Author Topic: Water By Difference in Glasses  (Read 1458 times)

Probeman

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    • John Donovan
Water By Difference in Glasses
« on: May 03, 2017, 11:11:33 pm »
Some time ago there was a discussion about the two methods for using EPMA to determine water in hydrated glasses. First there is the method for simply adding up all the elements (and their associated stoichiometric oxygen), and then subtracting that sum from 100 to obtain the so called water by difference. This water is then included in the matrix correction.

Note that one *cannot* simply perform this water by difference calculation in a spreadsheet, as the value of H2O obtained by difference needs to be iterated in the matrix correction for the other elements. Why?  Because the oxygen (in the water) absorbs the emission lines of the other elements, particularly Si. Think about it: by not including the H2O (by difference) in the matrix correction, the Si ka absorption correction will be underestimated for the simple reason that oxygen absorbs Si Ka more than silicon does!

This water by difference and the need for including it in the sample matrix correction is nicely demonstrated in the following post:

http://probesoftware.com/smf/index.php?topic=11.msg235#msg235

The other method is to calculate water in glass as suggested by Barbara Nash, where one measures oxygen in addition to the other cations, and then subtracts the oxygen calculated by stoichiometry (for the measured cations) from the measured oxygen to obtain an oxygen excess or deficit, that can then be converted into OH or H2O as desired. This method is described in more detail here (starting with point 9):

http://probesoftware.com/smf/index.php?topic=307.msg5427#msg5427

But this morning I decided to take the above water by measured oxygen run file, containing the data for the Withers glasses, and modify the calculation in Probe for EPMA to ignore the measured oxygen and instead perform the first method described above for water by difference (and included in the matrix correction).

First I made a copy of the Withers run and disabled the measured oxygen channel in the Elements/Cations dialog using the Disable Quant checkbox. Then I added oxygen as a specified (not measured) element, also in the Elements/Cations dialog. Then in the Calculation Options dialog I specified hydrogen by difference and then clicked the Calculate With Stoichiometric Oxygen option.

That done, here are the results for the first Withers glass which has little or no water (all analyses 15 keV, 10 nA, 20 um):

Un   12 Withers-NSL, Results in Oxide Weight Percents

ELEM:     Na2O     K2O      Cl     BaO       F    TiO2     FeO     MnO     CaO    SiO2   Al2O3     MgO     O-D     H2O       O   SUM
   514   5.763   4.302    .213   -.046    .111    .163   4.122    .033    .156  74.653  10.439    .013     ---    .080    .000 100.000
   515   5.119   4.352    .234   -.079    .108    .239   4.144    .109    .212  74.253  10.410    .009     ---    .890    .000 100.000
   516   5.508   4.109    .215    .054    .038    .228   4.135    .082    .210  74.471  10.473    .018     ---    .459    .000 100.000
   517   5.285   4.351    .291   -.009    .164    .168   4.120    .122    .166  74.723  10.499    .013     ---    .106    .000 100.000
   518   5.686   4.351    .234    .018    .069    .152   4.157    .114    .163  74.671  10.435    .014     ---    .000    .000 100.063
   519   5.560   4.501    .153    .007    .091    .168   4.087    .082    .185  74.357  10.382    .015     ---    .412    .000 100.000
   520   5.889   4.450    .210    .011    .097    .249   4.054    .088    .180  74.729  10.422    .012     ---    .000    .000 100.393
   521   5.795   4.548    .210    .022    .085    .222   4.128   -.004    .173  74.646  10.426    .023     ---    .000    .000 100.273
   522   5.771   4.466    .221   -.034    .056    .211   4.090    .069    .175  74.947  10.506    .016     ---    .000    .000 100.494
   523   5.578   4.507    .288   -.046    .079    .217   4.018    .049    .185  74.065  10.424    .014     ---    .621    .000 100.000
   524   5.697   4.485    .231    .031    .084    .260   4.085    .080    .185  74.333  10.413    .011     ---    .104    .000 100.000

AVER:    5.605   4.402    .227   -.006    .089    .207   4.104    .075    .181  74.532  10.439    .015     ---    .243    .000 100.111
SDEV:     .231    .126    .038    .040    .033    .038    .041    .037    .018    .258    .038    .004     ---    .306    .000    .185

