The "fast Monte Carlo" method discussed in this topic has finally been written up by myself, Philippe Pinard and Hendrix Demers. See the pdf attached below for the full paper which will be coming out in Microscopy & Microanalysis relatively soon:

In the meantime we thought we would mention that during the writing of the paper we discovered that we (Donovan!) had not properly handled the modeling of alpha factors for the gaseous elements in the periodic table, specifically N, O, Cl, F, Ar, Kr, and Xe and Rn.  Basically we had utilized the room temperature elemental densities for all the elements, but because the default "bulk" sample geometry file in Penepma (Penfluor/Fanal) utilizes a thickness of 0.1 cm, at moderate to high electron energies a 1mm thickness can not be considered "infinity" thick for the purposes of a bulk calculation.  That is to say, some of the electrons will not come to rest if the density is insufficiently low. This wasn't a problem when the binary composition was mostly a non gaseous element, but it could become a problem for pairs of gaseous elements or when the gaseous element comprised the major element of the binary composition.

Hence we started recalculating all the alpha factor for these gaseous elements about six months ago, but this time using a minimum density of 1.0 if the binary compositional density was less than that.  Again for binaries containing the gaseous elements already mentioned above. These calculations take a long time to complete but just so everyone knows, the current matrix.mdb file contains completed calculations for Xe and Rn binaries, and about half the periodic table for the other gaseous elements (both as emitters and absorbers).

Of course the point of these "fast Monte Carlo" alpha factors is to have a way to test our assumptions for the current analytically derived expressions (ZAF, phi-rho-z) which are generally "tuned" to some experimental k-ratios. The point being that these Penepma derived k-ratios are based on quantum mechanical models and therefore not tuned to any specific material datasets.

We suspect that the most interesting application of these Penepma based alpha factors will be for exotic materials where experimental k-ratios do not exist, and therefore have not been utilized in "tuning" our current analytical expressions for quantification.

Just to demonstrate that we are now correctly handling quantification of light elements using these "fast Monte Carlo" alpha factors here is a calculation using the Armstrong phi-rho-z analytical expression for a glass material (of course containing oxygen):

Un   30 MAM IW2 C4-ext-4, Results in Oxide Weight Percents

ELEM:     Na2O    SiO2     K2O   Al2O3     MgO     CaO    TiO2     MnO     FeO    P2O5   Cr2O3       O     H2O   SUM 
   241    .571  56.566    .502   8.301   7.801   8.146   1.547    .442  15.643    .416    .080    .000    .000 100.016
   242    .467  56.499    .473   8.160   7.843   8.064   1.459    .452  15.984    .398    .092    .000    .000  99.892
   243    .560  55.914    .526   8.032   4.472   8.648   1.696    .457  19.873    .400    .066    .000    .000 100.643
   244    .421  56.258    .480   8.020   6.266   8.415   1.501    .493  17.406    .408    .056    .000    .000  99.722
   245    .551  56.193    .500   8.070   5.606   8.627   1.482    .439  18.083    .407    .084    .000    .000 100.042
   246    .413  56.655    .471   8.268   7.487   8.015   1.474    .459  16.260    .407    .064    .000    .000  99.972

AVER:     .497  56.347    .492   8.142   6.579   8.319   1.526    .457  17.208    .406    .074    .000    .000 100.048
SDEV:     .072    .278    .021    .121   1.371    .283    .089    .019   1.597    .006    .014    .000    .000    .314
SERR:     .029    .113    .009    .050    .560    .115    .036    .008    .652    .003    .006    .000    .000
%RSD:    14.53     .49    4.33    1.49   20.84    3.40    5.80    4.19    9.28    1.59   18.89 -558.57     .00
STDS:      336     160     374     336     162     162      22      25     162     285     396     ---     ---

Now here is the same sample, but this time quantified using the Penepma based "fast Monte Carlo" alpha factor method:

