The Limits of EPMA Accuracy

[Probeman]

I was just going to post a similar graphic as you did, showing the proportional response range!  By the way, here's a plot of detector response as a function of barometric pressure from Jon Fellowes that I had forgotten about:

https://smf.probesoftware.com/index.php?topic=1614.msg12439#msg12439

Another very important benefits of reduced bias. GFPC ages - the anode gets contaminated with hydrocarbon gunk which impairs its performance.

That is good advice!  Though I will say that working with Andrew recently I noticed too late that he had been trying different bias voltages and although the PHA peak (for oxygen Ka) looked OK, when we performed quant analyses the results were not good extrapolating from MgO to MgAl2O4. Basically he accidentally set the bias voltage too low and apparently the detector was not quite stable for that low an energy x-ray.

I know that on most instruments the OEM engineer usually adjusts the gain level (8, 16, 32, 64, etc. for JEOL) for each Bragg crystal for x-ray energy range (LiF, PET,. TAP, etc.).  Of course on the Cameca the gain is more adjustable, but it also depends on whether one is using a 1 atm pressure detector or a 2 atm pressure detector (see screenshot of my SCALERS.DAT file below).  On the JEOL I am guessing that it similarly depends on whether one is using a P-10 detector or a xenon detector.  I remember from my ARL SEMQ days that as the xenon detectors age (leak) one requires more and more bias voltage to get a stable response but then they get more and more noisy, so it is suggested these sealed detectors get changed out every few years or so.

Why count rate starts to drop after going below ~1600V? (choose one/or both of reasons) a) as effective field around the anode in GFPC starts to be smaller than focused diffracted beam b) field is too weak to consistently produce Townsend avalanche from every X-ray produced photoelectron, and electrons are either reconnected to positive ions, or drifts without amplification to the anode where they are collected, but because no amplification they are invisible hidden in the noise of the anode.

My thinking is that one should utilize the lowest bias that provides a *stable* signal in the proportional response range of the detector, and yes, that seems to depend on the energy of the x-ray for a given Bragg crystal. Given that a stable instrument provides the most quantitative results...  for our SX100, I have defined these default bias voltages for each Bragg crystal in our SCALERS.DAT configuration file:



because as you mention, the lower the incoming x-ray energy, the more bias voltage that needs to be provided. Also note that spectrometers 3 and 5 are 2 atm pressure detectors and therefore require a significantly higher bias to achieve a stable proportional response.

How does one determine the proper bias voltage for a stable proportional response for a given detector for a given x-ray energy?  Well, I'm sure there are many ways to decide this, but what I do is to scan a range of bias voltages and see where the x-ray signal is first produced using the Acquire and Graph Bias Scan Distribution button here:



Then we see this output from the bias scan:



This tells me that we want our detector bias voltage to be some tens of volts above this peak, say 1400 to 1450v for O Ka on this spectrometer.  This seems to provide stable operation of the detector and it is optimized for the specific x-ray energy in question.  But I am open to other methods...

[Probeman]

Andrew and I continued with our testing of EPMA accuracy this time attempting to minimize absorption effects (which are very large in the MgAl2O4) and instead looking at elements/materials with large atomic number corrections (which are very small in MgAl2O4), for example, Fe Ka in various Fe silicates, sulfides and oxides.

Just as an example we analyzed Fe Ka on spectrometer 3 (LLIF, 2 atm P-10) and spectrometer 5 (LIF, 2 atm P-10). To start with, we aggregated the intensities of both spectrometers using the aggregate intensity feature in Probe for EPMA and we got these results for YIG (yttrium iron garnet) extrapolating from a natural magnetite (Fe3O4) as the primary standard:

Summary of All Calculated (averaged) Matrix Corrections:
St  854 Set   1 YIG single crystal (#258)
FFAST    Chantler (NIST v 2.1, 2005)

Elemental Weight Percents:
ELEM:       Fe      Fe       Y       O   TOTAL
     1  37.815    .000  36.140  26.020  99.975   Armstrong/Brown/Scott-Love (prZ)
     2  37.661    .000  36.140  26.020  99.821   Philibert/Duncumb-Reed
     3  38.150    .000  36.140  26.020 100.310   Heinrich/Duncumb-Reed
     4  37.753    .000  36.140  26.020  99.913   Love-Scott I
     5  37.826    .000  36.140  26.020  99.986   Love-Scott II
     6  37.491    .000  36.140  26.020  99.651   Packwood Phi(prZ) (EPQ-91)
     7  38.519    .000  36.140  26.020 100.679   Bastin (original) (prZ)
     8  37.693    .000  36.140  26.020  99.853   Bastin PROZA Phi (prZ) (EPQ-91)
     9  37.694    .000  36.140  26.020  99.854   Pouchou and Pichoir-Full (PAP)
    10  37.733    .000  36.140  26.020  99.893   Pouchou and Pichoir-Simplified (XPP)
    11  37.795    .000  36.140  26.020  99.955   PAP/Donovan and Moy BSC/BKS (prZ)

