Not sure if this really qualifies as a "trick" but I think it is worth examining a particularly nasty binary system and that is Si Ka in Hf.
I was running some trace zircon analyses and normally I don't measure Si (or Zr) because for trace analysis I usually just specify the ZrSiO4 formula by difference in the Calculation Options dialog for a complete matrix correction. But this time I did and when I analyzed my Hf standard for Si, I got some strange analyses.
I should say that this isn't the first time I've seen this as shown by the post from a couple of years ago:
http://probesoftware.com/smf/index.php?topic=158.msg815#msg815but this time I will follow up further on the quant question. By the way, I should also note that if I analyze the Hf in the Hf standard (HfSiO4 from John Hanchar) using pure Hf metal (using the Hf La line, so very energetic), I get almost exactly the expected Hf content in HfSiO4, so I'm pretty sure it's HfSiO4 (not sure if it could be anything else given only Hf, Si and O).
Anyway, here is the analysis of HfSiO4 using HfSiO4 as the Hf standard and ZrSiO4 as the Si standard:
ELEM: Zr Hf Si O
TYPE: ANAL ANAL ANAL SPEC
BGDS: LIN EXP LIN
TIME: 60.00 60.00 60.00 ---
BEAM: 29.89 29.89 29.89 ---
ELEM: Zr Hf Si O SUM
1533 .021 66.797 15.337 23.653 105.809
1534 -.014 66.405 14.935 23.653 104.979
1535 .028 66.587 15.288 23.653 105.556
AVER: .012 66.596 15.187 23.653 105.448
SDEV: .023 .196 .219 .000 .426
SERR: .013 .113 .127 .000
%RSD: 196.68 .29 1.44 .00
PUBL: n.a. 65.967 10.380 23.653 100.000
%VAR: --- (.95) 46.31 .00
DIFF: --- (.63) 4.807 .000
STDS: 257 19 257 ---
STKF: .4109 .5749 .1274 ---
STCT: 4215.7 14642.2 792.6 ---
UNKF: .0001 .5750 .0555 ---
UNCT: .6 14643.7 345.3 ---
UNBG: 9.4 245.2 3.4 ---
ZCOR: 2.0927 1.1582 2.7362 ---
KRAW: .0001 1.0001 .4357 ---
PKBG: 1.07 60.76 102.80 ---
I think we can all agree that a 46% relative error on a 10% value isn't very good! So then I ran all 10 matrix corrections in PFE and they all fail pretty miserably:
Summary of All Calculated (averaged) Matrix Corrections:
St 19 Set 6 HfSiO4 (Hafnon)
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Elemental Weight Percents:
ELEM: Zr Hf Si O TOTAL
1 .012 66.596 15.187 23.653 105.448 Armstrong/Love Scott (default)
2 .010 66.525 13.361 23.653 103.549 Conventional Philibert/Duncumb-Reed
3 .010 66.337 13.382 23.653 103.383 Heinrich/Duncumb-Reed
4 .011 66.464 13.954 23.653 104.083 Love-Scott I
5 .011 66.477 14.110 23.653 104.251 Love-Scott II
6 .010 66.482 13.564 23.653 103.709 Packwood Phi(pz) (EPQ-91)
7 .011 66.193 15.002 23.653 104.861 Bastin (original) Phi(pz)
8 .011 66.595 14.639 23.653 104.898 Bastin PROZA Phi(pz) (EPQ-91)
9 .011 66.492 13.905 23.653 104.061 Pouchou and Pichoir-Full (Original)
10 .010 66.446 13.630 23.653 103.740 Pouchou and Pichoir-Simplified (XPP)
AVER: .011 66.461 14.073 23.653 104.198
SDEV: .000 .120 .659 .000 .672
SERR: .000 .038 .208 .000
MIN: .010 66.193 13.361 23.653 103.383
MAX: .012 66.596 15.187 23.653 105.448
The Si concentrations range from 13.3 wt% to 15.1 wt%, but all are pretty far from the expected 10.38 wt% Si. So what is going on?
Well obviously there is an enormous atomic number correction for this system, and that is the main reason why there is so much variation in the different matrix corrections for Si Ka. Remember, all these matrix corrections are using the same MAC for Si Ka in Hf.
