Penepma/Penfluor/Fanal derived Alpha Factors For Matrix Corrections

[John Donovan]

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.

[John Donovan]

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

[John Donovan]

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

[John Donovan]

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:



These are available in the latest 10.1.7 of our software.
john

[Anette von der Handt]

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.

[Probeman]

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:



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://probesoftware.com/smf/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).

[Anette von der Handt]

That is very helpful. Thank you!

[John Donovan]

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.

[Anette von der Handt]

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!

[Probeman]

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://probesoftware.com/smf/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.

[Anette von der Handt]

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 Fe_XC_Y. 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?

[Probeman]

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 Fe_XC_Y. 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:



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...

[John Donovan]

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
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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
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06/09/2014  12:53 PM           249,082 28-90_40.txt
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06/09/2014  12:53 PM           193,911 13-90_40.txt
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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
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06/04/2014  10:37 AM           365,218 41-12_40.txt
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06/04/2014  10:37 AM           361,407 41-27_40.txt
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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
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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

[Probeman]

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 :



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:



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:



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.

[Probeman]

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):



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.