AVER:   37.830    .000  36.140  26.020  99.990
SDEV:     .278    .000    .000    .000    .278
SERR:     .084    .000    .000    .000

MIN:    37.491    .000  36.140  26.020  99.651
MAX:    38.519    .000  36.140  26.020 100.679

Percent Variances:
ELEM:       Fe      Fe       Y       O
PUBL:   37.840    n.a.  36.140  26.020
STDS:      895       0     ---     ---

ELEM:       Fe      Fe       Y       O
     1    -.07     .00     .00     .00           Armstrong/Brown/Scott-Love (prZ)
     2    -.47     .00     .00     .00           Philibert/Duncumb-Reed
     3     .82     .00     .00     .00           Heinrich/Duncumb-Reed
     4    -.23     .00     .00     .00           Love-Scott I
     5    -.04     .00     .00     .00           Love-Scott II
     6    -.92     .00     .00     .00           Packwood Phi(prZ) (EPQ-91)
     7    1.80     .00     .00     .00           Bastin (original) (prZ)
     8    -.39     .00     .00     .00           Bastin PROZA Phi (prZ) (EPQ-91)
     9    -.39     .00     .00     .00           Pouchou and Pichoir-Full (PAP)
    10    -.28     .00     .00     .00           Pouchou and Pichoir-Simplified (XPP)
    11    -.12     .00     .00     .00           PAP/Donovan and Moy BSC/BKS (prZ)

AVER:     -.03     .00     .00     .00        
SDEV:      .74     .00     .00     .00        
SERR:      .22     .00     .00     .00        

MIN:      -.92     .00     .00     .00        
MAX:      1.80     .00     .00     .00        

Plotting all the YIG analyses at both 15 and 20 keV we see this:



Similar accuracy was seen in the other oxides and silicates, here for example a synthetic fayalite also using Fe3O4 as the primary standard at 20 keV:

Summary of All Calculated (averaged) Matrix Corrections:
St  863 Set   4 Fayalite ORNL single crystal (#263)
FFAST    Chantler (NIST v 2.1, 2005)

Elemental Weight Percents:
ELEM:       Fe      Fe      Si       O   TOTAL
     1  54.510    .000  13.770  31.440  99.720   Armstrong/Brown/Scott-Love (prZ)
     2  54.986    .000  13.770  31.440 100.196   Philibert/Duncumb-Reed
     3  54.396    .000  13.770  31.440  99.606   Heinrich/Duncumb-Reed
     4  54.525    .000  13.770  31.440  99.735   Love-Scott I
     5  54.520    .000  13.770  31.440  99.730   Love-Scott II
     6  55.050    .000  13.770  31.440 100.260   Packwood Phi(prZ) (EPQ-91)
     7  54.619    .000  13.770  31.440  99.829   Bastin (original) (prZ)
     8  54.789    .000  13.770  31.440  99.999   Bastin PROZA Phi (prZ) (EPQ-91)
     9  54.776    .000  13.770  31.440  99.986   Pouchou and Pichoir-Full (PAP)
    10  54.782    .000  13.770  31.440  99.992   Pouchou and Pichoir-Simplified (XPP)
    11  54.502    .000  13.770  31.440  99.712   PAP/Donovan and Moy BSC/BKS (prZ)

AVER:   54.678    .000  13.770  31.440  99.888
SDEV:     .214    .000    .000    .000    .214
SERR:     .064    .000    .000    .000

MIN:    54.396    .000  13.770  31.440  99.606
MAX:    55.050    .000  13.770  31.440 100.260

Percent Variances:
ELEM:       Fe      Fe      Si       O
PUBL:   54.790    n.a.  13.770  31.440
STDS:      895       0     ---     ---

