A good introduction to the use of alpha and beta factors can be found here:
http://epmalab.uoregon.edu/bence.htm
Basically, the matrix elements are reduced to binaries for Monte-Carlo calculations (alpha factors) but later combined again for matrix corrections (beta factors) in real time.
This allows us to perform the Monte-carlo calculations in advance. Otherwise it would take the age of the universe.
Newly calculated binary intensity k-ratios derived from Penepma and fit to polynomial alpha factors for matrix corrections are listed here:
http://probesoftware.com/download/Calculated%20Alpha%20Binaries.txt
Note that one can check which Penepma derived alpha factors are being utilized by using the Run | List Current Alpha Factors menus in CalcZAF and Probe for EPMA.
All,
I have some free CPU cycles to devote to some specific Penepma Monte-Carlo k-ratio calculations for alpha factor matrix corrections if there are some specific compositions that anyone would like to have correction factors for.
I am currently running Na through Te and also some boride binaries: BAlSiTiVCrFeCoNiZrNbMoTaW and also some alloy binaries: NiTaHfReWZrAlHfReWCoCrMoZr.
But if there are some other specific binaries you would like calculated please let me know.
john
Dan R.
I will release a new matrix.mdb file this weekend and it will contain these binaries out of the list of elements you gave me to calculate:
Penepma K-Ratio Alpha Factors:
Xray Matrix Alpha1 Alpha2 Alpha3
Cr ka in Re .8563 -.0281 .0054 *From Penepma 2012 Calculations
Al ka in Re 1.0424 .2059 -.0454 *From Penepma 2012 Calculations
Cr ka in W .8499 -.0274 .0044 *From Penepma 2012 Calculations
Al ka in W 1.0170 .2395 -.0923 *From Penepma 2012 Calculations
Cr ka in Ta .8455 -.0274 .0037 *From Penepma 2012 Calculations
Al ka in Ta 1.0102 .2378 -.1299 *From Penepma 2012 Calculations
Cr ka in Hf .8401 -.0270 .0030 *From Penepma 2012 Calculations
Al ka in Hf .9952 .1649 -.0171 *From Penepma 2012 Calculations
Ni ka in Mo .8594 .0582 -.0523 *From Penepma 2012 Calculations
Co ka in Mo .9079 .1878 -.2327 *From Penepma 2012 Calculations
Cr ka in Mo .9692 .0493 -.0314 *From Penepma 2012 Calculations
Al ka in Mo 1.2327 .1265 -.0482 *From Penepma 2012 Calculations
Cr ka in Zr .9753 -.0919 .1539 *From Penepma 2012 Calculations
Al ka in Zr 1.1733 -.0328 .1521 *From Penepma 2012 Calculations
Mo la in Ni 1.3508 -.1958 .2462 *From Penepma 2012 Calculations
Co ka in Ni .9576 .1915 -.1545 *From Penepma 2012 Calculations
Cr ka in Ni .8962 .1128 -.0173 *From Penepma 2012 Calculations
Al ka in Ni 2.1889 -.0556 -.0531 *From Penepma 2012 Calculations
Mo la in Co 1.2272 -.0143 .0215 *From Penepma 2012 Calculations
Ni ka in Co .9548 .0922 -.1215 *From Penepma 2012 Calculations
Cr ka in Co .7883 .2836 -.1428 *From Penepma 2012 Calculations
Al ka in Co 1.9230 .0005 -.0369 *From Penepma 2012 Calculations
Mo la in Cr 1.1540 -.1365 .2223 *From Penepma 2012 Calculations
Zr la in Cr 1.1903 .1192 -.1659 *From Penepma 2012 Calculations
Ni ka in Cr 1.0569 .0065 .0061 *From Penepma 2012 Calculations
Co ka in Cr 1.1110 .0367 -.0460 *From Penepma 2012 Calculations
Al ka in Cr 1.6329 -.0741 .0844 *From Penepma 2012 Calculations
Re la in Al 1.4951 -.0453 .2212 *From Penepma 2012 Calculations
W la in Al 1.4685 .3313 -.3948 *From Penepma 2012 Calculations
Ta la in Al 1.4407 .1691 -.0636 *From Penepma 2012 Calculations
Hf la in Al 1.3648 .3420 -.3919 *From Penepma 2012 Calculations
Mo la in Al 1.4925 -.0440 .0442 *From Penepma 2012 Calculations
Zr la in Al 1.6290 .0734 -.1941 *From Penepma 2012 Calculations
Ni ka in Al 1.0526 .1093 -.1075 *From Penepma 2012 Calculations
Co ka in Al 1.0875 .1570 -.1566 *From Penepma 2012 Calculations
Cr ka in Al 1.0998 .0060 .0119 *From Penepma 2012 Calculations
The remaining binaries are continuing to calculate and I will let you know when they are ready. Note that x-ray lines listed above are just defaulted, but you can run any K, L or M (alpha or beta) line (that actually exists) for these elements at any beam energy between 5 and 50 keV.
The cool thing is that when you select the Penepma derived alpha factors from the ZAF Selections dialog, the low energy lines will be corrected using whatever phi-rho-z you are currently using (for the best absorption correction), and only emission lines above 1 keV will get pulled in the from the matrix.mdb file for improved characteristic and continuum fluorescence corrections.
john
I've compiled the latest calculated Penepma binaries for matrix correction polynomial alpha factors and they are listed here as usual:
http://probesoftware.com/download/Calculated%20Alpha%20Binaries.txt
A screen shot of the 42 most recent binaries for alloy work (for Dan Ruscitto) is here:
(https://smf.probesoftware.com/oldpics/i43.tinypic.com/nmcjzs.jpg)
These are available in the latest 10.1.7 of our software.
john
Hi John,
thanks for doing this. Could you please run these for Pt-Fe binaries? I am specifically interested in the Pt M lines but also Pt La.
Hi Anette,
This has been done and should be available next time you update PFE or CalcZAF. But just for fun I decided to look at the system too...
Here's Fe and Pt (La) for a 50:50 formula:
Current Mass Absorption Coefficients From:
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Z-LINE X-RAY Z-ABSOR MAC
Pt la Pt 1.3551e+02
Pt la Fe 1.9904e+02
Fe ka Pt 3.6733e+02
Fe ka Fe 6.8270e+01
ELEMENT ABSFAC ZEDFAC FINFAC STP-POW BKS-COR F(x)e
Pt la 1.0254 6.5808 6.7481 .1400 .9213 .9752
Fe ka 1.0157 4.3900 4.4588 .2087 .9161 .9846
SAMPLE: 32767, ITERATIONS: 0, Z-BAR: 66.4272
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Pt la 1.0008 1.0000 1.1057 1.1066 1.1236 .9841 .9745 11.5630 1.2972 149.651
Fe ka 1.0640 .9873 .7973 .8375 .7091 1.1244 .9254 7.1120 2.1091 300.771
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Pt la .00000 .70255 77.745 ----- 50.000 .500 15.00
Fe ka .00000 .26573 22.255 ----- 50.000 .500 15.00
TOTAL: 100.000 ----- 100.000 1.000
As expected the only correction that stands out is the atomic number correction for Fe Ka resulting in a significant matrix correction of over 15%.
Here is Fe and Pt (Ma), again 50:50:
Current Mass Absorption Coefficients From:
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Z-LINE X-RAY Z-ABSOR MAC
Pt ma Pt 1.0992e+03
Pt ma Fe 1.5038e+03
Fe ka Pt 3.6733e+02
Fe ka Fe 6.8270e+01
ELEMENT ABSFAC ZEDFAC FINFAC STP-POW BKS-COR F(x)e
Pt ma 1.4350 5.4113 7.7651 .1162 .6290 .6969
Fe ka 1.0157 4.3900 4.4588 .2087 .9161 .9846
SAMPLE: 32767, ITERATIONS: 0, Z-BAR: 66.4272
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Pt ma 1.0057 1.0000 1.0449 1.0509 1.1323 .9229 .6929 2.1220 7.0688 1189.27
Fe ka 1.0640 .9873 .7973 .8375 .7091 1.1244 .9254 7.1120 2.1091 300.771
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Pt ma .00000 .73979 77.745 ----- 50.000 .500 15.00
Fe ka .00000 .26573 22.255 ----- 50.000 .500 15.00
TOTAL: 100.000 ----- 100.000 1.000
Somewhat surprisingly the correction for Pt Ma is actually slightly smaller than for the Pt La in this system.
Now let's see what the correction for the Penepma alpha factors are by selecting these options in the Analytical | ZAF, Phi-rho-z, Alpha Factor, Calibration Curve Selections:
(https://smf.probesoftware.com/oldpics/i39.tinypic.com/zjcu88.jpg)
Now we get the following output for the Fe and Pt (Ma) 50:50 formula:
Initializing alpha-factors...
Number of alpha-factor binaries to be calculated = 1
Calculating alpha-factor binary Pt ma in Fe
AFactorPenepmaReadMatrix: Pt ma in Fe at 40 degrees and 15 keV
Conc Kratios Alpha
99.0000 98.545616 1.46109
95.0000 93.005249 1.42895
90.0000 86.158394 1.44588
80.0000 73.629623 1.43260
60.0000 51.153011 1.43238
50.0000 41.185459 1.42804
40.0000 31.916910 1.42209
20.0000 14.974282 1.41953
10.0000 7.275982 1.41598
5.00000 3.595938 1.41101
1.00000 .720174 1.39248
AFactorPenepmaReadMatrix: Fe ka in Pt at 40 degrees and 15 keV
Conc Kratios Alpha
99.0000 99.206398 .791950
95.0000 95.924782 .807186
90.0000 91.829765 .800744
80.0000 83.113754 .812681
60.0000 65.103020 .804041
50.0000 55.469604 .802789
40.0000 45.418430 .801166
20.0000 23.979267 .792567
10.0000 12.290772 .792909
5.00000 6.256991 .788533
1.00000 1.255476 .794455
NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 15
P=1, Pt#1, C=.9900, K=.9855, Alpha=1.4611
P=2, Pt#2, C=.9500, K=.9301, Alpha=1.4290
P=3, Pt#3, C=.9000, K=.8616, Alpha=1.4459
P=4, Pt#4, C=.8000, K=.7363, Alpha=1.4326
P=5, Pt#5, C=.6000, K=.5115, Alpha=1.4324
P=6, Pt#6, C=.5000, K=.4119, Alpha=1.4280
P=7, Pt#7, C=.4000, K=.3192, Alpha=1.4221
P=8, Pt#8, C=.2000, K=.1497, Alpha=1.4195
P=9, Pt#9, C=.1000, K=.0728, Alpha=1.4160
P=10, Pt#10, C=.0500, K=.0360, Alpha=1.4110
P=11, Pt#11, C=.0100, K=.0072, Alpha=1.3925
Xray Matrix Alpha1 Alpha2 Alpha3 %MaxDev
Pt ma in Fe 1.4041 .0530 -.0113 1.07
P=1, Pt#1, C=.9900, K=.9921, Alpha=.7919
P=2, Pt#2, C=.9500, K=.9592, Alpha=.8072
P=3, Pt#3, C=.9000, K=.9183, Alpha=.8007
P=4, Pt#4, C=.8000, K=.8311, Alpha=.8127
P=5, Pt#5, C=.6000, K=.6510, Alpha=.8040
P=6, Pt#6, C=.5000, K=.5547, Alpha=.8028
P=7, Pt#7, C=.4000, K=.4542, Alpha=.8012
P=8, Pt#8, C=.2000, K=.2398, Alpha=.7926
P=9, Pt#9, C=.1000, K=.1229, Alpha=.7929
P=10, Pt#10, C=.0500, K=.0626, Alpha=.7885
P=11, Pt#11, C=.0100, K=.0126, Alpha=.7945
Xray Matrix Alpha1 Alpha2 Alpha3 %MaxDev
Fe ka in Pt .7885 .0495 -.0377 1.09
St 1 Sample 1
TakeOff = 40.0 KiloVolt = 15.0 Density = 5.000
Standard Z-bar: 66.4272
ELEM: Pt Fe
ELWT: 77.745 22.255
NRWT: 77.745 22.255
BETA: 1.0924 .8478
The "bottom line" (so to speak) are the beta factors which are equivalent to the matrix correction. Doing the same for the Fe and Pt (La) emission line we obtain the following table:
ELEM: Pt Ma Pt La Fe Ka
ELWT: 77.745 77.745 22.255
Prz 1.0509 1.1066 .8375
BETA: 1.0924 1.1004 .8478
So about a 4% difference for Pt Ma.