But there is also a very large absorption correction, as seen from a formula calculation in CalcZAF:
ELEMENT ABSCOR FLUCOR ZEDCOR ZAFCOR STP-POW BKS-COR F(x)u Ec Eo/Ec MACs
Hf la .9854 .9999 1.2376 1.2194 1.3252 .9339 .9760 9.5610 1.5689 122.199
Si ka 2.3552 1.0000 .8271 1.9481 .6972 1.1864 .3845 1.8390 8.1566 3875.50
O ka 3.7987 .9998 .7433 2.8232 .6220 1.1950 .1845 .5317 28.2114 7904.62
ELEMENT K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL
Hf la .00000 .54099 65.967 ----- 16.667 .500 15.00
Si ka .00000 .05328 10.380 ----- 16.667 .500 15.00
O ka .00000 .08378 23.653 ----- 66.667 2.000 15.00
TOTAL: 100.000 ----- 100.000 3.000
and in fact if we examine the different available MACs for Si Ka in Hf we can see there is a large range:
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 = 5061.00 (USERMAC User Defined MAC Table)
in fact, the Henke value is the 2nd highest available. What if we utilize the FFAST value?
Summary of All Calculated (averaged) Matrix Corrections:
St 19 Set 6 HfSiO4 (Hafnon)
FFAST Chantler (NIST v 2.1, 2005)
Elemental Weight Percents:
ELEM: Zr Hf Si O TOTAL
1 .011 66.523 14.493 23.653 104.680 Armstrong/Love Scott (default)
2 .010 66.431 12.831 23.653 102.925 Conventional Philibert/Duncumb-Reed
3 .010 66.282 12.858 23.653 102.803 Heinrich/Duncumb-Reed
4 .010 66.387 13.326 23.653 103.377 Love-Scott I
5 .010 66.399 13.447 23.653 103.509 Love-Scott II
6 .010 66.388 12.922 23.653 102.972 Packwood Phi(pz) (EPQ-91)
7 .011 66.173 14.335 23.653 104.172 Bastin (original) Phi(pz)
8 .011 66.514 13.990 23.653 104.168 Bastin PROZA Phi(pz) (EPQ-91)
9 .010 66.417 13.321 23.653 103.402 Pouchou and Pichoir-Full (Original)
10 .010 66.372 13.049 23.653 103.084 Pouchou and Pichoir-Simplified (XPP)
AVER: .010 66.389 13.457 23.653 103.509
SDEV: .000 .102 .612 .000 .631
SERR: .000 .032 .193 .000
MIN: .010 66.173 12.831 23.653 102.803
MAX: .011 66.523 14.493 23.653 104.680
Better, but still pretty high compared to the expected 10.38 wt%. What if we try the fast Monte Carlo method?
ELEM: Zr Hf Si O SUM
1533 .019 66.368 12.375 23.653 102.415
1534 -.013 65.993 12.043 23.653 101.677
1535 .024 66.161 12.336 23.653 102.175
AVER: .010 66.174 12.251 23.653 102.089
SDEV: .020 .188 .181 .000 .377
SERR: .012 .109 .105 .000
%RSD: 196.62 .28 1.48 .00
PUBL: n.a. 65.967 10.380 23.653 100.000
%VAR: --- (.31) 18.03 .00
DIFF: --- (.21) 1.871 .000
STDS: 257 19 257 ---
STBE: 1.2931 1.1413 1.2894 ---
STCT: 4215.7 14642.2 792.6 ---
UNBE: 1.9602 1.1448 2.3660 ---
UNCT: .6 14643.7 345.3 ---
UNBG: 9.4 245.2 3.4 ---
KRAW: .0001 1.0001 .4357 ---
PKBG: 1.07 60.76 102.80 ---
So, it's better than the best matrix correction with the FFAST MAC but still off by some 18% relative.
So now let's pull out the "big gun", which is an empirical MAC I measured for Si Ka in Hf some years ago (3.4770e+03) using Pouchou's XMAC app and a number of measurements at multiple keVs, and see what we get:
ELEM: Zr Hf Si O SUM
1533 .020 66.308 11.493 23.653 101.474
1534 -.014 65.925 11.185 23.653 100.750
1535 .026 66.101 11.457 23.653 101.237
AVER: .011 66.111 11.378 23.653 101.154
SDEV: .022 .191 .169 .000 .369
SERR: .012 .111 .097 .000
%RSD: 196.65 .29 1.48 .00
PUBL: n.a. 65.967 10.380 23.653 100.000
%VAR: --- (.22) 9.62 .00
DIFF: --- (.14) .998 .000
STDS: 257 19 257 ---
STKF: .4045 .5730 .1304 ---
STCT: 4215.7 14642.2 792.6 ---
UNKF: .0001 .5730 .0568 ---
UNCT: .6 14643.7 345.3 ---
UNBG: 9.4 245.2 3.4 ---
ZCOR: 2.0110 1.1537 2.0020 ---
KRAW: .0001 1.0001 .4357 ---
PKBG: 1.07 60.76 102.80 ---
So we're still off by some 9.6% relative, but that's a heck of a lot better than an error of 46% relative!
And the beat goes on...