Note that it calculated 0.243 +/- 0.306 H2O.  So that is a zero within statistics and the measured water by FTIR was 0.13 wt%, so again, within statistics. I say within statistics, because being within 0.1 wt% absolute is what we call "spurious accuracy"!   :) 

For N1 glass we obtain:
Un   13 Withers-N1, Results in Oxide Weight Percents

ELEM:     Na2O     K2O      Cl     BaO       F    TiO2     FeO     MnO     CaO    SiO2   Al2O3     MgO     O-D     H2O       O   SUM
   526   5.428   4.385    .258    .067    .082    .233   4.247    .091    .196  72.389  10.504    .023     ---   2.096    .000 100.000
   527   5.779   4.227    .248    .014    .037    .277   4.139    .077    .208  72.751  10.459    .016     ---   1.767    .000 100.000
   528   5.849   4.808    .161    .090    .076    .212   4.214    .053    .176  72.137  10.455    .023     ---   1.747    .000 100.000
   529   5.214   4.672    .242    .054    .052    .212   4.123    .098    .198  72.407  10.434    .024     ---   2.271    .000 100.000
   530   5.664   4.566    .245   -.009    .092    .266   4.215    .046    .206  72.259  10.506    .017     ---   1.927    .000 100.000
   531   5.366   4.392    .239    .010    .064    .359   4.189    .046    .185  72.042  10.500    .015     ---   2.592    .000 100.000
   532   5.343   4.509    .186   -.003    .039    .250   4.179    .029    .201  72.244  10.492    .018     ---   2.514    .000 100.000
   533   5.272   4.460    .231    .014    .095    .223   4.124    .091    .208  72.276  10.562    .014     ---   2.431    .000 100.000
   534   5.343   4.409    .229    .006    .055    .294   4.112    .054    .189  72.349  10.513    .019     ---   2.429    .000 100.000
   535   5.067   4.216    .242   -.017    .108    .196   4.156    .102    .194  72.522  10.447    .016     ---   2.752    .000 100.000
   536   5.646   4.537    .169   -.022    .123    .282   4.183    .096    .227  72.480  10.461    .017     ---   1.800    .000 100.000
   537   5.281   4.385    .172    .009    .069    .261   4.143    .087    .187  72.534  10.433    .015     ---   2.423    .000 100.000

AVER:    5.438   4.464    .219    .018    .074    .255   4.169    .073    .198  72.366  10.480    .018     ---   2.229    .000 100.000
SDEV:     .242    .170    .035    .035    .027    .045    .043    .025    .013    .193    .039    .003     ---    .350    .000    .000

so a little higher than the expected 1.16 wt % by FTIR.  For the N3 glass we obtain:
Un   14 Withers-N3, Results in Oxide Weight Percents

ELEM:     Na2O     K2O      Cl     BaO       F    TiO2     FeO     MnO     CaO    SiO2   Al2O3     MgO     O-D     H2O       O   SUM
   538   5.172   4.310    .269    .003    .117    .261   4.034    .089    .181  72.031  10.287    .018     ---   3.226    .000 100.000
   539   5.383   3.983    .213    .005    .097    .256   4.059    .105    .178  71.788  10.252    .024     ---   3.659    .000 100.000
   540   5.213   4.288    .213    .031    .029    .196   3.988    .092    .208  72.293  10.276    .027     ---   3.147    .000 100.000
   541   5.796   4.384    .215    .049    .027    .250   4.110    .060    .213  71.777  10.212    .020     ---   2.887    .000 100.000
   542   5.215   4.571    .210    .084    .092    .234   4.032    .044    .176  72.471  10.287    .024     ---   2.562    .000 100.000
   543   5.974   4.128    .188    .047    .045    .250   4.118    .106    .186  72.015  10.254    .016     ---   2.672    .000 100.000
   544   5.324   4.479    .248    .003    .116    .109   3.980    .088    .199  71.832  10.241    .019     ---   3.361    .000 100.000
   545   5.356   4.092    .164   -.004    .066    .201   4.122    .013    .216  72.204  10.257    .020     ---   3.293    .000 100.000
   546   5.303   4.122    .224    .029    .055    .174   4.095    .075    .185  72.459  10.249    .020     ---   3.011    .000 100.000
   547   5.487   4.422    .213   -.028    .059    .201   4.037    .023    .179  71.855  10.223    .011     ---   3.318    .000 100.000
   548   5.259   4.382    .261    .035    .100    .245   4.053    .100    .186  72.281  10.242    .024     ---   2.832    .000 100.000
   549   5.385   4.193    .237   -.050    .090    .131   4.108    .134    .222  72.044  10.227    .022     ---   3.258    .000 100.000