Un   30 MAM IW2 C4-ext-4, Results in Oxide Weight Percents

ELEM:     Na2O    SiO2     K2O   Al2O3     MgO     CaO    TiO2     MnO     FeO    P2O5   Cr2O3       O     H2O   SUM 
   241    .569  56.703    .503   8.298   7.787   8.130   1.549    .442  15.616    .415    .080    .000    .000 100.092
   242    .465  56.643    .474   8.156   7.828   8.049   1.462    .451  15.957    .397    .092    .000    .000  99.974
   243    .557  56.111    .526   8.013   4.461   8.638   1.701    .457  19.838    .398    .066    .000    .000 100.767
   244    .420  56.424    .480   8.009   6.252   8.402   1.503    .492  17.375    .407    .056    .000    .000  99.820
   245    .549  56.367    .501   8.056   5.593   8.614   1.485    .439  18.052    .406    .085    .000    .000 100.146
   246    .411  56.806    .471   8.263   7.472   8.001   1.476    .459  16.232    .406    .064    .000    .000 100.060

AVER:     .495  56.509    .493   8.133   6.565   8.306   1.529    .457  17.178    .405    .074    .000    .000 100.143
SDEV:     .072    .257    .021    .127   1.370    .284    .089    .019   1.594    .006    .014    .000    .000    .326
SERR:     .029    .105    .009    .052    .559    .116    .036    .008    .651    .003    .006    .000    .000
%RSD:    14.50     .45    4.34    1.56   20.86    3.42    5.84    4.19    9.28    1.58   18.82  -36.51     .00
STDS:      336     160     374     336     162     162      22      25     162     285     396     ---     ---

Again, we have no reason to suspect that such a (low Z) material would benefit from such an "untuned" quantification model, but if anyone does run across a composition that does show significant differences between our current "tuned" phi-rho-z models and this "untuned" Penepma based model, we would be very interested in hearing about it.

After recalculating the SiO2 matrix effect in Penepma for a three material geometry, and editing the above post, here is a summary of the two matrices:

Expressing the Ti Ka k-ratios in PPM we get (for the beam in the center of a 20 um SiO2 inclusion adjacent to a 5 um TiO2 inclusion) in an epoxy matrix (at a 20 keV electron energy):

10 um from: 21 +/- 2 PPM
20 um from: 11 +/- 1 PPM
40 um from:  5 +/- 1 PPM

Expressing the Ti Ka k-ratios in PPM for the same but with an SiO2 matrix (at a 20 keV electron energy):

10 um from: 19 +/- 2 PPM
20 um from: 10 +/- 1 PPM
40 um from:  3 +/- 1 PPM

We can see the effect of less absorption of the continuum (greater SF effect) by the epoxy matrix, by modeling the x-ray absorption in CalcZAF using the Calculate Electron and X-Ray ranges menu as described here:

https://probesoftware.com/smf/index.php?topic=86.0

Doing that we can see that assuming a Cr or Mn Ka radiation as a proxy for continuum x-rays sufficient to excite the Ti K edge (at ~4.9 keV), for a distance of 10 um we get roughly a transmission of 0.8 for an SiO2 matrix, and a transmission of 0.95 for an epoxy matrix.

Therefore the epoxy matrix produces a slightly larger secondary fluorescence effect for Ti Ka than an SiO2 matrix.  Sorry for the earlier confusion!   

Hi Anne
Is there a reason you need to remove the C coat for laser. In my experience with geological samples moving from probe to laser, C coat is not too much of an issue other than affecting things visually on the reflected light image on the laser. Usually the C layer is ablated within the first second or so of acquisition which you usually get rid of anyway. Unless you are looking at specific elements with bad C polyatomic interferences?

Cheers

Xavier Llovet responded to both Mike and I and said we could post his comments. Here they are:

Hi John, Mike:

I've checked the electronic configuration of U and is 5f3 6d1 7s2 so in principle the O4 and O5 levels (5d) are filled. Those that are partially filled are the 5f levels, which would correspond to O6 and O7 levels. So if I'm correct, both two N6-O5 and N6-O4 lines should exist.

The problem could be in the relative intensity reported by Bearden. For instance, according to the PENELOPE database, the N6-O4 line (with energy 289 eV) is 10 times more intense that the N6-O5 line (with energy 298 eV), just the opposite than Bearden's data! You can find this information in the U.mat file:

15 20  0  7.40479E-05  2.89740E+02
15 21  0  4.72978E-06  2.98070E+02

(the transition "15 20 0" would correspond to the N6-O4 line and the transition "15 21 0" to the N6-O5 line)

So perhaps this could explain what you're seeing?

