Author Topic: Specifying Unanalyzed Elements For a Proper Matrix Correction  (Read 25545 times)

AndrewLocock

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #75 on: July 24, 2019, 01:08:25 pm »
Thus, I suspect that some (slight) divergence from ideality could similarly occur in the ferric/ferrous recalculation during the iterations of the matrix corrections.

Yes, indeed. Sometimes reality is not ideal!    ;)


Hi John,
Below is a graph of the C vs. Ca formula contents from multiple analyses of the Smithsonian calcite standard.

CO2 was added by stoichiometry (0.33333 C for every 1 O) prior to the matrix corrections.

The amount of C is perfectly anti-correlated with the amount of Ca.

My interpretation: this is an unfortunate consequence of the analytical uncertainty in Ca coupling with the algorithm loops in Probe-for-EPMA.

If Ca is low, PfE determines C as high. If Ca is high, PfE determines C as low. Of course the ideal is 1:1, CaCO3.

I am pretty sure that the Smithsonian calcite is electrically neutral (charge-balanced!), so the behaviour in this graph is an artifact of the data reduction process.

Take home message: at present, add CO2 in to get the best data reduction, then recalculate it for stoichiometry.
Cheers,
Andrew



John Donovan

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #76 on: July 24, 2019, 04:04:34 pm »
Hi Andrew,
Interesting.  Is the stoichiometry correlated in any way with the analytical total?

I ask because it seems to me this could also be an artifact of the normalization from weight percent to atoms.  When you get a chance please send me the MDB file and I'll look into it.
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AndrewLocock

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #77 on: July 25, 2019, 10:42:47 am »
Hi Andrew,
Interesting.  Is the stoichiometry correlated in any way with the analytical total?

I ask because it seems to me this could also be an artifact of the normalization from weight percent to atoms. 

Hi John,

The data are from back in 2015; I have attached the raw oxide data (CaO and CO2) and the molar proportions that result as an Excel file. There are actually two calcite samples present (which I previously confused, sorry).

The plots of the molar proportions show negative linear correlations (essentially identical for the two calcites):





Of course, the molar amount of CO2 should(!) be equal to the molar amount of CaO.
That is, these graphs should simply show y = x.

If one recalculates the wt% CO2 based on the stoichiometry CaCO3, it has a negative linear correlation with the wt% CO2 initially reported by Probe-for-EPMA:



The weight percent CO2 reported by Probe-for-EPMA (after the iterated matrix corrections) is not in stoichiometric proportion to the CaO content for these calcite analyses. 

In answer to your question about correlation with the analytical total, for the two calcites, the initial data reported by Probe-for-EPMA show a negative linear correlation between wt% CO2 and analytical total.

Whereas, when CO2 is calculated by stoichiometry to the CaO content, the wt% CO2 and the subsequent revised totals are positively correlated, in the ratio 2.2742. This is, of course, the ratio found in ideal calcite, CaCO3 (43.97 wt% CO2, 56.03 wt% CaO, total 100.00), where 100/43.97 = 2.2742.



I will send you this MDB file separately.

Best regards,
Andrew

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #78 on: July 25, 2019, 11:31:36 am »
In answer to your question about correlation with the analytical total, for the two calcites, the initial data reported by Probe-for-EPMA show a negative linear correlation between wt% CO2 and analytical total.

Whereas, when CO2 is calculated by stoichiometry to the CaO content, the wt% CO2 and the subsequent revised totals are positively correlated, in the ratio 2.2742. This is, of course, the ratio found in ideal calcite, CaCO3 (43.97 wt% CO2, 56.03 wt% CaO, total 100.00), where 100/43.97 = 2.2742.



I will send you this MDB file separately.

Best regards,
Andrew

Hi Andrew,
Yes, this is exactly what I suspected. For those analyses where the totals are not close to 100%, when the concentrations are normalized to 100% for the formula calculations, the CO2 stoichiometry gets "distorted" due to different atomic weights relative to atom proportions.

As evidence for this, please note that for those analyses in the above plot where the analytical totals are close to 100%, the stoichiometric CO2 values are almost exactly equal to the ideal concentration of 43.97 wt% CO2.