Note you can also run this calculation from the Secondary fluorescence window in Standard by specifying both the beam incident and boundary phases to be the same as described here:
http://smf.probesoftware.com/index.php?topic=58.0
I don't have the exact weight percent composition already calculated as PAR files, but when we do this for the Fe Pt (Ma) 20:80 mass composition we get these output to Excel (see attachments).
That is very helpful. Thank you!
We now have already calculated Penepma 2012 k-ratios for 6573 binaries:
http://probesoftware.com/download/Calculated%20Alpha%20Binaries.txt
Further Monte-Carlo calculations are proceeding...
If there is a system that you are particularly interested in and would like to know what results you can obtain from these new matrix corrections and we haven't already calculated the k-ratios for those binaries, just let us know and we will run them for you and add them to the Matrix.mdb database.
Hi John,
I have a new request. I am interested in carbon in the Fe-Ni-S system at 11kV. Would it be possible to run these as well? It is very much appreciated!
Quote from: Anette von der Handt on March 21, 2014, 11:52:54 AM
I have a new request. I am interested in carbon in the Fe-Ni-S system at 11kV. Would it be possible to run these as well? It is very much appreciated!
Yeah, I hear you. I'm still working on trying to get great light element analyses myself!
The problem for a Penepma/Penfluor Monte-Carlo approach is that these calculations for light elements are completely dominated by absorption (and chemical) effects. As our photoelastic cross section tables improve in accuracy, the absorption calculation will improve, but it will be a *long* time before we can model chemical effects from quantum principles!
Not to mention that to get good precision for these low energy lines, one must run for a long time because the interactions increase exponentially as the minimum photon/electron energy is reduced. For carbon at edge energy 283 eV (or so), this is slow going and then one is still left with dealing with the chemical effects.
Here's the approach I would take for carbon:
http://smf.probesoftware.com/index.php?topic=48.0
Why don't you describe a typical acquisition/analysis setup you are using now for carbon and show some results on standards (if you have a good Fe3C- cementite standard for example) and we can see if there anything else we can suggest...
In the meantime I will post some additional thoughts on carbon analyses in the topic linked above.
Well, the problem is that the system (Fe-Ni-S) does not or only rarely produce stable binary (or ternary) carbides (anyone has a cohenite standard to share?) beyond FeXCY. The problem I have is not so much the background positions and interferences (and APF's and...) but the matrix corrections. I played around with CalcZAF and the absorption correction when S is around is incredibly high which precludes in my opinion the use of simple iron carbides for calibration curves. I wanted to explore this system a little further to see how "robust" the current matrix corrections are. I guess then the best approach would be to try to determine empirical MAC's for our system. Otherwise, any thoughts on the validity/quality of the current MAC's for carbon?
Quote from: Anette von der Handt on March 28, 2014, 06:27:25 PM
Well, the problem is that the system (Fe-Ni-S) does not or only rarely produce stable binary (or ternary) carbides (anyone has a cohenite standard to share?) beyond FeXCY. The problem I have is not so much the background positions and interferences (and APF's and...) but the matrix corrections. I played around with CalcZAF and the absorption correction when S is around is incredibly high which precludes in my opinion the use of simple iron carbides for calibration curves. I wanted to explore this system a little further to see how "robust" the current matrix corrections are. I guess then the best approach would be to try to determine empirical MAC's for our system. Otherwise, any thoughts on the validity/quality of the current MAC's for carbon?
Hi Anette,
Wow, I had not noticed this quite nasty system previously!
Here is the output from the CalcZAF | Xray | Display MAC Emitter-Absorber Pair menu for the entry "C ka S":
MAC value for C ka in S = 47396.64 (LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV)
MAC value for C ka in S = 47940.00 (CITZMU Heinrich (1966) and Henke and Ebisu (1974))
MAC value for C ka in S = .00 (MCMASTER McMaster (LLL, 1969) (modified by Rivers))
MAC value for C ka in S = 50414.55 (MAC30 Heinrich (Fit to Goldstein tables, 1987))
MAC value for C ka in S = .00 (MACJTA Armstrong (FRAME equations, 1992))
MAC value for C ka in S = 46621.07 (FFAST Chantler (NIST v 2.1, 2005))
MAC value for C ka in S = 46621.07 (USERMAC User Defined MAC Table)
Those are very large absorption corrections indeed. Let's try a test material... you mentioned carbides so I assume you are interested in sulfur in carbides (though how would sulfur get in a carbide?). So let's make up something, say FeSC, where we assume the sulfur atom has replaced a carbon atom?
A calculation using Armstrong/Reed is shown here for starters:
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Fe ka 1.0053 1.0000 1.0781 1.0838 1.1077 .9733 .9794 7.1120 2.1091 94.5743
S ka 1.1339 .9975 .9528 1.0777 .9269 1.0279 .8211 2.4720 6.0680 719.626
C ka 9.2882 .9998 .8496 7.8889 .7765 1.0940 .0556 .2838 52.8467 23223.0
So the absorption correction for C ka in this particular composition is almost 1000% Yes, one thousand percent...
How does it fair with other absorption models? Here is PAP (original full treatment):
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Fe ka 1.0055 1.0000 1.0938 1.0998 1.1231 .9739 .9783 7.1120 2.1091 94.5743
S ka 1.1336 .9975 .9510 1.0754 .9290 1.0238 .8186 2.4720 6.0680 719.626
C ka 9.0369 .9998 .8018 7.2439 .7215 1.1112 .0541 .2838 52.8467 23223.0
So, yes, it would appear that absorption is the culprit and that means that the mass absorption coefficients (MACs) are the thing to look at as Anette suggests. So let's see what we have in the way of Empirical MACs by going to the Xray | Empirical MACs menu in CalcZAF:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/2ymepva.jpg)
So, apparently no one has measured this MAC previously...
If anyone can provide a suitable Fe carbide-sulfide I would be pleased to do some empirical determinations of the mass absorption coefficients a la Pouchou...
New Penepma Monte-Carlo binaries calculated for ultra fast matrix corrections:
06/09/2014 12:54 PM 368,435 41-73_40.txt
06/09/2014 12:54 PM 367,336 41-42_40.txt
06/09/2014 12:54 PM 365,812 41-74_40.txt
06/09/2014 12:54 PM 363,509 42-5_40.txt
06/09/2014 12:54 PM 361,811 42-11_40.txt
06/09/2014 12:53 PM 398,589 32-48_40.txt
06/09/2014 12:53 PM 398,323 32-49_40.txt
06/09/2014 12:53 PM 398,165 32-51_40.txt
06/09/2014 12:53 PM 397,931 32-47_40.txt
06/09/2014 12:53 PM 397,925 32-52_40.txt
06/09/2014 12:53 PM 397,280 32-50_40.txt
06/09/2014 12:53 PM 396,255 33-40_40.txt
06/09/2014 12:53 PM 396,057 33-36_40.txt
06/09/2014 12:53 PM 394,291 33-35_40.txt
06/09/2014 12:53 PM 393,589 33-37_40.txt
06/09/2014 12:53 PM 387,190 36-33_40.txt
06/09/2014 12:53 PM 387,166 35-33_40.txt
06/09/2014 12:53 PM 384,414 35-28_40.txt
06/09/2014 12:53 PM 382,325 37-33_40.txt
06/09/2014 12:53 PM 377,206 36-28_40.txt
06/09/2014 12:53 PM 372,527 40-90_40.txt
06/09/2014 12:53 PM 372,301 40-82_40.txt
06/09/2014 12:53 PM 370,440 41-16_40.txt
06/09/2014 12:53 PM 368,995 40-33_40.txt
06/09/2014 12:53 PM 367,922 41-15_40.txt
06/09/2014 12:53 PM 367,900 41-32_40.txt
06/09/2014 12:53 PM 364,261 42-16_40.txt
06/09/2014 12:53 PM 361,920 42-40_40.txt
06/09/2014 12:53 PM 361,640 42-23_40.txt
06/09/2014 12:53 PM 361,278 42-14_40.txt
06/09/2014 12:53 PM 361,168 42-13_40.txt
06/09/2014 12:53 PM 361,120 42-22_40.txt
06/09/2014 12:53 PM 361,058 42-15_40.txt
06/09/2014 12:53 PM 360,683 42-27_40.txt
06/09/2014 12:53 PM 360,427 42-25_40.txt
06/09/2014 12:53 PM 360,269 42-29_40.txt
06/09/2014 12:53 PM 356,695 42-24_40.txt
06/09/2014 12:53 PM 356,588 42-28_40.txt
06/09/2014 12:53 PM 354,732 42-26_40.txt
06/09/2014 12:53 PM 353,473 42-12_40.txt
06/09/2014 12:53 PM 271,174 16-47_40.txt
06/09/2014 12:53 PM 271,125 16-44_40.txt
06/09/2014 12:53 PM 271,089 16-45_40.txt
06/09/2014 12:53 PM 271,057 16-46_40.txt
06/09/2014 12:53 PM 271,040 16-42_40.txt
06/09/2014 12:53 PM 270,927 16-49_40.txt
06/09/2014 12:53 PM 270,920 16-43_40.txt
06/09/2014 12:53 PM 270,914 16-48_40.txt
06/09/2014 12:53 PM 270,767 16-51_40.txt
06/09/2014 12:53 PM 270,661 16-50_40.txt
06/09/2014 12:53 PM 270,173 16-41_40.txt
06/09/2014 12:53 PM 270,014 15-56_40.txt
06/09/2014 12:53 PM 260,828 22-90_40.txt
06/09/2014 12:53 PM 260,703 22-63_40.txt
06/09/2014 12:53 PM 258,656 22-92_40.txt
06/09/2014 12:53 PM 254,226 24-63_40.txt
06/09/2014 12:53 PM 252,136 24-56_40.txt
06/09/2014 12:53 PM 251,947 27-50_40.txt
06/09/2014 12:53 PM 251,800 27-45_40.txt
06/09/2014 12:53 PM 251,728 27-47_40.txt
06/09/2014 12:53 PM 251,391 27-90_40.txt
06/09/2014 12:53 PM 251,095 27-82_40.txt
06/09/2014 12:53 PM 250,224 27-46_40.txt
06/09/2014 12:53 PM 250,169 27-44_40.txt
06/09/2014 12:53 PM 249,952 27-49_40.txt
06/09/2014 12:53 PM 249,911 27-51_40.txt
06/09/2014 12:53 PM 249,907 27-52_40.txt
06/09/2014 12:53 PM 249,781 27-48_40.txt
06/09/2014 12:53 PM 249,082 28-90_40.txt
06/09/2014 12:53 PM 248,148 28-35_40.txt
06/09/2014 12:53 PM 247,901 28-36_40.txt
06/09/2014 12:53 PM 247,662 28-82_40.txt
06/09/2014 12:53 PM 193,911 13-90_40.txt
