Specifying Unanalyzed Elements For a Proper Matrix Correction

[AndrewLocock]

Hello,
Although end-member tremolite has the formula: □Ca2(Mg5)(Si8)O22(OH)2, where □ indicates a vacancy on the A-site of amphibole, other amphiboles have substitutions for Si (and for hydroxyl).

Thus, end-member kaersutite has the formula: NaCa2(Mg3TiAl)(Si6Al2)O22O2.
Similarly, end-member pargasite has the formula: NaCa2(Mg4Al)(Si6Al2)O22(OH)2.

For the hydroxyl group of amphiboles, if Cl and F are assumed to be absent, one could specify 2 hydroxyl groups.
In both end-member tremolite and end-member pargasite, the ratio of H to O would therefore be 2 to 24, or 0.083333:1.

It is critical that the output in weight percent be expressed as neutral oxides, that is, H2O.

End-member ideal tremolite has the following oxide weight percent composition:
SiO2 59.17, MgO 24.81, CaO 13.81, H2O 2.22 wt%, sum 100.01 (all rounded to 2 decimal places).

End-member ideal pargasite has the following oxide weight percent composition:
SiO2 43.13, Al2O3 18.30, MgO 19.29, CaO 13.42, Na2O 3.71, H2O 2.16 wt%, sum 100.01 (all rounded to 2 decimal places).

Because Si varies considerably (in principle from 5 atoms per formula unit in sadanagaite to 8 in tremolite), it is not a good choice as a basis for H calculation. Oxygen should be better (assuming no oxo-substitution).

All the best,
Andrew

[Probeman]

I'm completely confused now.  Some of that oxygen in the formula isn't associated with the cations.  If I just specify hydrogen elementally relative to the calculated oxygen, it won't add in the additional oxygen in hydroxl or water.  Correct? 

So what *exactly* would you do in the Calculation Options dialog?

[Probeman]

If I specify .08333 hydrogens to calculated oxygen I get:

Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element H is Calculated  .08333 Atoms Relative To 1.0 Atom of Oxygen

Using Conductive Coating Correction For Electron Absorption and X-Ray Transmission:
Sample Coating=C, Density=2.1 gm/cm3, Thickness=200 angstroms, Sin(Thickness)=311.145 angstroms

Un   13 AZ asbestos gr6, Results in Elemental Weight Percents
 
ELEM:       Na      Si       K      Al      Fe      Mg      Ca      Cl      Ti       F      Mn      Zn       O       H
TYPE:     ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    CALC    STOI
BGDS:      MAN     MAN     LIN     MAN     MAN     MAN     MAN     LIN     LIN     LIN     LIN     LIN
TIME:    40.00   40.00   20.00   40.00   40.00  165.00  150.00  120.00   30.00  120.00   30.00   30.00     ---     ---
BEAM:    29.92   29.92   29.92   29.92   29.92   29.92   29.92   29.92   29.92   29.92   29.92   29.92     ---     ---

ELEM:       Na      Si       K      Al      Fe      Mg      Ca      Cl      Ti       F      Mn      Zn       O       H   SUM 
   642   -.010  26.802    .093    .099   2.825  13.397   9.163    .004   -.026   -.065    .144    .022  47.925    .250 100.624
   643    .006  26.921    .071    .108   2.586  13.481   9.167    .000   -.019    .050    .168    .007  48.069    .250 100.866
   644    .008  26.967    .065    .097   2.687  13.505   9.162    .004   -.009   -.028    .138    .021  48.156    .250 101.025
   645    .047  26.935    .061    .087   2.477  13.540   9.253    .003    .007   -.073    .136    .023  48.138    .250 100.885
   646    .067  26.952    .066    .028   2.355  13.492   9.382   -.003   -.022   -.048    .107   -.033  48.059    .251 100.655

AVER:     .024  26.915    .071    .084   2.586  13.483   9.226    .002   -.014   -.033    .139    .008  48.070    .250 100.811
SDEV:     .032    .066    .013    .032    .182    .053    .096    .003    .013    .049    .021    .024    .091    .000    .169
SERR:     .014    .029    .006    .014    .081    .024    .043    .001    .006    .022    .010    .011    .041    .000
%RSD:   136.38     .24   18.19   38.02    7.03     .39    1.04  159.31  -97.92 -151.40   15.48  295.56     .19     .10
STDS:      336     162     374     336     162     162     162     285      22     835      25     660     ---     ---

STKF:    .0735   .2018   .1132   .1332   .0950   .0568   .1027   .0602   .5547   .1715   .7341   .4865     ---     ---
STCT:    58.60  246.04  197.64  255.36   19.35   72.74  178.88   61.41   44.86   13.54  136.63   66.08     ---     ---

UNKF:    .0001   .2126   .0006   .0006   .0215   .0926   .0838   .0000  -.0001  -.0001   .0011   .0001     ---     ---
UNCT:      .10  259.20    1.11    1.10    4.38  118.69  146.07     .01    -.01    -.01     .21     .01     ---     ---
UNBG:      .30     .20     .95     .80     .22     .52     .99     .37     .06     .05     .15     .36     ---     ---

ZCOR:   1.9014  1.2659  1.1175  1.4587  1.2014  1.4554  1.1004  1.2304  1.2048  4.1651  1.2217  1.2664     ---     ---
KRAW:    .0017  1.0535   .0056   .0043   .2265  1.6316   .8165   .0002  -.0002  -.0005   .0015   .0001     ---     ---
PKBG:     1.34 1319.20    2.18    2.37   20.95  228.69  149.12    1.04     .86     .90    2.43    1.03     ---     ---
INT%:     ----    ----    ----    ----    -.01    ----    ----    ----    ----   76.60    ----    ----     ---     ---

