OK, let's start again with the Armstrong/Reed/CITZMU phi-rho-z calculation of the SiIr alloy where we obtain what ostensibly appears to be Si55Ir45 (atomic):
#1 approx. Ir45Si55 (atomic) based on Ir3Si5 standard
SAMPLE: 1, ITERATIONS: 4, Z-BAR: 67.40733
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Ir la .9907 1.0000 1.0824 1.0723 1.1287 .9589 .9548 11.2150 1.7833 124.108
Si ka 1.6859 .9886 .7791 1.2986 .5819 1.3389 .5095 1.8390 10.8755 1456.45
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Ir la .79090 .79090 84.806 ----- 44.860 .449 20.00
Si ka .11730 .11730 15.232 ----- 55.140 .551 20.00
TOTAL: 100.038 ----- 100.000 1.000
Now we switch to alpha factor polynomial fitting using the Analytical | ZAF, Phi-Rho-Z, Alpha Factor, Calibration Curve Selection menu:
If we plot these alpha factors derived from the k-ratios from the Armstrong/Reed/CITZMU calculations (see the Analytical | Calculate and Plot Binary Alpha factors menu) we obtain this plot for Ir La at 20 keV:
and this plot for Si ka at 20 keV where we can see that even with a 2nd order polynomial, the fit is not perfect due to the non-linear nature of the absorption correction:
Now we get roughly similar results to the "straight" phi-rho-z calculation fitting the Armstrong/Reed/CITZMU k-ratios to polynomial alpha factors as seen here:
ELEMENT ir la si ka Total
UNK KRAT .7909 .1173
UNK WT% 84.990 14.951 99.941
UNK AT%
45.375 54.625 100.000
UNK BETA 1.0746 1.2746
ALPITER 6.0000
The point being that the polynomial alpha factor fitting allows one to pre-calculate the physics for each binary system, and subsequently combine them using the beta factor expression for arbitrary compositions as described here:
http://probesoftware.com/smf/index.php?topic=139.msg637#msg637Now we enable the Penepma 2012 k-ratios as seen here, again from the Analytical | ZAF, Phi-Rho-Z, Alpha Factor, Calibration Curve Selection menu:
and obtain these intermediate results using the Penepma 2012 Penfluor/Fanal derived k-ratios for Si and Ir:
Initializing alpha-factors...
Number of alpha-factor binaries to be calculated = 1
Calculating alpha-factor binary ir la in si
AFactorPenepmaReadMatrix: Ir la in Si at 40 degrees and 20 keV
Conc Kratios Alpha
99.0000 98.006218 2.01400
95.0000 92.924858 1.44663
90.0000 86.025154 1.46206
80.0000 73.216965 1.46322
60.0000 50.819466 1.45163
50.0000 40.913555 1.44418
40.0000 31.832989 1.42760
20.0000 15.031998 1.41312
10.0000 7.298365 1.41130
5.00000 3.682503 1.37660
1.00000 .738135 1.35835
AFactorPenepmaReadMatrix: Si ka in Ir at 40 degrees and 20 keV
Conc Kratios Alpha
99.0000 98.885162 1.11614
95.0000 93.915077 1.23104
90.0000 88.040230 1.22260
80.0000 76.524353 1.22709
60.0000 55.550423 1.20025
50.0000 45.765198 1.18507
40.0000 36.368473 1.16642
20.0000 18.166149 1.12619
10.0000 9.182739 1.09889
5.00000 4.624117 1.08557
1.00000 .924762 1.08218
NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 20
P=1, Pt#1, C=.9900, K=.9801, Alpha=2.0140
P=2, Pt#2, C=.9500, K=.9292, Alpha=1.4466
P=3, Pt#3, C=.9000, K=.8603, Alpha=1.4621
P=4, Pt#4, C=.8000, K=.7322, Alpha=1.4632
P=5, Pt#5, C=.6000, K=.5082, Alpha=1.4516
P=6, Pt#6, C=.5000, K=.4091, Alpha=1.4442
P=7, Pt#7, C=.4000, K=.3183, Alpha=1.4276
P=8, Pt#8, C=.2000, K=.1503, Alpha=1.4131
P=9, Pt#9, C=.1000, K=.0730, Alpha=1.4113
P=10, Pt#10, C=.0500, K=.0368, Alpha=1.3766
P=11, Pt#11, C=.0100, K=.0074, Alpha=1.3583
Xray Matrix Alpha1 Alpha2 Alpha3 %MaxDev
ir la in si 1.4124 -.3141 .5920 16.50
P=1, Pt#1, C=.9900, K=.9889, Alpha=1.1161
P=2, Pt#2, C=.9500, K=.9392, Alpha=1.2310
P=3, Pt#3, C=.9000, K=.8804, Alpha=1.2226
P=4, Pt#4, C=.8000, K=.7652, Alpha=1.2271
P=5, Pt#5, C=.6000, K=.5555, Alpha=1.2003
P=6, Pt#6, C=.5000, K=.4577, Alpha=1.1851
P=7, Pt#7, C=.4000, K=.3637, Alpha=1.1664
P=8, Pt#8, C=.2000, K=.1817, Alpha=1.1262
P=9, Pt#9, C=.1000, K=.0918, Alpha=1.0989
P=10, Pt#10, C=.0500, K=.0462, Alpha=1.0856
P=11, Pt#11, C=.0100, K=.0092, Alpha=1.0822
Xray Matrix Alpha1 Alpha2 Alpha3 %MaxDev
si ka in ir 1.0654 .3966 -.2790 6.13
Penepma K-Ratio Alpha Factors:
Xray Matrix Alpha1 Alpha2 Alpha3
Si ka in Ir 1.0654 .3966 -.2790 *From Penepma 2012 Calculations
Ir la in Si 1.4124 -.3141 .5920 *From Penepma 2012 Calculations
All Alpha Factors:
ir si
ir la 1.0000 1.4124
ir la .0000 -.3141
ir la .0000 .5920
si ka 1.0654 1.0000
si ka .3966 .0000
si ka -.2790 .0000
Plotted up these Penepma derived alpha-factors look like this for Ir La:
and this for Si Ka:
Obviously there are some fit problems as we approach the pure end-member. This is primarily a precision problem that occurs from subtracting two large numbers from each other, but they don't have a very significant effect on the results because the alpha factor for an element in itself is 1.0.