AVER:    5.405   4.280    .221    .017    .074    .209   4.061    .077    .194  72.087  10.251    .020     ---   3.102    .000 100.000
SDEV:     .244    .177    .029    .036    .032    .050    .049    .036    .017    .251    .024    .004     ---    .317    .000    .000

which is quite close to the FTIR value of 3.30 wt%.  For the N3.35 glass we obtain:
Un   15 Withers-N3.35, Results in Oxide Weight Percents

ELEM:     Na2O     K2O      Cl     BaO       F    TiO2     FeO     MnO     CaO    SiO2   Al2O3     MgO     O-D     H2O       O   SUM
   550   5.296   4.343    .229   -.078    .096    .283   4.280    .093    .208  70.317  10.258    .013     ---   4.663    .000 100.000
   551   4.849   4.032    .170   -.009    .108    .251   4.249    .086    .181  70.492  10.184    .014     ---   5.394    .000 100.000
   552   5.240   4.328    .213   -.050    .108    .212   4.212    .075    .178  70.826  10.242    .014     ---   4.403    .000 100.000
   553   4.964   4.326    .218    .046    .084    .207   4.156    .087    .199  70.550  10.246    .014     ---   4.904    .000 100.000
   554   5.336   4.339    .213   -.009    .033    .174   4.251    .045    .179  70.821  10.330    .014     ---   4.274    .000 100.000
   555   5.670   4.488    .229    .032    .086    .310   4.193    .124    .225  70.945  10.261    .011     ---   3.428    .000 100.000
   556   5.011   4.152    .213    .018    .063    .278   4.184    .106    .170  70.532  10.387    .016     ---   4.869    .000 100.000
   557   4.997   4.268    .240    .021    .046    .261   4.248    .142    .214  70.633  10.233    .022     ---   4.674    .000 100.000
   558   5.600   4.252    .156   -.037    .078    .262   4.164    .094    .170  69.915  10.287    .018     ---   5.041    .000 100.000
   559   4.658   3.848    .208   -.004    .067    .076   4.304    .149    .211  70.511  10.255    .011     ---   5.705    .000 100.000
   560   5.169   4.583    .215    .013    .092    .180   4.327    .096    .193  70.203  10.303    .027     ---   4.599    .000 100.000
   561   5.279   4.671    .153    .016    .076    .142   4.218    .121    .202  70.217  10.314    .017     ---   4.574    .000 100.000

AVER:    5.172   4.302    .205   -.003    .078    .220   4.232    .101    .194  70.497  10.275    .016     ---   4.711    .000 100.000
SDEV:     .295    .225    .029    .036    .023    .068    .054    .029    .018    .297    .053    .005     ---    .571    .000    .000

which is a little higher than the 3.51 wt% from FTIR. And for N4.6 we obtain:
Un   16 Withers-N4.6, Results in Oxide Weight Percents