Regards,
Xavier

The (modified) NIST x-ray database included with Probe for EPMA does include some N emission lines, but not all apparently. I guess we need a KLMN x-ray database!

Pd MZ2               43.3622  .285930  1.00000        ES 
Pd MZ1               43.3622  .285930  10.0000        ES 
Ne KB1      III      43.3814  .857410  .500000        JD 
Se SLB1``   V        43.4488  1.42680  .250000        JD 
Dy M2-N1    V        43.4610  1.42640  1.25000        JD 
Ni SLA3     III      43.4691  .855680  .500000        JD 
La MB       III      43.5016  .855040  45.0000        JD 
Bi N5-N6             43.5801  .284500  1.00000        ES 
Eu M4-O2    IV       43.5993  1.13750  .064000        JD 
Eu MA1      IV       43.6146  1.13710  64.0000        JD 
Ag MG       II       43.6422  .568190  16.0000        JD 
Eu MA2      IV       43.6492  1.13620  64.0000        JD 
Tm MZ1      IV       43.6607  1.13590  3.84000        JD 
Er M4-O2    V        43.6630  1.41980  .025000        JD 
Tl N4-N6             43.6707  .283910  1.00000        ES 
Tm MZ2      IV       43.6761  1.13550  .640000        JD 
Se LB1      V        43.6876  1.41900  9.71200        JD 
Ni LA2      III      43.7081  .851000  5.72500        JD 
Ni LA1      III      43.7081  .851000  50.0000        JD 
Mn Ln       II       43.7338  .567000  5.14300        JD 
Ga L2-N3    IV       43.7724  1.13300  .173000        JD 
Ce M2-N4    IV       43.8266  1.13160  5.12000        JD 
Ga SLB1``   IV       43.8421  1.13120  .640000        JD 
Ne KA1      III      43.8467  .848310  50.0000        JD 
Ne KA2      III      43.8467  .848310  25.0000        JD 
Ga LG5      IV       43.8886  1.13000  .141000        JD 
Tm M3-N1    V        43.9260  1.41130  .250000        JD 
Pr MG       IV       43.9938  1.12730  38.4000        JD 
C  KA1               44.0023  .281770  100.000        ES        <-- carbon emission
C  KA2               44.0023  .281770  50.0000        ES        <-- carbon emission
Er MA1      V        44.0039  1.40880  25.0000        JD 
Er MA2      V        44.0039  1.40880  25.0000        JD 
Cs M2-N1    III      44.0049  .845260  7.00000        JD 
Cs MZ1      II       44.0063  .563490  8.00000        JD 
Ga LB1      IV       44.0837  1.12500  10.6910        JD 
La M3-N1    III      44.1759  .841990  .650000        JD 
Pd M2-N4    II       44.2016  .561000  .800000        JD 
Gd MG       V        44.2205  1.40190  6.52500        JD 
Zr M3-N1             44.2789  .280010  1.00000        ES 
As Ll       IV       44.2805  1.12000  3.15500        JD 
Sm MZ2      III      44.4259  .837250  .500000        JD 
Ge LG3      V        44.4392  1.39500  .028000        JD 
Mn Ll       II       44.5991  .556000  10.6000        JD 
Se SLA4     V        44.6119  1.38960  .250000        JD 
La MA1      III      44.6414  .833210  50.0000        JD 
La MA2      III      44.6414  .833210  50.0000        JD 
Eu M3-N1    IV       44.6432  1.11090  .640000        JD 
Se SLA5     V        44.6569  1.38820  .250000        JD 
As LB4      V        44.6633  1.38800  .650000        JD 
As LB3      V        44.6633  1.38800  1.19200        JD 
Ho SMB2     V        44.6859  1.38730  .250000        JD 
Cu Ln       III      44.7068  .831990  1.37500        JD 
Kr Ll       V        44.7601  1.38500  1.12700        JD 
Ga SLA4     IV       44.7601  1.10800  .640000        JD 
Sm MZ1      III      44.7865  .830510  3.00000        JD 
Se SLA3     V        44.7924  1.38400  .250000        JD 
Zn LB4      IV       44.8005  1.10700  1.51000        JD 
Zn LB3      IV       44.8005  1.10700  .250000        JD 
Ru M4-O2             44.8021  .276740  .010000        ES 
Ga SLA5     IV       44.8086  1.10680  .640000        JD 
W  MZ1      V        44.8118  1.38340  .336000        JD 
Ho MB       V        44.8280  1.38290  14.8610        JD 
La M4-O2    III      44.8313  .829680  .050000        JD 
Sm M2-N4    V        44.8832  1.38120  .300000        JD 
Se LA2      V        44.9548  1.37900  2.85500        JD 
Se LA1      V        44.9548  1.37900  25.0000        JD 
W  MZ2      V        44.9679  1.37860  1.12800        JD 
Ga SLA3     IV       44.9956  1.10220  .640000        JD 
Pb N5-N6             45.0021  .275510  1.00000        ES 
Sm MB       IV       45.0815  1.10010  56.3200        JD 
I  MG       III      45.1064  .824620  10.0000        JD 
Ga LA2      IV       45.1677  1.09800  7.30900        JD 
Ga LA1      IV       45.1677  1.09800  64.0000        JD 
Sb M2-M4             45.2023  .274290  .010000        ES 
Hg N4-N6             45.2023  .274290  1.00000        ES 
Na SKB^4    IV       45.2584  1.09580  .640000        JD 
Tb M2-N1    V        45.3495  1.36700  1.25000        JD 
Te M2-N4    III      45.3511  .820170  .500000        JD 
Nd M2-N1    IV       45.3993  1.09240  2.56000        JD 
Er MZ1      IV       45.4867  1.09030  3.84000        JD 
Er MZ2      IV       45.5118  1.08970  .640000        JD 
Ho M4-O2    V        45.5728  1.36030  .025000        JD 
Er M3-N1    V        45.5996  1.35950  .250000        JD 
Sm MA1      IV       45.7173  1.08480  64.0000        JD 
Sm MA2      IV       45.7173  1.08480  64.0000        JD 
Sm M4-O2    IV       45.7216  1.08470  .064000        JD 
Cd M2-N1    II       45.8018  .541400  4.00000        JD 
Ho MA2      V        45.8085  1.35330  25.0000        JD 
Ho MA1      V        45.8085  1.35330  25.0000        JD 
Cu Ll       III      45.8639  .811000  2.07000        JD 
In M3-N1    II       45.9503  .539650  .800000        JD 

