Now that Probe for EPMA contains methods to utilize so called "effective takeoff" angles for quantitative analysis, I thought it might be worth a try. See here for an introduction:
https://smf.probesoftware.com/index.php?topic=40.msg12018#msg12018
Essentially one utilizes simultaneous k-ratio measurements on multiple spectrometers to determine how closely the k-ratios from different WDS spectrometers agree with each other, when measuring the same emission line and primary and secondary materials. The idea being that (at low count rates to avoid dead time effects), the k-ratios of all spectrometers (regardless of the Bragg crystal), should be similar, within statistics.
If they are not similar, there must be problem with either the spectrometer alignment or perhaps the Bragg crystal is diffracting asymmetrically. Of course the stage might also not be perpendicular to the electron beam or the sample could tilted in the sample holder, so these other possibilities need to be addressed first. Note that the latter problem (sample tilt) can easily be determined by checking the Z focus on the sample using the light optics, while the former issue (stage tilt) is more subtle and not so easily resolved.
A instrument purchase specification for simultaneous k-ratios is described in this post:
https://smf.probesoftware.com/index.php?topic=369.msg1948#msg1948
These issues are discussed further in this post:
https://smf.probesoftware.com/index.php?topic=1535.msg11937#msg11937
Moving on, a method for calculating these effective take off angle k-ratios is found in the (free) CalcZAF application here:
https://smf.probesoftware.com/index.php?topic=598.msg12062#msg12062
For these tests I utilized SiO2 as a primary standard and SRM K-412 as a secondary standard (tuning all 5 spectrometers to Si Ka), at 15 keV (I should have utilized 25 keV or more to increase the absorption correction for improved sensitivity to the effective take off angles). Here is a model calculation from CalcZAF for this system:
Effective K-Ratios for Primary Standard: 14 SiO2 synthetic
Secondary Standard: 160 NBS K-412 mineral glass
Emission line: si ka at 15 keV
Absorption Correction Method: Phi(pz) Absorption of Armstrong/Packwood-Brown 1981 MAS
MAC File: LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Percent (absolute) k-ratio change per degree at 40 degrees: .113340
Percent (relative) k-ratio change per degree at 40 degrees: .285936
Takeoff Angle: 35.0000, K-Ratio: .388863
Takeoff Angle: 35.5000, K-Ratio: .389578
Takeoff Angle: 36.0000, K-Ratio: .390275
Takeoff Angle: 36.5000, K-Ratio: .390955
Takeoff Angle: 37.0000, K-Ratio: .391619
Takeoff Angle: 37.5000, K-Ratio: .392266
Takeoff Angle: 38.0000, K-Ratio: .392897
Takeoff Angle: 38.5000, K-Ratio: .393513
Takeoff Angle: 39.0000, K-Ratio: .394115
Takeoff Angle: 39.5000, K-Ratio: .394702
Takeoff Angle: 40.0000, K-Ratio: .395275
Takeoff Angle: 40.5000, K-Ratio: .395835
Takeoff Angle: 41.0000, K-Ratio: .396381
Takeoff Angle: 41.5000, K-Ratio: .396915
Takeoff Angle: 42.0000, K-Ratio: .397437
Takeoff Angle: 42.5000, K-Ratio: .397946
Takeoff Angle: 43.0000, K-Ratio: .398444
Takeoff Angle: 43.5000, K-Ratio: .398930
Takeoff Angle: 44.0000, K-Ratio: .399405
Takeoff Angle: 44.5000, K-Ratio: .399870
Takeoff Angle: 45.0000, K-Ratio: .400323
Note that at 40 degrees takeoff angle the measured k-ratio should be 0.395 for this system. Here is what I obtained with actual measurements last weekend:
(https://smf.probesoftware.com/gallery/395_08_10_23_8_57_28.png)
Note that spectrometer 4 plots somewhat below the other spectrometers, so by "consensus" one might hypothesize that spectrometer 4 (TAP) is not diffracting symmetrically (assuming the sample is not tilted in the sample holder!). On the other hand, it could be that all 4 other spectrometers are problematic in a consistent manner. However we note that the theoretical k-ratio for this system is 0.395, which falls in the middle of the pack, so let us assume that spectrometer #4 is the outlier.
After editing the effective takeoff angle as described in the above posts to a value of 37 degrees, we now calculate the composition to utilize the effective k-ratio in the absorption correction for this spectrometer.
Note that we must perform a matrix correction to utilize the edited effective takeoff angle, but because we have measured a major element on multiple spectrometers, the matrix correction is not accurate, because too much Si will be included in the calculations also resulting in a very high total. Normally we would be utilizing the aggregate feature in Probe for EPMA for an accurate matrix correction when duplicate major or minor elements are present.
However, since we are merely looking for consistency between our spectrometers, we can perform the matrix correction with duplicate major elements. Here is a plot of the concentrations first, without the effective takeoff angle applied:
(https://smf.probesoftware.com/gallery/395_08_10_23_8_57_54.png)
And here with the effective takeoff angle feature enabled:
(https://smf.probesoftware.com/gallery/395_08_10_23_8_58_13.png)
Note that spectrometer 4 now plots in the "middle of the pack" after editing the effective takeoff angle from 40 to 37 degrees.