ELEM:     Na2O     K2O      Cl     BaO       F    TiO2     FeO     MnO     CaO    SiO2   Al2O3     MgO     O-D     H2O       O   SUM
   562   4.976   4.283    .234   -.027   -.009    .338   4.011    .100    .184  71.539  10.240    .017     ---   4.115    .000 100.000
   563   5.113   4.355    .180    .012    .115    .240   3.965    .106    .196  71.564  10.260    .020     ---   3.874    .000 100.000
   564   5.773   4.116    .215    .042    .107    .228   3.967    .145    .207  71.525  10.220    .019     ---   3.436    .000 100.000
   565   4.816   4.508    .223    .025    .064    .191   4.115    .090    .211  71.138  10.202    .019     ---   4.400    .000 100.000
   566   5.336   4.332    .156    .051    .082    .272   3.943    .095    .226  70.918  10.280    .025     ---   4.284    .000 100.000
   567   4.879   4.218    .234    .000    .048    .163   3.973    .060    .195  71.469  10.341    .019     ---   4.401    .000 100.000
   568   5.053   4.147    .218    .019    .037    .191   3.909    .068    .198  70.828  10.319    .020     ---   4.993    .000 100.000
   569   4.963   3.944    .259   -.019    .080    .245   3.892    .097    .198  70.910  10.234    .022     ---   5.174    .000 100.000
   570   5.395   4.282    .250   -.049    .067    .114   3.891    .078    .201  71.323  10.241    .015     ---   4.191    .000 100.000
   571   4.943   4.125    .256   -.018    .152    .153   3.831    .083    .214  71.425  10.176    .015     ---   4.646    .000 100.000
   572   4.615   4.141    .251    .029    .033    .278   3.870    .096    .175  71.119  10.214    .018     ---   5.161    .000 100.000
   573   5.047   4.244    .232    .031    .078    .174   3.939    .075    .221  71.371  10.242    .022     ---   4.323    .000 100.000

AVER:    5.076   4.225    .226    .008    .071    .216   3.942    .091    .202  71.261  10.247    .019     ---   4.417    .000 100.000
SDEV:     .304    .144    .031    .031    .042    .063    .074    .022    .015    .268    .047    .003     ---    .517    .000    .000

which is quite close to the FTIR value of 4.11 wt%. And finally for N5 we get:
Un   17 Withers-N5, Results in Oxide Weight Percents

ELEM:     Na2O     K2O      Cl     BaO       F    TiO2     FeO     MnO     CaO    SiO2   Al2O3     MgO     O-D     H2O       O   SUM
   574   4.151   4.261    .205    .033    .086    .180   4.044    .078    .227  70.035  10.241    .028     ---   6.430    .000 100.000
   575   4.936   4.282    .207    .018    .084    .207   4.018    .102    .207  70.694  10.169    .020     ---   5.056    .000 100.000
   576   4.308   3.994    .181    .036    .100    .229   4.039    .108    .180  70.560  10.079    .010     ---   6.178    .000 100.000
   577   4.622   4.275    .259    .046    .110    .164   4.078    .075    .164  70.409  10.304    .008     ---   5.486    .000 100.000
   578   4.645   4.219    .259   -.015    .083    .120   4.092    .104    .162  70.132  10.171    .024     ---   6.004    .000 100.000
   579   4.725   4.288    .240   -.088    .070    .207   4.111    .106    .182  70.305  10.285    .018     ---   5.550    .000 100.000
   580   4.362   4.254    .224    .018    .088    .169   4.030    .070    .184  70.304  10.113    .007     ---   6.177    .000 100.000
   581   5.017   4.163    .248   -.021    .120    .196   3.992    .064    .212  70.749  10.158    .018     ---   5.083    .000 100.000
   582   4.488   4.222    .164   -.028    .080    .224   4.122    .065    .167  70.989  10.186    .024     ---   5.297    .000 100.000
   583   4.580   4.138    .218   -.069    .033    .246   4.080    .040    .199  70.575  10.218    .014     ---   5.726    .000 100.000
   584   4.596   4.073    .213    .004    .033    .207   4.028    .083    .185  70.887  10.096    .015     ---   5.579    .000 100.000
   585   4.022   4.346    .191    .033    .071    .202   4.060    .079    .224  70.688  10.186    .019     ---   5.879    .000 100.000

AVER:    4.538   4.210    .217   -.003    .080    .196   4.058    .081    .191  70.527  10.184    .017     ---   5.704    .000 100.000
SDEV:     .294    .101    .030    .043    .026    .034    .039    .021    .022    .295    .070    .007     ---    .442    .000    .000

which is also close to the FTIR value of 5.06 wt%. Here a summary of these glasses which contain water measured by FTIR of the following values:

glass   FTIR    EPMA (H2O by diff)
NSL     0.13    0.24
N1      1.16    2.23
N3      3.30    3.10
N3.35   3.51    4.71
N4.6    4.11    4.42
N5      5.06    5.70

