Matrix correction issues for Fe-Ga

[Warren Straszheim]

I've been operating an 8200 for Ames Laboratory for almost four years now. I've worked with SEM and EDS since about 1980 and trying to push it for all its worth.

Currently, I am having challenges analyzing FeGa compounds. Many are in the neighborhood of 15% Ga.

I have been using Fe and GaAs as standards and I have a sample of about 65 at% Ga that has FeGa3 and Fe3Ga4 phases present. The FeGa3 is supposed to be a line compound but the Fe3Ga4 has almost 2 at% width to the phase.

I've run my regular probe analyses and included the FeGa3 as an unknown to check. While the composition is supposed to be 79 wt% Ga and 21 wt% Fe, I measured 77% Ga and 23% Fe when using Fe and GaAs as standards. I had to adjust the Fe standard down in intensity about 8% to get the proper composition for FeGa3. Then the Fe3Ga4 phase came out with 36% Fe where it is supposed to be 37.5%.  I'm not sure if that is due to error in matrix correction or the width of the phase diagram favoring the Ga-rich side. However, the Ga analyses came out pretty much on the mark.

I tried setting up the FeGa3 as a standard for both Fe and Ga. It gave the right results for FeGa3, of course. It also gave the right answer for Ga in Fe3Ga4, but it gave a low value for Fe like before. It also gave a value of 92% for my Fe std.

I have tested the same materials with an Oxford EDS system which used Fe and GaP as a standard. It ends up giving a close answer for the two FeGa phases in my standard. Now I suppose I need to turn off normalization and see how the numbers come out.

I've calculated the ZAF factors for various compositions of Fe and Ga using the CalcZAF program.

I found a ZAF factor as low as 0.83 for 1% Fe in Ga. About 70% of the correction was due to the fluorescence effect. The other 30% was due to Z.

The ZAF factor was as high as 1.12 for 1% Ga in Fe. About 60% was due to Z and 40% due to absorption.

The ZAF factor was 0.88 for Fe and 1.03 for Ga at the FeGa3 composition. The probe gave a factor of 0.91 for Fe at that composition; thus there seems to be a 3% difference in correction between CalcZAF and the probe. EDS gave 0.90 for Fe.


I know that it's best to have a standard in the neighborhood of the unknowns so that uncertainties in the matrix correction cancel out. That's not really an option for me here yet, but I am working on it. Still, shouldn't the matrix corrections work over a broader range? I wonder why the WDS analyses can't match the apparent accuracy of the EDS results. Is there something about the probe matrix correction that isn't up to par for this particular mix of elements?


The bottom line is that the matrix correction appears to be significant and not all that good over a wide range of compositions, especially for the probe. The Oxford EDS systems may be using a different set of physical constants which may be more correct

[Probeman]

Hi Warren,
Interesting example!

I'd like to respond to your post in several parts as it will give me time to treat it properly and allow others to chime in as well (you know who you are!). Also I can walk everyone through the steps in CalcZAF that one might take to shed light on the physics that you have mentioned.  We'll treat it as a "worked example".   

But first off, would you mind posting the beam energy you are utilizing and also, if you have a Fe-Ga compound that you trust the composition of, please post the raw and/or pure element normalized k-ratios (relative to Fe and GaAs standards sound good to me) that you have measured so we can compare to some calculations...

[Warren Straszheim]

I hate to ask and run, but I will probably have to do just that. I didn't take much time off around Christmas and am going to bug out next week. I might be able to scare up the K-ratios in my old e-mails.

I can tell you certainly that the the accelerating voltage was 20 kV so I could safely use K lines for both Fe and Ga.

I can also say that I specified compositions ranging from 99% Fe to 99% Ga to get an idea of what ZAF factors would be over the range. I'd like to follow up to see how to specify other sets of physical constants to see how they affect the results.

ws

[Probeman]

Hi Warren,
Been a busy week for me too, but the real reason for the delay is that I'm currently running 11 compositions of the Fe-Ga binary in the full Penepma (Penelope) app before I discuss this binary and that calculation takes over a week!