The calculation utilizing these Penepma derived alpha factors is here (primary intensity from Penfluor Monte-Carlo, fluorescence from Fanal analytical model:
ELEMENT ir la si ka Total
UNK KRAT .7909 .1173
UNK WT% 83.343 13.746 97.089
UNK AT% 46.977 53.023 100.000
UNK BETA 1.0538 1.1719
ALPITER 5.0000Somewhat ambiguous one might say. Now we limit the polynomial fit to avoid low precision calculations as the pure element concentrations are approached by selecting this option:
Initializing alpha-factors...
Number of alpha-factor binaries to be calculated = 1
Calculating alpha-factor binary ir la in si
AFactorPenepmaReadMatrix: Ir la in Si at 40 degrees and 20 keV
Conc Kratios Alpha
99.0000 98.006218 2.01400
95.0000 92.924858 1.44663
90.0000 86.025154 1.46206
80.0000 73.216965 1.46322
60.0000 50.819466 1.45163
50.0000 40.913555 1.44418
40.0000 31.832989 1.42760
20.0000 15.031998 1.41312
10.0000 7.298365 1.41130
5.00000 3.682503 1.37660
1.00000 .738135 1.35835
AFactorPenepmaReadMatrix: Si ka in Ir at 40 degrees and 20 keV
Conc Kratios Alpha
99.0000 98.885162 1.11614
95.0000 93.915077 1.23104
90.0000 88.040230 1.22260
80.0000 76.524353 1.22709
60.0000 55.550423 1.20025
50.0000 45.765198 1.18507
40.0000 36.368473 1.16642
20.0000 18.166149 1.12619
10.0000 9.182739 1.09889
5.00000 4.624117 1.08557
1.00000 .924762 1.08218
NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 20
P=3, Pt#1, C=.9000, K=.8603, Alpha=1.4621
P=4, Pt#2, C=.8000, K=.7322, Alpha=1.4632
P=5, Pt#3, C=.6000, K=.5082, Alpha=1.4516
P=6, Pt#4, C=.5000, K=.4091, Alpha=1.4442
P=7, Pt#5, C=.4000, K=.3183, Alpha=1.4276
P=8, Pt#6, C=.2000, K=.1503, Alpha=1.4131
P=9, Pt#7, C=.1000, K=.0730, Alpha=1.4113
P=10, Pt#8, C=.0500, K=.0368, Alpha=1.3766
P=11, Pt#9, C=.0100, K=.0074, Alpha=1.3583
Xray Matrix Alpha1 Alpha2 Alpha3 %MaxDev
ir la in si 1.3700 .2149 -.1261 1.50
P=3, Pt#1, C=.9000, K=.8804, Alpha=1.2226
P=4, Pt#2, C=.8000, K=.7652, Alpha=1.2271
P=5, Pt#3, C=.6000, K=.5555, Alpha=1.2003
P=6, Pt#4, C=.5000, K=.4577, Alpha=1.1851
P=7, Pt#5, C=.4000, K=.3637, Alpha=1.1664
P=8, Pt#6, C=.2000, K=.1817, Alpha=1.1262
P=9, Pt#7, C=.1000, K=.0918, Alpha=1.0989
P=10, Pt#8, C=.0500, K=.0462, Alpha=1.0856
P=11, Pt#9, C=.0100, K=.0092, Alpha=1.0822
Xray Matrix Alpha1 Alpha2 Alpha3 %MaxDev
si ka in ir 1.0743 .2858 -.1283 .52
Penepma K-Ratio Alpha Factors:
Xray Matrix Alpha1 Alpha2 Alpha3
Si ka in Ir 1.0743 .2858 -.1283 *From Penepma 2012 Calculations
Ir la in Si 1.3700 .2149 -.1261 *From Penepma 2012 Calculations
All Alpha Factors:
ir si
ir la 1.0000 1.3700
ir la .0000 .2149
ir la .0000 -.1261
si ka 1.0743 1.0000
si ka .2858 .0000
si ka -.1283 .0000
Plotting up these 90% limited alpha factors we obtain more precise fits as seen here for Ir la:
and here for Si Ka:
And we now obtain these results, which are somewhat better, though still not as unequivocal as one would hope.
ELEMENT ir la si ka Total
UNK KRAT .7909 .1173
UNK WT% 83.604 13.990 97.595
UNK AT% 46.617 53.383 100.000
UNK BETA 1.0571 1.1927
ALPITER 5.0000Though it is closer to Si55Ir45 as expected. But this is the "state of the art" for this particular Monte-Carlo physics!