I'm really not sure what one can do about this except try to obtain better analytical totals!   :P

In principle I guess one could concoct a "correction" for those analyses which don't total close to 100%, but this seems to me to be a little problematic for several reasons. 

The good news is that averaging these analyses together should average out this normalization effect.  Assuming the average analytical total is close to 100%!  :)

Thank-you for your help on this.
« Last Edit: July 25, 2019, 12:08:50 pm by John Donovan »
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AndrewLocock

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #79 on: July 25, 2019, 01:08:05 pm »
Hi Andrew,
Yes, this is exactly what I suspected. For those analyses where the totals are not close to 100%, when the concentrations are normalized to 100% for the formula calculations, the CO2 stoichiometry gets "distorted" due to different atomic weights relative to atom proportions.

As evidence for this, please note that for those analyses in the above plot where the analytical totals are close to 100%, the stoichiometric CO2 values are almost exactly equal to the ideal concentration of 43.97 wt% CO2.

I'm really not sure what one can do about this except try to obtain better analytical totals!   :P

In principle I guess one could concoct a "correction" for those analyses which don't total close to 100%, but this seems to me to be a little problematic for several reasons. 

The good news is that averaging these analyses together should average out this normalization effect.  Assuming the average analytical total is close to 100%!  :)

Thank-you for your help on this.

Hi John,
I am confused as to why (or how) oxygen is handled vs. how CO2 is handled in Probe-for-EPMA. Both are added in prior to the iterative matrix corrections (yes?). But the behaviour of a simple oxide compound seems different than that of a simple carbonate.

For example, I just measured Mg in periclase (20 points). The results are given as elements in weight percent, with oxygen calculated by stoichiometry in Probe-for-EPMA. The totals are between 99.6 and 100.6 wt%.

A graph of the oxygen wt% vs. analytical total follows the ideal ratio of 2.5191:



Probe-for-EPMA can figure out the exact stoichiometric amount of oxygen in MgO for a series of points with differing amounts of Mg (and therefore differing analytical totals).

Why are the results for the calculation of CO2 in CaCO3 any different?
Or how is it that the CO2 is handled that causes the results to differ from stoichiometry?

Thanks,
Andrew


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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #80 on: July 25, 2019, 01:25:46 pm »
Hi Andrew,
It's a good question. I'm not quite sure myself but as I said, I think it's because of the normalization to atoms for the CO2 calculation. My code is based on Armstrong's code and it's all on Github so you can check it out yourself.

https://github.com/openmicroanalysis/calczaf

You'll want to look at procedure ZAFSMP in code module ZAF.bas. The calculation for an element in relative atoms to stoichiometric oxygen is calculated in two places, here is the first approximation calculation:

Code: [Select]
' Add in elements calculated relative to stoichiometric element (in0%)
For i% = 1 To zaf.in1%
If zaf.il%(i%) = 15 Then
zaf.krat!(i%) = (zaf.krat!(zaf.in0%) / zaf.atwts!(zaf.in0%)) * sample(1).StoichiometryRatio! * zaf.atwts!(i%)
zaf.krat!(zaf.in0%) = zaf.krat!(zaf.in0%) + zaf.krat!(i%) * zaf.p1!(i%)
zaf.ksum! = zaf.ksum! + zaf.krat!(i%) + zaf.krat!(i%) * zaf.p1!(i%)
End If
Next i%
End If

The relative element calculation code inside the iteration loop is:

Code: [Select]
' Calculate element relative to stoichiometric oxygen based on previous iteration calculation of oxygen
If zaf.il%(zaf.in0%) = 0 Then    ' if calculating oxygen by stoichiometry
For i% = 1 To zaf.in1%
If zaf.il%(i%) = 15 Then
r1!(i%) = (r1!(zaf.in0%) / zaf.atwts!(zaf.in0%)) * sample(1).StoichiometryRatio! * zaf.atwts!(i%)
zaf.ksum! = zaf.ksum! + r1!(i%)
zaf.krat!(i%) = r1!(i%)
End If
Next i%

The integer "15" is the flag for an element calculated by stocihiometry to stoichiometric oxygen.

krat is the k-ratio
ksum is the k-ratio sum

If you see anything you think we should modify please let me know and send me a test file to try it.  Maybe we'll figure this out together!
john
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John Donovan

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #81 on: July 25, 2019, 01:56:32 pm »
Andrew,
But really I don't think the relative element calculation is the real problem.  I suspect that the real problem comes at the end of the iteration loop when it de-normalizes everything to get back to the actual analytical total.

