Quantitative Spectral Interference Corrections

[John Donovan]

But first, a bit of history... to better explain what Andrew saw and we subsequently found to be the issue.

In the mid 1990s we implemented the quantitative interference correction in Probe for EPMA using an iterative method.  An iterative method is necessary when the correction in question is compositionally dependent, for example the MAN background correction depends on the average Z of the material to estimate the continuum production, and the average Z of the material is in turn dependent on the composition:

https://smf.probesoftware.com/index.php?topic=1378.0

Similarly the quantitative spectral interference correction is dependent on the concentration of the interfering element (not the intensity of the interfering element!):

https://epmalab.uoregon.edu/publ/Improved%20Interference%20(Micro.%20Anal,%201993).pdf

The same can be said for the Area-Peak Factor (APF) correction for peak shape/shift when using the "compound" APF feature:

https://smf.probesoftware.com/index.php?topic=536.0

and to some extent, also the volatile (TDI) correction:

https://smf.probesoftware.com/index.php?topic=11.0

although the TDI correction really only needs to be applied *prior* to the matrix correction for accuracy.

In any case, when the quantitative interference correction (and the other compositionally dependent corrections) was implemented in the mid 1990s, we utilized the existing iteration loop already used for the MAN background correction. At that time the MAN iteration loop was fixed to utilize a maximum of 10 iterations because one never needed more than 10 iterations to converge.

However, in the late 1990s Probeman started pushing the limits of the interference correction and found that in some of the most extreme pathological overlaps situations, e.g., Pb La and As Ka, we found that additional iterations were necessary to converge the iterations to accuracy. And the reason turns out to be because when calibrating As Ka and Pb La, it will be found that the intensity of the As overlap on the Pb Ma signal is actually *larger* than the Pb La signal, even though the concentration of the As in the GaAs standard is lower than the Pb in the Pb S standard.  This is due to the fact that the As Ka emission is more efficient than the Pb La production, as seen here in the List Standard Intensities output in Probe for EPMA:

Drift array background intensities (cps/49.005nA) for standards:
ELMXRY:    pb la   as ka    s ka
MOTCRY:  3   LIF 2   LIF 5   PET
INTEGR:        0       0       0
STDASS:      731     662     730
STDVIR:        0       0       0
           224.5   124.6    42.2
           226.1   124.3    42.5

Drift array standard intensities (cps/49.005nA) (background corrected):
ELMXRY:    pb la   as ka    s ka
MOTCRY:  3   LIF 2   LIF 5   PET
STDASS:      731     662     730
STDVIR:        0       0       0
          3550.2  4257.7 12340.3
          3566.3  4266.5 12365.8

Drift array interference standard intensities (cps/49.005nA):

1st assigned interference elements
ELMXRY:    pb la   as ka    s ka
INTFELM:     as      pb         
INTFSTD:     662     731       
          4076.5  2736.3       
          4094.6  2763.6       

Because of this "inverted" concentration to intensity ratio, the iteration becomes quite extended, as seen here:



Sorry about the quality of the above plot, it comes from the 1990s! The point is that this sort of pathological interference correction requires over 50 iterations! While a typical spectral interference only required 4 or 5 iterations. It's actually sort of amazing that this iteration even converges at all!

Anyway, it turns out that years later, in the late 2010s, we started working on the quantitative x-ray mapping method, which requires a full quantitative correction of every pixel, just as one would with an analytical point analysis:

https://smf.probesoftware.com/index.php?topic=1212.0

Some vendors attempt to quantify x-ray maps using a calibration curve, but there's a reason that we don't use calibration curves for our quantitative point analyses: it's not very quantitative!   

Anyway, the downside of applying a full dead time, standard intensity drift, background, matrix and of course also interference and TDI (volatile) corrections, to every pixel is that it can be a bit time consuming to apply a complete quant correction to quantify hundreds of thousands of pixels.

The quant code in Probe for EPMA is pretty darn efficient, but still we tried modifying a few parameters to improve the iteration speed, and yup, you guessed it, we reduced the number of iterations for the MAN (and interference) corrections in the late 2010s because we found that we really didn't need so many iterations, forgetting about the rare cases of the extreme Pb la and As ka situation! 

Anyway, this is all fixed in the latest version of Probe for EPMA (and CalcImage), so please update when you get a chance. And this doesn't seem to have affected the quantification speed in CalcImage for x-ray map quant.

