So, here is where I would like to introduce a new TDI extrapolation model, the Logarithmic extrapolation or log-log fit or "double-exponential" model. The previously existing linear and hyper-exponential TDI methods are summarized in the previous post. Let's take a look first at the TDI plots using this new double exponential fit:
The extrapolations are much improved, at least to the eye, so now let's look at the quant results again:
St 173 Set 24 K-0375 NBS glass
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 100. Beam Size = 10
(Magnification (analytical) = 40000), Beam Mode = Analog Spot
(Magnification (default) = 400, Magnification (imaging) = 800)
Image Shift (X,Y): .00, .00
from John Rutledge
Number of Data Lines: 5 Number of 'Good' Data Lines: 5
First/Last Date-Time: 05/10/2012 02:30:56 AM to 05/10/2012 02:38:17 AM
WARNING- Using Exponential Off-Peak correction for si ka
WARNING- Using Exponential Off-Peak correction for p ka
WARNING- Using Time Dependent Intensity (TDI) Element Correction
Average Total Oxygen: .000 Average Total Weight%: 97.309
Average Calculated Oxygen: .000 Average Atomic Number: 16.572
Average Excess Oxygen: .000 Average Atomic Weight: 22.868
Average ZAF Iteration: 4.00 Average Quant Iterate: 2.00
St 173 Set 24 K-0375 NBS glass, Results in Elemental Weight Percents
SPEC: Zn Ba U O
TYPE: SPEC SPEC SPEC SPEC
AVER: 4.940 10.370 .110 42.320
SDEV: .000 .000 .000 .000
ELEM: Na Si Ca Fe P
BGDS: LIN EXP LIN LIN EXP
TIME: 20.00 20.00 20.00 20.00 20.00
BEAM: 100.72 100.72 100.72 100.72 100.72
ELEM: Na Si Ca Fe P SUM
371 7.358 33.896 .001 .007 .004 99.006
372 5.900 33.248 .005 -.008 .012 96.897
373 6.969 32.999 .008 -.014 .014 97.717
374 5.572 33.286 .001 -.029 .008 96.579
375 5.781 32.830 .001 .013 -.021 96.344
AVER: 6.316 33.252 .003 -.006 .003 97.309
SDEV: .795 .406 .003 .017 .014 1.082
SERR: .355 .181 .001 .008 .006
%RSD: 12.58 1.22 87.96 -272.99 412.40
PUBL: 10.420 31.830 n.a. n.a. n.a. 99.990
%VAR: -39.39 4.47 --- --- ---
DIFF: -4.104 1.422 --- --- ---
STDS: 336 14 285 162 285
STKF: .0735 .4101 .3596 .0950 .1599
STCT: 77.91 79.30 603.55 66.49 40.15
UNKF: .0302 .2643 .0000 -.0001 .0000
UNCT: 32.04 51.11 .05 -.04 .01
UNBG: 3.34 .16 1.23 .99 .05
ZCOR: 2.0906 1.2580 1.0656 1.1519 1.4697
KRAW: .4113 .6446 .0001 -.0006 .0001
PKBG: 10.59 315.92 1.04 .97 1.26
TDI%: 3412.187 -5.918 .962 ---- ----
DEV%: 11.8 .4 33.2 ---- ----
TDIF: LOG-LOG LOG-LOG LOG-LIN ---- ----
TDIT: 74.20 74.40 71.80 ---- ----
TDII: 31.8 51.1 1.28 ---- ----
Ok, so that is better and now we are "only" off in accuracy for Na by around 40% relative (6.3 wt% compared to the published value of 10.4 wt%). Interestingly our Si value is very slightly worse than the "hyper-exponential" fit. The total averages 97% which is not good, but much better than before.
Are we done, well maybe... if we look again at the log-log plots it does appear that we are still slightly under estimating the TDI correction in the first few seconds. What can we do?