06/09/2014 12:53 PM 193,895 13-92_40.txt
06/09/2014 12:53 PM 193,870 13-63_40.txt
06/09/2014 12:53 PM 193,798 12-92_40.txt
06/04/2014 10:37 AM 370,493 41-40_40.txt
06/04/2014 10:37 AM 370,334 41-5_40.txt
06/04/2014 10:37 AM 368,352 41-23_40.txt
06/04/2014 10:37 AM 368,304 41-11_40.txt
06/04/2014 10:37 AM 368,165 41-26_40.txt
06/04/2014 10:37 AM 367,991 41-14_40.txt
06/04/2014 10:37 AM 367,981 41-13_40.txt
06/04/2014 10:37 AM 365,907 41-22_40.txt
06/04/2014 10:37 AM 365,783 41-24_40.txt
06/04/2014 10:37 AM 365,218 41-12_40.txt
06/04/2014 10:37 AM 365,157 41-28_40.txt
06/04/2014 10:37 AM 361,407 41-27_40.txt
06/02/2014 02:30 PM 374,394 39-32_40.txt
06/02/2014 02:30 PM 374,321 39-33_40.txt
06/02/2014 02:30 PM 373,263 40-16_40.txt
06/02/2014 02:30 PM 373,129 40-5_40.txt
06/02/2014 02:30 PM 372,688 40-42_40.txt
06/02/2014 02:30 PM 372,663 40-15_40.txt
06/02/2014 02:30 PM 370,987 40-72_40.txt
06/02/2014 02:30 PM 370,791 40-23_40.txt
06/02/2014 02:30 PM 370,680 40-24_40.txt
06/02/2014 02:30 PM 370,632 40-41_40.txt
06/02/2014 02:30 PM 370,557 40-22_40.txt
06/02/2014 02:30 PM 370,441 40-74_40.txt
06/02/2014 02:30 PM 370,319 40-73_40.txt
06/02/2014 02:30 PM 370,317 40-25_40.txt
06/02/2014 02:30 PM 370,113 40-75_40.txt
06/02/2014 02:30 PM 370,108 40-27_40.txt
06/02/2014 02:30 PM 370,105 40-12_40.txt
06/02/2014 02:30 PM 370,034 40-26_40.txt
06/02/2014 02:30 PM 369,983 39-27_40.txt
06/02/2014 02:30 PM 369,725 40-13_40.txt
06/02/2014 02:30 PM 369,686 40-28_40.txt
06/02/2014 02:30 PM 369,479 40-11_40.txt
06/02/2014 02:30 PM 369,418 40-8_40.txt
06/02/2014 02:30 PM 369,179 40-14_40.txt
06/02/2014 02:30 PM 365,469 39-38_40.txt
06/02/2014 02:30 PM 354,944 39-26_40.txt
06/02/2014 02:30 PM 371,049 40-32_40.txt
This is a very silly thing to plot, but since I haven't finished calculating all the binary pairs in the POUCHOU2.DAT kratio dataset, I thought it might be a fun thing to try in the meantime...
So here is the Pouchou dataset calculated using the default JTA (Armstrong)/Reed p/r/z :
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/kb3dp5.jpg)
As you can see, it does an excellent job with an average of 1.0085 and a variance of 0.0466 (4.6%).
Running the same calculation using the same JTA/Reed p/r/z physics, but with the k-ratios fit to three coefficient alpha factors, we see a slight degradation due to the fact that a 2nd order polynomial doesn't provide a perfect fit to these hyperbolic relationships:
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/sfe645.jpg)
But with an average of 1.009 and a variance of 0.0469 (4.6%), the results are very similar.
Now let's try the alpha factor regression again but this time replacing analytically calculated k-ratios with Penfluor/Fanal MC calculated k-ratios. Why are we doing this? Remember, if we can utilize pre-calculated MC k-ratios for alpha factors, we can essentially perform Monte-Carlo calculations for arbitrary compositions in a few seconds. Note that only a small fraction of the binaries are replaced and yet we see an improvement even over the full JTA/Reed p/r/z:
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/1zcic7q.jpg)
Where we can see an average of 1.0029 and a variance of 0.0448 (4.4%) utilizing what Penfluor/Fanal k-ratios were available. So a visible improvement using the MC derived k-ratios.
I will post further Pouchou error distributions as I obtain a more complete set of Penfluor/Fanal binaries.
A bunch of new fast Monte-Carlo derived k-ratios for alpha factors has been added to the matrix.mdb database.
Running the Pouchou2.dat dataset again gives the following results (compare to the above histogram):
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/6rt1xw.jpg)
Again, a small improvement, but still an improvement...
Quick addition: I finally also ran the full Pouchou2.dat dataset using full PAR files calculated for the actual compositions (without the use of binary alpha factors) and here is what we obtain:
AverageA .993658
StdDevA .038908
MinimumA .719737
MaximumA 1.20810
AverageB .000000
StdDevB .000000
MinimumB .000000
MaximumB .000000
Problematic k-ratio errors (< 0.8 or > 1.2)
Line ConcA ConcB t0 e0 K-Exp K-Cal K-Err
3 al ka in fe .241000 .759000 52.5000 30.0000 .083000 .065567 .789963
618 al ka in ti .398000 .602000 40.0000 40.0000 .142900 .172638 1.20810
648 au la in cu .508000 .492000 40.0000 13.0000 .417400 .300418 .719737
The above three k-ratios produce the largest errors.
Taking the last k-ratio (Au La in Cu) and running it in CalcZAF as a standard we obtain the following (with the warnings for a low overvoltage situation):
Sample 1
Warning: Overvoltage of Au la, edge energy 11.918 KeV, is 1.090787
Warning: Overvoltage of Au la is only 1.090787
Warning: Overvoltage of Au la, edge energy 11.918 KeV, is 1.090787
Warning: Overvoltage of Au la is only 1.090787
Current Mass Absorption Coefficients From:
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Z-LINE X-RAY Z-ABSOR MAC
Au la Au 1.3232e+02
Au la Cu 2.3420e+02
Cu ka Au 2.1412e+02
Cu ka Cu 5.0035e+01
ELEMENT ABSFAC ZEDFAC FINFAC STP-POW BKS-COR F(x)e
Au la 1.0119 7.1804 7.2660 .1369 .9827 .9882
Cu ka 1.0071 4.7798 4.8137 .1994 .9531 .9930
SAMPLE: 32767, ITERATIONS: 0, Z-BAR: 54.4
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Au la 1.0027 1.0000 1.2378 1.2412 1.2455 .9938 .9855 11.9180 1.0908 182.447
Cu ka 1.0133 .9921 .8513 .8558 .8235 1.0337 .9799 8.9790 1.4478 133.391
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Au la .00000 .40929 50.800 ----- 24.987 .250 13.00
Cu ka .00000 .57491 49.200 ----- 75.013 .750 13.00
TOTAL: 100.000 ----- 100.000 1.000
Note also the very large atomic number correction.
Latest version of the matrix.mdb file contains a large number of new binaries.
197K k-ratios for 1562 binary pairs.
Here is the error histogram plotted for the full Pouchou2.dat dataset using specific compositions calculated using Penfluor/Fanal (Penepma for primary intensities and Fanal for analytical fluorescence):
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/1omvzd.jpg)
Quite good really, but lets look closer at a few of the outliers by plotting k-ratio error as a function of concentration as seen here (the data labels are the line numbers in the first column in the Pouchou2.dat file):
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/eqcleb.jpg)
As one can see, many of these are at very high overvoltages where the absorption correction is very large, except for the Au La measurement at 13 keV which is a low overvoltage measurement.
For comparison with the analytical phi-rho-z calculations here is the same plot using the default phi-rho-z in CalcZAF:
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/2q89et3.jpg)
The Pouchou2.dat file is included with your CalcZAF.msi installation, but I attach it below for convenience.
For comparison, results using the full-blown PENEPMA.
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/aln293.jpg)
The points in red are those highlighted by Probeman in the PENFLUOR/FANAL graph. Note that the limits of the y-axis are different.
Edit by John: This is excellent! Would it be possible to re-plot the data with the same axes as the others? Which version of Penepma was utilized? Do you see a difference between say Penepma 2008 and 2012?
Same scaling.
(https://smf.probesoftware.com/oldpics/i62.tinypic.com/2ch7rlc.jpg)
The results are from PENEPMA/PENELOPE 2011. The simulations were run until an relative uncertainty of 1% was obtained for the x-ray line of interest. The detector was centered as the specified take-off angle and had an opening of +- 9 deg.
Hi Philippe,
I am surprised that there is so much difference between the Penfluor/Fanal and Penepema results given that the main difference between them is the treatment of fluorescence (Fanal does the fluorescence analytically).
I've got a back burner project to start calculating k-ratios for alpha factors from the full Penepma, but now it's going to get more attention...
Ok, here's another thing I realize after some thinking: if I compare the two graphs directly:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/23mr8ms.jpg)
and
(https://smf.probesoftware.com/oldpics/i59.tinypic.com/9jj3ud.jpg)
it appears to me that the high concentrations errors are more similar and that the Penfluor errors increase as the concentrations are lower. Since the default in Penfluor is to only calculate 3600 sec for each voltage this could mean that the Penfluor k-ratios used to calculate the alpha-factors are of insufficient precision.
I am going to do some comparisons with the full blown Penepma and check this idea...
No, it wasn't a precision issue after all. Instead I found a silly mistake with the formatting of the takeoff angle in the Fanal input file! Re-extracting the data using Fanal provides significantly improved error distributions and many of the remaining outliers seem to be highly fluorescent systems- see updated graphs above.
Edit by John: it could be the low overvoltage situations (Au La) may be precision related- I will check that as well.
A new Matrix.mdb database has been released for CalcZAF and Probe for EPMA which includes some light element binaries (many more coming soon) and newly recalculated k-ratios with double precision pure element standards for improved calculations.
To see what binaries are currently available please see the following link:
http://probesoftware.com/download/Calculated%20Matrix%20Binaries.txt
I would be very pleased if you have any experimental data comparing these new fast Monte-Carlo alpha factors with traditional analytical calculations.