Just for fun, I will post some examples of the Pb La and As Ka analyses in the next post.

[John Donovan]

Before I present an examples of these "pathological" spectral interferences, here is an early flow chart of the double iteration loop that is utilized for the interference (and MAN, TDI and APF) corrections:



Note that the inner iteration loop contains the matrix correction for the analyzed elements, along with any unanalyzed elements that need to be included in the matrix correction. That is, elements by stoichiometry, difference, and/or charge balance.

The outer loop contains the correction of spectral interferences (and also the MAN background, TDI (volatile) and Area Peak factor (APF) corrections).

This double iteration loop is the "secret sauce" in Probe for EPMA and CalcImage that allows for compositionally dependent corrections to be utilized in the matrix correction for best accuracy. Think of it this way: if you perform an interference or TDI correction to the composition, and the magnitude of the these corrections are greater than ~ 1%, you will want to re-calculate your matrix correction to reflect this modified composition. Here is a more detailed, but more complex flow chart of the same double iteration loop which we published in our 2019 quant mapping paper:



https://www.probesoftware.com/wp-content/uploads/2024/08/donovan_2021_amer_min_2021-7739.pdf

Performing these interference corrections *after* the matrix correction, will result in poor accuracy for your analyzed elements. Even an analyzed element such as Fe (Ka) can be significantly affected by these changes to the compositions as shown here:

https://smf.probesoftware.com/index.php?topic=92.105

[John Donovan]

OK, so back to actual interference corrections. In the case of a "self interfering" interferences such as As K a and Pb La, the changes in composition can be quite large. For example here is an analysis of a PbAs sulfide (Sartorite) WITHOUT the quantitative interference correction:

Un    7 Sartorite (rim high z )
TakeOff = 40.0  KiloVolt = 20.0  Beam Current = 50.0  Beam Size =    0
(Magnification (analytical) =   4000),        Beam Mode = Analog  Spot
(Magnification (default) =        0, Magnification (imaging) =    100)
Image Shift (X,Y):                                         .00,    .00
Number of Data Lines:   8             Number of 'Good' Data Lines:   6
First/Last Date-Time: 05/08/1998 05:37:49 PM to 05/08/1998 05:46:56 PM

Average Total Oxygen:         .000     Average Total Weight%:  172.947
Average Calculated Oxygen:    .000     Average Atomic Number:   60.812
Average Excess Oxygen:        .000     Average Atomic Weight:   93.989
Average ZAF Iteration:        4.00     Average Quant Iterate:     2.00

Un    7 Sartorite (rim high z ), Results in Elemental Weight Percents
 
ELEM:       Pb      As       S       O       H
TYPE:     ANAL    ANAL    ANAL    SPEC    SPEC
BGDS:      LIN     LIN     LIN
TIME:    30.00   30.00   30.00     ---     ---
BEAM:    50.02   50.02   50.02     ---     ---

ELEM:       Pb      As       S       O       H   SUM  
   991 106.124  41.202  24.532    .000    .000 171.859
   992 106.800  41.229  24.262    .000    .000 172.291
   994 108.183  41.744  24.609    .000    .000 174.537
   995 105.893  41.153  24.681    .000    .000 171.726
   996 106.981  41.826  25.485    .000    .000 174.291
   997 106.486  41.643  24.851    .000    .000 172.980

AVER:  106.744  41.466  24.737    .000    .000 172.947
SDEV:     .813    .304    .414    .000    .000   1.220
SERR:     .332    .124    .169    .000    .000
%RSD:      .76     .73    1.68     .00     .00
STDS:      731     662     730     ---     ---

STKF:    .8033   .4962   .4761     ---     ---
STCT:   3566.3  4266.5 12365.8     ---     ---

UNKF:    .9285   .4512   .2039     ---     ---
UNCT:   4121.9  3879.9  5296.9     ---     ---
UNBG:    167.1   161.4    57.2     ---     ---

ZCOR:   1.1497   .9190  1.2130     ---     ---
KRAW:   1.1558   .9094   .4283     ---     ---
PKBG:    25.67   25.05   93.78     ---     ---

OK, so we see the totals are around 175 wt%, so just a slight error!      Also note that the sulfur (which is not interfered with) averages ~24.7 wt% with this matrix (uncorrected for interferences). We'll see how this value changes when the interference correction is applied below.