TDI%:    2.963    .033  -2.002  -3.947   -.711    .000    .000    .000    .000    .000    .000    .000     ---     ---
DEV%:       .2      .1    18.6    23.1     3.4      .0      .0      .0      .0      .0      .0      .0     ---     ---
TDIF:  HYP-EXP LOG-LIN LOG-LIN LOG-LIN LOG-LIN    ----    ----    ----    ----    ----    ----    ----     ---     ---
TDIT:   111.80  112.60   78.00  111.00  115.40     .00     .00     .00     .00     .00     .00     .00     ---     ---
TDII:     .369    259.    2.01    1.84    4.57    ----    ----    ----    ----    ----    ----    ----     ---     ---
TDIL:    -.996    5.56    .697    .611    1.52    ----    ----    ----    ----    ----    ----    ----     ---     ---

Un   13 AZ asbestos gr6, Results in Oxide Weight Percents

ELEM:     Na2O    SiO2     K2O   Al2O3     FeO     MgO     CaO      Cl    TiO2       F     MnO     ZnO       O      HO   SUM 
   642   -.014  57.339    .112    .187   3.634  22.216  12.821    .004   -.044   -.065    .186    .028    .000   4.219 100.624
   643    .009  57.593    .086    .204   3.327  22.356  12.827    .000   -.032    .050    .216    .009    .000   4.221 100.866
   644    .011  57.691    .078    .183   3.457  22.396  12.820    .004   -.015   -.028    .179    .026    .000   4.222 101.025
   645    .063  57.623    .073    .164   3.187  22.454  12.947    .003    .012   -.073    .176    .029    .000   4.226 100.885
   646    .091  57.660    .079    .054   3.030  22.373  13.128   -.003   -.036   -.048    .139   -.042    .000   4.229 100.655

AVER:     .032  57.581    .086    .158   3.327  22.359  12.909    .002   -.023   -.033    .179    .010    .000   4.223 100.811
SDEV:     .043    .140    .016    .060    .234    .088    .134    .003    .022    .049    .028    .030    .000    .004    .169
SERR:     .019    .063    .007    .027    .105    .039    .060    .001    .010    .022    .012    .013    .000    .002
%RSD:   136.38     .24   18.19   38.02    7.03     .39    1.04  159.31  -97.92 -151.40   15.48  295.56  418.33     .10
STDS:      336     162     374     336     162     162     162     285      22     835      25     660     ---     ---

[AndrewLocock]

I'm completely confused now.  Some of that oxygen in the formula isn't associated with the cations.  If I just specify hydrogen elementally relative to the calculated oxygen, it won't add in the additional oxygen in hydroxl or water.  Correct? 

So what *exactly* would you do in the Calculation Options dialog?

Sorry to cause confusion.
The program actually does better than you might expect!

Let me explain with the example of apophyllite, ideal formula: KCa4Si8O20(OH)·8H2O
The ratio of hydrogen to oxygen in this formula is 17 to 29, or about 0.58621:1.
From the Handbook of Mineralogy entry for hydroxyapophyllite, the ideal oxide weight percents are:
SiO2 53.10, CaO 24.78, K2O 5.20, H2O 16.92 wt%, sum 100.00.

I ran some apophyllite analyses last year.
The measured oxides were: Na2O, SiO2, K2O, Al2O3, CaO, MgO, and BaO.
In the Calculation Options window, I selected:
Stoichiometry to Calculated Oxygen 0.58621 Atoms of H to 1 Oxygen
(This is shown in the attached MS-Word document entitled "apophyllite example.docx").

The results (also in the attached MS-Word document) are:
              Na2O   SiO2   K2O   Al2O3   CaO   MgO   BaO   H2O   Total
Average: 0.03   52.98   4.81   0.02   24.52   0.01  0.00   16.98   99.36

Thus, the program has calculated the presence of 16.98 wt% H2O.
If I calculate the formula proportions (on the basis of 8 Si+Al), I get:

Si7.998 Al0.002 Ca3.966 Na0.010 K0.926 H17.101, with 28.98 O by charge balance.
(Remember, the ideal is Si8, Ca4, K1, H17, O29).

I consider this to be pretty good initial results for a hydroxylated- and hydrated-mineral.

The take-home message is that Probe-for-EPMA can calculate the appropriate content of H2O.
Just try it!
(I have equally good results for analcime, NaAlSi2O6·H2O).

Best regards,
Andrew

[AndrewLocock]

I should also note that the major element composition of that apophyllite without any calculated OH & H2O was:
SiO2 51.23, K2O 4.65 CaO 23.79, sum 79.67 wt%.

Thus, the calculated OH & H2O content made significant changes (about 3% relative) in these major elements during the data reduction process.
The major element results:
               SiO2   K2O    CaO    H2O   
Average: 52.98   4.81  24.52   16.98

Cheers,
Andrew

[Probeman]

Sorry to cause confusion.
The program actually does better than you might expect!

Let me explain with the example of apophyllite, ideal formula: KCa4Si8O20(OH)·8H2O
The ratio of hydrogen to oxygen in this formula is 17 to 29, or about 0.58621:1.
From the Handbook of Mineralogy entry for hydroxyapophyllite, the ideal oxide weight percents are:
SiO2 53.10, CaO 24.78, K2O 5.20, H2O 16.92 wt%, sum 100.00.

I ran some apophyllite analyses last year.
The measured oxides were: Na2O, SiO2, K2O, Al2O3, CaO, MgO, and BaO.
In the Calculation Options window, I selected:
Stoichiometry to Calculated Oxygen 0.58621 Atoms of H to 1 Oxygen
(This is shown in the attached MS-Word document entitled "apophyllite example.docx").

The results (also in the attached MS-Word document) are:
              Na2O   SiO2   K2O   Al2O3   CaO   MgO   BaO   H2O   Total
Average: 0.03   52.98   4.81   0.02   24.52   0.01  0.00   16.98   99.36

Thus, the program has calculated the presence of 16.98 wt% H2O.
If I calculate the formula proportions (on the basis of 8 Si+Al), I get:

Si7.998 Al0.002 Ca3.966 Na0.010 K0.926 H17.101, with 28.98 O by charge balance.
(Remember, the ideal is Si8, Ca4, K1, H17, O29).