ELEM:       Fe      Fe      Si       O
     1    -.51     .00     .00     .00           Armstrong/Brown/Scott-Love (prZ)
     2     .36     .00     .00     .00           Philibert/Duncumb-Reed
     3    -.72     .00     .00     .00           Heinrich/Duncumb-Reed
     4    -.48     .00     .00     .00           Love-Scott I
     5    -.49     .00     .00     .00           Love-Scott II
     6     .47     .00     .00     .00           Packwood Phi(prZ) (EPQ-91)
     7    -.31     .00     .00     .00           Bastin (original) (prZ)
     8     .00     .00     .00     .00           Bastin PROZA Phi (prZ) (EPQ-91)
     9    -.03     .00     .00     .00           Pouchou and Pichoir-Full (PAP)
    10    -.01     .00     .00     .00           Pouchou and Pichoir-Simplified (XPP)
    11    -.53     .00     .00     .00           PAP/Donovan and Moy BSC/BKS (prZ)

AVER:     -.20     .00     .00     .00        
SDEV:      .39     .00     .00     .00        
SERR:      .12     .00     .00     .00        

MIN:      -.72     .00     .00     .00        
MAX:       .47     .00     .00     .00        

And here extrapolating from Fe3O4 to the NIST K-412 mineral glass:

Summary of All Calculated (averaged) Matrix Corrections:
St  807 Set   2 NBS K-412 mineral glass (#160)
FFAST    Chantler (NIST v 2.1, 2005)

Elemental Weight Percents:
ELEM:       Fe      Fe      Si      Mg      Ca      Al      Mn       O   TOTAL
     1   7.677    .000  21.190  11.650  10.900   4.910    .070  43.597  99.994   Armstrong/Brown/Scott-Love (prZ)
     2   7.863    .000  21.190  11.650  10.900   4.910    .070  43.597 100.180   Philibert/Duncumb-Reed
     3   7.605    .000  21.190  11.650  10.900   4.910    .070  43.597  99.922   Heinrich/Duncumb-Reed
     4   7.687    .000  21.190  11.650  10.900   4.910    .070  43.597 100.005   Love-Scott I
     5   7.685    .000  21.190  11.650  10.900   4.910    .070  43.597 100.002   Love-Scott II
     6   7.946    .000  21.190  11.650  10.900   4.910    .070  43.597 100.263   Packwood Phi(prZ) (EPQ-91)
     7   7.723    .000  21.190  11.650  10.900   4.910    .070  43.597 100.040   Bastin (original) (prZ)
     8   7.830    .000  21.190  11.650  10.900   4.910    .070  43.597 100.147   Bastin PROZA Phi (prZ) (EPQ-91)
     9   7.818    .000  21.190  11.650  10.900   4.910    .070  43.597 100.136   Pouchou and Pichoir-Full (PAP)
    10   7.828    .000  21.190  11.650  10.900   4.910    .070  43.597 100.145   Pouchou and Pichoir-Simplified (XPP)
    11   7.668    .000  21.190  11.650  10.900   4.910    .070  43.597  99.985   PAP/Donovan and Moy BSC/BKS (prZ)

AVER:    7.757    .000  21.190  11.650  10.900   4.910    .070  43.597 100.074
SDEV:     .105    .000    .000    .000    .000    .000    .000    .000    .105
SERR:     .032    .000    .000    .000    .000    .000    .000    .000

MIN:     7.605    .000  21.190  11.650  10.900   4.910    .070  43.597  99.922
MAX:     7.946    .000  21.190  11.650  10.900   4.910    .070  43.597 100.263

Percent Variances:
ELEM:       Fe      Fe      Si      Mg      Ca      Al      Mn       O
PUBL:    7.740    n.a.  21.190  11.650  10.900   4.910    .070  43.597
STDS:      895       0     ---     ---     ---     ---     ---     ---

ELEM:       Fe      Fe      Si      Mg      Ca      Al      Mn       O
     1    -.82     .00     ---     ---     ---     ---     ---     ---           Armstrong/Brown/Scott-Love (prZ)
     2    1.59     .00     ---     ---     ---     ---     ---     ---           Philibert/Duncumb-Reed
     3   -1.75     .00     ---     ---     ---     ---     ---     ---           Heinrich/Duncumb-Reed
     4    -.68     .00     ---     ---     ---     ---     ---     ---           Love-Scott I
     5    -.72     .00     ---     ---     ---     ---     ---     ---           Love-Scott II
     6    2.67     .00     ---     ---     ---     ---     ---     ---           Packwood Phi(prZ) (EPQ-91)
     7    -.22     .00     ---     ---     ---     ---     ---     ---           Bastin (original) (prZ)
     8    1.16     .00     ---     ---     ---     ---     ---     ---           Bastin PROZA Phi (prZ) (EPQ-91)
     9    1.01     .00     ---     ---     ---     ---     ---     ---           Pouchou and Pichoir-Full (PAP)
    10    1.14     .00     ---     ---     ---     ---     ---     ---           Pouchou and Pichoir-Simplified (XPP)
    11    -.93     .00     ---     ---     ---     ---     ---     ---           PAP/Donovan and Moy BSC/BKS (prZ)

AVER:      .22     .00     .00     .00     .00     .00     .00     .00        
SDEV:     1.36     .00     .00     .00     .00     .00     .00     .00        
SERR:      .41     .00     .00     .00     .00     .00     .00     .00        

MIN:     -1.75     .00     .00     .00     .00     .00     .00     .00        
MAX:      2.67     .00     .00     .00     .00     .00     .00     .00        

Still with sub percent level accuracy for DAM/PAP... and this is at 20 keV!