Now let's turn on the interference correction of Pb by As and As by Pb:



Note that we utilized GaAs as the interference standard for Pb La (contains a known concentration of the interfering element As, but none of the interfered element Pb) and PbS as the interference standard for As Ka (again, contains a known concentration of the interfering element Pb, but none of the interfered element As).

Now, finally(!), here are the interference corrected results for the above mineral:

Un    7 Sartorite (rim high z )
TakeOff = 40.0  KiloVolt = 20.0  Beam Current = 50.0  Beam Size =    0
(Magnification (analytical) =   4000),        Beam Mode = Analog  Spot
(Magnification (default) =        0, Magnification (imaging) =    100)
Image Shift (X,Y):                                         .00,    .00
Number of Data Lines:   8             Number of 'Good' Data Lines:   6
First/Last Date-Time: 05/08/1998 05:37:49 PM to 05/08/1998 05:46:56 PM

Average Total Oxygen:         .000     Average Total Weight%:   99.342
Average Calculated Oxygen:    .000     Average Atomic Number:   50.041
Average Excess Oxygen:        .000     Average Atomic Weight:   70.501
Average ZAF Iteration:        4.00     Average Quant Iterate:    58.00


Un    7 Sartorite (rim high z ), Results in Elemental Weight Percents
 
ELEM:       Pb      As       S       O       H
TYPE:     ANAL    ANAL    ANAL    SPEC    SPEC
BGDS:      LIN     LIN     LIN
TIME:    30.00   30.00   30.00     ---     ---
BEAM:    50.02   50.02   50.02     ---     ---

ELEM:       Pb      As       S       O       H   SUM 
   991  43.299  30.282  25.168    .000    .000  98.749
   992  45.643  29.386  24.768    .000    .000  99.796
   994  46.395  29.681  25.111    .000    .000 101.188
   995  42.864  30.405  25.339    .000    .000  98.608
   996  41.166  31.912  26.299    .000    .000  99.377
   997  40.860  31.810  25.667    .000    .000  98.337

AVER:   43.371  30.579  25.392    .000    .000  99.342
SDEV:    2.269   1.062    .533    .000    .000   1.050
SERR:     .926    .434    .217    .000    .000
%RSD:     5.23    3.47    2.10     .00     .00
STDS:      731     662     730     ---     ---

STKF:    .8033   .4962   .4761     ---     ---
STCT:   3566.3  4266.5 12365.8     ---     ---

UNKF:    .3500   .3100   .2039     ---     ---
UNCT:   1554.0  2665.8  5296.9     ---     ---
UNBG:    167.1   161.4    57.2     ---     ---

ZCOR:   1.2394   .9862  1.2450     ---     ---
KRAW:    .4357   .6248   .4283     ---     ---
PKBG:    10.30   17.53   93.78     ---     ---
INT%:   -62.31  -31.29    ----     ---     ---

Just a slight improvement in the totals!      Also note that sulfur average value went from ~24.7 to ~25.4 wt%, which is roughly a 2.8% relative change in the sulfur concentrations. And remember, the sulfur itself was not affected by any interferences in this example, the change in the sulfur concentration is completely due to the change in the matrix correction due to the interference correction of Pb and As!

Just for laughs and giggles I've attached below, a rough transcription of the talk I gave back in 1998 (using 35 mm slides!) and the original 1993 interference iteration paper.

[John Donovan]

In summary, the important point of the last few posts in this topic, is that that when we modified the interference, MAN, TDI and APF iteration loop back in 2018 in an attempt to further speed up the x-ray mapping quantification by reducing the maximum iterations from 100 to 10, we accidentally caused the interference corrections to fail when more than 10 iterations are required, specifically in the case of "self interferences" such as As Ka and Pb La:

Average Total Oxygen:         .000     Average Total Weight%:   99.342
Average Calculated Oxygen:    .000     Average Atomic Number:   50.041
Average Excess Oxygen:        .000     Average Atomic Weight:   70.501
Average ZAF Iteration:        4.00     Average Quant Iterate:    58.00

I'm not sure if there any other "self interferences" as bad as As Ka and Pb la, but it doesn't seem to slow down the x-ray map quantification time for "normal" interferences in our testing...

Hey, would someone be willing to acquire an x-ray map of an As,Pb sulfide and try to quantify it?   

Thank-you to Andrew Locock for noticing this issue and bringing it to our attention!

Update Probe for EPMA as usual using the Help menu to obtain this v. 13.9.4 update.