Of course the cool thing about CalcZAF (or Probe for EPMA), is that once we've run a full Monte-Carlo on a binary, I can fit them to polynomial alpha factors as described here for use with *any* composition in seconds!

http://epmalab.uoregon.edu/posters/High%20Speed%20Monte%20Carlo%20By%20Binary%20Methods_EMAS_2013-A0.pdf

I have found that Penepma does a surprisingly good job for absorption compared to analytical methods, but really excels with the fluorescence effects. The Fe-Ga Monte-Carlo calculations should be done early next week, so I'll take up the torch then!

Edit 01/15/2014: had to restart the Monte-Carlo computer a few times for Windows updates so the calculations will be complete over the weekend- I'll post the results next week

[Probeman]

Hi Warren,
The Penepma Fe-Ga Monte-carlo calculations at 20 keV finally finished. I calculated 11 binaries from 1 to 99% and Fe and Si end-members all at 20 keV, and also GaAs so you can re-normalize everything to that standard for your measurements.

There are a lot of files, but I can drop them in DropBox if that works for you.  In the meantime here's some results, first using just the normal CalcZAF analytical calculations at 20 keV:

Current Mass Absorption Coefficients From:
LINEMU   Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV

  Z-LINE   X-RAY Z-ABSOR     MAC
      Ga      ka      Ga  4.0534e+01
      Ga      ka      Fe  2.0981e+02
      Fe      ka      Ga  1.1390e+02
      Fe      ka      Fe  6.8270e+01

 ELEMENT  ABSFAC  ZEDFAC  FINFAC STP-POW BKS-COR   F(x)e
   Ga ka  1.0150  4.3624  4.4276   .2085   .9094   .9853
   Fe ka  1.0280  4.0572  4.1710   .2195   .8906   .9727

SAMPLE: 32767, ITERATIONS: 0, Z-BAR: 28.5

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ga ka  1.0300  1.0000  1.0346  1.0656  1.0451   .9899   .9566 10.3670  1.9292 125.170
   Fe ka  1.0100   .9598   .9709   .9412   .9580  1.0134   .9630  7.1120  2.8121 91.0860

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
   Ga ka  .00000  .46923  50.000   -----  44.476    .445   20.00
   Fe ka  .00000  .53121  50.000   -----  55.524    .555   20.00
   TOTAL:                100.000   ----- 100.000   1.000

Fe is significantly fluoresced by Ga is the most notable correction. These types of calculations are described here in more detail:

http://probesoftware.com/smf/index.php?topic=81.msg545#msg545

Next we can try the FeGa binary in the Penfluor/Fanal calculations as described here by specifying the same material for both the beam incident and the boundary material as described here:

http://probesoftware.com/smf/index.php?topic=151.0

Now if we look at the Penfluor/Fanal k-ratios calculated for say a 50:50 weight fraction composition we get this table for Fe Ka:



and the display shows that both CalcZAF (Armstrong/Reed) give very similar results:



and this table for Ga Ka also at 20 keV but note we changed the line to Ga Ka and standard to Ga:



and this for the display:



We can see there is a small but significant difference between the analytical and Monte-carlo models for Ga Ka.

Next we can try the full blown Penepma 2012 Monte-Carlo as described here:

http://probesoftware.com/smf/index.php?topic=151.0

The results from the full Penepma Monte-Carlo are shown here  by simply opening any of the k-ratio files in Excel. Here is the Ka lines file for Fe and Ga:



The k-ratio (%) and alpha factors are shown. Again we can see that Fe is significantly fluoresced and Ga Ka significantly absorbed.  We can compare these to the Penfluor/Fanal results for Ga Ka at 20 keV from above as seen here:

[Probeman]

Note that the alpha factors are "only" the effect for the element by another element. To convert the alpha factors to a matrix correction, or "beta" factors as they are usually referred to, one must compound them using the method described in the attached poster below.

Why, because we need to include the effect of the element by itself as an absorber, which is 1.0 by definition of course. So we need to take the fraction of the Fe-Ga binary but also the fraction of the Fe-Fe and Ga-Ga binaries which again by definition are 1.0.

