Armstrong's Famous Si-Ir Binary Alloy

[Probeman]

Some of you have already seen John Armstrong's excellent presentation of Si-Ir alloy data he and Paul Carpenter acquired for JPL when John and Paul were still at Cal Tech.  It is a wonderful example of why we need more than one matrix correction method.

Basically the presentation starts by John explaining how JPL was sure that the alloy in question was either Si50Ir50 (atomic) or Si55Ir45 (atomic), but they didn't know which phase it was. So John proceeds to show his measurements, which when calculated using his default matrix corrections (Armstrong/Reed/CITZMU) gave this result:



So, it must be the Si55Ir45 phase right?  Maybe...

But let's run the other matrix corrections to be sure by checking the Use All Matrix Corrections box as seen here:



Then we obtain these results after clicking the Calculate button as seen here:



Please note that matrix correction #1, the one we showed above does give the Si55Ir45 composition, but now look at the very next matrix correction, a traditional one going back to Philibert, which gives a 50:50 atomic ratio- also one of the "expected" compositions!

So which one is right?  Well we could start playing the game where we evaluate the ability of these different matrix corrections to give the right answer for this particular system, and yes, the atomic number correction is significant, so perhaps the more "primitive", Philibert correction is more suspect, but in the end John and Paul were able to utilize a SiIr alloy of known composition as a primary standard and the Si55Ir45 (atomic) composition is the correct composition, but using pure element standards the choice seems arbitrary based on the results above.

This is just one more reason why the professional analyst needs to rely on more than a single matrix correction- for the simple reason that they have all been "optimized" to particular empirical data sets and therefore work better on some compositions than others.

In the meantime let's look at the original Armstrong/Reed correction  which gave us the Si55Ir45 (atomic)  composition using the Heinrich/CitZAF MACs as originally implemented by John as seen here again:

SAMPLE: 1, ITERATIONS: 4, Z-BAR: 67.40733

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ir la   .9907  1.0000  1.0824  1.0723  1.1287   .9589   .9548 11.2150  1.7833 124.108
   Si ka  1.6859   .9886   .7791  1.2986   .5819  1.3389   .5095  1.8390 10.8755 1456.45

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
   Ir la  .79090  .79090  84.806   -----  44.860    .449   20.00
   Si ka  .11730  .11730  15.232   -----  55.140    .551   20.00
   TOTAL:                100.038   ----- 100.000   1.000


Let's try a different set of MACs, the Henke MACs for example as seen here:

SAMPLE: 1, ITERATIONS: 3, Z-BAR: 67.89716

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ir la   .9911  1.0000  1.0780  1.0684  1.1220   .9608   .9544 11.2150  1.7833 123.152
   Si ka  1.5841   .9880   .7773  1.2166   .5782  1.3444   .5368  1.8390 10.8755 1302.59

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
   Ir la  .79090  .79090  84.498   -----  46.387    .464   20.00
   Si ka  .11730  .11730  14.271   -----  53.613    .536   20.00
   TOTAL:                 98.769   ----- 100.000   1.000


Somewhat more ambiguous to say the least. Let's run all the matrix corrections again but with the same (Henke) mass absorption coefficients:

Summary of All Calculated (averaged) Matrix Corrections:
#1  approx. Ir45Si55 (atomic) based on Ir3Si5 standard
LINEMU   Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV

Elemental Weight Percents:
ELEM:       Ir      Si   TOTAL
     1  84.498  14.271  98.769   Armstrong/Love Scott (default)
     2  86.704  11.747  98.451   Conventional Philibert/Duncumb-Reed
     3  84.857  12.874  97.731   Heinrich/Duncumb-Reed
     4  84.334  12.785  97.119   Love-Scott I
     5  84.324  12.798  97.122   Love-Scott II
     6  84.203  11.044  95.247   Packwood Phi(pz) (EPQ-91)
     7  86.125  13.959 100.084   Bastin (original) Phi(pz)
     8  84.607  13.656  98.263   Bastin PROZA Phi(pz) (EPQ-91)
     9  84.525  12.801  97.326   Pouchou and Pichoir-Full (Original)
    10  84.289  12.599  96.888   Pouchou and Pichoir-Simplified (XPP)