This code is in the same procedure and is after the iteration loop completes to the specified precision:

Code: [Select]
' Un-Normalize
3400:
For i% = 1 To zaf.in0%
zaf.conc!(i%) = zaf.conc!(i%) * zaf.ksum!
Next i%

What I think is happening is that because the matrix physics and unanalyzed element calculations are all performed in concentration units and during the iteration everything is normalized to total 1.0, when the loop exits, the program takes these concentrations and de-normalizes them for the actual analytical total.

But because the atomic proportion calculations are based on the number of atoms, a divergence from the previously calculated stoichiometry occurs, depending on the difference to a 100% analytical total. Because concentrations scale differently than concentrations.

Does this make any sense to you?   

By the way, if you turn on DebugMode you will get a lot more output of the intermediate calculations, maybe more than you want!  So maybe use the CalcZAF output menu in the PFE Analyze! window by right clicking the sample, and export a sample to CalcZAF format and perform the Debug calculations there...
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Paul Carpenter

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #82 on: July 25, 2019, 02:30:17 pm »
I suggest that beam sensitivity is a contributing factor here. For the analysis of calcite, many exhibit differing beam sensitive behavior. During beam damage, CO2 is released and the residual beam volume becomes progressively an oxide residue. Ultimately the analysis would be of Ca oxide after complete CO2 loss.

The calculation of CO2 by stoichiometry is made by associating a carbon with the oxygen calculated from the measured cations in the sample, Ca, Mg, Fe, etc. So if a differential amount of CO2 is lost, then the cation concentration increases, and the calculated CO2 amount also increases. This results in a high total as there is too much CO2 calculated because the analytical volume is a more cation-rich composition.

So when doing conventional analysis, a low total indicates beam damage. When calculating CO2 by stoichiometry a high total indicates the same.

There is also the possibility of organic material in biogenically produced calcite or aragonite. I have analyzed a number of these materials and they exhibit significant beam sensitivity. But the point here is that there are organic materials that could also be in the carbonate. Not knowing what the specific material is, it is also possible that there are small inclusions of quartz or sulfate.

This may not be the whole story here, but that is my take.

Paul

Paul Carpenter
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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #83 on: July 25, 2019, 04:54:44 pm »
Andrew,
Do you have a nice simple example of this formula normalization issue, but not a beam sensitive sample?  In an MDB file?

Paul is correct that sample sensitivity to the beam can be an issue, especially with carbonates, but my intuition is that this (anti)-correlation with the analytical totals is essentially a normalization issue of some kind.
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AndrewLocock

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #84 on: July 25, 2019, 05:14:31 pm »
I suggest that beam sensitivity is a contributing factor here. For the analysis of calcite, many exhibit differing beam sensitive behavior. During beam damage, CO2 is released and the residual beam volume becomes progressively an oxide residue. Ultimately the analysis would be of Ca oxide after complete CO2 loss.

The calculation of CO2 by stoichiometry is made by associating a carbon with the oxygen calculated from the measured cations in the sample, Ca, Mg, Fe, etc. So if a differential amount of CO2 is lost, then the cation concentration increases, and the calculated CO2 amount also increases. This results in a high total as there is too much CO2 calculated because the analytical volume is a more cation-rich composition.

So when doing conventional analysis, a low total indicates beam damage. When calculating CO2 by stoichiometry a high total indicates the same.