I consider this to be pretty good initial results for a hydroxylated- and hydrated-mineral.

The take-home message is that Probe-for-EPMA can calculate the appropriate content of H2O.
Just try it!
(I have equally good results for analcime, NaAlSi2O6·H2O).

Best regards,
Andrew

Hi Andrew,
OK, wow, that makes more sense.  So if I specify 0.08333 hydrogens to each oxygen (and specifying hydrogen oxide as H2O), I get this:

Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element H is Calculated  .08333 Atoms Relative To 1.0 Atom of Oxygen

Using Conductive Coating Correction For Electron Absorption and X-Ray Transmission:
Sample Coating=C, Density=2.1 gm/cm3, Thickness=200 angstroms, Sin(Thickness)=311.145 angstroms

Un   13 AZ asbestos gr6, Results in Elemental Weight Percents
 
ELEM:       Na      Si       K      Al      Fe      Mg      Ca      Cl      Ti       F      Mn      Zn       O       H
TYPE:     ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    CALC    STOI
BGDS:      MAN     MAN     LIN     MAN     MAN     MAN     MAN     LIN     LIN     LIN     LIN     LIN
TIME:    40.00   40.00   20.00   40.00   40.00  165.00  150.00  120.00   30.00  120.00   30.00   30.00     ---     ---
BEAM:    29.92   29.92   29.92   29.92   29.92   29.92   29.92   29.92   29.92   29.92   29.92   29.92     ---     ---

ELEM:       Na      Si       K      Al      Fe      Mg      Ca      Cl      Ti       F      Mn      Zn       O       H   SUM 
   642   -.011  26.791    .093    .099   2.822  13.344   9.163    .004   -.026   -.064    .144    .022  45.847    .244  98.472
   643    .006  26.909    .071    .108   2.583  13.427   9.167    .000   -.019    .050    .167    .007  45.989    .245  98.711
   644    .007  26.955    .065    .097   2.684  13.452   9.162    .004   -.009   -.028    .138    .021  46.076    .245  98.870
   645    .046  26.923    .061    .087   2.474  13.486   9.253    .003    .007   -.072    .136    .023  46.055    .245  98.728
   646    .066  26.940    .066    .028   2.353  13.437   9.382   -.003   -.022   -.048    .107   -.033  45.974    .245  98.494

AVER:     .023  26.904    .071    .084   2.583  13.429   9.225    .002   -.014   -.032    .139    .008  45.988    .245  98.655
SDEV:     .032    .065    .013    .032    .182    .053    .096    .003    .013    .049    .021    .024    .090    .000    .169
SERR:     .014    .029    .006    .014    .081    .024    .043    .001    .006    .022    .010    .011    .040    .000
%RSD:   140.42     .24   18.19   38.06    7.04     .39    1.04  159.31  -97.92 -151.40   15.48  295.57     .20     .10
STDS:      336     162     374     336     162     162     162     285      22     835      25     660     ---     ---

STKF:    .0735   .2018   .1132   .1332   .0950   .0568   .1027   .0602   .5547   .1715   .7341   .4865     ---     ---
STCT:    58.60  246.04  197.64  255.36   19.35   72.74  178.88   61.41   44.86   13.54  136.63   66.08     ---     ---

UNKF:    .0001   .2126   .0006   .0006   .0215   .0926   .0838   .0000  -.0001  -.0001   .0011   .0001     ---     ---
UNCT:      .10  259.20    1.11    1.10    4.38  118.68  146.06     .01    -.01    -.01     .21     .01     ---     ---
UNBG:      .30     .20     .95     .81     .22     .53     .99     .37     .06     .05     .15     .36     ---     ---

ZCOR:   1.8912  1.2654  1.1175  1.4576  1.2006  1.4496  1.1004  1.2318  1.2048  4.1235  1.2210  1.2653     ---     ---
KRAW:    .0016  1.0535   .0056   .0043   .2264  1.6315   .8165   .0002  -.0002  -.0005   .0015   .0001     ---     ---
PKBG:     1.32 1312.38    2.18    2.37   20.78  226.62  148.12    1.04     .86     .90    2.43    1.03     ---     ---
INT%:     ----    ----    ----    ----    -.01    ----    ----    ----    ----   76.60    ----    ----     ---     ---

TDI%:    2.963    .033  -2.002  -3.947   -.711    .000    .000    .000    .000    .000    .000    .000     ---     ---
DEV%:       .2      .1    18.6    23.1     3.4      .0      .0      .0      .0      .0      .0      .0     ---     ---
TDIF:  HYP-EXP LOG-LIN LOG-LIN LOG-LIN LOG-LIN    ----    ----    ----    ----    ----    ----    ----     ---     ---
TDIT:   111.80  112.60   78.00  111.00  115.40     .00     .00     .00     .00     .00     .00     .00     ---     ---
TDII:     .369    259.    2.01    1.84    4.57    ----    ----    ----    ----    ----    ----    ----     ---     ---
TDIL:    -.996    5.56    .697    .611    1.52    ----    ----    ----    ----    ----    ----    ----     ---     ---

Un   13 AZ asbestos gr6, Results in Oxide Weight Percents

ELEM:     Na2O    SiO2     K2O   Al2O3     FeO     MgO     CaO      Cl    TiO2       F     MnO     ZnO       O     H2O   SUM 
   642   -.015  57.315    .112    .186   3.631  22.128  12.821    .004   -.044   -.064    .186    .028    .000   2.184  98.472
   643    .008  57.568    .086    .204   3.323  22.266  12.826    .000   -.032    .050    .216    .009    .000   2.186  98.711
   644    .010  57.667    .078    .183   3.453  22.307  12.819    .004   -.015   -.028    .179    .026    .000   2.186  98.870
   645    .062  57.598    .073    .164   3.183  22.364  12.947    .003    .012   -.072    .176    .029    .000   2.188  98.728
   646    .089  57.634    .079    .053   3.027  22.283  13.127   -.003   -.036   -.048    .139   -.042    .000   2.190  98.494