Well let's try "weighting" the first few data points in the acquisition, since these measurements should obviously be the closer to the zero time intensity, by utilizing this option in the Analytical | Analysis Options dialog as seen here:
By entering a value to "2", we weight the first point times 2, if we enter say "3" we weight the first point times 3 and the second point times 2, if we enter a "4" we weight the first point 4 times, second point 3 times, third point 2 times, etc., etc. Here is what we obtain quantitatively with just weighting the first point times 2:
St 173 Set 24 K-0375 NBS glass
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 100. Beam Size = 10
(Magnification (analytical) = 40000), Beam Mode = Analog Spot
(Magnification (default) = 400, Magnification (imaging) = 800)
Image Shift (X,Y): .00, .00
from John Rutledge
Number of Data Lines: 5 Number of 'Good' Data Lines: 5
First/Last Date-Time: 05/10/2012 02:30:56 AM to 05/10/2012 02:38:17 AM
WARNING- Using Exponential Off-Peak correction for si ka
WARNING- Using Exponential Off-Peak correction for p ka
WARNING- Using Time Dependent Intensity (TDI) Element Correction
WARNING- Using Time Dependent Intensity (TDI) Weighting Factor of 2
Average Total Oxygen: .000 Average Total Weight%: 98.071
Average Calculated Oxygen: .000 Average Atomic Number: 16.519
Average Excess Oxygen: .000 Average Atomic Weight: 22.855
Average ZAF Iteration: 4.00 Average Quant Iterate: 2.00
St 173 Set 24 K-0375 NBS glass, Results in Elemental Weight Percents
SPEC: Zn Ba U O
TYPE: SPEC SPEC SPEC SPEC
AVER: 4.940 10.370 .110 42.320
SDEV: .000 .000 .000 .000
ELEM: Na Si Ca Fe P
BGDS: LIN EXP LIN LIN EXP
TIME: 20.00 20.00 20.00 20.00 20.00
BEAM: 100.72 100.72 100.72 100.72 100.72
ELEM: Na Si Ca Fe P SUM
371 8.221 33.420 .001 .007 .004 99.394
372 7.202 33.052 .005 -.008 .012 98.003
373 8.104 32.753 .008 -.014 .014 98.605
374 6.835 32.904 .001 -.029 .008 97.459
375 6.694 32.465 .001 .013 -.021 96.893
AVER: 7.411 32.919 .003 -.006 .003 98.071
SDEV: .712 .354 .003 .017 .014 .975
SERR: .318 .159 .001 .008 .006
%RSD: 9.60 1.08 88.39 -272.99 412.33
PUBL: 10.420 31.830 n.a. n.a. n.a. 99.990
%VAR: -28.88 3.42 --- --- ---
DIFF: -3.009 1.089 --- --- ---
STDS: 336 14 285 162 285
STKF: .0735 .4101 .3596 .0950 .1599
STCT: 77.82 79.39 604.17 66.49 40.15
UNKF: .0356 .2607 .0000 -.0001 .0000
UNCT: 37.74 50.48 .05 -.04 .01
UNBG: 3.34 .16 1.23 .99 .05
ZCOR: 2.0801 1.2625 1.0652 1.1517 1.4679
KRAW: .4849 .6358 .0001 -.0006 .0001
PKBG: 12.30 311.92 1.04 .97 1.26
TDI%: 4041.216 -7.094 1.268 ---- ----
DEV%: 12.1 .4 32.6 ---- ----
TDIF: LOG-LOG LOG-LOG LOG-LIN ---- ----
TDIT: 74.20 74.40 71.80 ---- ----
TDII: 37.6 50.5 1.29 ---- ----
As you can see, there is further improvement. Our total average is now 98%, our Na value is now 7.4 wt% compared to the published value of 10.4 wt%- still a 28% error, but note that the correction is approximately 4000%! Yes, you read that correctly- over 4000% correction. The Si is now within 3.4 % relative accuracy.