OK, I've recalculated the Pouchou binaries using Penfluor/Fanal (without B Ka just as Philippe did above) and here is what I get now:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/14uf50l.jpg)
As you can see the outliers are now all very low overvoltage situations. This is because I used the default 3600 seconds per beam energy to obtain the intensities and at very low overvoltages the precision is insufficient under these circumstances. But this is very promising compared to the analytical codes in CalcZAF.
The advantage of the Penfluor code is that once you have a composition, you can extract multiple elements, x-rays at different takeoff angles and beam energies in seconds. Because these intensities will be used to calculate k-ratios for alpha factors for matrix corrections for arbitrary compositions within the binary one cannot specify the precision in advance, as one can with Philippe's Penepma runs shown above.
Next I will compare to a 7200 sec per beam energy calculation to see how that improves the precision for these low overvoltage situations. Meanwhile the Monte-Carlo modeling continues...
The latest version of CalcZAF (and Probe for EPMA) now contain an updated matrix.mdb k-ratio database for over 2000 binaries at beam energies between 1 and 50 keV for a total of over 229,000 k-ratios. That's about half the periodic table calculated at normal precision using the Penepma (Penfluor/Fanal) code.
Most of the new additions are for REEs and actinide elements.
For a list of the binaries already calculated see this link:
http://probesoftware.com/download/Calculated%20Matrix%20Binaries.txt
Oh, and there are a significant number of new light element binaries for carbon, nitrogen, etc. Please remember that while these light element matrix corrections are well modeled, they do not include chemical bonding effects which affect peak shape and position. For these chemical bonding effects, area peak factor (APF) corrections are still required as discussed here:
http://smf.probesoftware.com/index.php?topic=248.msg1186#msg1186
To compare the difference between the default precision Penfluor/Fanal calculation with higher precision calculations see the graphs below of the Ag, Cu, Au alloy measurements in the Pouchou2.dat (without the Cu La measurements). That gives us 232 measurements to compare, and the nice thing about this system is that there are all sorts of physics here, high absorption and large fluorescences.
First here is the original CalcZAF (Armstrong/Reed) calculation without beta fluorescence for reference:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/15pj0co.jpg)
This can be compared to the new CalcZAF fluorescence code with beta lines fluorescence seen here:
http://smf.probesoftware.com/index.php?topic=490.msg2710#msg2710
Now here are the same measurements, but calculated using Penfluor/Fanal derived k-ratio alpha factors using the default precision (3600 sec per beam energy). All k-ratios for 11 compositions in each binary all precalculated in advance:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/97jzft.jpg)
The high side outlier is a low overvoltage situation.
Now here are the same data, but this time using "high precision" Penfluor k-ratios (7200 sec per beam energy):
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/2uzf68k.jpg)
Similar, but note that the variance is improved considerably over the default precision calculations (much smaller). And the low overvoltage outlier is no longer visible!
In fact these 7200 sec k-ratios fitted to alpha factors compares quite well to the full Penfluor/Fanal calculations on the specific Ag, Cu, Au conditions and compositions in the Pouchou2 database as seen here:
AverageA .995590
StdDevA .026136
MinimumA .881889
MaximumA 1.12403
The work continues...
I'm looking to further test the Penepma derived k-ratio alpha factor matrix corrections for extreme fluorescence situations.
The Pouchou binary k-ratio database was apparently selected to avoid large fluorescence situations and mainly test the Z and A terms in the matrix corrections at that time.
But if anyone has a high quality set of measurements on stainless steel or high alloy steel standard materials and they would be willing to share it, I would be very interested in obtaining such a database for testing these Monte-Carlo characteristic (and continuum) fluorescence matrix corrections. The elements of interest would be Fe, Ni, Cr, Co, W, Nb, etc, etc...
I have recently improved the handling of Penepma Monte-Carlo derived k-ratios for alpha factor matrix corrections to show whether the binary is question has already been calculated and loaded or not (if not, the calculation falls through to the current phi-rho-z method to analytically calculate the missing k-ratios).
This is can seen in the following output from CalcZAF. Normally, the binary has been loaded from the Penepma matrix.mdb database (or not,) in both emitter-matrix directions, for example as seen here:
NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 20
P=1, C=.9900, K=.9883, Alpha=1.1735
P=2, C=.9500, K=.9416, Alpha=1.1793
P=3, C=.9000, K=.8753, Alpha=1.2822
P=4, C=.8000, K=.7586, Alpha=1.2729
P=5, C=.6000, K=.5420, Alpha=1.2675
P=6, C=.5000, K=.4421, Alpha=1.2620
P=7, C=.4000, K=.3467, Alpha=1.2563
P=8, C=.2000, K=.1668, Alpha=1.2485
P=9, C=.1000, K=.0818, Alpha=1.2475
P=10, C=.0500, K=.0405, Alpha=1.2461
P=11, C=.0100, K=.0080, Alpha=1.2505
Xray Matrix Alpha1 Alpha2 Alpha3 Alpha4 %AvgDev *from Penepma 2012 Calculations
pr la in p 4.6916 3.1333 2.6693 -3.4302 1.49763
P=1, C=.0100, K=.0048, Alpha=2.1103
P=2, C=.0500, K=.0245, Alpha=2.0975
P=3, C=.9000, K=.8059, Alpha=2.1672
P=4, C=.8000, K=.6481, Alpha=2.1724
P=5, C=.6000, K=.4089, Alpha=2.1688
P=6, C=.5000, K=.3160, Alpha=2.1645
P=7, C=.4000, K=.2360, Alpha=2.1576
P=8, C=.2000, K=.1053, Alpha=2.1252
P=9, C=.1000, K=.0501, Alpha=2.1059
P=10, C=.0500, K=.0245, Alpha=2.0952
P=11, C=.0100, K=.0048, Alpha=2.0868
Xray Matrix Alpha1 Alpha2 Alpha3 Alpha4 %AvgDev *from Penepma 2012 Calculations
p ka in pr 2.6245 .6932 .2787 -.5319 .295767
In this example one element binary (emitting element and matrix element) are found in the matrix.mdb database, but the other binary is not:
NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 15
P=1, C=.9900, K=.9889, Alpha=1.1146
P=2, C=.9500, K=.9440, Alpha=1.1280
P=3, C=.9000, K=.8877, Alpha=1.1389
P=4, C=.8000, K=.7765, Alpha=1.1511
P=5, C=.6000, K=.5636, Alpha=1.1615
P=6, C=.5000, K=.4621, Alpha=1.1641
P=7, C=.4000, K=.3638, Alpha=1.1660
P=8, C=.2000, K=.1762, Alpha=1.1686
P=9, C=.1000, K=.0868, Alpha=1.1696
P=10, C=.0500, K=.0430, Alpha=1.1700
P=11, C=.0100, K=.0086, Alpha=1.1703
Xray Matrix Alpha1 Alpha2 Alpha3 Alpha4 %AvgDev
Rb la in c 1.8420 .6163 .4769 -.6695 .159128
P=1, C=.0100, K=.0009, Alpha=11.3800
P=2, C=.0500, K=.0046, Alpha=11.4613
P=3, C=.9000, K=.5033, Alpha=8.8820
P=4, C=.8000, K=.3013, Alpha=9.2778
P=5, C=.6000, K=.1342, Alpha=9.6748
P=6, C=.5000, K=.0932, Alpha=9.7260
P=7, C=.4000, K=.0646, Alpha=9.6565
P=8, C=.2000, K=.0259, Alpha=9.3892
P=9, C=.1000, K=.0120, Alpha=9.1567
P=10, C=.0500, K=.0058, Alpha=9.0326
P=11, C=.0100, K=.0011, Alpha=8.9032
Xray Matrix Alpha1 Alpha2 Alpha3 Alpha4 %AvgDev *from Penepma 2012 Calculations
c ka in Rb 69.4274 51.9633 47.0268-59.1578 8.38180
This is merely a sanity check comparing the fit error from using polynomial (3 coefficient) and non-linear (4 coefficient) alpha factors for the Pouchou Au, Cu, Ag dataset with the actual calculated k-ratios from Penepma (Penfluor/Fanal).
As you can see, both fit methods look excellent, the non-linear fit is slightly closer to 1.000 (no error) and has a slightly worse deviation, than the polynomial fit alpha factors.
The reason why the comparison is not exactly always equal to one, is due to limitations of precision in the Monte Carlo calculations, so there will be always be some small amount of variance in the fit (see image attachments below). But, here is where it gets interesting: because the fit is essentially regressing the "noise" it should provide a *more accurate* calculation than just using a single Monte Carlo calculation!
Interesting that the alpha factor magnitudes are similar but the slopes are different!
I been making progress on utilizing Penepma Monte-Carlo derived k-ratios for fast matrix corrections in CalcZAF (and Probe for EPMA and CalcImage), and can show some new results (with newly extracted k-ratios with self-consistent precision levels) starting with the Au, Cu, Ag binary systems in the Pouchou k-ratio database.
First Au, Cu and Ag binaries calculated at 3600 per keV (x10) times 11 binary compositions (from 1 to 99%) or 110 hours per binary system:
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/27x1d07.jpg)
Note that while the preliminary Monte Carlo calculations take a long time, the actual matrix correction runs in seconds, quite comparable to the traditional analytical expressions we all use every day. Next here are the same Au, Cu and Ag binaries but calculated to a significantly higher precision at 14400 sec/keV (x10) times 11 binary compositions or 440 hours per binary system:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/4j24vs.jpg)
Note that the higher precision calculation gives both a better error average (closer to 1.000) and has a smaller variance. This is mostly due to several very low overvoltage situations in the Pouchou database. Note: as we attempt even lower overvoltage measurements on FEG instruments to reduce our interaction volumes these, very low overvoltage calculations become much more critical.
But the good news is that already we are already getting better accuracy with the above fast Monte-Carlo k-ratios compared to the traditional analytical expressions. For comparison check the same binary compositions calculated using the JTA/Reed phi-rho-z, first without beta line fluorescence:
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/23lxx0h.jpg)
and now with the beta fluorescence:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/2dkjte1.jpg)
The average error calculation with beta fluorescence is slightly higher than without beta lines (as one would expect), but the variance is improved (smaller) by including beta lines. I will have more on this, as I am still adjusting the relative line weights in the Reed fluorescence correction for more exotic fluorescence situations...
I've updated the matrix.mdb file for many new binaries. In fact most (though not all) of the binary systems in the Pouchou database have been calculated. For example, I have not yet extracted k-ratios for 75 degree takeoff angles yet!
But enough binaries have been calculated that it's worth comparing to traditional analytical physics expression accuracy. Both calculations below were done using the Pouchou database *without* B Ka and Cu La (there are bigger analytical issues with these emission lines!).
First here is the JTA phi-rho-z with beta fluorescence:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/123rvhl.jpg)
A decent average error of 1.01 and a variance of around 4.5%. Now let's try the Penepma derived fast Monte-Carlo k-ratios fitted using polynomial alpha factors.
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/1zdmzhx.jpg)
As you can see, an even better average error and the variance has decreased to around 3.4%! I believe the era of fast Monte-Carlo has arrived...
Pretty impressive!
Quote from: Mike Jercinovic on July 17, 2015, 06:21:03 AM
Pretty impressive!
Thanks, Mike!