AVER:   84.847  12.853  97.700
SDEV:     .858    .969   1.299
SERR:     .271    .306

MIN:    84.203  11.044  95.247
MAX:    86.704  14.271 100.084

Atomic Percents:
ELEM:       Ir      Si   TOTAL
     1  46.387  53.613 100.000   Armstrong/Love Scott (default)
     2  51.891  48.109 100.000   Conventional Philibert/Duncumb-Reed
     3  49.063  50.937 100.000   Heinrich/Duncumb-Reed
     4  49.082  50.918 100.000   Love-Scott I
     5  49.053  50.947 100.000   Love-Scott II
     6  52.699  47.301 100.000   Packwood Phi(pz) (EPQ-91)
     7  47.413  52.587 100.000   Bastin (original) Phi(pz)
     8  47.516  52.485 100.000   Bastin PROZA Phi(pz) (EPQ-91)
     9  49.107  50.893 100.000   Pouchou and Pichoir-Full (Original)
    10  49.435  50.565 100.000   Pouchou and Pichoir-Simplified (XPP)

AVER:   49.164  50.836 100.000
SDEV:    1.930   1.930    .000
SERR:     .610    .610

MIN:    46.387  47.301 100.000
MAX:    52.699  53.613 100.000


Pretty hard to tell what the correct answer is!   So, what can we do next?  Well I then ran Penepma 2012 for around 10 days and modeled 11 binary compositions in the Si-Ir system and here are some results for Si Ka at 20 keV:



The weight percents of Si and k-ratio (also in percent) are shown circled in red.  Here is the Ir La line at 20 keV:



Currently I haven't yet provided a way to automatically insert these Penepma Monte-Carlo calculations into the matrix.mdb database (though it is on the "to do list"), but next we'll look at utilizing the Penfluor/Fanal Si-Ir binary which contains a full Monte-Carlo calculation for the primary intensity and an analytical expression for the fluorescence.

[Probeman]

OK, let's start again with the Armstrong/Reed/CITZMU phi-rho-z calculation of the SiIr alloy where we obtain what ostensibly appears to be Si55Ir45 (atomic):

#1  approx. Ir45Si55 (atomic) based on Ir3Si5 standard

SAMPLE: 1, ITERATIONS: 4, Z-BAR: 67.40733

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Ir la   .9907  1.0000  1.0824  1.0723  1.1287   .9589   .9548 11.2150  1.7833 124.108
   Si ka  1.6859   .9886   .7791  1.2986   .5819  1.3389   .5095  1.8390 10.8755 1456.45

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
   Ir la  .79090  .79090  84.806   -----  44.860    .449   20.00
   Si ka  .11730  .11730  15.232   -----  55.140    .551   20.00
   TOTAL:                100.038   ----- 100.000   1.000


Now we switch to alpha factor polynomial fitting using the Analytical | ZAF, Phi-Rho-Z, Alpha Factor, Calibration Curve Selection menu:



If we plot these alpha factors derived from the k-ratios from the Armstrong/Reed/CITZMU calculations (see the Analytical | Calculate and Plot Binary Alpha factors menu) we obtain this plot for Ir La at 20 keV:



and this plot for Si ka at 20 keV where we can see that even with a 2nd order polynomial, the fit is not perfect due to the non-linear nature of the absorption correction:



Now we get roughly similar results to the "straight" phi-rho-z calculation fitting the Armstrong/Reed/CITZMU k-ratios to polynomial alpha factors as seen here:

ELEMENT    ir la   si ka   Total
UNK KRAT   .7909   .1173
UNK WT%   84.990  14.951  99.941
UNK AT%   45.375  54.625 100.000
UNK BETA  1.0746  1.2746
ALPITER   6.0000

The point being that the polynomial alpha factor fitting allows one to pre-calculate the physics for each binary system, and subsequently combine them using the beta factor expression for arbitrary compositions as described here:

http://probesoftware.com/smf/index.php?topic=139.msg637#msg637

Now we enable the Penepma 2012 k-ratios as seen here, again from the Analytical | ZAF, Phi-Rho-Z, Alpha Factor, Calibration Curve Selection menu:



and obtain these intermediate results using the Penepma 2012 Penfluor/Fanal derived k-ratios for Si and Ir:

Initializing alpha-factors...
Number of alpha-factor binaries to be calculated =  1
Calculating alpha-factor binary ir la in si