[aducharme]

Regarding the earlier PHA discussion, see the below table in Hall's 1993 article in Surface Engineering on suggested PHA settings for measuring light elements on a JEOL instrument. Despite never considering it, the upper limits on the differential mode window are high enough that measurements are either very similar to, or essentially are in, integral mode.



Paper can be found here: https://doi.org/10.1179/sur.1993.9.3.205
I have a pdf if anyone wants to read the full article, but there's not a ton more PHA discussion hiding within the text.

[Probeman]

A more general question regarding EPMA accuracy is how can EDS quant use a pure metal standard to accurately analyze oxide materials but WDS cannot? 

As mentioned in this post here regarding "peak shift matching" for relatively low energy lines, I think it's because WDS has much greater spectral resolution than EDS, and therefore is more sensitive to chemical states:

https://smf.probesoftware.com/index.php?topic=127.msg14013#msg14013

As seen in the post linked above, if we adjust the WDS spectrometer position to the actual peak position on each material, we can get accurate analyses for even S ka, assuming our dead times are properly calibrated and our PHA setting are properly tuned. But even Fe Ka can exhibit subtle peak shift issues between oxidized and reduced phases. Here is analyzing NBS K-412 glass using Fe metal (#526) as a standard:

St  807 Set   3 NBS K-412 mineral glass (#160), Results in Elemental Weight Percents
 
ELEM:       Fe      Fe      Si      Mg      Ca      Al      Mn       O
TYPE:     ANAL    ANAL    SPEC    SPEC    SPEC    SPEC    SPEC    SPEC
BGDS:      LIN     LIN
TIME:    60.00     .00     ---     ---     ---     ---     ---     ---
BEAM:    29.87     .00     ---     ---     ---     ---     ---     ---
AGGR:        2             ---     ---     ---     ---     ---     ---

ELEM:       Fe      Fe      Si      Mg      Ca      Al      Mn       O   SUM  
XRAY:     (ka)    (ka)      ()      ()      ()      ()      ()      ()
   424   7.503    .000  21.190  11.650  10.900   4.910    .070  43.597  99.820
   425   7.540    .000  21.190  11.650  10.900   4.910    .070  43.597  99.857
   426   7.550    .000  21.190  11.650  10.900   4.910    .070  43.597  99.867
   427   7.521    .000  21.190  11.650  10.900   4.910    .070  43.597  99.838
   428   7.520    .000  21.190  11.650  10.900   4.910    .070  43.597  99.837

AVER:    7.527    .000  21.190  11.650  10.900   4.910    .070  43.597  99.844
SDEV:     .019    .000    .000    .000    .000    .000    .000    .000    .019
SERR:     .008    .000    .000    .000    .000    .000    .000    .000
%RSD:      .25   .0000     .00     .00     .00     .00     .00     .00

PUBL:    7.740    n.a.  21.190  11.650  10.900   4.910    .070  43.597 100.057
%VAR:    -2.76     .00     .00     .00     .00     .00     .00     .00
DIFF:    -.213     ---    .000    .000    .000    .000    .000    .000
STDS:      526       0     ---     ---     ---     ---     ---     ---

So this error is due to the "peak shift" issues we discussed previously in the S Ka anhydrite/pyrite post. But by re-assigning our primary standard to Fe3O4 (#895) we obtain this analysis:

St  807 Set   3 NBS K-412 mineral glass (#160), Results in Elemental Weight Percents
 
ELEM:       Fe      Fe      Si      Mg      Ca      Al      Mn       O
TYPE:     ANAL    ANAL    SPEC    SPEC    SPEC    SPEC    SPEC    SPEC
BGDS:      LIN     LIN
TIME:    60.00     .00     ---     ---     ---     ---     ---     ---
BEAM:    29.87     .00     ---     ---     ---     ---     ---     ---
AGGR:        2             ---     ---     ---     ---     ---     ---