Here are some additional thoughts on this new "fast Monte-Carlo" method:
I should mention at the outset that matrix k-ratios utilized for this method, can be derived from *any* Monte-Carlo program. One only needs to calculate k-ratios for a range of composition for each binary (for each takeoff-angle, each beam energy and each emitting x-ray). I have chosen to utilize these compositions for each emitting binary (that is what is in the matrix.mdb file):
1 : 99, 5 : 95, 10 : 90, 20 : 80, 40 : 60, 50 : 50, 60 : 40, 80 : 20, 90 : 10, 95 : 5, 99 : 1
For the k-ratio extractions I've mostly performed 40 degree takeoff angle calculations (and some 52.5 and 75 degree geometries for comparison to the empirical Pouchou k-ratio database) and beam energies from 1 to 50 keV in 1 keV steps. Note Penfluor only calculates down to 5 keV by default so I should probably not scan in k-ratios for beam energies below 5 keV into the matrix.mdb database (note to self). Though of course we can utilize k-ratios calculated for any instrument/beam condition of interest.
This means that *any* MC program can be utilized for these k-ratio calculations though currently I use Penepma (Penfluor) and Fanal for my k-ratios because it is MC based for the primary and continuum intensities, though the fluorescence calculation is analytical. One aspect to these MC calculations is that because one does not know the actual composition in advance (after all this is for matrix correction of arbitrary measured unknowns), the k-ratio calculation must be run to an arbitrary precision. This is mostly an issue for very weak emission lines and/or low over voltage situations.
Currently I am Running Penepma (Penfluor) for 3600 sec for each of the 10 beam energies for each binary composition. That is then 10 hours times 11 compositions or 110 hours per binary. The nice thing about using Penfluor is that once one has the Penfluor .PAR file for a specific composition, one can then "extract" k-ratios for *any* takeoff angle, for *any* beam energy (up to 50 keV), for any emitting line. In addition, because 11 compositions are being regressed to the alpha vs. concentration fit for each binary, statistical noise is actually reduced compared to single composition calculations as seen here:
http://smf.probesoftware.com/index.php?topic=47.msg3019#msg3019
In any event, because the MC k-ratio calculations occur off-line on one's MC servers, the speed of the MC program performing the k-ratio calculations isn't as important as the *accuracy*. That is because once the k-ratios are pre-calculated to some arbitrary precision, they can be utilized in the matrix iteration by use of the alpha and beta expressions described here:
http://epmalab.uoregon.edu/bence.htm
for arbitrary compositions!
The situation today reminds me of the early days of microanalysis when everyone was trying to implement analytical expressions for electron-solid physics on computers that were simply too slow to handle a full blown treatment of all the parameters. That is why approximations were introduced into these early analytical expressions (with the possible exception of COR from NIST). More recently some investigators have modified these traditional codes to make them more rigorous (John Armstrong comes to mind).
However, now that computers today are so much faster, we can perform even more rigorous treatments of the physics in analytical expressions and some investigators (Hendrix Demers and Nicholas Ritchie are two that come to mind) have done just that.
But... computers today are *still too slow* for on-line Monte Carlo calculation of matrix corrections. And that is why I am proposing that we perform these time consuming binary k-ratio calculations for the periodic table off-line (to arbitrary precision) and save the k-ratios for a range of composition for each binary and then utilize these k-ratios on-line in alpha expressions for high accuracy MC matrix corrections of arbitrary compositions.
In other words, there is no more need to "optimize" MC calculations for speed since we now have a way to utilize them for *fast* on-line matrix corrections. Instead we should be solely concentrating on creating the most *accurate* MC programs for electron-solid physics...
Let's not compromise the physics for speed as was done 20 years ago because of computer technology limitations.
And it just keeps getting better and better...
This is a error distribution from the Pouchou database (without B ka and Cu la) now with the 52.5 degree k-ratios included.
(https://smf.probesoftware.com/oldpics/i62.tinypic.com/2nuirna.jpg)
As you can see it is even better than before (smaller variance). I should also point out that a significant portion of the above variance is due to two low over voltage binaries as seen here:
Problematic k-ratio errors (< 0.8 or > 1.2)
Line ConcA ConcB TOA eO Uo K-Exp K-Cal K-Err
715 Cu ka in Ni .565000 .435000 40.0000 10.1000 1.12485 .558000 .719701 1.28979
722 Cu kb in Ni .565000 .435000 40.0000 10.2000 1.13598 .549400 .719902 1.31034
But this can be improved from increasing the modeling time from 3600 to 7200 sec per keV. See the last error plot in this post calculated at 7200 sec:
http://smf.probesoftware.com/index.php?topic=47.msg2680#msg2680
By the way, the entire Pouchou database was calculated in about the same time as using Phi-rho-z, so yes, it is fast.
This version of the matrix.mdb database will be distributed in v. 10.9.6 of CalcZAF (and Probe for EPMA).
Hi John,
Very interesting results.
However, I don't completely agree with your statement "there is no more need to "optimize" MC calculations for speed". I think we need both: accurate MC and sometime we need very fast MC. Outside the microanalysis world, we use MC to simulate imaging conditions and detector and still the MC are too slow (especially for SE micrograph). Event for x-ray microanalysis, most our sample now have feature size less than 50-10 nm and we need to be able to simulate different geometry "quickly".
But I agree we need the most accurate MC programs for electron-solid physics as we need to able to validate with a good reference other MC programs or analytical models.
Regards,
Hendrix
Quote from: hdemers on July 21, 2015, 11:57:32 AM
However, I don't completely agree with your statement "there is no more need to "optimize" MC calculations for speed". I think we need both: accurate MC and sometime we need very fast MC. Outside the microanalysis world, we use MC to simulate imaging conditions and detector and still the MC are too slow (especially for SE micrograph). Event for x-ray microanalysis, most our sample now have feature size less than 50-10 nm and we need to be able to simulate different geometry "quickly".
Hi Hendrix,
Ok, I'll rephrase the statement to this: "there is no more need to optimize MC calculations for speed in order to perform quantitative matrix corrections on arbitrary compositions". Does that work for you?
I agree with you that we also need to perform full arbitrary geometry calculations and that will require a fast MC (and/or much faster computers).
My point was mainly that I don't want us to sacrifice MC accuracy for speed as was done 20 and 30 years ago with the analytical expression modeling approximations.
On a related note, Xavier once said to me: why don't you implement a fully rigorous fundamental parameters matrix correction in your software. And I replied: give me the equations and I'll do it! I even have a place holder for it in the software already:
(https://smf.probesoftware.com/oldpics/i61.tinypic.com/ws0krs.jpg)
As soon as you guys send me the code I'll implement it with full attribution!
john
Hi John
Quote from: Probeman on July 21, 2015, 12:31:54 PM
Ok, I'll rephrase the statement to this: "there is no more need to optimize MC calculations for speed in order to perform quantitative matrix corrections on arbitrary compositions". Does that work for you?
OK for me
Quote from: Probeman on July 21, 2015, 12:31:54 PM
On a related note, Xavier once said to me: why don't you implement a fully rigorous fundamental parameters matrix correction in your software. And I replied: give me the equations and I'll do it! I even have a place holder for it in the software already:
As soon as you guys send me the code I'll implement it with full attribution!
Interesting idea, you just need to solve the electron transport equation in the sample and calculate the x-ray generation from the electron distribution (energy and position) to get the phirhoz curve. The work of Rex and Dapor should be a good starting point.
Regards,
Hendrix
Quote from: hdemers on July 22, 2015, 03:23:15 PM
Quote from: Probeman on July 21, 2015, 12:31:54 PM
On a related note, Xavier once said to me: why don't you implement a fully rigorous fundamental parameters matrix correction in your software. And I replied: give me the equations and I'll do it! I even have a place holder for it in the software already:
As soon as you guys send me the code I'll implement it with full attribution!
Interesting idea, you just need to solve the electron transport equation in the sample and calculate the x-ray generation from the electron distribution (energy and position) to get the phirhoz curve. The work of Rex and Dapor should be a good starting point.
That sounds simple... not! :-\
In any event here is the Pouchou database re-calculated with some 75 degree k-ratios extracted and added to the matrix.mdb file:
(https://smf.probesoftware.com/oldpics/i60.tinypic.com/2ir12qx.jpg)
Basically the same results, just very slightly worse in the 4th or 5th decimal place. Again the main problem here are the low over voltage Cu Kb in Ni measurements as noted in the image above. I will be adding higher precision MC calculations to the matrix.mdb file shortly which will take care of this for many elements.
I am pleased to report that after re-calculating the Ni-Cu binary at 7200 sec per beam energy (20 hours per binary for 11 binary compositions or 220 hours), the Pouchou database calculated errors from using the Penfluor/Fanal derived k-ratio for alpha factor fits looks even better (error variance down to 2.9 % compared to 3.2 % from the previous post above), as seen here:
(https://smf.probesoftware.com/oldpics/i57.tinypic.com/bg7ktt.jpg)
This new matrix k-ratio database will be folded into the main CalcZAF/PFE release this weekend.
Edit by John: well it came together faster than I thought. The current release of CalcZAF or Probe for EPMA now has the matrix.mdb file used to produce the Pouchou database error distribution in the above post.
In case anyone is wondering (because I have an assortment of different kratios with different precisions), I always contruct the release matrix.mdb in the following fashion:
1. Copy the default precision files, then the high precision files, then the very high precision files (which are only CuAuAg binaries at the moment), so the higher precision calculations overwrite the lower precision calculations.
2. I then do the same for the files where the minimum energy was limited to 1 keV. These files are best for calculating matrix corrections for emitters absorbed by low Z elements where a low minimum energy calculation would provide insufficient precision for high energy emission line matrix corrections.
The latest matrix.mdb penepma k-ratio database is available here:
http://probesoftware.com/download/Matrix.mdb
Over 266K binary k-ratios.
john
I'm uploading the latest matrix.mdb now (which comes with the last version of PFE v. 11.05, though you'll need to re-run the latest CalcZAF.msi installer to get it).
This version contains a number of new binaries, particularly for actinide elements, e.g., oxygen in U, Np and Pu.
Sounds cool. Let me know what I can do to provide some experimental data.
Quote from: Philipp Poeml on September 17, 2015, 04:16:19 AM
Sounds cool. Let me know what I can do to provide some experimental data.
Can you post some beam conditions (keV) and k-ratios here?
And of course also post what the actual concentrations are... based on, what?
The latest "fast" Monte-Carlo matrix.mdb file now contains many of the actinide binaries as seen here:
07/15/2015 11:59 AM 116,568 84-85_40.txt
07/15/2015 11:59 AM 116,671 84-86_40.txt
07/15/2015 11:59 AM 116,513 84-87_40.txt
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08/12/2015 04:54 PM 197,472 92-15_40.txt
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08/12/2015 04:54 PM 193,668 92-33_40.txt
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166 File(s) 26,862,286 bytes
I've recently updated the matrix.mdb file for fast Monte-Carlo matrix corrections. The new binaries include additional light elements, actinides and rare-earth binaries, particularly Ce, La, P, U, Th and Pb.