There is also the possibility of organic material in biogenically produced calcite or aragonite. I have analyzed a number of these materials and they exhibit significant beam sensitivity. But the point here is that there are organic materials that could also be in the carbonate. Not knowing what the specific material is, it is also possible that there are small inclusions of quartz or sulfate.

This may not be the whole story here, but that is my take.

Paul


Hi Paul,

I take your point about the considerable beam sensitivity of calcite.

I just examined the Smithsonian siderite reference material, and ran 10 points with a 10-micron defocussed beam at 15 kV and 10 nA, with a count time of 30 s on peak, and 6 time-dependent-intensity (TDI) intervals for the Fe measurement.

The behaviour of Fe as a function of time is shown below:



As the Fe signal does not vary significantly with time, I turned off the TDI correction.
(I do not consider this siderite to be beam sensitive under the analytical conditions used here.)

The initial analytical totals range from 99.7 to 100.3 wt%.

However, the molar proportions of CO2 derived from the wt% CO2 reported by Probe-for-EPMA are negatively correlated with the molar proportions of the sum of FeO + MnO:



As I cannot attribute this behaviour to the sample, I concur with John that this is probably a result of how the CO2 is handled during the matrix corrections.

I will have to do some work to understand the Basic code provided (I am not a programmer).

But, I suspect that, although the initial amount of CO2 provided at the start of the matrix corrections may be in the correct stoichiometric ratio to the Fe+Mn of this siderite, by the time the iterations converge, this stoichiometric relationship has been altered. As John suggests, this may have to do with exactly how the algorithm proceeds (normalization to help with convergence?).

Best regards,
Andrew

AndrewLocock

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #85 on: July 26, 2019, 07:01:44 am »
Andrew,
Do you have a nice simple example of this formula normalization issue, but not a beam sensitive sample?  In an MDB file?

Paul is correct that sample sensitivity to the beam can be an issue, especially with carbonates, but my intuition is that this (anti)-correlation with the analytical totals is essentially a normalization issue of some kind.

Hi John,
Here is the MDB file for 4 lines of 10-point analyses on Smithsonian siderite.

The material does not exhibit beam damage (no significant change of intensity of Fe with time) under the conditions used.

Also attached is the formatted Excel file of the results.
As before, the CO2 wt% results reported by Probe-for-EPMA are close to, but systematically different from, the ideal stoichiometry.

Best regards,
Andrew
« Last Edit: July 26, 2019, 10:04:06 am by John Donovan »

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #86 on: July 26, 2019, 10:54:22 am »
Hi Andrew,
Thanks. This will be useful.

Here's another approach in my KISS (keep it simple stupid) philosophy: run Probe for EPMA in simulation mode! Then there's no instrumental or sample issues!

You might already know that you can run PFE in "demo" or "simulation" mode. In PFE's simulation mode one can peak elements, acquire wavescans, acquire standards and if you specify an unknown name that is already a standard in your simulation run, it will utilize the physics for that standard composition as the unknown. 

See the attached simulation run below where all I ran was Ca using a pure CaCO3 standard.  I then added C as a specified (unanalyzed) element, and specified 0.3333 atoms of carbon for each atom of stoichiometric oxygen.

So here is the CaCO3 standard analyzed as an unknown:

St  136 Set   2 CaCO3, Results in Elemental Weight Percents
 
ELEM:       Ca       C       O
TYPE:     ANAL    STOI    CALC
BGDS:      LIN
TIME:    10.00     ---     ---
BEAM:    30.01     ---     ---

ELEM:       Ca       C       O   SUM 
     6  39.888  12.010  47.920  99.817
     7  39.875  12.011  47.917  99.803
     8  40.341  11.970  47.994 100.305
     9  40.025  11.997  47.942  99.964

AVER:   40.032  11.997  47.943  99.972
SDEV:     .216    .019    .036    .233
SERR:     .108    .009    .018
%RSD:      .54     .16     .07

PUBL:   40.044  12.000  47.956 100.000
%VAR:   (-.03)    -.03    -.03
DIFF:   (-.01)   -.003   -.013
STDS:      136     ---     ---

STKF:    .3790     ---     ---
STCT:   128.04     ---     ---

UNKF:    .3789     ---     ---
UNCT:   128.00     ---     ---
UNBG:      .17     ---     ---

ZCOR:   1.0567     ---     ---
KRAW:    .9997     ---     ---
PKBG:   756.80     ---     ---

St  136 Set   2 CaCO3, Results Based on 1 Atoms of ca

ELEM:       Ca       C       O   SUM 
     6   1.000   1.005   3.009   5.014
     7   1.000   1.005   3.010   5.015
     8   1.000    .990   2.980   4.970
     9   1.000   1.000   3.001   5.001

AVER:    1.000   1.000   3.000   5.000    <---- sanity check!
SDEV:     .000    .007    .014    .021
SERR:     .000    .003    .007
%RSD:      .00     .70     .46

Note that the standard intensity varies because we add noise to the simulation, but the average is as expected.  Within the precision of the noise.  Now here is an analysis of an unknown which was named CaCO3, so the standard composition is automatically utilized for calculating the intensities from the composition (running the matrix correction backwards!):

Un    3 CaCO3, Results in Elemental Weight Percents
 
ELEM:       Ca       C       O
TYPE:     ANAL    STOI    CALC
BGDS:      LIN
TIME:    10.00     ---     ---
BEAM:    30.02     ---     ---

ELEM:       Ca       C       O   SUM 
     3  39.880  12.010  47.918  99.808
     4  39.845  12.013  47.912  99.771
     5  39.689  12.027  47.887  99.604

AVER:   39.805  12.017  47.906  99.728       <---- note slightly low total
SDEV:     .101    .009    .017    .109
SERR:     .059    .005    .010
%RSD:      .25     .07     .03
STDS:      136     ---     ---

STKF:    .3790     ---     ---
STCT:   128.28     ---     ---

UNKF:    .3767     ---     ---
UNCT:   127.50     ---     ---
UNBG:      .15     ---     ---

ZCOR:   1.0568     ---     ---
KRAW:    .9939     ---     ---
PKBG:   866.07     ---     ---

Un    3 CaCO3, Results Based on 1 Atoms of ca

ELEM:       Ca       C       O   SUM 
     3   1.000   1.005   3.010   5.015
     4   1.000   1.006   3.012   5.018
     5   1.000   1.011   3.022   5.034

AVER:    1.000   1.007   3.015   5.022      <---- note slightly high C and O formula atoms
SDEV:     .000    .003    .007    .010
SERR:     .000    .002    .004
%RSD:      .00     .33     .22

Note that the totals are a little low (random noise) *and* that the C and O are a little high relative to Ca.  Now another unknown, but this time with slightly high totals:

Un    4 CaCO3, Results in Elemental Weight Percents
 
ELEM:       Ca       C       O
TYPE:     ANAL    STOI    CALC
BGDS:      LIN
TIME:    10.00     ---     ---
BEAM:    30.00     ---     ---

ELEM:       Ca       C       O   SUM 
    10  40.197  11.982  47.970 100.150
    11  40.088  11.992  47.952 100.032

AVER:   40.142  11.987  47.961 100.091     <---- note slightly high totals
SDEV:     .077    .007    .013    .083
SERR:     .055    .005    .009
%RSD:      .19     .06     .03
STDS:      136     ---     ---

STKF:    .3790     ---     ---
STCT:   128.00     ---     ---

UNKF:    .3799     ---     ---
UNCT:   128.33     ---     ---
UNBG:      .16     ---     ---

ZCOR:   1.0566     ---     ---
KRAW:   1.0025     ---     ---
PKBG:   812.48     ---     ---

Un    4 CaCO3, Results Based on 1 Atoms of ca

ELEM:       Ca       C       O   SUM 
    10   1.000    .995   2.989   4.984
    11   1.000    .998   2.996   4.995

AVER:    1.000    .996   2.993   4.989      <---- note slightly low C and O atoms
SDEV:     .000    .002    .005    .007
SERR:     .000    .002    .004
%RSD:      .00     .25     .17

Now note that the C and O are slightly low when the totals are slightly high.