AVER:     .031  57.556    .086    .158   3.323  22.270  12.908    .002   -.023   -.032    .179    .010    .000   2.187  98.655
SDEV:     .043    .140    .016    .060    .234    .087    .134    .003    .022    .049    .028    .030    .000    .002    .169
SERR:     .019    .063    .007    .027    .105    .039    .060    .001    .010    .022    .012    .013    .000    .001
%RSD:   140.42     .24   18.19   38.06    7.04     .39    1.04  159.31  -97.92 -151.40   15.48  295.57   69.72     .10
STDS:      336     162     374     336     162     162     162     285      22     835      25     660     ---     ---

And as you and Brian said, the total is a little low, probably out of focus. Looking at another sample I get this:

Oxygen Calculated by Cation Stoichiometry and Included in the Matrix Correction
Element H is Calculated  .08333 Atoms Relative To 1.0 Atom of Oxygen

Using Conductive Coating Correction For Electron Absorption and X-Ray Transmission:
Sample Coating=C, Density=2.1 gm/cm3, Thickness=200 angstroms, Sin(Thickness)=311.145 angstroms

Un    3 AZ asbestos gr1, Results in Elemental Weight Percents
 
ELEM:       Na      Si       K      Al      Fe      Mg      Ca      Cl      Ti       F      Mn      Zn       O       H
TYPE:     ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    CALC    STOI
BGDS:      MAN     MAN     LIN     MAN     MAN     MAN     MAN     LIN     LIN     LIN     LIN     LIN
TIME:    40.00   40.00   20.00   40.00   40.00  165.00  150.00  120.00   30.00  120.00   30.00   30.00     ---     ---
BEAM:    29.90   29.90   29.90   29.90   29.90   29.90   29.90   29.90   29.90   29.90   29.90   29.90     ---     ---

ELEM:       Na      Si       K      Al      Fe      Mg      Ca      Cl      Ti       F      Mn      Zn       O       H   SUM 
   138    .008  26.996    .051    .014   2.275  13.729   9.586    .004    .026   -.031    .082    .025  46.289    .245  99.298
   139    .008  27.285    .040    .033   2.379  13.658   9.453    .006    .008    .040    .133   -.028  46.554    .245  99.813
   140    .030  27.073    .065    .050   2.282  13.667   9.501    .002    .013   -.032    .080   -.048  46.323    .245  99.251
   141    .055  27.055    .032    .055   2.533  13.677   9.358    .000    .011    .009    .136   -.010  46.350    .245  99.505
   142    .037  27.221    .028    .016   2.592  13.659   9.399    .004    .014    .005    .107    .017  46.519    .245  99.861
   143    .059  27.190    .059    .042   2.310  13.713   9.476    .004   -.002    .004    .101    .037  46.501    .245  99.740
   144    .082  27.189    .043    .080   2.457  13.619   9.446   -.001   -.019   -.052    .028    .004  46.468    .245  99.589

AVER:     .040  27.144    .045    .041   2.404  13.674   9.460    .003    .007   -.008    .095    .000  46.429    .245  99.580
SDEV:     .027    .104    .014    .023    .126    .037    .073    .002    .014    .031    .037    .030    .106    .000    .242
SERR:     .010    .039    .005    .009    .048    .014    .028    .001    .005    .012    .014    .011    .040    .000
%RSD:    68.48     .38   30.26   56.41    5.25     .27     .78   93.90  205.40 -385.54   38.60-8861.00     .23     .08
STDS:      336     162     374     336     162     162     162     285      22     835      25     660     ---     ---

STKF:    .0735   .2018   .1132   .1332   .0950   .0568   .1027   .0602   .5547   .1715   .7341   .4865     ---     ---
STCT:    55.79  246.63  196.50  255.38   19.50   71.86  178.02   66.46   44.04   14.00  136.85   66.47     ---     ---

UNKF:    .0002   .2145   .0004   .0003   .0200   .0945   .0860   .0000   .0001   .0000   .0008   .0000     ---     ---
UNCT:      .16  262.18     .70     .55    4.11  119.57  149.02     .02     .00     .00     .15     .00     ---     ---
UNBG:      .30     .21     .96     .82     .22     .54    1.01     .36     .05     .05     .17     .38     ---     ---

ZCOR:   1.8837  1.2652  1.1173  1.4579  1.2011  1.4474  1.1006  1.2318  1.2033  4.1276  1.2215  1.2656     ---     ---
KRAW:    .0029  1.0631   .0036   .0021   .2106  1.6638   .8371   .0003   .0001  -.0001   .0011   .0000     ---     ---
PKBG:     1.53 1227.91    1.74    1.67   20.07  223.49  149.16    1.07    1.12     .98    1.91    1.00     ---     ---
INT%:     ----    ----    ----    ----    -.01    ----    ----    ----    ---- -129.12    ----    ----     ---     ---

TDI%:    7.889    .289  -4.914   1.125    .386    .000    .000    .000    .000    .000    .000    .000     ---     ---
DEV%:       .2      .1    29.7    56.7     3.6      .0      .0      .0      .0      .0      .0      .0     ---     ---
TDIF:  HYP-EXP LOG-LIN LOG-LIN LOG-LIN LOG-LIN    ----    ----    ----    ----    ----    ----    ----     ---     ---
TDIT:   116.14  116.14   81.43  114.71  120.57     .00     .00     .00     .00     .00     .00     .00     ---     ---
TDII:     .435    262.    1.58    1.33    4.32    ----    ----    ----    ----    ----    ----    ----     ---     ---
TDIL:    -.832    5.57    .460    .286    1.46    ----    ----    ----    ----    ----    ----    ----     ---     ---