But to take an example using CalcZAF we can enter a nominal FeGa 50:50 wt% compound as seen here:



We also need to enter 20 keV in the Analytical |Operating Conditions menu. Then we click the Calculate button:



Again we see a significant fluorescence for Fe Ka and significant absorption for Ga Ka.  Let's change things up by switching to alpha-factor calculations from the Analytical | ZAF, Phi-Rho-Z, Alpha factor and Calibration Curve Selections menu.

This way we can see the same k-ratios from our Armstrong/Reed analytical model expressed as polynomial fit alpha factors. First we select alpha-factors:



Then we click the Calculate button again and get much more output, finally this summary:

NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 20
P=1, Pt#1, C=.9900, K=.9887, Alpha=1.1302
P=2, Pt#2, C=.9500, K=.9439, Alpha=1.1302
P=3, Pt#3, C=.9000, K=.8884, Alpha=1.1303
P=4, Pt#4, C=.8000, K=.7796, Alpha=1.1305
P=5, Pt#5, C=.6000, K=.5701, Alpha=1.1309
P=6, Pt#6, C=.5000, K=.4692, Alpha=1.1312
P=7, Pt#7, C=.4000, K=.3708, Alpha=1.1314
P=8, Pt#8, C=.2000, K=.1809, Alpha=1.1318
P=9, Pt#9, C=.1000, K=.0894, Alpha=1.1320
P=10, Pt#10, C=.0500, K=.0444, Alpha=1.1321
P=11, Pt#11, C=.0100, K=.0088, Alpha=1.1322
Xray  Matrix   Alpha1  Alpha2  Alpha3 %MaxDev
Ga ka in Fe    1.1322  -.0021   .0000     .00
P=1, Pt#1, C=.0100, K=.0118, Alpha=.8429
P=2, Pt#2, C=.0500, K=.0584, Alpha=.8485
P=3, Pt#3, C=.1000, K=.1151, Alpha=.8545
P=4, Pt#4, C=.2000, K=.2244, Alpha=.8640
P=5, Pt#5, C=.4000, K=.4317, Alpha=.8775
P=6, Pt#6, C=.5000, K=.5312, Alpha=.8825
P=7, Pt#7, C=.6000, K=.6285, Alpha=.8867
P=8, Pt#8, C=.8000, K=.8174, Alpha=.8937
P=9, Pt#9, C=.9000, K=.9094, Alpha=.8966
P=10, Pt#10, C=.9500, K=.9549, Alpha=.8979
P=11, Pt#11, C=.9900, K=.9910, Alpha=.8989
Xray  Matrix   Alpha1  Alpha2  Alpha3 %MaxDev
Fe ka in Ga     .8437   .1021  -.0478     .22

St    3 Sample 3
TakeOff = 40.0  KiloVolt = 20.0  Density =  5.000
Standard Z-bar:  28.5

ELEM:       Ga      Fe
ELWT:   50.000  50.000
NRWT:   50.000  50.000
BETA:   1.0656   .9414


So these "beta" factors are essentially the matrix correction factors for this composition at 20 keV and as one can see they are very close to the pure Phi-rho-z calculations above.

Ga Ka 1.0656 compared to 1.0656
Fe Ka 0.9414 compared to 0.9412

Now it gets interesting.  Let's now utilize the Penepma Penfluor/Fanal Fe-Ga binary k-ratios as alpha factors by checking this box here:



Now we click calculate again and here is our output, notice the k-ratios loaded from the matrix.mdb database:

Initializing alpha-factors...
Number of alpha-factor binaries to be calculated =  1
Calculating alpha-factor binary Ga ka in Fe

AFactorPenepmaReadMatrix: Ga ka in Fe at 40 degrees and 20 keV
   Conc      Kratios    Alpha   
    99.0000   98.690285    1.31383
    95.0000   94.231575    1.16309
    90.0000   88.327248    1.18938
    80.0000   77.508125    1.16075
    60.0000   56.482689    1.15568
    50.0000   46.362133    1.15693
    40.0000   36.643017    1.15269
    20.0000   17.789076    1.15536
    10.0000   8.803622     1.15100
    5.00000   4.372882     1.15096
    1.00000   .870474      1.15030