See the link here for a list:
http://probesoftware.com/download/Calculated%20Matrix%20Binaries.txt
Again here is a comparison of a monazite composition with traditional phi-rho-z:
Un 11 Montel Madagascar 4-1, Results in Elemental Weight Percents
ELEM: Ca Si Al Y Pr Nd Sm Gd Ce La P U Pb Th Dy Er O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL CALC
BGDS: LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN
TIME: 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 20.00 20.00 20.00 240.00 240.00 240.00 80.00 80.00 ---
BEAM: 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 ---
ELEM: Ca Si Al Y Pr Nd Sm Gd Ce La P U Pb Th Dy Er O SUM
183 .550 1.078 .010 .071 2.525 8.165 .811 .381 24.575 12.188 11.662 .097 .252 11.320 .039 .004 26.428 100.157
184 .550 1.105 .010 .068 2.535 8.119 .806 .374 24.392 12.079 11.445 .108 .238 11.385 .050 .008 26.131 99.404
185 .537 1.131 .010 .091 2.440 8.067 .820 .386 24.441 11.911 11.544 .114 .249 11.713 .052 .003 26.294 99.802
AVER: .546 1.105 .010 .077 2.500 8.117 .812 .381 24.470 12.059 11.550 .106 .246 11.473 .047 .005 26.284 99.788
SDEV: .007 .027 .000 .012 .052 .049 .007 .006 .095 .140 .109 .008 .008 .210 .007 .003 .149 .377
SERR: .004 .015 .000 .007 .030 .028 .004 .003 .055 .081 .063 .005 .004 .122 .004 .002 .086
%RSD: 1.33 2.42 1.17 15.97 2.10 .60 .83 1.55 .39 1.16 .94 7.98 3.06 1.83 15.54 52.36 .57
STDS: 305 305 305 1016 1010 1009 1011 1005 1001 1007 1001 15 17 16 1002 1003 ---
STKF: .0862 .1608 .1137 .4593 .5438 .5479 .5534 .5556 .5348 .5384 .0783 .8994 .7907 .7095 .5626 .5656 ---
STCT: 122.89 443.60 303.18 42.38 58.63 69.20 90.67 109.30 47.53 40.77 30.38 214.22 199.42 136.30 125.91 139.67 ---
UNKF: .0051 .0057 .0000 .0005 .0226 .0732 .0072 .0032 .2188 .1072 .0701 .0010 .0019 .1026 .0004 .0000 ---
UNCT: 7.29 15.61 .10 .04 2.44 9.24 1.17 .62 19.45 8.12 27.19 .23 .47 19.71 .08 .01 ---
UNBG: 2.10 2.91 1.68 .23 .54 .69 .87 .96 .49 .39 .27 1.36 .68 1.06 1.20 1.47 ---
ZCOR: 1.0668 1.9521 2.5987 1.5967 1.1047 1.1093 1.1340 1.2080 1.1182 1.1251 1.6481 1.0858 1.3164 1.1182 1.2381 1.2413 ---
KRAW: .0593 .0352 .0003 .0010 .0416 .1336 .0129 .0057 .4092 .1991 .8950 .0011 .0024 .1446 .0007 .0001 ---
PKBG: 4.47 6.36 1.06 1.19 5.52 14.34 2.35 1.65 40.45 22.03 101.47 1.17 1.70 19.66 1.07 1.01 ---
INT%: .00 -4.29 -.03 ---- -24.42 -.90 -18.24 -83.12 ---- -.16 ---- -55.80 -.53 ---- -52.11 -44.11 ---
and the same composition with the latest matrix.mdb fast Monte-Carlo binaries:
Un 11 Montel Madagascar 4-1, Results in Elemental Weight Percents
ELEM: Ca Si Al Y Pr Nd Sm Gd Ce La P U Pb Th Dy Er O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL ANAL CALC
BGDS: LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN LIN
TIME: 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 20.00 20.00 20.00 240.00 240.00 240.00 80.00 80.00 ---
BEAM: 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 149.50 ---
ELEM: Ca Si Al Y Pr Nd Sm Gd Ce La P U Pb Th Dy Er O SUM
183 .547 .996 .009 .068 2.540 8.176 .814 .399 24.405 12.055 11.415 .105 .264 11.526 .038 .004 25.997 99.357
184 .546 1.021 .009 .065 2.550 8.130 .809 .392 24.221 11.946 11.200 .117 .249 11.590 .049 .008 25.700 98.601
185 .534 1.045 .009 .087 2.455 8.079 .822 .404 24.265 11.776 11.295 .123 .260 11.924 .051 .003 25.856 98.987
AVER: .542 1.020 .009 .073 2.515 8.128 .815 .398 24.297 11.926 11.303 .115 .258 11.680 .046 .005 25.851 98.982
SDEV: .007 .025 .000 .012 .052 .049 .007 .006 .096 .141 .108 .009 .008 .214 .007 .003 .149 .378
SERR: .004 .014 .000 .007 .030 .028 .004 .003 .056 .081 .062 .005 .005 .124 .004 .002 .086
%RSD: 1.35 2.40 1.18 15.95 2.08 .60 .84 1.52 .40 1.18 .95 7.97 3.07 1.83 15.86 52.38 .57
STDS: 305 305 305 1016 1010 1009 1011 1005 1001 1007 1001 15 17 16 1002 1003 ---
STBE: 1.1015 1.6109 1.5555 1.0815 1.1033 1.1045 1.1121 1.1192 1.1052 1.1074 1.7178 1.0285 1.0041 1.0602 1.1277 1.1331 ---
STCT: 122.89 443.60 303.18 42.38 58.63 69.20 90.67 109.30 47.53 40.77 30.38 214.22 199.42 136.30 125.91 139.67 ---
UNBE: 1.0523 1.9534 2.5985 1.5694 1.1233 1.1249 1.1499 1.2111 1.1264 1.1310 1.6553 1.2332 1.4100 1.1961 1.2438 1.2452 ---
UNCT: 7.29 15.59 .10 .04 2.45 9.24 1.18 .65 19.45 8.12 27.19 .23 .47 19.71 .08 .01 ---
UNBG: 2.10 2.91 1.68 .23 .54 .69 .87 .96 .49 .39 .27 1.36 .68 1.06 1.20 1.47 ---
KRAW: .0593 .0351 .0003 .0010 .0418 .1336 .0130 .0059 .4092 .1991 .8950 .0011 .0024 .1446 .0007 .0001 ---
PKBG: 4.47 6.35 1.06 1.19 5.54 14.34 2.36 1.68 40.45 22.03 101.47 1.17 1.70 19.66 1.07 1.01 ---
INT%: .00 -4.43 -.03 ---- -24.06 -.89 -18.07 -82.33 ---- -.17 ---- -55.73 -.53 ---- -53.13 -44.13 ---
Scroll to the bottom of each "code" window to compare. It would be interesting for someone to calculate the differences in the U-Th-Pb "chemical dating" results between the two matrix corrections...
Quote from: Probeman on October 25, 2015, 10:18:16 AM
I've recently updated the matrix.mdb file for fast Monte-Carlo matrix corrections. The new binaries include additional light elements, actinides and rare-earth binaries, particularly Ce, La, P, U, Th and Pb.
I should add that I have one or two Monte-Carlo servers that could be pressed into service for some additional particular binaries or compositions that haven't yet been calculated...
Suggestions?
Julien Allaz asked me to calculate the Ti-Pt binary using Penepma (Penfluor/Fanal) and I've finished part of the calculation (Ti Ka in Pt)... here are the results:
Ti Ka in Pt calculated using the default Phi-rho-z from Armstrong/Love Scott/Reed with non-linear alpha factors:
(https://smf.probesoftware.com/oldpics/i63.tinypic.com/29ct8p3.jpg)
and here is the same binary, but using Penepma derived k-ratios:
(https://smf.probesoftware.com/oldpics/i65.tinypic.com/29mavkh.jpg)
Interesting that both both methods give about the same absolute correction, a small fluorescence correction, but with opposite slopes! However, it should be pointed out that the different analytical methods don't agree very much either, and they are shown here all using the same fluorescence correction!
(https://smf.probesoftware.com/oldpics/i68.tinypic.com/16bawex.jpg)
Most surprising to me is that the old Heinrich method appears to yield the best agreement with the Penepma Monte-Carlo method! Luck or skill?
Although oxygen is not a major constituent of Julien's Ti-Pt alloy, I thought I would also compare O in Ti and O in Pt for fun. Here is O Ka in Ti using the default Armstrong/Love-Scott/Reed corrections for calculating alpha factors:
(https://smf.probesoftware.com/oldpics/i65.tinypic.com/2801p3n.jpg)
Now here is the same binary using Penepma Monte-Carlo derived k-ratios:
(https://smf.probesoftware.com/oldpics/i66.tinypic.com/30jmohc.jpg)
Considering the magnitude of the matrix correction (very large MAC), they are is rough agreement. Now for O in Pt, again using the default Armstrong/Love-Scott/Reed corrections for calculating alpha factors:
(https://smf.probesoftware.com/oldpics/i68.tinypic.com/5due51.jpg)
and again using Penepma Monte-Carlo derived k-ratios:
(https://smf.probesoftware.com/oldpics/i66.tinypic.com/20qnwy1.jpg)
All in all, in basic agreement...
Although nitrogen is also not a significant component of Julien's Ti-Pt system, I decided to look at the N-Ti binary out of curiosity because as some of you may know, there is a nasty absorption edge there that produces a significant matrix correction (not to mention a nasty spectral interference). Unfortunately the matrix correction (and interference correction) is quite dependent on the chemical state if the Ti atom because it's a Ti L series interference and the M shell is involved in the chemical bonding state. But aside from all that this binary system display an interesting Monte-Carlo statistical issue that is worth mentioning.
Here is the N-Ti using the default Armatring/LogveScott/Reed analytical matrix corrections:
(https://smf.probesoftware.com/oldpics/i67.tinypic.com/30xk0nb.jpg)
It looks pretty reasonable. Now here is the same binary calculated using fast Monte-Carlo k-ratios from Penfluor/Fanal (matrix.mdb):
(https://smf.probesoftware.com/oldpics/i66.tinypic.com/259g6cn.jpg)
Holy donut holes Batman! That does not look good. What is going on? The problem is statistics. Because of the low energies involved, the default binary calculation time of 110 hours is insufficient to obtain decent statistics for N ka, so we could calculate longer, or... we could just remove the high N concentration binaries from our fit by selecting the Penepma Limits option at say 90%, in the ZAF/Phi-Rho-Z/Alpha factor and Calibration Curve Options menu dialog as seen here:
(https://smf.probesoftware.com/oldpics/i58.tinypic.com/2j6ptk.jpg)
After we select this we get this:
(https://smf.probesoftware.com/oldpics/i66.tinypic.com/2difwqv.jpg)
Not perfect but good, and if we choose the non-linear fit we do even better:
(https://smf.probesoftware.com/oldpics/i67.tinypic.com/23sydg0.jpg)
Finally we look at the Pt Ma in Ti binary. Again here is the default Armstrong/Love-Scott/Reed Phi-rho-z:
(https://smf.probesoftware.com/oldpics/i66.tinypic.com/11c9pbb.jpg)
and note the significant difference with the Penepma Monte-Carlo:
(https://smf.probesoftware.com/oldpics/i63.tinypic.com/j95y0n.jpg)
With the latest Penepma (Penfluor/fanal) binary k-ratio database update (see matrix.mdb), the following results are obtained with the Pouchou k-ratio database (without the B ka and Cu La measurements):
(https://smf.probesoftware.com/oldpics/i67.tinypic.com/95vips.jpg)
Compared to the previous result here:
http://smf.probesoftware.com/index.php?topic=47.msg3263#msg3263
this latest error distribution is slightly higher for the average and slightly improved for the standard deviation.