AFactorPenepmaReadMatrix: Ir la in Si at 40 degrees and 20 keV
   Conc      Kratios    Alpha   
    99.0000   98.006218    2.01400
    95.0000   92.924858    1.44663
    90.0000   86.025154    1.46206
    80.0000   73.216965    1.46322
    60.0000   50.819466    1.45163
    50.0000   40.913555    1.44418
    40.0000   31.832989    1.42760
    20.0000   15.031998    1.41312
    10.0000   7.298365     1.41130
    5.00000   3.682503     1.37660
    1.00000   .738135      1.35835

AFactorPenepmaReadMatrix: Si ka in Ir at 40 degrees and 20 keV
   Conc      Kratios    Alpha   
    99.0000   98.885162    1.11614
    95.0000   93.915077    1.23104
    90.0000   88.040230    1.22260
    80.0000   76.524353    1.22709
    60.0000   55.550423    1.20025
    50.0000   45.765198    1.18507
    40.0000   36.368473    1.16642
    20.0000   18.166149    1.12619
    10.0000   9.182739     1.09889
    5.00000   4.624117     1.08557
    1.00000   .924762      1.08218

 NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 20
P=1, Pt#1, C=.9900, K=.9801, Alpha=2.0140
P=2, Pt#2, C=.9500, K=.9292, Alpha=1.4466
P=3, Pt#3, C=.9000, K=.8603, Alpha=1.4621
P=4, Pt#4, C=.8000, K=.7322, Alpha=1.4632
P=5, Pt#5, C=.6000, K=.5082, Alpha=1.4516
P=6, Pt#6, C=.5000, K=.4091, Alpha=1.4442
P=7, Pt#7, C=.4000, K=.3183, Alpha=1.4276
P=8, Pt#8, C=.2000, K=.1503, Alpha=1.4131
P=9, Pt#9, C=.1000, K=.0730, Alpha=1.4113
P=10, Pt#10, C=.0500, K=.0368, Alpha=1.3766
P=11, Pt#11, C=.0100, K=.0074, Alpha=1.3583
Xray  Matrix   Alpha1  Alpha2  Alpha3 %MaxDev
ir la in si    1.4124  -.3141   .5920   16.50
P=1, Pt#1, C=.9900, K=.9889, Alpha=1.1161
P=2, Pt#2, C=.9500, K=.9392, Alpha=1.2310
P=3, Pt#3, C=.9000, K=.8804, Alpha=1.2226
P=4, Pt#4, C=.8000, K=.7652, Alpha=1.2271
P=5, Pt#5, C=.6000, K=.5555, Alpha=1.2003
P=6, Pt#6, C=.5000, K=.4577, Alpha=1.1851
P=7, Pt#7, C=.4000, K=.3637, Alpha=1.1664
P=8, Pt#8, C=.2000, K=.1817, Alpha=1.1262
P=9, Pt#9, C=.1000, K=.0918, Alpha=1.0989
P=10, Pt#10, C=.0500, K=.0462, Alpha=1.0856
P=11, Pt#11, C=.0100, K=.0092, Alpha=1.0822
Xray  Matrix   Alpha1  Alpha2  Alpha3 %MaxDev
si ka in ir    1.0654   .3966  -.2790    6.13

Penepma K-Ratio Alpha Factors:
Xray  Matrix   Alpha1  Alpha2  Alpha3
Si ka in Ir    1.0654   .3966  -.2790    *From Penepma 2012 Calculations
Ir la in Si    1.4124  -.3141   .5920    *From Penepma 2012 Calculations

All Alpha Factors:
                 ir         si   
   ir la     1.0000     1.4124   
   ir la      .0000     -.3141   
   ir la      .0000      .5920   
   si ka     1.0654     1.0000   
   si ka      .3966      .0000   
   si ka     -.2790      .0000   


Plotted up these Penepma derived alpha-factors look like this for Ir La:



and this for Si Ka:



Obviously there are some fit problems as we approach the pure end-member. This is primarily a precision problem that occurs from subtracting two large numbers from each other, but they don't have a very significant effect on the results because the alpha factor for an element in itself is 1.0.