This is what I've been trying to say all along.  That is, I think that the atomic proportionality gets slightly distorted when the normalized composition in the matrix iteration loop is de-normalized after the iteration loop is exited. This is how Armstrong coded this many years ago in his CITZAF/TRYZAF code.

I think we can use this test run to see the effect most clearly since it is such a simple example.  Maybe Paul Carpenter also has some ideas on this code as he worked on it with John Armstrong many years ago.

Edit by John: I just realized the output of the CaCO3 standard as an "unknown" had the C and O specified by concentration.  That is now fixed, so that C is now specified as 0.3333 atoms for each atom of stoichiometric oxygen as previously stated. The attached MDB file below has been updated to reflect this.
« Last Edit: July 26, 2019, 05:05:33 pm by John Donovan »
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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #87 on: July 27, 2019, 09:29:02 am »
Previously I wondered if the de-normalization of the concentrations to the analytical total after the matrix iteration loop is exited, was affecting the conversion to atoms. But I just checked, and no, that's not the issue:

Un    4 CaCO3, Results in Elemental Weight Percents
 
ELEM:       Ca       C       O
TYPE:     ANAL    STOI    CALC
BGDS:      LIN
TIME:    10.00     ---     ---
BEAM:    30.00     ---     ---

ELEM:       Ca       C       O   SUM 
    10  40.137  11.964  47.899 100.000
    11  40.075  11.988  47.937 100.000

AVER:   40.106  11.976  47.918 100.000
SDEV:     .044    .017    .027    .000
SERR:     .031    .012    .019
%RSD:      .11     .14     .06
STDS:      136     ---     ---

STKF:    .3790     ---     ---
STCT:   128.00     ---     ---

UNKF:    .3799     ---     ---
UNCT:   128.33     ---     ---
UNBG:      .16     ---     ---

ZCOR:   1.0566     ---     ---
KRAW:   1.0025     ---     ---
PKBG:   812.48     ---     ---

Un    4 CaCO3, Results Based on 1 Atoms of ca

ELEM:       Ca       C       O   SUM 
    10   1.000    .995   2.989   4.984
    11   1.000    .998   2.996   4.995

AVER:    1.000    .996   2.993   4.989
SDEV:     .000    .002    .005    .007
SERR:     .000    .002    .004
%RSD:      .00     .25     .17

So, with the de-normalization code commented out, the analytical totals are now 100.000, but the atoms for C and O are still low. In fact they are exactly the same numbers as before when they were de-normalized to the actual analytical totals.

I'm beginning to wonder if non-stoichiometric results are unavoidable when one obtains the "wrong" Ca concentration. Afterall, if one measures too high or too low a Ca concentration in a carbonate (for whatever reason!), why would one expect the atom proportions to be calculated correctly?
« Last Edit: July 27, 2019, 11:44:17 am by John Donovan »
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John Donovan

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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #88 on: July 27, 2019, 11:55:34 am »
Hi Andrew,
I again return to this plot of analytical totals versus Ca concentration you posted earlier.  With some additional annotations.



I'm probably missing something, so please correct me if you see something, but it seems to me that when making a measurement of CaCO3, why would one expect to obtain the exactly correct stoichiometry for CO2, when the Ca measurement is not exactly correct?

We already know the code calculates the correct CO2 when the correct Ca is provided (relative to the standard of course). So if the measured Ca concentration is different than the expected Ca, the matrix correction will be different and the concentration of stoichiometric carbon, based on the calculated oxygen, which is itself based on the measured Ca content, will also be different.

Am I making any sense?

In fact I think the answer is laying right in front of our noses. In Reply#86 look at the ZCOR values for Ca Ka for the standard CaCO3, the slightly high total CaCO3 and the slightly low total CaCO3. I summarize them here:

ZCOR:   1.0567     ---     ---     <--- close to 100% total
ZCOR:   1.0568     ---     ---     <--- slightly high total
ZCOR:   1.0566     ---     ---     <--- slightly low total

In short, different Ca concentrations are calculated for each different case, meaning that different amounts of stoichiometric oxygen are calculated for each composition, and hence different amounts of carbon are calculated for each composition. Only when the correct Ca is measured, does the correct stoichiometric oxygen get calculated, and subsequently only then does the correct carbon by stoichiometry to oxygen get calculated. 