Progress...
I'm about to release a new matrix.mdb k-ratio database from my ongoing Penepma Monte-Carlo calculations.
In particular, many of these latest binary compositions are for the REEs and actinide series elements. And I would like to perform and post some comparisons between traditional analytical expressions and these new Penepma binary calculations for these elements, particularly the actinides...
Can those of you working in the EPMA nuclear characterization field please provide some examples of actinide binary pairs that you would find most helpful for your matrix corrections? For example, Am La/Ma in Pu???
Al, Am, C, Fe, Ga, Ni, O and U would be the top requests in my list.
...and Pu
Quote from: Mike Matthews on January 05, 2016, 09:19:27 PM
Al, Am, C, Fe, Ga, Ni, O and U would be the top requests in my list.
Hi Mike,
Perfect.
The Penepma binaries that are already calculated for these elements are as follows:
Penepma K-Ratio Alpha Factors:
Xray Matrix Alpha1 Alpha2 Alpha3 Alpha4
Ni ka in U .7367 .1837 -.1886 .0000 *from Penepma 2012 Calculations
Fe ka in U .8127 .0905 -.0362 .0000 *from Penepma 2012 Calculations
Al ka in U 1.5105 .4800 -.1656 .0000 *from Penepma 2012 Calculations
O ka in U 3.5118 -5.5011 9.6713 .0000 *from Penepma 2012 Calculations
Ni ka in Ga .7277 .3683 -.3001 .0000 *from Penepma 2012 Calculations
Fe ka in Ga .8370 .2470 -.2436 .0000 *from Penepma 2012 Calculations
Al ka in Ga 2.6465 -.0290 -.0772 .0000 *from Penepma 2012 Calculations
O ka in Ga 3.0362 -7.2413 10.7289 .0000 *from Penepma 2012 Calculations
C ka in Ga 5.6139 1.7763 -1.9722 .0000 *from Penepma 2012 Calculations
U ma in Ni 1.3002 .1365 -.0661 .0000 *from Penepma 2012 Calculations
Ga ka in Ni 1.1508 .0200 -.0086 .0000 *from Penepma 2012 Calculations
Fe ka in Ni .7620 .4592 -.3626 .0000 *from Penepma 2012 Calculations
Al ka in Ni 2.4398 -.1169 -.0413 .0000 *from Penepma 2012 Calculations
O ka in Ni 2.6317 -7.4839 10.9035 .0000 *from Penepma 2012 Calculations
C ka in Ni 4.4830 .5990 -.8225 .0000 *from Penepma 2012 Calculations
U ma in Fe 1.2105 .1559 -.0372 .0000 *from Penepma 2012 Calculations
Ga ka in Fe 1.1250 .0983 -.1315 .0000 *from Penepma 2012 Calculations
Ni ka in Fe 1.0798 .0256 -.0120 .0000 *from Penepma 2012 Calculations
Al ka in Fe 2.0251 .0243 -.0913 .0000 *from Penepma 2012 Calculations
O ka in Fe 2.2125 -7.4945 10.9570 .0000 *from Penepma 2012 Calculations
C ka in Fe 3.2583 .4177 -.4456 .0000 *from Penepma 2012 Calculations
U ma in Al 1.4492 .0996 -.0010 .0000 *from Penepma 2012 Calculations
Ga ka in Al 1.1008 .3902 -.3712 .0000 *from Penepma 2012 Calculations
Ni ka in Al 1.0528 .0758 -.0400 .0000 *from Penepma 2012 Calculations
Fe ka in Al 1.0780 .2010 -.2520 .0000 *from Penepma 2012 Calculations
O ka in Al 3.0586 -7.4658 10.7455 .0000 *from Penepma 2012 Calculations
C ka in Al 7.8972 .6031 -1.9221 .0000 *from Penepma 2012 Calculations
U ma in O 1.3779 .3482 -.1499 .0000 *from Penepma 2012 Calculations
Ga ka in O 1.1752 .6630 -.2488 .0000 *from Penepma 2012 Calculations
Ni ka in O 1.1135 .2717 -.0710 .0000 *from Penepma 2012 Calculations
Fe ka in O 1.1522 .4001 -.4122 .0000 *from Penepma 2012 Calculations
Al ka in O 1.6517 -.0568 -.1022 .0000 *from Penepma 2012 Calculations
C ka in O 1.8118 -.1394 .0949 .0000 *from Penepma 2012 Calculations
U ma in C 1.3601 .2630 .0155 .0000 *from Penepma 2012 Calculations
Ga ka in C 1.0964 2.1334 -2.3743 .0000 *from Penepma 2012 Calculations
Ni ka in C 1.0986 .5467 -.3687 .0000 *from Penepma 2012 Calculations
Fe ka in C 1.1466 .4063 -.2857 .0000 *from Penepma 2012 Calculations
Al ka in C 1.3034 -.2479 .3163 .0000 *from Penepma 2012 Calculations
O ka in C 6.9004 -8.8507 10.6434 .0000 *from Penepma 2012 Calculations
I will check for the others as soon as the calculations are ready.
john
A good introduction to the use of alpha and beta factors can be found here:
http://epmalab.uoregon.edu/bence.htm
Basically, the matrix elements are reduced to binaries for off-line Monte-Carlo calculations (alpha factors) in advance, but later combined again for matrix corrections (beta factors) in real time.
This allows us to perform the Monte-Carlo calculations in advance. Otherwise it would take the age of the universe. :o
I'd suggest the following pairs:
U ma Pu mb
U ma Np ma
U ma Am mb
Pu mb Np ma
Pu mb Am mb
Np ma Am mb
U ma C ka
U ma O ka
U ma Zr la
Pu mb Zr la
U ma Mo la
U ma Nd la
Thanks for your efforts!
Hi Karen,
No need to specify the x-ray lines, as all available lines are calculated automatically with the Penepma Monte-Carlo code. By the way, some of these binary pairs are calculated and available already, and here's how one can find out if they are:
1. Run CalcZAF and click the Enter Composition by Formula String button as seen here:
(https://smf.probesoftware.com/oldpics/i67.tinypic.com/2r4o9pd.jpg)
2. Enter the elements (all of them) that you are interested in as seen here:
(https://smf.probesoftware.com/oldpics/i66.tinypic.com/23rvfwx.jpg)
For some of these actinide elements you may get some overvoltage warnings if your default operating voltage is under 20 keV. Just ignore these, or if you prefer, change the default keV to 20 in the Analytical | Operating Conditions menu and try again.
Note also that you may get warnings regarding missing MAC values for some of these actinide elements (e.g., Am) if your x-ray databases do not have values for these elements. These modified database files are available on request (and you already have them!) but, these missing MAC values are *not* necessary for the Penepma calculations as the k-ratio intensities are calculated from fundamental parameters!
3. From the Analytical | ZAF, Phi-Rho-Z, Alpha factor and Calibration Curve Selections menu, click the Polynomial Alpha Factors option and then check the Use Penepma K-ratios checkbox as seen here:
(https://smf.probesoftware.com/oldpics/i63.tinypic.com/2mpdgn6.jpg)
4. Finally click the Run | List Current Alpha Factors menu and see which binary pairs are available from Penepma Monte-Carlo calculations as seen here:
Penepma K-Ratio Alpha Factors:
Xray Matrix Alpha1 Alpha2 Alpha3 Alpha4
O ka in Pu 2.7028 -.6135 2.3234 .0000 *from Penepma 2012 Calculations
O ka in Np 3.6677 .2544 1.4957 .0000 *from Penepma 2012 Calculations
Mo la in U 1.1164 -.0435 .1787 .0000 *from Penepma 2012 Calculations
Zr la in U 1.2261 .0781 .0284 .0000 *from Penepma 2012 Calculations
O ka in U 4.1551 .6973 1.1366 .0000 *from Penepma 2012 Calculations
O ka in Nd 2.3311 -1.5983 2.8928 .0000 *from Penepma 2012 Calculations
C ka in Nd 2.1652 .9365 -.5294 .0000 *from Penepma 2012 Calculations
Zr la in Mo 1.0175 -.0331 .0910 .0000 *from Penepma 2012 Calculations
O ka in Mo 9.2251 1.2504 -1.1877 .0000 *from Penepma 2012 Calculations
C ka in Mo 9.6890 4.9851 -5.2894 .0000 *from Penepma 2012 Calculations
U ma in Zr 1.7090 -.0252 -.0740 .0000 *from Penepma 2012 Calculations
Mo la in Zr 1.8058 -.1545 .0953 .0000 *from Penepma 2012 Calculations
O ka in Zr 8.0640 .2963 -.0162 .0000 *from Penepma 2012 Calculations
C ka in Zr 10.9231 6.1915 -6.7884 .0000 *from Penepma 2012 Calculations
Pu la in O 3.4332-13.5762 20.2590 .0000 *from Penepma 2012 Calculations
Np la in O 3.7503-19.0111 29.3622 .0000 *from Penepma 2012 Calculations
U ma in O 1.1949 .4583 -.2719 .0000 *from Penepma 2012 Calculations
Nd la in O 1.2222 .1731 -.0761 .0000 *from Penepma 2012 Calculations
Mo la in O 1.1821 .0278 .0545 .0000 *from Penepma 2012 Calculations
Zr la in O 1.2404 -.0669 .1358 .0000 *from Penepma 2012 Calculations
C ka in O 2.0980 -.1984 .1442 .0000 *from Penepma 2012 Calculations
U ma in C 1.1587 .2905 .0099 .0000 *from Penepma 2012 Calculations
Nd la in C 1.2121 .0938 .1284 .0000 *from Penepma 2012 Calculations
Mo la in C 1.0433 .0165 .1176 .0000 *from Penepma 2012 Calculations
Zr la in C 1.0258 .1284 -.0654 .0000 *from Penepma 2012 Calculations
O ka in C 8.6296 -3.8210 2.4080 .0000 *from Penepma 2012 Calculations
Note that there is a fitting problem with C ka in U that I am fixing this weekend (not shown). Next week I should have a bunch more actinide pairs to release, so stay tuned! :)
Here is a comparison of the carbon-lead binary between the JTA correction and the fast Monte-Carlo method.
Some significant differences, but which one is "correct"? :o
See attachments below.
The matrix.mdb Penepma (Penfluor/Fanal) binary k-ratio database now contains over 300,000 k-ratios (2805 binaries). That's almost 2/3 of the periodic table.