Un    3 AZ asbestos gr1, Results in Oxide Weight Percents

ELEM:     Na2O    SiO2     K2O   Al2O3     FeO     MgO     CaO      Cl    TiO2       F     MnO     ZnO       O     H2O   SUM 
   138    .011  57.754    .061    .026   2.927  22.766  13.413    .004    .043   -.031    .106    .031    .000   2.187  99.298
   139    .011  58.372    .048    .062   3.061  22.648  13.227    .006    .013    .040    .172   -.035    .000   2.188  99.813
   140    .041  57.919    .078    .095   2.936  22.664  13.294    .002    .021   -.032    .103   -.060    .000   2.190  99.251
   141    .074  57.880    .039    .105   3.258  22.681  13.094    .000    .018    .009    .176   -.013    .000   2.185  99.505
   142    .049  58.235    .033    .030   3.335  22.651  13.151    .004    .023    .005    .139    .021    .000   2.185  99.861
   143    .079  58.170    .071    .079   2.971  22.741  13.259    .004   -.004    .004    .131    .046    .000   2.187  99.740
   144    .110  58.167    .052    .152   3.161  22.585  13.216   -.001   -.032   -.052    .037    .005    .000   2.189  99.589

AVER:     .054  58.071    .055    .078   3.093  22.676  13.236    .003    .012   -.008    .123    .000    .000   2.187  99.580
SDEV:     .037    .222    .017    .044    .162    .061    .103    .002    .024    .031    .048    .038    .000    .002    .242
SERR:     .014    .084    .006    .017    .061    .023    .039    .001    .009    .012    .018    .014    .000    .001
%RSD:    68.48     .38   30.26   56.41    5.25     .27     .78   93.90  205.40 -385.54   38.60-8860.99     .00     .08
STDS:      336     162     374     336     162     162     162     285      22     835      25     660     ---     ---

Which is much better. Dang, geology is complicated compared to physics!

Now I'm almost afraid to ask, but can you tell me why the tremolite formula is stated as Ca2(Mg5)(Si8)O22(OH)2 when Ca2(Mg5)(Si8)O23(H2O) is chemically the same? Which to me makes more sense considering how hydrogen (oxide) needs to be treated.

[AndrewLocock]

Now I'm almost afraid to ask, but can you tell me why the tremolite formula is stated as Ca2(Mg5)(Si8)O22(OH)2 when Ca2(Mg5)(Si8)O23(H2O) is chemically the same? Which to me makes more sense considering how hydrogen (oxide) needs to be treated.

It has to do with how the hydrogen is present in the crystal structure.

In the case of hydroxyl, the hydrogen is located at about 0.9 to 1 angstrom away from an oxygen atom.

In the case of an H2O molecule ("water molecule"), two hydrogen atoms are located about 0.9 to 1 angstrom away from a single oxygen atom.

The H2O molecule is not linear, so in a crystal structure the central oxygen also tends to be attracted to a cation.
And, the hydrogen atoms of this H2O group may be weakly attracted to other oxygen atoms (usually within 2 to 3 angstroms distance) - this is the so-called "hydrogen bonding", for which the best example is ice.

Although it is possible to express a formula in different ways, e.g., Mg(OH)2 could be expressed as MgO·H2O, it is best to use the formula the reflects what is present in the crystal structure (or glass). In the example of apophyllite KCa4Si8O20(OH)·8H2O, both hydroxyl and H2O are present. And in tremolite, hydroxyl groups are present, but H2O groups are not.

Finally, in a chemical analysis that is expressed at neutral oxides, the hydrogen content should be expressed as H2O, regardless of how it is present in the crystal structure or glass.

Cheers,
Andrew

[Probeman]

Now I'm almost afraid to ask, but can you tell me why the tremolite formula is stated as Ca2(Mg5)(Si8)O22(OH)2 when Ca2(Mg5)(Si8)O23(H2O) is chemically the same? Which to me makes more sense considering how hydrogen (oxide) needs to be treated.

It has to do with how the hydrogen is present in the crystal structure.

In the case of hydroxyl, the hydrogen is located at about 0.9 to 1 angstrom away from an oxygen atom.

In the case of an H2O molecule ("water molecule"), two hydrogen atoms are located about 0.9 to 1 angstrom away from a single oxygen atom.

The H2O molecule is not linear, so in a crystal structure the central oxygen also tends to be attracted to a cation.
And, the hydrogen atoms of this H2O group may be weakly attracted to other oxygen atoms (usually within 2 to 3 angstroms distance) - this is the so-called "hydrogen bonding", for which the best example is ice.

Although it is possible to express a formula in different ways, e.g., Mg(OH)2 could be expressed as MgO·H2O, it is best to use the formula the reflects what is present in the crystal structure (or glass). In the example of apophyllite KCa4Si8O20(OH)·8H2O, both hydroxyl and H2O are present. And in tremolite, hydroxyl groups are present, but H2O groups are not.

Finally, in a chemical analysis that is expressed at neutral oxides, the hydrogen content should be expressed as H2O, regardless of how it is present in the crystal structure or glass.

Cheers,
Andrew

Hi Andrew,
Thank-you. This sort of makes sense, even to a non-geologist like me!   

[John Donovan]

Most of us understand the effects of "unanalyzed" elements in the matrix correction and how it is important to include these elements either by specification, difference or by stoichiometry to other analyzed elements, in order to obtain an accurate matrix correction.

For example the issue of unanalyzed water in hydrous glasses, where one gets a results with a total of say 95% and one might be forgiven to think that, OK, I've got 5 wt% H2O there because 100 - 95 = 5 in Excel.  But that would be wrong because Excel doesn't know anything about matrix correction physics.  In fact what we see when we specify water by difference is described in this and other posts in this topic:

https://probesoftware.com/smf/index.php?topic=92.msg7701#msg7701

Basically adding oxygen (and hydrogen) to our glass matrix correction results in a significant change in the concentration of other elements.  In a generic example of a silicate glass, the Si (and other element) concentrations increases significantly.  Why is this? Because it turns out that Si Ka is not well absorbed by Si atoms, but they are well absorbed by oxygen atoms!  Once the matrix correction "knows" about the extra oxygen (water), the absorption correction increases correspondingly.

