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#msg235The 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#msg5427But 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