The complete list is here:
http://probesoftware.com/download/Calculated%20Matrix%20Binaries.txt
I just released a new matrix.mdb k-ratio database with many new binaries, but because it doesn't get automatically updated unless you run the CalcZAF.msi file, I've provided a link below to allow one to download it manually. It should be copied to the C:\ProgramData\Probe Software\Probe for EPMA folder (or under XP the C:\Documents and Settings\All Users\Probe Software\Probe for EPMA folder).
http://www.probesoftware.com/download/Matrix.mdb
Here is the Pouchou database calculated using phi-rho-z (JTA/improved Reed):
(https://smf.probesoftware.com/gallery/395_02_03_16_10_50_50.png)
And here with polynomial alpha factors fitted to k-ratios from Penepma (Penfluor/Fanal):
(https://smf.probesoftware.com/gallery/395_02_03_16_10_52_06.png)
Cool.
The latest matrix.mdb (see above post for link) contains an additional 59 binaries, mostly REE and actinides.
That makes over 326K binary k-ratios! 8)
The error distributions for the Pouchou dataset comparing traditional analytical expressions (JTA/Modified Reed) and the new fast Monte-Carlo matrix correction methods have been previously compared here:
http://smf.probesoftware.com/index.php?topic=47.msg4159#msg4159
But I thought it would be interesting to try the same comparison for the Bastin k-ratio dataset which I obtained from Brian Joy earlier this year. There is some overlap between the two datasets, but the Bastin dataset has some crazy large overvoltages that should really stress the corrections, so let's see how they do. First the Bastin dataset using the traditional analytical expressions (JTA/Modified Reed):
(https://smf.probesoftware.com/gallery/395_13_04_16_10_55_39.png)
The average is good, but the standard deviation is larger than what we get from the Pouchou dataset and the reason is the very high overvoltage outliers (plus one very low overvoltage k-ratio) seen circled in the image and listed here:
Problematic k-ratio errors (< 0.8 or > 1.2)
Line ConcA ConcB TOA eO Uo K-Exp K-Cal K-Err
121 Ag la in Au .199600 .800400 52.5000 48.5000 14.4690 .079500 .063394 .797408
348 Al ka in Mg .091000 .909000 75.0000 40.0000 25.6410 .012300 .015082 1.22615
360 Al ka in Mg .091000 .909000 20.0000 40.0000 25.6410 .006900 .008550 1.23914
436 Nb la in V .080000 .920000 20.0000 40.0000 16.8705 .053000 .064454 1.21612
These high overvoltage outliers also tend to be low concentrations, so accuracy errors in the "known" compositions could be an additional factor as seen here:
(https://smf.probesoftware.com/gallery/395_13_04_16_11_00_50.png)
Note that I've included the complete k-ratio dataset including the B ka in carbon k-ratios, but these low energy emission lines do not seem to be problematic.
Now let's try the same thing using the Penfluor/Fanal fast Monte-Carlo method on this Bastin k-ratio dataset using polynomial alpha factor fitting:
(https://smf.probesoftware.com/gallery/395_13_04_16_11_26_35.png)
Something has gone south on us and it's those very high overvoltage k-ratios as seen here:
Problematic k-ratio errors (< 0.8 or > 1.2)
Line ConcA ConcB TOA eO Uo K-Exp K-Cal K-Err
14 Au ma in Cu .300000 .700000 40.0000 31.5000 14.2792 .177300 .216098 1.21883
15 Au ma in Cu .300000 .700000 40.0000 36.6000 16.5911 .171700 .207533 1.20869
16 Au ma in Cu .300000 .700000 40.0000 39.7000 17.9964 .168900 .202966 1.20169
227 Au ma in Cu .201200 .798800 52.5000 30.0000 13.5993 .122000 .146576 1.20144
228 Au ma in Cu .201200 .798800 52.5000 40.0000 18.1324 .110000 .134807 1.22552
345 Al ka in Mg .091000 .909000 75.0000 25.0000 16.0256 .025800 .033720 1.30698
346 Al ka in Mg .091000 .909000 75.0000 30.0000 19.2308 .019800 .027770 1.40252
347 Al ka in Mg .091000 .909000 75.0000 35.0000 22.4359 .015200 .023329 1.53478
348 Al ka in Mg .091000 .909000 75.0000 40.0000 25.6410 .012300 .019971 1.62368
351 Al ka in Mg .091000 .909000 52.5000 20.0000 12.8205 .030200 .037609 1.24535
352 Al ka in Mg .091000 .909000 52.5000 25.0000 16.0256 .022100 .029937 1.35460
353 Al ka in Mg .091000 .909000 52.5000 30.0000 19.2308 .016800 .024434 1.45442
355 Al ka in Mg .091000 .909000 20.0000 15.0000 9.61539 .025200 .030915 1.22677
356 Al ka in Mg .091000 .909000 20.0000 20.0000 12.8205 .016900 .022333 1.32147
357 Al ka in Mg .091000 .909000 20.0000 25.0000 16.0256 .012200 .017164 1.40685
358 Al ka in Mg .091000 .909000 20.0000 30.0000 19.2308 .009500 .013918 1.46507
359 Al ka in Mg .091000 .909000 20.0000 35.0000 22.4359 .007900 .011811 1.49501
360 Al ka in Mg .091000 .909000 20.0000 40.0000 25.6410 .006900 .010408 1.50844
367 Al ka in Fe .100000 .900000 75.0000 40.0000 25.6410 .021800 .027727 1.27190
371 Al ka in Fe .100000 .900000 52.5000 25.0000 16.0256 .033500 .040724 1.21563
372 Al ka in Fe .100000 .900000 52.5000 30.0000 19.2308 .026600 .033607 1.26343
375 Al ka in Fe .100000 .900000 20.0000 20.0000 12.8205 .024900 .030930 1.24219
376 Al ka in Fe .100000 .900000 20.0000 25.0000 16.0256 .018500 .024065 1.30079
377 Al ka in Fe .100000 .900000 20.0000 30.0000 19.2308 .014900 .019693 1.32171
378 Al ka in Fe .100000 .900000 20.0000 35.0000 22.4359 .012600 .016823 1.33512
379 Al ka in Fe .100000 .900000 20.0000 40.0000 25.6410 .011400 .014890 1.30614
436 Nb la in V .080000 .920000 20.0000 40.0000 16.8705 .053000 .065254 1.23122
645 Al ka in Ni .125000 .875000 40.0000 31.9000 20.4487 .023300 .028246 1.21229
646 Al ka in Ni .125000 .875000 40.0000 37.2000 23.8462 .019500 .023487 1.20444
650 Al ka in Ni .049000 .951000 40.0000 21.2000 13.5897 .014300 .017270 1.20770
651 Al ka in Ni .049000 .951000 40.0000 26.6000 17.0513 .009800 .013345 1.36171
652 Al ka in Ni .049000 .951000 40.0000 31.9000 20.4487 .007500 .010757 1.43433
653 Al ka in Ni .049000 .951000 40.0000 37.2000 23.8462 .006800 .008957 1.31725
Yes, these are overvoltages of 10 or 20 and higher so it's not good, but not surprising when running Al Ka at 30 or 40 keV!
Let's examine one or two of these cases in more detail, for example Al Ka in Mg at 30 keV. Here is a plot of the alpha factors for all analytical expression matrix corrections but first at a more normal 15 keV:
(https://smf.probesoftware.com/gallery/395_13_04_16_11_39_24.png)
There is a significant difference of opinion here, with about a 10% variation in the correction factor. If we plot the same thing at 30 keV, there is even more disagreement in the analytical expressions:
(https://smf.probesoftware.com/gallery/395_13_04_16_11_43_00.png)
The variation is now around 15% between the different models. So where does our Penfluor/Fanal based Monte-Carlo method put us?
(https://smf.probesoftware.com/gallery/395_13_04_16_11_46_54.png)
Pretty much "smack dab in the middle of the pack". The lesson here is that even a small difference in the matrix corrections can make a significant difference in accuracy, when their magnitude is this large. I guess the other lesson is: don't run your analyses with an overvoltage of 20 or 30 if you want accuracy. For improving sensitivity? Maybe a larger analytical volume will help. But certainly not for accuracy.
Just for fun, let's run these Bastin k-ratios with the PAP correction (XPP):
(https://smf.probesoftware.com/gallery/395_13_04_16_11_54_23.png)
Significantly better. Of course this makes sense as the PAP correction was optimized using a related dataset from Pouchou which was selected for large absorption corrections.
My "bottom line"? If you are going to have excessively large absorption corrections, whether they be from very high overvoltages or from very low energy emission lines, I would stick with the analytical expressions. But for large atomic number corrections or large fluorescence corrections I think the Penfluor/Fanal corrections will be your best bet.
As they say: your mileage (or kilometerage) may vary! ;D
The latest distribution of CalcZAF (v. 11.5.1) contains an updated matrix.mdb k-ratio database with 3087 binaries (over 337K k-ratios) for the fast Monte-Carlo matrix correction option.
See here for the complete list:
http://probesoftware.com/download/Calculated%20Matrix%20Binaries.txt
The latest CalcZAF.msi deployment contains a new matrix.mdb file for fast Monte-Carlo matrix corrections.
This database now contains 346K k-ratios for most element pairs in the periodic table (I'd be interested if anyone had the inclination to visualize these k-ratios in some way- it might make for interesting "science art").
(https://smf.probesoftware.com/gallery/395_30_06_16_8_22_43.png)
This latest error distribution for the Pouchou binary database shows a slightly better average, and slightly worse variance than the previous database. Still with a standard deviation of under 3%, this is better than any analytical based matrix correction I am aware of.
I decided to try the new 4 coefficient non-linear alpha factor fit to the Pouchou binary k-ratio database and indeed the accuracy and variance are both improved slightly (compared to the previous post using polynomial alpha factors) as seen here:
(https://smf.probesoftware.com/gallery/395_05_07_16_1_09_14.png)
I am now focusing on calculating k-ratios at higher precision to deal with low concentration and low overvoltage situations and will post these results soon...
The latest CalcZAF.msi contains a new matrix.mdb k-ratio database with over 367K binary k-ratios from Monte-Carlo calculations that further improves accuracy for the fast Monte-Carlo based matrix corrections. The previous error histogram from the Pouchou k-ratio database was here (the post just above the non-linear post):
http://smf.probesoftware.com/index.php?topic=47.msg4740#msg4740
The new matrix database is slightly improved in accuracy and with a smaller variance as seen here:
(https://smf.probesoftware.com/gallery/395_26_08_16_11_42_05.png)
The main outliers are from extremely high overvoltage measurements for relatively low energy emission lines such as Al Ka in Ni at 48 keV... which is simply a limitation of the accuracy of the photon scattering factor tables utilized by the Penepma code.
The latest matrix.mdb contains over 377K k-ratios for fast Monte Carlo calculations for matrix corrections. Most of the new additions are mid z element pairs.
john
The latest matrix.mdb k-ratio database now contains over 380K k-ratios for binary compositions from Penfluor-Fanal calculations. The new additions are mostly high emitters absorbed by low matrices, e.g., Nb La in B or C. You can update by using the CalcZAF Help | Update CalcZAF menu or downloading the matrix.mdb directly here:
http://www.probesoftware.com/download/Matrix.mdb
john
The latest version of CalcZAF/Probe for EPMA (v. 11.9.6) contains a new update to the matrix.mdb k-ratio database for fast Monte Carlo based matrix corrections.
This latest release adds about 100K more k-ratios for a total of ~394K k-ratios in the matrix.mdb database. Many of the new binaries are for REE and actinide binaries.
Please let me know if you have any questions.
john