The calculation utilizing these Penepma derived alpha factors is here (primary intensity from Penfluor Monte-Carlo, fluorescence from Fanal analytical model:

ELEMENT    ir la   si ka   Total
UNK KRAT   .7909   .1173
UNK WT%   83.343  13.746  97.089
UNK AT%   46.977  53.023 100.000
UNK BETA  1.0538  1.1719
ALPITER   5.0000

Somewhat ambiguous one might say.  Now we limit the polynomial fit to avoid low precision calculations as the pure element concentrations are approached by selecting this option:



Initializing alpha-factors...
Number of alpha-factor binaries to be calculated =  1
Calculating alpha-factor binary ir la in si

AFactorPenepmaReadMatrix: Ir la in Si at 40 degrees and 20 keV
   Conc      Kratios    Alpha   
    99.0000   98.006218    2.01400
    95.0000   92.924858    1.44663
    90.0000   86.025154    1.46206
    80.0000   73.216965    1.46322
    60.0000   50.819466    1.45163
    50.0000   40.913555    1.44418
    40.0000   31.832989    1.42760
    20.0000   15.031998    1.41312
    10.0000   7.298365     1.41130
    5.00000   3.682503     1.37660
    1.00000   .738135      1.35835

AFactorPenepmaReadMatrix: Si ka in Ir at 40 degrees and 20 keV
   Conc      Kratios    Alpha   
    99.0000   98.885162    1.11614
    95.0000   93.915077    1.23104
    90.0000   88.040230    1.22260
    80.0000   76.524353    1.22709
    60.0000   55.550423    1.20025
    50.0000   45.765198    1.18507
    40.0000   36.368473    1.16642
    20.0000   18.166149    1.12619
    10.0000   9.182739     1.09889
    5.00000   4.624117     1.08557
    1.00000   .924762      1.08218

 NON-LINEAR Alpha Factors, Takeoff= 40, KeV= 20
P=3, Pt#1, C=.9000, K=.8603, Alpha=1.4621
P=4, Pt#2, C=.8000, K=.7322, Alpha=1.4632
P=5, Pt#3, C=.6000, K=.5082, Alpha=1.4516
P=6, Pt#4, C=.5000, K=.4091, Alpha=1.4442
P=7, Pt#5, C=.4000, K=.3183, Alpha=1.4276
P=8, Pt#6, C=.2000, K=.1503, Alpha=1.4131
P=9, Pt#7, C=.1000, K=.0730, Alpha=1.4113
P=10, Pt#8, C=.0500, K=.0368, Alpha=1.3766
P=11, Pt#9, C=.0100, K=.0074, Alpha=1.3583
Xray  Matrix   Alpha1  Alpha2  Alpha3 %MaxDev
ir la in si    1.3700   .2149  -.1261    1.50
P=3, Pt#1, C=.9000, K=.8804, Alpha=1.2226
P=4, Pt#2, C=.8000, K=.7652, Alpha=1.2271
P=5, Pt#3, C=.6000, K=.5555, Alpha=1.2003
P=6, Pt#4, C=.5000, K=.4577, Alpha=1.1851
P=7, Pt#5, C=.4000, K=.3637, Alpha=1.1664
P=8, Pt#6, C=.2000, K=.1817, Alpha=1.1262
P=9, Pt#7, C=.1000, K=.0918, Alpha=1.0989
P=10, Pt#8, C=.0500, K=.0462, Alpha=1.0856
P=11, Pt#9, C=.0100, K=.0092, Alpha=1.0822
Xray  Matrix   Alpha1  Alpha2  Alpha3 %MaxDev
si ka in ir    1.0743   .2858  -.1283     .52

Penepma K-Ratio Alpha Factors:
Xray  Matrix   Alpha1  Alpha2  Alpha3
Si ka in Ir    1.0743   .2858  -.1283    *From Penepma 2012 Calculations
Ir la in Si    1.3700   .2149  -.1261    *From Penepma 2012 Calculations

All Alpha Factors:
                 ir         si   
   ir la     1.0000     1.3700   
   ir la      .0000      .2149   
   ir la      .0000     -.1261   
   si ka     1.0743     1.0000   
   si ka      .2858      .0000   
   si ka     -.1283      .0000   


Plotting up these 90% limited alpha factors we obtain more precise fits as seen here for Ir la:



and here for Si Ka:



And we now obtain these results, which are somewhat better, though still not as unequivocal as one would hope.