So in our generic example of a 95% total in a hydrous glass, once we add H2O by difference and include it in the matrix correction, because the Si (and other elements) increase by about 1%, we instead obtain about 4% H2O by difference.  This effect was described in the Roman et al. paper referenced here:

https://probesoftware.com/smf/index.php?topic=61.msg4303#msg4303

Now this makes some intuitive sense to me because Si Ka is a fairly low energy emission line and therefore fairly well absorbed by other elements, but I never expected this to be the case for Fe Ka at 6.4 keV!

Here's an example for a magnetite sample where the Fe is expressed, as we usually do in EPMA, as FeO:

Un   96 7138_PPO-2_Mgt4_HO-1, Results in Elemental Weight Percents
 
ELEM:       Fe      Mg      Si      Ti       V      Mn      Cr      Al       O
TYPE:     ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    CALC
BGDS:      MAN     MAN     MAN     MAN     EXP     LIN     MAN     MAN
TIME:    40.00  120.00   40.00   80.00   30.00   30.00   80.00  120.00     ---
BEAM:    45.93   45.93   45.93   45.93   45.93   45.93   45.93   45.93     ---

ELEM:       Fe      Mg      Si      Ti       V      Mn      Cr      Al       O   SUM 
   146  60.944   1.463    .058   5.329    .265    .422    .375   1.542  23.842  94.240

AVER:   60.944   1.463    .058   5.329    .265    .422    .375   1.542  23.842  94.240
SDEV:     .000    .000    .000    .000    .000    .000    .000    .000    .000    .000
SERR:     .000    .000    .000    .000    .000    .000    .000    .000    .000
%RSD:      .00     .00     .00     .00     .00     .00     .00     .00     .00
STDS:      396     396      14      22      23      25     396     396     ---

STKF:    .1836   .0330   .4101   .5547   .6328   .7341   .3060   .0469     ---
STCT:   1119.3  3499.0  4307.2  9290.4  8344.6 14435.6  1338.8  1992.0     ---

UNKF:    .5710   .0066   .0004   .0548   .0028   .0040   .0043   .0088     ---
UNCT:   3481.1   701.1     4.3   917.6    37.1    77.9    18.9   373.9     ---
UNBG:     12.2    47.8     2.8    32.9    15.3    29.2     6.1    29.4     ---

ZCOR:   1.0674  2.2108  1.4127   .9728   .9416  1.0658   .8682  1.7520     ---
KRAW:   3.1102   .2004   .0010   .0988   .0044   .0054   .0141   .1877     ---
PKBG:   286.31   15.65    2.55   28.88    3.43    3.67    4.10   13.70     ---
INT%:      .00    ----    ----    ----  -15.76    ----   -1.38    ----     ---

As one can see our Fe concentration is 60.944 and our total is 94.240. So we're missing about 5% of something and that something of course is mostly the excess oxygen in the Fe2O3 molecule in magnetite. Now how much of an effect can this ~5% missing oxygen have on our Fe concentration? What would you guess?  I wouldn't have guessed this much:

Un   96 7138_PPO-2_Mgt4_HO-1, Results in Elemental Weight Percents
 
ELEM:       Fe      Mg      Si      Ti       V      Mn      Cr      Al       O
TYPE:     ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    ANAL    DIFF
BGDS:      MAN     MAN     MAN     MAN     EXP     LIN     MAN     MAN
TIME:    40.00  120.00   40.00   80.00   30.00   30.00   80.00  120.00     ---
BEAM:    45.93   45.93   45.93   45.93   45.93   45.93   45.93   45.93     ---

ELEM:       Fe      Mg      Si      Ti       V      Mn      Cr      Al       O   SUM 
   146  61.421   1.451    .057   5.379    .267    .425    .383   1.532  29.085 100.000

AVER:   61.421   1.451    .057   5.379    .267    .425    .383   1.532  29.085 100.000
SDEV:     .000    .000    .000    .000    .000    .000    .000    .000    .000    .000
SERR:     .000    .000    .000    .000    .000    .000    .000    .000    .000
%RSD:      .00     .00     .00     .00     .00     .00     .00     .00     .00
STDS:      396     396      14      22      23      25     396     396     ---

STKF:    .1836   .0330   .4101   .5547   .6328   .7341   .3060   .0469     ---
STCT:   1119.3  3499.0  4307.2  9290.4  8344.6 14435.6  1338.8  1992.0     ---

UNKF:    .5710   .0066   .0004   .0548   .0028   .0040   .0044   .0088     ---
UNCT:   3481.6   701.6     4.3   918.5    37.1    77.9    19.1   374.1     ---
UNBG:     11.8    47.3     2.8    32.0    15.3    29.2     5.9    29.2     ---

ZCOR:   1.0756  2.1904  1.4061   .9808   .9506  1.0740   .8773  1.7396     ---
KRAW:   3.1106   .2005   .0010   .0989   .0044   .0054   .0143   .1878     ---
PKBG:   296.98   15.83    2.54   29.68    3.43    3.67    4.25   13.80     ---
INT%:      .00    ----    ----    ----  -15.75    ----   -1.36    ----     ---

Holy cow!  Our Fe concentration went from 60.944 to 61.421 which is almost 0.5 wt% absolute. And note how the ZCOR (matrix correction) for Fe Ka went from 1.0674 to 1.0756.  But even more mind blowing is to compare the *other* elements we measured: Mg, Ti, Al, etc.  What happened to them?  Well they went slightly *down* in concentration!  Why? Because they are more absorbed by Fe than by O.  It just goes to show you that one cannot intuit physics, you have to just run the darn calculation.