By the way, I also searched Philipp Poeml's modified replacement NIST x-ray database, which has additional emission lines for the actinide elements, and it doesn't have these N emission lines for U either.

I’m actually analysing C in U right at the moment and talked about this very interference problem at the AMAS symposium a couple of months ago. You can’t completely separate the C and U lines but you can reduce the degree of interference by using the 2nd order C Ka line on either an LDE1/PC1 or a Pb-stearate. This puts the line at the top end of the spectrometer range, where the resolution is better. The stearate has the highest resolution of the light element crystals, and almost completely separates the two peaks but the intensity is really lousy (<200th that of the LDE2/PC2). Both still need overlap correction (really easy to set up in PfE, thanks John!). I’m using the LDE1/PC1 as a compromise between level of correction and useable count rate (~20th that of LDE2/PC2). Thanks to Ben Buse for suggesting this method. As John says, the k-ratio values that PfE outputs include the overlap correction.

I have a sort of linked question though: The interfering U line is the N6-O4 at 0.286keV, with a relative intensity of 0.01% (Bearden, 1967), but there should also be a N6-O5 line at 0.294keV which Bearden lists with a relative intensity of 1% (i.e. 100 times bigger than the N6-O4 line), but I see no evidence of this peak. My working theory is that the O5 shell in U isn’t normally occupied so the line can’t be fluoresced and the 1% intensity in Bearden is just a default value when the actual intensity hasn’t been measured. However, my understanding of how shells are occupied is very limited and I might be completely misunderstanding the diagrams. Can anyone confirm or deny this hypothesis?

Mike