ELEM:       Fe      Fe      Si      Mg      Ca      Al      Mn       O   SUM  
XRAY:     (ka)    (ka)      ()      ()      ()      ()      ()      ()
   424   7.673    .000  21.190  11.650  10.900   4.910    .070  43.597  99.990
   425   7.712    .000  21.190  11.650  10.900   4.910    .070  43.597 100.029
   426   7.722    .000  21.190  11.650  10.900   4.910    .070  43.597 100.039
   427   7.692    .000  21.190  11.650  10.900   4.910    .070  43.597 100.009
   428   7.691    .000  21.190  11.650  10.900   4.910    .070  43.597 100.008

AVER:    7.698    .000  21.190  11.650  10.900   4.910    .070  43.597 100.015
SDEV:     .019    .000    .000    .000    .000    .000    .000    .000    .019
SERR:     .008    .000    .000    .000    .000    .000    .000    .000
%RSD:      .25   .0000     .00     .00     .00     .00     .00     .00

PUBL:    7.740    n.a.  21.190  11.650  10.900   4.910    .070  43.597 100.057
%VAR:     -.55     .00     .00     .00     .00     .00     .00     .00
DIFF:    -.042     ---    .000    .000    .000    .000    .000    .000
STDS:      895       0     ---     ---     ---     ---     ---     ---

That's an impressive extrapolation from the pure oxide to the NIST glass for both the dead time correction and the PHA tuning not to mention the atomic number correction!

Yes, for light elements the chemical effects are so large that we may still need to "peak shape match" or utilize Area Peak Factors.

But it seems to me that with a properly calibrated instrument we can accurately analyze any oxide/silicate materials with a pure oxide primary standard.

Yes, this is all preparation for the release of the FIGMAS synthetic mineral mount that Will Nachlas is working on!

[Probeman]

I plotted up the quantitative results from the work Andrew and I did last weekend at 15 and 20 keV for Fe Ka on spectormeters 3 and 5 and aggregated the results using the aggregate intensities feature in PFE:

https://smf.probesoftware.com/index.php?topic=1316.0

because it's so easy!  But I also calculated the data for each spectrometer separately but they all agree quite well, so why not improve precision if one can?

Here are results for Fe Ka using Fe metal as a primary standard measuring a pure natural pyrite as a secondary standard:



The relative accuracy errors are less that 0.5% and all within the variance.  Next I plotted up synthetic YIG (yttrium iron garnet) using Fe3O4 as a primary standard (because of the subtle chemical shift between oxidized and reduced iron which the LiF WDS crystal can resolve):



and again excellent accuracy at both 15 and 20 keV. Now to test the dead time extrapolation and the atomic number correction we measured the NBS K-412 mineral glass again with Fe3O4 as the primary standard:



Excellent accuracy at 15 keV and about a 1% relative error at 20 keV (approximately a difference of ~800 PPM from the published value, so not too bad!

Now, here's the shocking part. Let's look at the PHA scans for these two spectrometers, first we'll start with spectrometer 5 LiF (2 atm P-10):



Looks pretty normal, right?  Now let's see the LLIF diffractor PHA scan on spectrometer 3 (which would dominate these aggregated intensities because it's a *large* LIF):



Don't be surprised. Remember, all photons to the right will be counted in integral PHA mode!  The key is that your PHA peak needs to be *completely* above the PHA baseline when measuring the highest intensity you expect to measure, usually ones primary standard, in this case Fe metal, to ensure a linear response from your counting electronics.

[Probeman]

"If one is aiming for +/-30% accuracy, well nothing really matters, though if one is looking for +/-10% accuracy, well then a few things matter, but if one is trying to obtain +/-1% accuracy, then everything matters!    🙂

Over the last few months Andrew and I have been doing some measurements on our Cameca instrument, and we're finally starting to put two and two together:

https://smf.probesoftware.com/index.php?topic=1831.0

In other words, here's the gist of why some people still think they need to "matrix match" their standard and their unknown:

1. Due to the high spectral resolution of WDS (unlike EDS!) we must at least utilize a rough "peak shift" match. That is, we must use an oxide (oxidized) standard for oxides/silicates and an elemental (reduced) standard for alloys/sulfides:

https://smf.probesoftware.com/index.php?topic=1423.msg11809#msg11809

Though interestingly we don't need to "peak shift match" if we adjust our WDS peak position for each phase:

https://smf.probesoftware.com/index.php?topic=127.msg14013#msg14013

Yes, for very light elements (e.g., O, N, C, etc.) the chemical effects are so large for WDS that we may still need to "peak shape match" or utilize Area Peak Factors.

