The "fast Monte Carlo" method discussed in this topic has finally been written up by myself, Philippe Pinard and Hendrix Demers. See the pdf attached below for the full paper which will be coming out in Microscopy & Microanalysis relatively soon:
In the meantime we thought we would mention that during the writing of the paper we discovered that we (Donovan!) had not properly handled the modeling of alpha factors for the gaseous elements in the periodic table, specifically N, O, Cl, F, Ar, Kr, and Xe and Rn. Basically we had utilized the room temperature elemental densities for all the elements, but because the default "bulk" sample geometry file in Penepma (Penfluor/Fanal) utilizes a thickness of 0.1 cm, at moderate to high electron energies a 1mm thickness can not be considered "infinity" thick for the purposes of a bulk calculation. That is to say, some of the electrons will not come to rest if the density is insufficiently low. This wasn't a problem when the binary composition was mostly a non gaseous element, but it could become a problem for pairs of gaseous elements or when the gaseous element comprised the major element of the binary composition.
Hence we started recalculating all the alpha factor for these gaseous elements about six months ago, but this time using a minimum density of 1.0 if the binary compositional density was less than that. Again for binaries containing the gaseous elements already mentioned above. These calculations take a long time to complete but just so everyone knows, the current matrix.mdb file contains completed calculations for Xe and Rn binaries, and about half the periodic table for the other gaseous elements (both as emitters and absorbers).
Of course the point of these "fast Monte Carlo" alpha factors is to have a way to test our assumptions for the current analytically derived expressions (ZAF, phi-rho-z) which are generally "tuned" to some experimental k-ratios. The point being that these Penepma derived k-ratios are based on quantum mechanical models and therefore not tuned to any specific material datasets.
We suspect that the most interesting application of these Penepma based alpha factors will be for exotic materials where experimental k-ratios do not exist, and therefore have not been utilized in "tuning" our current analytical expressions for quantification.
Just to demonstrate that we are now correctly handling quantification of light elements using these "fast Monte Carlo" alpha factors here is a calculation using the Armstrong phi-rho-z analytical expression for a glass material (of course containing oxygen):
Un 30 MAM IW2 C4-ext-4, Results in Oxide Weight Percents
ELEM: Na2O SiO2 K2O Al2O3 MgO CaO TiO2 MnO FeO P2O5 Cr2O3 O H2O SUM
241 .571 56.566 .502 8.301 7.801 8.146 1.547 .442 15.643 .416 .080 .000 .000 100.016
242 .467 56.499 .473 8.160 7.843 8.064 1.459 .452 15.984 .398 .092 .000 .000 99.892
243 .560 55.914 .526 8.032 4.472 8.648 1.696 .457 19.873 .400 .066 .000 .000 100.643
244 .421 56.258 .480 8.020 6.266 8.415 1.501 .493 17.406 .408 .056 .000 .000 99.722
245 .551 56.193 .500 8.070 5.606 8.627 1.482 .439 18.083 .407 .084 .000 .000 100.042
246 .413 56.655 .471 8.268 7.487 8.015 1.474 .459 16.260 .407 .064 .000 .000 99.972
AVER: .497 56.347 .492 8.142 6.579 8.319 1.526 .457 17.208 .406 .074 .000 .000 100.048
SDEV: .072 .278 .021 .121 1.371 .283 .089 .019 1.597 .006 .014 .000 .000 .314
SERR: .029 .113 .009 .050 .560 .115 .036 .008 .652 .003 .006 .000 .000
%RSD: 14.53 .49 4.33 1.49 20.84 3.40 5.80 4.19 9.28 1.59 18.89 -558.57 .00
STDS: 336 160 374 336 162 162 22 25 162 285 396 --- ---
Now here is the same sample, but this time quantified using the Penepma based "fast Monte Carlo" alpha factor method:
Un 30 MAM IW2 C4-ext-4, Results in Oxide Weight Percents
ELEM: Na2O SiO2 K2O Al2O3 MgO CaO TiO2 MnO FeO P2O5 Cr2O3 O H2O SUM
241 .569 56.703 .503 8.298 7.787 8.130 1.549 .442 15.616 .415 .080 .000 .000 100.092
242 .465 56.643 .474 8.156 7.828 8.049 1.462 .451 15.957 .397 .092 .000 .000 99.974
243 .557 56.111 .526 8.013 4.461 8.638 1.701 .457 19.838 .398 .066 .000 .000 100.767
244 .420 56.424 .480 8.009 6.252 8.402 1.503 .492 17.375 .407 .056 .000 .000 99.820
245 .549 56.367 .501 8.056 5.593 8.614 1.485 .439 18.052 .406 .085 .000 .000 100.146
246 .411 56.806 .471 8.263 7.472 8.001 1.476 .459 16.232 .406 .064 .000 .000 100.060
AVER: .495 56.509 .493 8.133 6.565 8.306 1.529 .457 17.178 .405 .074 .000 .000 100.143
SDEV: .072 .257 .021 .127 1.370 .284 .089 .019 1.594 .006 .014 .000 .000 .326
SERR: .029 .105 .009 .052 .559 .116 .036 .008 .651 .003 .006 .000 .000
%RSD: 14.50 .45 4.34 1.56 20.86 3.42 5.84 4.19 9.28 1.58 18.82 -36.51 .00
STDS: 336 160 374 336 162 162 22 25 162 285 396 --- ---
Again, we have no reason to suspect that such a (low Z) material would benefit from such an "untuned" quantification model, but if anyone does run across a composition that does show significant differences between our current "tuned" phi-rho-z models and this "untuned" Penepma based model, we would be very interested in hearing about it.