.00   60.00     ---     ---
BEAM:    29.98   29.98   29.98     ---     ---

ELEM:       Si      Ti      Fe      Al       O   SUM  
   357    .020    .020  70.278    .200  27.640  98.158
   358    .018    .028  70.214    .200  27.640  98.100
   359    .025    .029  70.326    .200  27.640  98.220
   360    .023    .018  70.633    .200  27.640  98.513
   361    .013    .032  70.014    .200  27.640  97.899

AVER:     .020    .025  70.293    .200  27.640  98.178
SDEV:     .005    .006    .224    .000    .000    .223
SERR:     .002    .003    .100    .000    .000
%RSD:    22.84   24.83     .32     .00     .00

PUBL:     .020    .010  72.080    .200  27.640  99.950
%VAR:     -.32  154.16   -2.48     ---     ---
DIFF:     .000    .015  -1.787     ---     ---
STDS:      514     522     526     ---     ---

By the way, these percent variance values from the published are quite reproducible as I ran each standard twice and got almost exactly the same numbers a second time.  But it is odd that the largest variance was for Si while the smallest was for Ti, while Fe was in the middle (and error is in the opposite direction!).  I suspect this speaks to some complications regarding the physics.

Anyway, these results say to me that the problem is not really due to a peak shift effect but rather a peak shape effect. The reason I had originally suspected this was a peak shift issue, was due to some efforts I did back in 2004/2005 where I found that for S Ka, the quantitative effect was almost entirely due to a peak shift, not a peak shape change. Here is an analysis (aggregated from 3 spectrometers) for S Ka in anhydrite using pyrite as a primary standard:

St  327 Set   1 Anhydrite (CaSO4) UC # 5555, Results in Elemental Weight Percents

SPEC:       Ca       O      Sr
TYPE:     SPEC    SPEC    SPEC

AVER:   29.380  46.881    .300
SDEV:     .000    .000    .000
 
ELEM:        S       S       S
BGDS:      LIN     LIN     LIN
TIME:    10.00     .00     .00
BEAM:    30.14     .00     .00
AGGR:        3                

ELEM:        S       S       S   SUM  
XRAY:     (ka)    (ka)    (ka)
    11  23.769    .000    .000 100.330
    12  23.644    .000    .000 100.205
    13  23.655    .000    .000 100.216
    14  23.643    .000    .000 100.204
    15  23.770    .000    .000 100.331

AVER:   23.696    .000    .000 100.257
SDEV:     .068    .000    .000    .068
SERR:     .030    .000    .000
%RSD:      .29   .0000   .0000

PUBL:   23.499    n.a.    n.a. 100.060
%VAR:      .84     .00     .00
DIFF:     .197     ---     ---
STDS:      730       0       0

But it's odd because simply utilizing different peak positions for the pyrite:

On and Off Peak Positions:
ELEM:     s ka    s ka    s ka
CRYST:     PET     PET     PET
ONPEAK 61219.0 61677.0 61456.0
OFFSET 196.453 -261.55 -40.547
HIPEAK 62419.0 62877.0 62656.0
LOPEAK 60019.0 60477.0 60256.0
HI-OFF 1200.00 1200.00 1200.00
LO-OFF -1200.0 -1200.0 -1200.0

And the anhydrite:

On and Off Peak Positions:
ELEM:     s ka    s ka    s ka
CRYST:     PET     PET     PET
ONPEAK 61192.0 61648.0 61428.0
OFFSET 223.453 -232.55 -12.547
HIPEAK 62392.0 62848.0 62628.0
LOPEAK 59992.0 60448.0 60228.0
HI-OFF 1200.00 1200.00 1200.00
LO-OFF -1200.0 -1200.0 -1200.0

We obtain very quantitative data as seen above, so S Ka appears to be an outlier in that it is a pure peak shift between the oxide and the sulfide (I don't have a sulfur "metal" standard!)

Also see here for more details on sulfur shifts:

https://smf.probesoftware.com/index.php?topic=127.0

Next we'll perform "integrated intensity" scans where we utilized the area between the off-peak positions to obtain the full integrated intensities of the emission lines, to be continued...

[Probeman]

Next we'll perform "integrated intensity" scans where we utilized the area between the off-peak positions to obtain the full integrated intensities of the emission lines, to be continued...

The integrated intensity acquisition feature (see the Elements/Cations dialog) in Probe for EPMA allows one to acquire the full integrated intensity of an emission line for quantification:



by using a spline fit to perform the intensity integration for the full emission peak shape. This allows the software to eliminate peak shift/shape changes between phases that could affect the quantification accuracy for light elements, or as we shall see, even more subtle peak shape changes for higher Z elements even up to Fe Ka between the metal and oxide!

Note that this feature is designed to perform lower resolution steps at low intensities, with the step size decreasing as the intensity increases in order to improve counting statistics on the emission line peak.