Of course we really should calculate the excess oxygen in our magnetites/ilmenites using a ferric/ferrous calculation (and more on that later), but the oxygen by difference calculation demonstrates that once we obtain our ferric/ferrous ratio, we really need to calculate the excess oxygen from that and specify it in Probe for EPMA, to obtain a more accurate Fe concentration for our mineral thermodynamic calculations.

Now, I'm no geologist but perhaps one should then recalculate our ferric/ferrous ratios, this time using our improved Fe concentration. Again, more on this later...

The idea of calculating excess oxygen and including that excess oxygen into the matrix correction physics is a very appealing idea.  Based on the preliminary calculations quoted above, it appears that the effect of excess oxygen could, at least in some cases, affect the accuracy of various geological thermometers/barometers.  Simply because the addition of excess oxygen in the matrix calculations causes some element concentrations to increase, while other elements will show a decrease in concentrations.

So we've chatted with a few geologists about adding such a calculation for ferric/ferrous ratios into Probe for EPMA, it seems that there needs to be a separate calculation (normalization) for each (non-hydrous) mineral species, e.g., magnetite/ilmenite, garnet, etc., etc. 

There also seems to be some various approaches to this ferric/ferrous calculation, apparently optimized for different mineral species.  That is, Gihorso, Droop, Stormer, etc.

Geologists: what are your thoughts on this?  What mineral species should we perform these ferric/ferrous excess oxygen calculations for, and what method should we utilize? We'd like to get a consensus from the geological community before starting work on the coding.

[AndrewLocock]

Hello,
The general principles of charge-balanced formulas are best laid out by Droop (1987) Min. Mag. 51, Issue 361, pp. 431-435.

A given mineral is assumed to have a set number of cation positions for a set number of oxygen atoms, with iron being the only element with variable valence state. The proportion of ferric iron is calculated to reach the ideal number of cations and of oxygen atoms.

It is important to realize the effects of propagation-of-uncertainty on the calculation of structural formulas.
This is outlined by Giaramita and Day (1990) Am. Min. 75, pp. 170-182.

As an example, below is solid-solution in the spinel group of magnetite - ulvospinel - spinel.
For the weight-percent oxides, we will assume some reasonable standard deviations, as might be found in a set of electron microprobe analyses:

MgO   Al2O3   TiO2   FeOtot   sum wt%   4.86   12.30   9.64   69.34   96.14 sd    0.25   0.45   0.35   0.60   n/a RSD   5.1%   3.7%   3.6%   0.9%  n/a

The resulting formula, calculated for 3 cations and 4 oxygen, is:

Mg       Al       Ti       Fe2+   Fe3+     O     cations average   0.250   0.500   0.250   1.000   1.000   4.000   3.000 std dev   0.012   0.016   0.009   0.016   0.021   0.000   0.000 RSD   4.8%   3.2%   3.4%   1.6%   2.1%   0.0%   0.0%

Although the starting relative uncertainty in FeO was 0.9%, the propagated relative uncertainty is considerably higher; for Fe2+ it is 1.6% and for Fe3+ it is 2.1%.

The example of augite based on the analysis and uncertainties given by Giaramita and Day (1990) follows:

oxide   Na2O   MgO   Al2O3   SiO2   CaO   TiO2   Cr2O3   MnO   FeOtot   sum mean   1.20   16.59   8.04   50.16   15.97   0.84   0.15   0.15   6.18   99.28 std dev   0.04   0.14   0.08   0.23   0.15   0.05   0.05   0.04   0.16   0.37 RSD   3.3%   0.8%   1.0%   0.5%   0.9%   6.0%   33.1%   27.1%   2.6%   0.4%

The resulting formula, calculated for 4 cations and 6 oxygen, is:

element     Na     Mg     Al      Si       Ca     Ti      Cr      Mn      Fe2+      Fe3+   O     cations average   0.085   0.901   0.345   1.826   0.623   0.023   0.004   0.005   0.152   0.036   6.000   4.000 std dev   0.003   0.007   0.003   0.007   0.005   0.001   0.001   0.001   0.014   0.015   0.000   0.000 RSD   3.3%   0.7%   1.0%   0.4%   0.8%   6.0%   33.1%   27.1%   9.2%   40.2%   0.0%   0.0%

Although the starting relative uncertainty in FeO was 2.6%, the propagated relative uncertainty is (very) considerably higher; for Fe2+ it is 9.2% and for Fe3+ it is 40.2% (in part, because of the small absolute amount of ferric iron).

These latter relative uncertainties would apply to the recalculated weight-percent FeO and Fe2O3.

Cheers,
Andrew

[John Donovan]

Hi Andrew,
Thanks for responding.  OK, so you think the Droop method is the way to go forward on this recalculation.  Let's see if anyone else objects, but that decision is fine by me.  I assume you already have written code that performs these calculations?

On the uncertainties issue, thanks for the info but let's not get ahead of ourselves. You said:

A given mineral is assumed to have a set number of cation positions for a set number of oxygen atoms, with iron being the only element with variable valence state. The proportion of ferric iron is calculated to reach the ideal number of cations and of oxygen atoms.

So let's discuss how the user will specify this "given mineral" in the software interface. Will the user select a mineral species from a drop down list, or will they specify a "a set number of cation positions for a set number of oxygen atoms". How does your code expect this specification?

[AndrewLocock]

So let's discuss how the user will specify this "given mineral" in the software interface. Will the user select a mineral species from a drop down list, or will they specify a "a set number of cation positions for a set number of oxygen atoms". How does your code expect this specification?

Hello,
Attached is an example Excel spreadsheet of how this charge-balance calculation could work.