ELEMENT    ir la   si ka   Total
UNK KRAT   .7909   .1173
UNK WT%   83.604  13.990  97.595
UNK AT%   46.617  53.383 100.000
UNK BETA  1.0571  1.1927
ALPITER   5.0000

Though it is closer to Si55Ir45 as expected. But this is the "state of the art" for this particular Monte-Carlo physics!

[Probeman]

Just for "funsies" I ran the last calculation using an 80% limit for the best possible Penepma 2012 alpha factor extrapolation which you set here:



and, which looks like this for Ir la:



and this for Si Ka:



and the result is further improvement to the "truth"... though perhaps it would be worthwhile at this point to use a larger dataset...

ELEMENT    ir la   si ka   Total
UNK KRAT   .7909   .1173
UNK WT%   83.630  14.074  97.703
UNK AT%   46.477  53.523 100.000
UNK BETA  1.0574  1.1998
ALPITER   5.0000

For further investigation let's examine the Pb-Si system which is a good proxy for the Si-Ir system due to the large difference in A/Z between the two elements (remember, we need to eliminate all normalizations to mass in  this physics!), and instead utilize a single crystal of PbSiO3 for which the stoichiometry is perfect as only Nature can accomplish (you know, most recently the Tsumeb locality). 

http://www.minersoc.org/pages/Archive-MM/Volume_29/29-218-933.pdf

By the way:

Element        A/Z
    Ir             2.49
    Pb            2.52
    Si             2.00

Next week we'll do some measurements on this material!

[Probeman]

But before we do that I just wanted to make sure everyone saw the interesting comparison between the analytical expressions and the Monte-carlo as seen here for Ir La which are actually fairly similar in magnitude though somewhat different in slope:



But this isn't too surprising since Ir La is a very energetic x-ray around 10 keV. 

The bigger surprise is for Si Ka which though a fairly simple atom is experiencing some very different physics depending on who's doing the calculation as seen here:

[Probeman]

Related to the Si-Ir problem is the ability to measure Si ka in various matrices. Here are results from some silicate measurements I recently did.  SiO2 was the primary standard (20 keV, 30 nA, 10 um beam). These are:

SiO2               yes, I know it's technically *not* a silicate
Mg2SiO4            synthetic (Japan, Takei)
Fe2SiO4            synthetic (Oak Ridge, Boatner)
Mn2SiO4            synthetic (Purdue)
Co2SiO4            synthetic (Purdue)
ZrSiO4             synthetic (Hanchar)
PbSiO3             natural (Tsumeb)
HfSiO4             synthetic (Hanchar)
ThSiO4             synthetic (Hanchar)
CaMgSi2O6          natural (Chesterman)

I will also post some Penepma 2012 calculations for these silicates for comparison. To start here are all the standard plotted using our Evaluate application which allows one to easily compare standard accuracy. I thank Paul Carpenter and John Fournelle for helping me with this app.



Here we can see that there are a few "outliers" particularly HfSiO4, which is a mass absorption coefficient problem for Si Ka by Hf which is close to an absorption edge. CalcZAF reports the following MACs from this binary from various sources:

MAC value for Si ka in Hf =    5449.15  (LINEMU   Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV)
MAC value for Si ka in Hf =    5151.30  (CITZMU   Heinrich (1966) and Henke and Ebisu (1974))
MAC value for Si ka in Hf =    5635.09  (MCMASTER McMaster (LLL, 1969) (modified by Rivers))
MAC value for Si ka in Hf =    5037.41  (MAC30    Heinrich (Fit to Goldstein tables, 1987))
MAC value for Si ka in Hf =    5152.54  (MACJTA   Armstrong (FRAME equations, 1992))
MAC value for Si ka in Hf =    4926.87  (FFAST    Chantler (NIST v 2.1, 2005))
MAC value for Si ka in Hf =    4926.87  (USERMAC  User Defined MAC Table)

We can see that the more modern FFAST value is smaller, which should help the correction, so we specify the FFAST MAC table from the Analytical | ZAF, Phi-Rho-Z, Alpha factor and Calibration Curve Selections menu dialog (MACs button) and get this somewhat better result, though some of the other standards are now slightly worse:



So let's try some other corrections, for example the PAP correction, which shows considerable improvement (at least the HfSiO4 now agrees with the other secondary standards!), even though all these secondary standards are a little low compared with the SiO2 priamry standard:



So, now let's try the XPP (PAP) correction which gives similar results:



Bastin's Proza correction is however, yields quite different results: