The Limits of EPMA Accuracy

[Probeman]

Do you want to "break" the EPMA 1% accuracy barrier?  You need to make sure your PHA peaks are completely above the baseline level at the highest count rate you anticipate measuring and be in *integral* PHA mode.

Paul Carpenter, 2008: "Avoid tight PHA window, use integral mode unless a PHA interference is observed" and "Use integral mode unless PHA energy discrimination required" (https://epmalab.uoregon.edu/Workshop2/Carpenter_Oregon_Workshop_2007.pdf)

Nice find. 

Yes, Paul has been saying this all along, but there's a critical component that I'm not seeing in his presentation.

For example, he says: "Low energy pulses must be discriminated from baseline noise. Need proper setting of noise threshold, baseline, and window settings of WDS pulse height analyzer."

And that is certainly true. But it would be better to merely say: make sure that the PHA peak is completely above the baseline level at the highest count rate that one intends to measure.

Then there is no need to perform "count rate matching" as he claims a bit later on: "Pulse energy shift with varying count rate results in instability. At high count rates pulses are poorly discriminated from baseline noise. Use similar count rates on standard and sample".  I say we don't need to "count rate match" if we tune our PHAs properly...

Also, it's not "instability" that occurs with "pulse energy shift" or what I would call "pulse height depression".  What occurs when the PHA peaks starts to shift lower (at higher count rates) or shifts higher (at lower count rates), is not "instability" but rather "non-linearity".  This is exactly why people seem to think that they need to "count rate match" their standard and unknown, but it is simply not necessary as long as one sets their PHA gain or bias high enough so that the PHA peak is *completely* above the baseline level at the highest count rate that one expects to measure (usually the highest concentration (primary std) at the highest beam current to be utilized).

That is, as the PHA shifts higher or lower, the baseline either cuts off pulse counts or includes more pulse counts from the left side tail of the PHA peak, thus introducing a non-linear response as a function of count rate.

Paul then mentions this: "Avoid tight PHA window, use integral mode unless a PHA interference is observed." But I would modify this to say: Because the use of PHA differential mode does not help with same Bragg order interferences, instead allow all interferences (same or higher order) to be counted and deal with the interferences properly using the quantitative interference correction.

I say this because, even in the case of higher order interferences, one cannot be sure that the interference pulses are cleanly separated from the interfered pulses. 

It is far better to obtain a linear response from our detectors/counting electronics and deal with any interference corrections in software. The one exception I can think of is maybe analyzing trace oxygen in a Na compound because it's difficult to find a material containing a known amount of Na but no oxygen, for use as an interference standard!

[Probeman]

Here's an example from a week ago where we analyzed PbSiO3 (natural Alamosite assumed stoichiometry) using SiO2 as the primary standard. Here are the results for all 11 matrix corrections:

Summary of All Calculated (averaged) Matrix Corrections:
St  386 Set   8 Alamosite (PbSiO3)
FFAST    Chantler (NIST v 2.1, 2005)

Elemental Weight Percents:
ELEM:       Si      Mg      Mn      Fe      Pb       O   TOTAL
     1  10.370   -.013   -.005    .011  73.151  16.939 100.454   Armstrong/Brown/Scott-Love (prZ)
     2   9.228   -.010   -.005    .011  73.151  16.939  99.314   Philibert/Duncumb-Reed
     3   9.691   -.011   -.005    .012  73.151  16.939  99.777   Heinrich/Duncumb-Reed
     4   9.302   -.011   -.005    .011  73.151  16.939  99.388   Love-Scott I
     5   9.423   -.011   -.005    .011  73.151  16.939  99.509   Love-Scott II
     6   8.037   -.010   -.004    .010  73.151  16.939  98.123   Packwood Phi(prZ) (EPQ-91)
     7  10.056   -.012   -.005    .012  73.151  16.939 100.141   Bastin (original) (prZ)
     8   9.481   -.011   -.005    .011  73.151  16.939  99.566   Bastin PROZA Phi (prZ) (EPQ-91)
     9   9.314   -.011   -.005    .011  73.151  16.939  99.399   Pouchou and Pichoir-Full (PAP)
    10   9.146   -.011   -.005    .011  73.151  16.939  99.232   Pouchou and Pichoir-Simplified (XPP)
    11   9.996   -.012   -.005    .011  73.151  16.939 100.080   Armstrong/Donovan and Moy BSC/BKS (prZ)

AVER:    9.459   -.011   -.005    .011  73.151  16.939  99.544
SDEV:     .612    .001    .000    .000    .000    .000    .612
SERR:     .185    .000    .000    .000    .000    .000

MIN:     8.037   -.013   -.005    .010  73.151  16.939  98.123
MAX:    10.370   -.010   -.004    .012  73.151  16.939 100.454

Percent Variances:
ELEM:       Si      Mg      Mn      Fe      Pb       O
PUBL:    9.910    n.a.    n.a.    n.a.  73.151  16.939
STDS:       14      12      25     395     ---     ---

ELEM:       Si      Mg      Mn      Fe      Pb       O
     1    4.65     ---     ---     ---     ---     ---           Armstrong/Brown/Scott-Love (prZ)
     2   -6.88     ---     ---     ---     ---     ---           Philibert/Duncumb-Reed
     3   -2.21     ---     ---     ---     ---     ---           Heinrich/Duncumb-Reed
     4   -6.13     ---     ---     ---     ---     ---           Love-Scott I
     5   -4.91     ---     ---     ---     ---     ---           Love-Scott II
     6  -18.90     ---     ---     ---     ---     ---           Packwood Phi(prZ) (EPQ-91)
     7    1.47     ---     ---     ---     ---     ---           Bastin (original) (prZ)
     8   -4.33     ---     ---     ---     ---     ---           Bastin PROZA Phi (prZ) (EPQ-91)
     9   -6.01     ---     ---     ---     ---     ---           Pouchou and Pichoir-Full (PAP)
    10   -7.71     ---     ---     ---     ---     ---           Pouchou and Pichoir-Simplified (XPP)
    11     .87     ---     ---     ---     ---     ---           Armstrong/Donovan and Moy BSC/BKS (prZ)

AVER:    -4.55     .00     .00     .00     .00     .00        
SDEV:     6.18     .00     .00     .00     .00     .00        
SERR:     1.86     .00     .00     .00     .00     .00        

MIN:    -18.90     .00     .00     .00     .00     .00        
MAX:      4.65     .00     .00     .00     .00     .00        

That's pretty wild, right?

Note the magnitude of the atomic number correction (from DebugMode in PFE or CalcZAF), for the last data point:

SAMPLE: 2545, ITERATIONS: 3, Z-BAR: 48.30882

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs  STDNUM uZAF/sZAF
   Si ka  1.6104   .9949   .7741  1.2402   .6403  1.2089   .5346  1.8390 10.8755 1355.02      14    1.0382
   Mg ka  2.4771  1.0000   .7735  1.9161   .6260  1.2358   .3264  1.3050 15.3257 2742.98      12    1.3592
   Mn ka  1.1342  1.0000   .8759   .9935   .8040  1.0894   .8562  6.5390  3.0586 356.758      25    .95158
   Fe ka  1.1032   .9854   .8580   .9327   .7936  1.0811   .8833  7.1120  2.8121 289.657     395    .88853

 ELEMENT   K-RAW K-RATIO ELEMWT% OXIDWT% ATOMIC% FORMULA TAKEOFF KILOVOL                                        
   Si ka  .20530  .08033   9.962   -----  20.085    .000   40.00   20.00                                        
   Mg ka -.00019 -.00008   -.016   -----   -.037    .000   40.00   20.00                                        
   Mn ka -.00008 -.00006   -.006   -----   -.006    .000   40.00   20.00                                        
   Fe ka  .00024  .00016    .015   -----    .015    .000   40.00   20.00                                        
   Pb                     73.151   -----  19.993    .000
   O                      16.939   -----  59.950    .000
   TOTAL:                100.045   ----- 100.000    .000

And here for those interested are the analysis for all data points using the Armstrong/Donovan and Moy matrix correction:

St  386 Set   8 Alamosite (PbSiO3)
TakeOff = 40.0  KiloVolt = 20.0  Beam Current = 30.0  Beam Size =   10
(Magnification (analytical) =  20000),        Beam Mode = Analog  Spot
(Magnification (default) =     1000, Magnification (imaging) =    100)
Image Shift (X,Y):                                         .00,    .00

Tsumeb, South West Africa
From Mineralogical Research, CA
(assumed stoichiometric)
Number of Data Lines:   6             Number of 'Good' Data Lines:   6
First/Last Date-Time: 04/19/2026 10:56:41 PM to 04/19/2026 11:08:42 PM

Average Total Oxygen:         .000     Average Total Weight%:  100.080
Average Calculated Oxygen:    .000     Z-Bar (Z Fraction^0.7):  48.289
Average Excess Oxygen:        .000     Average Atomic Weight:   56.630
Average ZAF Iteration:        3.00     Average Quant Iterate:     2.00

St  386 Set   8 Alamosite (PbSiO3), Results in Elemental Weight Percents
 
ELEM:       Si      Mg      Mn      Fe      Pb       O
TYPE:     ANAL    ANAL    ANAL    ANAL    SPEC    SPEC
BGDS:      LIN     LIN     LIN     LIN
TIME:    60.00   60.00   60.00   60.00     ---     ---
BEAM:    29.88   29.88   29.88   29.88     ---     ---

ELEM:       Si      Mg      Mn      Fe      Pb       O   SUM  
  2540  10.013   -.014   -.001    .008  73.151  16.939 100.096
  2541  10.000   -.007   -.011    .011  73.151  16.939 100.083
  2542  10.020   -.009   -.001    .009  73.151  16.939 100.109
  2543  10.001   -.020   -.005    .009  73.151  16.939 100.074
  2544   9.982   -.009   -.003    .014  73.151  16.939 100.074
  2545   9.962   -.016   -.006    .015  73.151  16.939 100.045

AVER:    9.996   -.012   -.005    .011  73.151  16.939 100.080
SDEV:     .021    .005    .004    .003    .000    .000    .022
SERR:     .009    .002    .001    .001    .000    .000
%RSD:      .21  -38.89  -76.31   27.89     .00     .00

PUBL:    9.910    n.a.    n.a.    n.a.  73.151  16.939 100.000
%VAR:      .87     ---     ---     ---     ---     ---
DIFF:     .086     ---     ---     ---     ---     ---
STDS:       14      12      25     395     ---     ---

STKF:    .3913   .4276   .7418   .6867     ---     ---
STCT:  2304.52  745.26  466.57 1036.19     ---     ---

UNKF:    .0806  -.0001   .0000   .0001     ---     ---
UNCT:   474.75    -.11    -.03     .18     ---     ---
UNBG:    11.48    1.53    1.62    5.04     ---     ---

ZCOR:   1.2402  1.9158   .9936   .9328     ---     ---
KRAW:    .2060  -.0002  -.0001   .0002     ---     ---
PKBG:    42.37     .93     .98    1.04     ---     ---

[Probeman]

Here's your 1% EPMA accuracy from pure oxide primary standards post of the day!

Si Ka in albite using SiO2 as a primary standard:



Yes, this albite is a natural specimen, but it was assumed stoichiometric minus the traces...  now here is Al Ka in the same albite, using Al2O3 as the primary standard:



This is good because Will Nachlas will probably be using a natural (alpine) albite from Julien Allaz for the FIGMAS standard mount. This albite might be the only natural mineral in the FIGMAS mount because there doesn't seem to be any synthetic (beam stable and water insoluble) Na minerals commercially available.

Unless anyone knows of something?

[Probeman]

Now let's look at accuracy when measuring Ti Ka extrapolating from TiO2 at 15 and 20 keV.  Let's start with SrTiO3:



All points close to 1% relative accuracy!  Now for RbTiOPO4 again at 15 and 20 keV:



Again, very close to 1% accuracy!

I'm sure many of you have synthetic TiO2 and SrTiO3 materials, and I'll bet a few of you have RbTiOPO4, which by the way can be obtained from Marc Schier for $100 a gram:

https://calchemist.com/

and makes a wonderful Rb standard and is completely beam stable.  So what are you waiting for?  Just be sure to tune your PHAs properly. Here's what Andrew and I used for these measurements:



Note that the PHA peak is completely above the baseline level. Yes, we had to amplify the detector a bit to get this accomplished, but with this gain/bias setting and in PHA integral mode, you will get 1% accuracy on suitable standards extrapolating from pure synthetic oxides!

[Probeman]

More "breaking the EPMA 1% accuracy barrier" of the day. Here's Si Ka measured in natural diopside (assumed stoichiometry minus traces) extrapolated from SiO2:



and here is Mg Ka extrapolated from the MgO primary std:



Wouldn't it be nice if every EPMA lab in the world were using the same synthetic SiO2, MgO, Fe3O4, TiO2, Al2O3, etc., primary standards? And we could check them against secondary standards such as synthetic MgAl2O4, Mg2SiO4, SrTiO3, etc?

That is exactly what Will Nachlas is working towards... hopefully he can give us an update on his global FIGMAS mount.

The Focused Interest Group on MicroAnalytical Standards (FIGMAS), a FIG of the Microscopy Society of America (MSA) and co-sponsored by the Microanalysis Society (MAS), is organizing a series of round robin exercises to begin investigating synthetic standard materials for developing a universal standards mount and accompanying database of community k-ratios. Details of the round robin and a survey to express interest are included in the link below. All labs who meet the stated criteria are welcome to participate.

https://docs.google.com/forms/d/e/1FAIpQLSd8nttQYcex9UmnHJyD3iHE-vpL7gG5XVpNumX8-fqrWrgb9A/viewform