In this spreadsheet, the user inputs the desired # of cations, # of oxygen, and the weight-percentages of nine common oxides: Na2O   MgO   Al2O3   SiO2   CaO   TiO2   Cr2O3   MnO   FeOtotal

The spreadsheet calculates:
- the sum of these oxides
- the molar amounts of the elements, including oxygen, assuming only ferrous iron
- the atomic proportions of the elements, including oxygen, assuming only ferrous iron, based on the input # of cations
- the charge-balanced proportions of the elements, based on the input # of cations and # of oxygen

The atomic ratio of ferric iron to total iron (Fe3+/ΣFe) is given, as are the recalculated weight percentages of FeO and Fe2O3, along with a revised sum of the oxides.

There are 6 analyses in this example file:
1) The augite from Giaramita and Day (1990), based on 4 cations and 6 oxygen.
2) The augite from Giaramita and Day (1990), based on 8 cations and 12 oxygen.
3) A magnetite-spinel-ulvospinel solid solution, based on 3 cations and 4 oxygen.
4) The garnet from Knowles (1987), based on 8 cations and 12 oxygen.
5) A mostly grossular garnet (#5) from Table 58 of volume 1A of the second edition of Deer, Howie and Zussman.
6) A mostly almandine garnet (#12) from Table 55 of volume 1A of the second edition of Deer, Howie and Zussman.

For the augite examples, the proportions of ferric iron are identical, as the ratios of cations to oxygen are identical.

The magnetite etc. solid solution is a hypothetical (fictive) composition, and so the total is exactly 100.00%.

For the garnet of Knowles (1987), charge balance is achieved with 0.59 wt% Fe2O3, and the final sum is 100.57 wt%.

For the mostly grossular garnet, all of the iron is recalculated as ferric iron, and exact charge balance is still not achieved; the oxygen remains as 11.973 atoms per 8 cations.

For the mostly almandine garnet, all of the iron remains as ferrous iron, and exact charge balance is still not achieved; the oxygen remains as 12.085 atoms per 8 cations.

In these latter two cases, the compositions do NOT achieve charge balance (indeed, they cannot). This is probably because of errors and uncertainties in the analyses.

The key formula in this Excel spreadsheet is the calculation of the proportion of ferric iron, which is handled with a nested IF formula:

IF(AI3<B3,IF(2*(B3-AI3)<=AH3,2*(B3-AI3),AH3),0)

If (the atomic proportion of oxygen is Less Than the input # of oxygen,
     If (two times (the input # of oxygen Minus the atomic proportion of oxygen) is Less Than or Equal To the atomic proportion of ferrous iron,
          then Calculate two times (the input # of oxygen Minus the atomic proportion of oxygen),
          Otherwise use the atomic proportion of ferrous iron,
     Otherwise report zero.

I hope that this spreadsheet and explanation will prove useful.
Regards,
Andrew

[John Donovan]

For the mostly grossular garnet, all of the iron is recalculated as ferric iron, and exact charge balance is still not achieved; the oxygen remains as 11.973 atoms per 8 cations.

For the mostly almandine garnet, all of the iron remains as ferrous iron, and exact charge balance is still not achieved; the oxygen remains as 12.085 atoms per 8 cations.

In these latter two cases, the compositions do NOT achieve charge balance (indeed, they cannot). This is probably because of errors and uncertainties in the analyses.

The key formula in this Excel spreadsheet is the calculation of the proportion of ferric iron, which is handled with a nested IF formula:

IF(AI3<B3,IF(2*(B3-AI3)<=AH3,2*(B3-AI3),AH3),0)

If (the atomic proportion of oxygen is Less Than the input # of oxygen,
     If (two times (the input # of oxygen Minus the atomic proportion of oxygen) is Less Than or Equal To the atomic proportion of ferrous iron,
          then Calculate two times (the input # of oxygen Minus the atomic proportion of oxygen),
          Otherwise use the atomic proportion of ferrous iron,
     Otherwise report zero.

I hope that this spreadsheet and explanation will prove useful.
Regards,
Andrew

Hi Andrew,
This is a good explanation, thanks. I will start working on this soon, but probably not until after M&M.

It occurs to me, with the two examples you gave that did not achieve charge balance, I wonder if these compositions would achieve charge balance if the additional excess oxygen was added back into the matrix correction physics and the charge balance re-calculated?

This is the approach that I will be taking for this calculation, as I already do with the interference and MAN corrections.

Thanks again.

[AndrewLocock]

Hi Andrew,
This is a good explanation, thanks. I will start working on this soon, but probably not until after M&M.

It occurs to me, with the two examples you gave that did not achieve charge balance, I wonder if these compositions would achieve charge balance if the additional excess oxygen was added back into the matrix correction physics and the charge balance re-calculated?

This is the approach that I will be taking for this calculation, as I already do with the interference and MAN corrections.

Thanks again.

Hi John,
It is conceivable that such an addition-and-recalculation might improve these analyses, if they had been obtained by electron microprobe analysis, but I think that they were both wet chemical analyses.

There are a few other points of concern with adding the ferric/ferrous recalculation into the matrix corrections:

1) The recalculation assumes that Fe is the ONLY element with variable valence, and that there are NO significant vacancies (cation or anion) in the material. This is mostly applicable to anhydrous oxides.

2) The result generated by the Probe-for-EPMA software during the iteration of the matrix corrections will probably need to be recalculated by the user after the fact, as it will probably diverge from the ideal during such iterations.

My reasoning is based on the case of carbonate minerals such as calcite, CaCO3, for which the CO2 content is calculated by stoichiometry and added into the iteration loop(s) of the matrix corrections.

In the case of calcite analyses, the final amount of CO2 reported by Probe-for-EPMA is usually NOT in perfect stoichiometric ratio to the divalent cations (it is usually close, but rarely perfect).

It is definitely preferable to have that CO2 present for the matrix corrections.

However, the user should (must) recalculate elsewhere the final proportion of CO2 to match stoichiometry.

Thus, I suspect that some (slight) divergence from ideality could similarly occur in the ferric/ferrous recalculation during the iterations of the matrix corrections.

Cheers,
Andrew

[John Donovan]

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!