AFactorPenepmaReadMatrix: Fe ka in Ga at 40 degrees and 20 keV
   Conc      Kratios    Alpha   
    99.0000   99.153847    .844841
    95.0000   95.536354    .887718
    90.0000   90.900276    .900960
    80.0000   81.657516    .898508
    60.0000   62.794140    .888758
    50.0000   53.077549    .884036
    40.0000   43.177395    .877351
    20.0000   22.564974    .857912
    10.0000   11.565740    .849581
    5.00000   5.906283     .838480
    1.00000   1.207044     .826737

 NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 20
P=1, Pt#1, C=.9900, K=.9869, Alpha=1.3138
P=2, Pt#2, C=.9500, K=.9423, Alpha=1.1631
P=3, Pt#3, C=.9000, K=.8833, Alpha=1.1894
P=4, Pt#4, C=.8000, K=.7751, Alpha=1.1607
P=5, Pt#5, C=.6000, K=.5648, Alpha=1.1557
P=6, Pt#6, C=.5000, K=.4636, Alpha=1.1569
P=7, Pt#7, C=.4000, K=.3664, Alpha=1.1527
P=8, Pt#8, C=.2000, K=.1779, Alpha=1.1554
P=9, Pt#9, C=.1000, K=.0880, Alpha=1.1510
P=10, Pt#10, C=.0500, K=.0437, Alpha=1.1510
P=11, Pt#11, C=.0100, K=.0087, Alpha=1.1503
Xray  Matrix   Alpha1  Alpha2  Alpha3 %MaxDev
Ga ka in Fe    1.1623  -.1413   .2145    6.18
P=1, Pt#1, C=.9900, K=.9915, Alpha=.8448
P=2, Pt#2, C=.9500, K=.9554, Alpha=.8877
P=3, Pt#3, C=.9000, K=.9090, Alpha=.9010
P=4, Pt#4, C=.8000, K=.8166, Alpha=.8985
P=5, Pt#5, C=.6000, K=.6279, Alpha=.8888
P=6, Pt#6, C=.5000, K=.5308, Alpha=.8840
P=7, Pt#7, C=.4000, K=.4318, Alpha=.8774
P=8, Pt#8, C=.2000, K=.2256, Alpha=.8579
P=9, Pt#9, C=.1000, K=.1157, Alpha=.8496
P=10, Pt#10, C=.0500, K=.0591, Alpha=.8385
P=11, Pt#11, C=.0100, K=.0121, Alpha=.8267
Xray  Matrix   Alpha1  Alpha2  Alpha3 %MaxDev
Fe ka in Ga     .8257   .2086  -.1624    3.33

St    1 Sample 1
TakeOff = 40.0  KiloVolt = 20.0  Density =  5.000
Standard Z-bar:  28.5

ELEM:       Ga      Fe
ELWT:   50.000  50.000
NRWT:   50.000  50.000
BETA:   1.0727   .9447


Close to the Armstrong/Reed analytical calculations but but little different.  Which is is more correct?  For these high energy lines I would say the Penfluor/Fanal calculations, but one would want to compare these calculations with measurements on standards.

By the way, any time one wants to know if the alpha factors are from the Penepma calculations or not, simply click the Run | List Current Alpha Factors menu here:



and then you will get output for all currently utilized binaries as seen here:

Penepma K-Ratio Alpha Factors:
Xray  Matrix   Alpha1  Alpha2  Alpha3
Fe ka in Ga     .8257   .2086  -.1624    *From Penepma 2012 Calculations
Ga ka in Fe    1.1623  -.1413   .2145    *From Penepma 2012 Calculations

All Alpha Factors:
                 Ga         Fe   
   Ga ka     1.0000     1.1623   
   Ga ka      .0000     -.1413   
   Ga ka      .0000      .2145   
   Fe ka      .8257     1.0000   
   Fe ka      .2086      .0000   
   Fe ka     -.1624      .0000