I think this water by difference method is useful, but one does need to account for all minor (and trace?) cations (and CO2?), and also the FeO/Fe2O3 ratios for correctly calculating the stoichiometric oxygen from the cations.
john
« Last Edit: May 06, 2017, 07:09:31 am by Probeman »
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Probeman

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Re: Water By Difference in Glasses
« Reply #1 on: May 04, 2017, 06:57:14 am »
By the way, the water by difference calculations shown above (that is, *not* estimating water by measuring oxygen), were performed without the blank correction (which was used to improve oxygen accuracy, based on the NIST mineral glasses, for the water by oxygen measurement method).

And in case anyone is interested in playing with this data themselves, I've attached the MDB files for both methods below. Also since the original data file was from 2008, it does not contain the standard compositions as is the case for more recent MDB files. So I'm also attaching my standard.mdb file for reprocessing. So you should browse to this standard database first from the Standard | Select Standard Database menu, before opening either of the two Withers glass files.

Let me know if you have any questions.
john
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Probeman

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Re: Water By Difference in Glasses
« Reply #2 on: May 04, 2017, 10:45:15 pm »
This may be a subtle point but I think it could be important when measuring very small water contents using the WBD (water by difference) method.

When measuring very small concentrations of water, the totals will tend to be very close to 100% if all cations are measured. In fact if zero water was present and all the traces measured and stoichiometric oxygen is properly specified, the average total of all elements should be close to 100%. And of course some points will total less than 100%, and some more than 100% just due to statistics.

For points with totals less than 100% we perform the WBD method which gives us a positive concentration of water.  If the total is more than 100%, one generally does not calculate water by difference- but when averaging the water content for all points, this procedure causes a bias in the average water by difference because we are adding in the statistical variance for low totals but not the variance for high totals.  This will bias our small concentrations of water in a positive (higher concentration) direction when the WBD is performed and the points are subsequently averaged. See here:

Un   12 Withers-NSL, Results in Oxide Weight Percents

ELEM:     Na2O     K2O      Cl     BaO       F    TiO2     FeO     MnO     CaO    SiO2   Al2O3     MgO     O-D     H2O       O   SUM 
   514   5.763   4.302    .213   -.046    .111    .163   4.122    .033    .156  74.653  10.439    .013     ---    .080    .000 100.000
   515   5.119   4.352    .234   -.079    .108    .239   4.144    .109    .212  74.253  10.410    .009     ---    .890    .000 100.000
   516   5.508   4.109    .215    .054    .038    .228   4.135    .082    .210  74.471  10.473    .018     ---    .459    .000 100.000
   517   5.285   4.351    .291   -.009    .164    .168   4.120    .122    .166  74.723  10.499    .013     ---    .106    .000 100.000
   518   5.686   4.351    .234    .018    .069    .152   4.157    .114    .163  74.671  10.435    .014     ---    .000    .000 100.063
   519   5.560   4.501    .153    .007    .091    .168   4.087    .082    .185  74.357  10.382    .015     ---    .412    .000 100.000
   520   5.889   4.450    .210    .011    .097    .249   4.054    .088    .180  74.729  10.422    .012     ---    .000    .000 100.393
   521   5.795   4.548    .210    .022    .085    .222   4.128   -.004    .173  74.646  10.426    .023     ---    .000    .000 100.273
   522   5.771   4.466    .221   -.034    .056    .211   4.090    .069    .175  74.947  10.506    .016     ---    .000    .000 100.494
   523   5.578   4.507    .288   -.046    .079    .217   4.018    .049    .185  74.065  10.424    .014     ---    .621    .000 100.000
   524   5.697   4.485    .231    .031    .084    .260   4.085    .080    .185  74.333  10.413    .011     ---    .104    .000 100.000

AVER:    5.605   4.402    .227   -.006    .089    .207   4.104    .075    .181  74.532  10.439    .015     ---    .243    .000 100.111
SDEV:     .231    .126    .038    .040    .033    .038    .041    .037    .018    .258    .038    .004     ---    .306    .000    .185

The lines in red have totals greater than 100% so no water by difference was calculated. But if we want an accurate *average* of the WBD, then we really should calculate a "negative" water concentration for these high total points, which then can be included in the calculation of the average water by difference.