2. But when adjusting our PHA settings, we *do not* need to "count rate match" our standard and unknown. That is, if we adjust the PHA bias/gain properly (there's the rub!) and utilize integral mode using just the baseline level. Properly tuning our PHA allows the use of high purity synthetic metal or oxide materials  as primary standards when the count rates are very different compared to our unknowns, even with severe pulse height depression. 

But what if there are high order spectral interferences?  That's OK. Let them in and correct for them quantitatively using software!  But don't use the PHA window differential to induce a non-linear response in our counting electronics!

https://smf.probesoftware.com/index.php?topic=1466.msg13955#msg13955

https://smf.probesoftware.com/index.php?topic=1831.msg14015#msg14015

3. Our quantitative accuracy will improve significantly when we no longer rely on heterogeneous natural "matrix matched" standards. Because our counting electronics response will be totally linear with this method of PHA tuning.  By following these steps we can achieve high accuracy quantitative EPMA:

https://smf.probesoftware.com/index.php?topic=1831.msg14011#msg14011

https://smf.probesoftware.com/index.php?topic=1823.msg13926#msg13926

4. And of course if we no longer need to "count rate match" our standard and unknown, we need to have carefully calibrated our dead time constants using the constant k-ratio method, and possibly utilize the non-linear dead time expression:

https://smf.probesoftware.com/index.php?topic=1466.msg13255#msg13255

As I said at the beginning of this post: 2 + 2 = 4!   

Thus, we can achieve sub 1% quantitative accuracy in EPMA if we utilize high purity, end member synthetic standards with a minimal "peak shift match" for oxidized vs. reduced chemical states, follow the PHA tuning steps described above, along with well calibrated dead time constants. Let's test this hypothesis on more instruments!

[Probeman]

If anyone would like to see the data from our Fe Ka testing that Andrew and I did last weekend I've attached it below.  See this post for some examples and conclusions:

https://smf.probesoftware.com/index.php?topic=1831.msg14015#msg14015

One comment: the chromite "standard" (#896) is a natural material I sourced from the Berkeley mineral collection back in the 1980s and should not be considered to have an accurate composition in any sense.  Same goes for the pyrrhotite "standard" (#757), it's just a natural mineral with an assumed composition originally used for peak shift tests.

[Probeman]

I found some Pb and As analyses I did back in 2015 and it appears I never posted them probably because using the Armstrong pr(z) matrix corrections they didn't come out very well (as we all know, the Pb La and As Ka overlap is the worst!).

Here is the analysis of PbS using FeS2 as the primary sulfur standard using Pb La and the Armstrong pr(z) (and Henke MACs):

St  731 Set   2 Galena U.C. #7400, Results in Elemental Weight Percents
 
ELEM:        S      Pb      As
TYPE:     ANAL    ANAL    ANAL
BGDS:      LIN     EXP     EXP
TIME:    80.00   80.00   80.00
BEAM:    29.88   29.88   29.88

ELEM:        S      Pb      As   SUM  
   333  14.997  87.319   -.148 102.167
   334  14.976  87.067   -.055 101.988
   335  15.051  86.071    .521 101.643

AVER:   15.008  86.819    .106 101.933
SDEV:     .039    .660    .363    .266
SERR:     .022    .381    .209
%RSD:      .26     .76  342.11

PUBL:   13.400  86.600    n.a. 100.000
%VAR:    12.00   (.25)     ---
DIFF:    1.608   (.22)     ---
STDS:      730     731     662

Note that the sulfur analysis here is off by ~12% relative, so not very good.  Let's switch to the FFAST MACs:

St  731 Set   2 Galena U.C. #7400, Results in Elemental Weight Percents
 
ELEM:        S      Pb      As
TYPE:     ANAL    ANAL    ANAL
BGDS:      LIN     EXP     EXP
TIME:    80.00   80.00   80.00
BEAM:    29.88   29.88   29.88

ELEM:        S      Pb      As   SUM  
   333  14.357  87.101   -.143 101.315
   334  14.336  86.837   -.050 101.123
   335  14.413  85.806    .537 100.756

AVER:   14.368  86.581    .115 101.065
SDEV:     .040    .684    .369    .284
SERR:     .023    .395    .213
%RSD:      .28     .79  320.88

PUBL:   13.400  86.600    n.a. 100.000
%VAR:     7.23  (-.02)     ---
DIFF:     .968  (-.02)     ---
STDS:      730     731     662

Well that's a little better as the error is now only ~7% relative.  OK now let's try again using the Donovan and Moy DAM/PAP matrix correction using Z fractions for the backscatter correction:

St  731 Set   2 Galena U.C. #7400, Results in Elemental Weight Percents
 
ELEM:        S      Pb      As
TYPE:     ANAL    ANAL    ANAL
BGDS:      LIN     EXP     EXP
TIME:    80.00   80.00   80.00
BEAM:    29.88   29.88   29.88

ELEM:        S      Pb      As   SUM  
   333  13.218  86.664   -.132  99.750
   334  13.200  86.404   -.040  99.563
   335  13.285  85.339    .555  99.179

AVER:   13.234  86.136    .128  99.498
SDEV:     .045    .702    .373    .291
SERR:     .026    .405    .215
%RSD:      .34     .82  292.39

PUBL:   13.400  86.600    n.a. 100.000
%VAR:    -1.24  (-.54)     ---
DIFF:    -.166  (-.46)     ---
STDS:      730     731     662

OK, I can live with an ~1.2% relative error!

But just for fun, lets try the DAM "zero" exponent which calculates the exponent based on Andrew Ducharme and Aurelien Moy's work:

https://smf.probesoftware.com/index.php?topic=1566.msg12051#msg12051

https://academic.oup.com/mam/article/30/Supplement_1/ozae044.088/7719396

St  731 Set   2 Galena U.C. #7400, Results in Elemental Weight Percents
 
ELEM:        S      Pb      As
TYPE:     ANAL    ANAL    ANAL
BGDS:      LIN     EXP     EXP
TIME:    80.00   80.00   80.00
BEAM:    29.88   29.88   29.88

ELEM:        S      Pb      As   SUM  
   333  13.248  86.676   -.132  99.791
   334  13.230  86.415   -.040  99.605
   335  13.316  85.351    .556  99.223

AVER:   13.264  86.147    .128  99.539
SDEV:     .045    .702    .374    .290
SERR:     .026    .405    .216
%RSD:      .34     .81  292.74

PUBL:   13.400  86.600    n.a. 100.000
%VAR:    -1.01  (-.52)     ---
DIFF:    -.136  (-.45)     ---
STDS:      730     731     662

OK, now we have only 1% relative error extrapolating from FeS2 to PbS. That's a difference in average atomic number between of FeS2 and PbS standard of ~20 to 67 with an ~30% atomic number correction!

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs  STDNUM uZAF/sZAF
   S  ka  1.3328  1.0000   .7185   .9576   .5736  1.2526   .6745  2.4720  8.0906 783.125     730    .85342
   Pb la   .9944   .9999  1.0869  1.0807  1.1167   .9733   .9677 13.0340  1.5344 95.6487     731    1.0016
   As ka  1.0249  1.0000   .8357   .8565   .7829  1.0675   .9651 11.8670  1.6853 95.8321     662    .82411

Try it for yourself...

[Probeman]

...And yes, there are a few "black holes" in the periodic table that may require a roughly similar matrix, e.g., Si Ka in Hf due to disagreement in mass absorption coefficients.  But geological silicates and oxides are pretty well handled by modern matrix corrections."

While Andrew Ducharme and I are waiting for some time on the instrument, I decided to take a look back at some old runs I did on our old SX50 (which has long been scrapped), and see if I examined any of the synthetic silicates standards we had obtained from various sources when I was at UC Berkeley. I found the following run from 2014 when I was still using differential PHA tuning, which we now know produces less accurate results as described here:

https://smf.probesoftware.com/index.php?topic=1831.msg13978#msg13978

So while we wait to re-run these materials using SiO2 as the primary standard on our Sx100, here are the results from the Evaluate program for Si Ka in these materials:

https://smf.probesoftware.com/index.php?topic=340.0

2  St   12 Set   1 MgO synthetic                         
3  St   14 Set   1 SiO2 synthetic                        
4  St   16 Set   1 ThSiO4 (Thorite)                      
5  St   19 Set   1 HfSiO4 (Hafnon)                       
6  St   25 Set   1 MnO synthetic                         
7  St  257 Set   1 Zircon crystal (synthetic)            
8  St  263 Set   1 Fe2SiO4 (synthetic fayalite)          
9  St  272 Set   1 Ni2SiO4 (synthetic)                   
10  St  273 Set   1 Mg2SiO4 (magnesium olivine) synthetic
11  St  274 Set   1 Co2SiO4 (cobalt olivine) synthetic   
12  St  275 Set   1 Mn2SiO4 (manganese olivine) synthetic
13  St  358 Set   1 Diopside (Chesterman)                
14  St  386 Set   1 Alamosite (PbSiO3)                   