In the previous post we saw that even when adjusting the peak position of the emission line for both the metal and the oxide, we still observed quantification inaccuracy on the order to 2 to 4 percent for Si, Ti and Fe. Now we will acquire the full integrated intensities for both materials between the off-peak background positions, starting with Si which we can see displayed here for both the metal and the oxide:



It doesn't look like much of a difference, yet we saw in the previous post that this produced an ~4% inaccuracy when extrapolating from Si metal to SiO2.  Here are the results when using this integrated intensity feature:

St  914 Set   2 SiO2 (elemental) (#14), Results in Elemental Weight Percents
 
ELEM:       Si      Ti      Fe       O
TYPE:     ANAL    ANAL    ANAL    SPEC
BGDS:      INT     INT     INT
TIME:      .23     .24     .21     ---
BEAM:    30.08   30.08   30.08     ---

ELEM:       Si      Ti      Fe       O   SUM  
  3549  46.838   -.112    .257  53.260 100.243
  3550  46.976    .036    .168  53.260 100.440
  3551  46.910   -.276   -.415  53.260  99.479
  3552  46.860    .012   -.320  53.260  99.812
  3553  47.310   -.025    .262  53.260 100.807

AVER:   46.979   -.073   -.009  53.260 100.156
SDEV:     .193    .126    .330    .000    .522
SERR:     .086    .057    .148    .000
%RSD:      .41 -173.00-3478.60     .00

PUBL:   46.740    n.a.    n.a.  53.260 100.000
%VAR:      .51     ---     ---     ---
DIFF:     .239     ---     ---     ---
STDS:      514     522     526     ---

As you can see we are now within ~0.5% relative accuracy!

Now for Ti Ka using Ti metal as the primary standard and TiO2 as the secondary standard:

St  922 Set   2 TiO2 (elemental) (#22), Results in Elemental Weight Percents
 
ELEM:       Si      Ti      Fe       O
TYPE:     ANAL    ANAL    ANAL    SPEC
BGDS:      INT     INT     INT
TIME:      .23     .24     .21     ---
BEAM:    30.08   30.08   30.08     ---

ELEM:       Si      Ti      Fe       O   SUM  
  3554   -.042  59.598   -.300  40.000  99.256
  3555    .053  60.279  -1.550  40.000  98.782
  3556   -.016  59.640   -.146  40.000  99.478
  3557    .212  59.188   -.032  40.000  99.368
  3558    .081  59.677    .569  40.000 100.328

AVER:     .058  59.677   -.292  40.000  99.443
SDEV:     .100    .390    .777    .000    .562
SERR:     .045    .175    .347    .000
%RSD:   173.53     .65 -266.48     .00

PUBL:     .000  59.990    .000  40.000  99.990
%VAR:      .00    -.52     .00     ---
DIFF:     .000   -.313    .000     ---
STDS:      514     522     526     ---

Again ~0.5% accuracy and now for Fe Ka (metal to oxide):

St  895 Set   2 Magnetite (std #395), Results in Elemental Weight Percents
 
ELEM:       Si      Ti      Fe      Al       O
TYPE:     ANAL    ANAL    ANAL    SPEC    SPEC
BGDS:      INT     INT     INT
TIME:      .23     .24     .21     ---     ---
BEAM:    30.07   30.07   30.07     ---     ---

ELEM:       Si      Ti      Fe      Al       O   SUM  
  3544   -.019    .168  71.713    .200  27.640  99.703
  3545    .047    .177  71.280    .200  27.640  99.343
  3546    .049    .054  71.398    .200  27.640  99.341
  3547   -.011    .041  71.163    .200  27.640  99.033
  3548   -.061   -.028  71.838    .200  27.640  99.589

AVER:     .001    .082  71.479    .200  27.640  99.402
SDEV:     .047    .088    .287    .000    .000    .259
SERR:     .021    .039    .128    .000    .000
%RSD:  5515.12  106.81     .40     .00     .00

PUBL:     .020    .010  72.080    .200  27.640  99.950
%VAR:   -95.74  724.41    -.83     ---     ---
DIFF:    -.019    .072   -.601     ---     ---
STDS:      514     522     526     ---     ---

Better than 1% accuracy!

The point is that there are indeed subtle chemical peak shifts even for Fe Ka as was originally brought to our attention by Rom a few years ago:

Some addition things which might give somebody good ideas. In all cases of the list lower the Standards - 100% metal.

1. Incorrect result of measuring metal in oxide/silicate we obtain for many (I suppose for all) metals.
2. More often the measured concentration of metal (Fe, Ni, Pb,....) in its oxide/silicate is lower then we expected but sometimes higher (Sb, Cu).
3. Differences between measured and expected (published) concentration can be from ~1-2 rel% (Sb in oxide) to ~2 rel% (Fe in oxides, Ni in silicates) and more: ~2-3 rel% (Pb in oxide, silicate).

https://smf.probesoftware.com/index.php?topic=1423.msg11788#msg11788

While we have known for decades of these peak shape changes for low energy emission lines such as O Ka, N Ka, C Ka, etc. we had not noticed these effects for higher energy emission lines as discussed above. I myself had wrongly assumed that these quantification problems were solely due to peak shift issues (as in my discussion of sulfur in the previous post).

The good news is that the integrated intensity feature in Probe for EPMA allows us to investigate these effects. BTW, once you have integrated intensities acquired in PFE, you can investigate them using the Run | Display Integrated Intensities menu dialog as seen here:



Search for "integrated" in the Probe for EPMA User's Reference manual more more details on this integrated intensity feature.