What do you think?
« Last Edit: July 27, 2019, 03:15:12 pm by John Donovan »
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Re: Specifying Unanalyzed Elements For a Proper Matrix Correction
« Reply #89 on: July 29, 2019, 10:55:55 am »
Hi Andrew,
I again return to this plot of analytical totals versus Ca concentration you posted earlier.  With some additional annotations.



I'm probably missing something, so please correct me if you see something, but it seems to me that when making a measurement of CaCO3, why would one expect to obtain the exactly correct stoichiometry for CO2, when the Ca measurement is not exactly correct?

We already know the code calculates the correct CO2 when the correct Ca is provided (relative to the standard of course). So if the measured Ca concentration is different than the expected Ca, the matrix correction will be different and the concentration of stoichiometric carbon, based on the calculated oxygen, which is itself based on the measured Ca content, will also be different.

Am I making any sense?

In fact I think the answer is laying right in front of our noses. In Reply#86 look at the ZCOR values for Ca Ka for the standard CaCO3, the slightly high total CaCO3 and the slightly low total CaCO3. I summarize them here:

ZCOR:   1.0567     ---     ---     <--- close to 100% total
ZCOR:   1.0568     ---     ---     <--- slightly high total
ZCOR:   1.0566     ---     ---     <--- slightly low total

In short, different Ca concentrations are calculated for each different case, meaning that different amounts of stoichiometric oxygen are calculated for each composition, and hence different amounts of carbon are calculated for each composition. Only when the correct Ca is measured, does the correct stoichiometric oxygen get calculated, and subsequently only then does the correct carbon by stoichiometry to oxygen get calculated. 

What do you think?


Hi John,
Let us look at how Probe-for-EPMA handles a binary oxide, MgO, in comparison to a simple carbonate, siderite (Fe,Mn)CO3.

In the case of MgO, I measured the Mg K-alpha intensity for 20 points, and for the usual reasons, we have uncertainty in the results. The Mg concentrations range from 60.05 to 60.65 wt%, and the analytical totals from about 99.6 to 100.6 wt%.

However, regardless of this analytical uncertainty, for every point, Probe-for-EPMA reports oxygen-by-stoichiometry in the ideal ratio of 1:1 (with rounding in the fifth decimal place):



In the case of siderite, I measured the Fe K-alpha and Mn K-alpha intensities for 40 points, and for the usual reasons, we have uncertainty in the results (but beam damage was not an issue). The (Fe+Mn) concentrations range from 47.9 to 48.6 wt%, and the analytical totals from Probe-for-EPMA are reported between 99.7 and 100.4 wt%.

However, Probe-for-EPMA reports CO2-by-stoichiometry as a function of concentration!



Only when the concentration is extremely close to 100.00 wt% is the correct, stoichiometric, amount of CO2 reported.


So, in the case of MgO, regardless of analytical uncertainty, the stoichiometric ratio of 1:1 Mg:O is maintained.

But in the case of a carbonate, such as calcite CaCO3 or siderite (Fe,Mn)CO3, stoichiometry is not maintained.
Rather, the proportion of CO2 reported by Probe-for-EPMA is a function of concentration.

To follow up on your above post:
"In short, different Ca concentrations are calculated for each different case, meaning that different amounts of stoichiometric oxygen are calculated for each composition, and hence different amounts of carbon are calculated for each composition. Only when the correct Ca is measured, does the correct stoichiometric oxygen get calculated, and subsequently only then does the correct carbon by stoichiometry to oxygen get calculated."

Yes, in Probe-for-EPMA, different amounts of Ca result in different amounts of C and O being calculated.
Unfortunately, they are not calculated in the stoichiometric ratio for CaCO3 where Ca : C : O should be 1:1:3.

The question is why do we see this behaviour?
We need to look into the matrix correction code more closely.

Best regards,
Andrew