Does this make sense?  It's a little bit analogous to the problem when measuring a zero concentration element. Simply due to statistics, some trace element points will give a small positive number and some points will give a small negative number.  Both positive and negative results are equally valid for averaging the concentration.  If one insists on zeroing out negative k-ratios or concentrations (as some do), this will bias the average trace concentration in a positive (higher concentration) direction, because only the values zero or higher will be averaged.

This is not a problem for the WBD method if the totals for all points are less than 100% (just as it's not a problem to zero negative k-ratios or concentrations, if all trace element values are greater than zero!), but it could be a problem for glasses that contain zero or very small amounts of water.

I'm going to try this "negative water by difference" correction when I get home from EMAS and will let you all know what I find.  Please chime in with your own thoughts!
john

Edit by John: come to think of it, this point about "negative" WBD concentrations for more accurate averaging, also applies to *any* element by difference (not just hydrogen!), if the concentration of that element by difference approaches zero...
« Last Edit: May 04, 2017, 11:27:42 pm by Probeman »
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Probeman

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Re: Water By Difference in Glasses
« Reply #3 on: May 05, 2017, 04:24:39 am »
After taking a nice slow walk around the "old town" of Konstantz, I got back to the hotel and decided to try the "negative" water by difference idea, and here are the results for the same sample in the previous post:

Un   12 Withers-NSL, Results in Oxide Weight Percents

ELEM:     Na2O     K2O      Cl     BaO       F    TiO2     FeO     MnO     CaO    SiO2   Al2O3     MgO     O-D     H2O       O   SUM 
   514   5.763   4.302    .213   -.046    .111    .163   4.122    .033    .156  74.653  10.439    .013     ---    .080    .000 100.000
   515   5.119   4.352    .234   -.079    .108    .239   4.144    .109    .212  74.253  10.410    .009     ---    .890    .000 100.000
   516   5.508   4.109    .215    .054    .038    .228   4.135    .082    .210  74.471  10.473    .018     ---    .459    .000 100.000
   517   5.285   4.351    .291   -.009    .164    .168   4.120    .122    .166  74.723  10.499    .013     ---    .106    .000 100.000
   518   5.685   4.350    .234    .018    .069    .152   4.157    .114    .163  74.665  10.434    .014     ---   -.055    .000 100.000
   519   5.560   4.501    .153    .007    .091    .168   4.087    .082    .185  74.357  10.382    .015     ---    .412    .000 100.000
   520   5.883   4.449    .210    .011    .097    .249   4.052    .088    .180  74.692  10.414    .012     ---   -.338    .000 100.000
   521   5.791   4.546    .210    .022    .085    .222   4.127   -.004    .173  74.620  10.421    .023     ---   -.236    .000 100.000
   522   5.764   4.464    .220   -.034    .056    .211   4.087    .069    .175  74.901  10.496    .016     ---   -.425    .000 100.000
   523   5.578   4.507    .288   -.046    .079    .217   4.018    .049    .185  74.065  10.424    .014     ---    .621    .000 100.000
   524   5.697   4.485    .231    .031    .084    .260   4.085    .080    .185  74.333  10.413    .011     ---    .104    .000 100.000

AVER:    5.603   4.401    .227   -.006    .089    .207   4.103    .075    .181  74.521  10.437    .015     ---    .147    .000 100.000
SDEV:     .230    .126    .038    .040    .033    .038    .042    .037    .018    .246    .037    .004     ---    .412    .000    .000

As you can see, the lines in red had totals higher then 100%, so the water by difference becomes "negative" thus slightly lowering the average WBD. The average water by difference for this Withers glass is now a little closer to the FTIR value of 0.13 wt%.  In fact it's so close I'm calling it "spurious accuracy". That is: too good to be true... either way, all within a single standard deviation of 0.13 wt% H2O.
john
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