Ok, let's try with a weighting of "4" and see what that does:
St 173 Set 24 K-0375 NBS glass
TakeOff = 40.0 KiloVolt = 15.0 Beam Current = 100. Beam Size = 10
(Magnification (analytical) = 40000), Beam Mode = Analog Spot
(Magnification (default) = 400, Magnification (imaging) = 800)
Image Shift (X,Y): .00, .00
from John Rutledge
Number of Data Lines: 5 Number of 'Good' Data Lines: 5
First/Last Date-Time: 05/10/2012 02:30:56 AM to 05/10/2012 02:38:17 AM
WARNING- Using Exponential Off-Peak correction for si ka
WARNING- Using Exponential Off-Peak correction for p ka
WARNING- Using Time Dependent Intensity (TDI) Element Correction
WARNING- Using Time Dependent Intensity (TDI) Weighting Factor of 4
Average Total Oxygen: .000 Average Total Weight%: 98.809
Average Calculated Oxygen: .000 Average Atomic Number: 16.471
Average Excess Oxygen: .000 Average Atomic Weight: 22.847
Average ZAF Iteration: 4.00 Average Quant Iterate: 2.00
St 173 Set 24 K-0375 NBS glass, Results in Elemental Weight Percents
SPEC: Zn Ba U O
TYPE: SPEC SPEC SPEC SPEC
AVER: 4.940 10.370 .110 42.320
SDEV: .000 .000 .000 .000
ELEM: Na Si Ca Fe P
BGDS: LIN EXP LIN LIN EXP
TIME: 20.00 20.00 20.00 20.00 20.00
BEAM: 100.72 100.72 100.72 100.72 100.72
ELEM: Na Si Ca Fe P SUM
371 9.103 33.145 .001 .007 .004 100.000
372 8.228 32.857 .005 -.008 .012 98.834
373 9.077 32.640 .008 -.014 .014 99.465
374 7.914 32.672 .001 -.029 .008 98.307
375 7.449 32.258 .001 .013 -.021 97.441
AVER: 8.354 32.715 .003 -.006 .003 98.809
SDEV: .726 .325 .003 .017 .014 .997
SERR: .325 .145 .001 .008 .006
%RSD: 8.70 .99 88.90 -273.00 412.36
PUBL: 10.420 31.830 n.a. n.a. n.a. 99.990
%VAR: -19.83 2.78 --- --- ---
DIFF: -2.066 .885 --- --- ---
STDS: 336 14 285 162 285
STKF: .0735 .4101 .3596 .0950 .1599
STCT: 77.78 79.47 604.98 66.49 40.15
UNKF: .0404 .2584 .0000 -.0001 .0000
UNCT: 42.72 50.07 .05 -.04 .01
UNBG: 3.34 .16 1.23 .99 .05
ZCOR: 2.0704 1.2661 1.0649 1.1516 1.4666
KRAW: .5492 .6301 .0001 -.0006 .0001
PKBG: 13.79 309.41 1.04 .97 1.26
TDI%: 4588.661 -7.842 1.467 ---- ----
DEV%: 11.2 .4 31.9 ---- ----
TDIF: LOG-LOG LOG-LOG LOG-LIN ---- ----
TDIT: 74.20 74.40 71.80 ---- ----
TDII: 42.6 50.1 1.29 ---- ----
OK, so even more improvement! Our total average is now almost 99% and our relative accuracy error on Na and Si is now 20% and 2.8%. In the case of Na, the TDI% correction is now over 4500%!
We could keep going, but I think we all get the point... which is: we would most likely never want to perform such an acquisition on such a beam sensitive sample at such a high (100 nA) beam current! But... if we absolutely had to, we could give it a go using these new TDI tools!
By the way, here is the Na TDI plot with the 4 times point weighting:
And here are the quantitative results with 10x weighting log-log fit to the first TDI intervals:
St 173 Set 24 K-0375 NBS glass, Results in Elemental Weight Percents
ELEM: Na Si Ca Fe P Zn Ba U O
TYPE: ANAL ANAL ANAL ANAL ANAL SPEC SPEC SPEC SPEC
BGDS: LIN EXP LIN LIN EXP
TIME: 20.00 20.00 20.00 20.00 20.00
BEAM: 100.72 100.72 100.72 100.72 100.72
ELEM: Na Si Ca Fe P Zn Ba U O SUM
371 9.642 32.967 .001 .007 .004 4.940 10.370 .110 42.320 100.361
372 8.822 32.773 .005 -.008 .012 4.940 10.370 .110 42.320 99.344
373 9.654 32.545 .008 -.014 .014 4.940 10.370 .110 42.320 99.947
374 8.532 32.488 .001 -.029 .008 4.940 10.370 .110 42.320 98.740
375 7.915 32.109 .001 .013 -.021 4.940 10.370 .110 42.320 97.757
AVER: 8.913 32.576 .003 -.006 .003 4.940 10.370 .110 42.320 99.230
SDEV: .747 .323 .003 .017 .014 .000 .000 .000 .000 1.027
SERR: .334 .145 .001 .008 .006 .000 .000 .000 .000
%RSD: 8.38 .99 89.41 -273.00 412.34 .00 .00 .00 .00
PUBL: 10.420 31.830 n.a. n.a. n.a. 4.940 10.370 .110 42.320 99.990
%VAR: -14.46 2.34 --- --- --- .00 .00 .00 .00
DIFF: -1.507 .746 --- --- --- .000 .000 .000 .000
Maybe not perfect, but certainly better than the alternative!
Edit by John: The observant eye will note that the Na numbers decrease with each point acquisition in the last analysis above. This is due to the beam diameter being 10 um and the points 10 um apart, therefore each acquisition effectively pre-heats the subsequent acquisition volume which reduces the "incubation" time" and therefore decreases the Na intensity more quickly.