The big outlier is Si Ka in HfSiO4 (hafnon) synthesized by John Hanchar. Note the 45% relative accuracy in the quant:

St   19 Set   2 HfSiO4 (Hafnon), Results in Elemental Weight Percents

SPEC:       Th      Hf      Pb      Co      Ni      Zr      Al      Ca      Ti       O
TYPE:     SPEC    SPEC    SPEC    SPEC    SPEC    SPEC    SPEC    SPEC    SPEC    SPEC

AVER:     .000  65.967    .000    .000    .000    .000    .000    .000    .000  23.653
SDEV:     .000    .000    .000    .000    .000    .000    .000    .000    .000    .000
 
ELEM:       Si      Mg      Mn      Fe
BGDS:      MAN     MAN     MAN     MAN
TIME:    60.00   60.00   60.00   60.00
BEAM:    30.13   30.13   30.13   30.13

ELEM:       Si      Mg      Mn      Fe   SUM  
    86  15.092    .026    .043    .032 104.813
    87  15.126    .024    .030    .035 104.835
    88  15.122    .029    .038    .039 104.848
    89  15.094    .027    .039    .031 104.811
    90  15.078    .025    .047    .030 104.799

AVER:   15.102    .026    .040    .034 104.821
SDEV:     .021    .002    .006    .004    .020
SERR:     .009    .001    .003    .002
%RSD:      .14    6.98   15.97   10.86

PUBL:   10.380    n.a.    n.a.    n.a. 100.000
%VAR:    45.49     ---     ---     ---
DIFF:    4.722     ---     ---     ---
STDS:       14      12      25     395

STKF:    .3884   .4222   .7420   .6869
STCT:  1002.33  906.18  379.64  336.38

UNKF:    .0565   .0002   .0004   .0004
UNCT:   145.83     .35     .21     .18
UNBG:     2.03    1.43     .89    1.10

ZCOR:   2.6725  1.6261   .9765   .9241
KRAW:    .1455   .0004   .0005   .0005
PKBG:    72.96    1.24    1.23    1.16

This is because of the large absorption correction due to the Si Ka line being near the Hf M edge. The MAC from FFAST is only very slightly better. Remember in cases of large absorption corrections our matrix corrections are only as good as our mass absorption coefficients!

What I did at the time was to empirically measure the MAC for Si Ka in Hf using the method of Pouchou:

https://smf.probesoftware.com/index.php?topic=1340.msg9631#msg9631

After utilizing this experimental MAC from the EMPMAC.DAT file:

we now obtain these results:



Here for comparison is the HfSiO4 again:

St   19 Set   2 HfSiO4 (Hafnon), Results in Elemental Weight Percents

SPEC:       Th      Hf      Pb      Co      Ni      Zr      Al      Ca      Ti       O
TYPE:     SPEC    SPEC    SPEC    SPEC    SPEC    SPEC    SPEC    SPEC    SPEC    SPEC

AVER:     .000  65.967    .000    .000    .000    .000    .000    .000    .000  23.653
SDEV:     .000    .000    .000    .000    .000    .000    .000    .000    .000    .000
 
ELEM:       Si      Mg      Mn      Fe
BGDS:      MAN     MAN     MAN     MAN
TIME:    60.00   60.00   60.00   60.00
BEAM:    30.13   30.13   30.13   30.13

ELEM:       Si      Mg      Mn      Fe   SUM  
    86  10.924    .027    .039    .027 100.636
    87  10.950    .024    .025    .030 100.649
    88  10.947    .029    .034    .034 100.664
    89  10.925    .027    .035    .026 100.633
    90  10.914    .025    .042    .025 100.625

AVER:   10.932    .026    .035    .028 100.641
SDEV:     .016    .002    .006    .004    .015
SERR:     .007    .001    .003    .002
%RSD:      .14    7.01   17.95   12.71

PUBL:   10.380    n.a.    n.a.    n.a. 100.000
%VAR:     5.32     ---     ---     ---
DIFF:     .552     ---     ---     ---
STDS:       14      12      25     395

STKF:    .3884   .4222   .7420   .6869
STCT:  1002.33  906.18  379.64  336.38

UNKF:    .0562   .0002   .0004   .0003
UNCT:   145.00     .34     .18     .15
UNBG:     2.85    1.43     .91    1.13

ZCOR:   1.9456  1.6431   .9672   .9145
KRAW:    .1447   .0004   .0005   .0005
PKBG:    51.81    1.24    1.20    1.13

5% accuracy is a lot better than 45%!

The other silicates are all around ~1 to 2% accuracy. Can't wait to re-run these materials using integral PHA mode on a more modern instrument.