Does this mean that my spectrometer #4 TAP crystal is diffracting asymmetrically? You decide...
Yesterday, we belatedly realized that we had provided a mechanism to specify the effective takeoff angles for each WDS spectrometer and Bragg crystal combination by editing the SCALERS.DAT file as described in this post:
https://smf.probesoftware.com/index.php?topic=40.msg12018#msg12018
That is all well and good of course, but we decided we ought to also to support an "effective" take off angle for the EDS spectrometer. So now there is a new keyword in the [hardware] section of the Probewin.ini file as follows:
[hardware]
EDSEffectiveTakeoff=40
Now some might argue that the effective takeoff angle of an EDS spectrometer (being a fixed detector with no mechanical movement per se) should be very close to the nominal takeoff angle, so why bother? OK, good point, but in any event it is now available in version 13.5.8 of Probe for EPMA "just in case"!.
In fact the above post brings to mind an important point, which is because we don't know for certain what the actual k-ratio of our two materials should be from modeling, because each analytical model (e.g., Armstrong/Brown vs. PAP or XPP) provides a slightly different k-ratio and also due to carbon coat variation and sample surface contamination, there are some other small uncertainties associated with the k-ratio measurement, it would be nice to have a "known" k-ratio.
So perhaps, the k-ratio measured on an EDS spectrometer could provide that "reference" for the purposes of evaluating the effective k-ratios of our WDS spectrometers? I mean given that an EDS spectrometer should have a pretty accurate takeoff angle...
In the previous post above I showed the range of k-ratios for my 5 WDS spectrometers on TAP and PET crystals using Si ka in SRM K-411 and SiO2 at 15 keV:
Quote from: Probeman on October 08, 2023, 09:37:39 AM
Note that at 40 degrees takeoff angle the measured k-ratio should be 0.395 for this system. Here is what I obtained with actual measurements last weekend:
(https://smf.probesoftware.com/gallery/395_08_10_23_8_57_28.png)
Note that the measured k-ratios are all fairly close to the modeled k-ratio using the Armstrong/Brown absorption correction which was 0.395275, but using the PAP correction we obtain for these two materials at 40 degrees a value of 0.395334, so pretty close.
Also note that the range of measured k-ratios is well within the modeled range, which is a relief, I guess! :)
But, as I mentioned previously I really should have utilized a beam energy of 25 keV or more to increase the absorption correction which is what I will do next time. Also I probably should have also looked more at various secondary standards to find a pair with the largest absorption correction possible. Along that line of thinking I'm going to look next at Si Ka at 25 keV using SiO2 and perhaps my Fe2SiO4 synthetic which produces a ranges of k-ratios seen here (0.66 degrees relative percent change per degree):
Effective K-Ratios for Primary Standard: 14 SiO2 synthetic
Secondary Standard: 263 Fe2SiO4 (synthetic fayalite)
Emission line: si ka at 25 keV
Absorption Correction Method: Phi(pz) Absorption of Armstrong/Packwood-Brown 1981 MAS
MAC File: LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Percent (absolute) k-ratio change per degree at 40 degrees: .130966
Percent (relative) k-ratio change per degree at 40 degrees: .662938
Takeoff Angle: 35.0000, K-Ratio: .189129
Takeoff Angle: 35.5000, K-Ratio: .189898
Takeoff Angle: 36.0000, K-Ratio: .190655
Takeoff Angle: 36.5000, K-Ratio: .191398
Takeoff Angle: 37.0000, K-Ratio: .192130
Takeoff Angle: 37.5000, K-Ratio: .192849
Takeoff Angle: 38.0000, K-Ratio: .193556
Takeoff Angle: 38.5000, K-Ratio: .194251
Takeoff Angle: 39.0000, K-Ratio: .194934
Takeoff Angle: 39.5000, K-Ratio: .195606
Takeoff Angle: 40.0000, K-Ratio: .196266
Takeoff Angle: 40.5000, K-Ratio: .196915
Takeoff Angle: 41.0000, K-Ratio: .197553
Takeoff Angle: 41.5000, K-Ratio: .198181
Takeoff Angle: 42.0000, K-Ratio: .198797
Takeoff Angle: 42.5000, K-Ratio: .199403
Takeoff Angle: 43.0000, K-Ratio: .199998
Takeoff Angle: 43.5000, K-Ratio: .200584
Takeoff Angle: 44.0000, K-Ratio: .201159
Takeoff Angle: 44.5000, K-Ratio: .201724
Takeoff Angle: 45.0000, K-Ratio: .202279
Even better would be the Ni2SiO4 synthetic seen here:
Effective K-Ratios for Primary Standard: 14 SiO2 synthetic
Secondary Standard: 272 Ni2SiO4 (synthetic)
Emission line: si ka at 25 keV
Absorption Correction Method: Phi(pz) Absorption of Armstrong/Packwood-Brown 1981 MAS
MAC File: LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Percent (absolute) k-ratio change per degree at 40 degrees: .134306
Percent (relative) k-ratio change per degree at 40 degrees: .803700
Takeoff Angle: 35.0000, K-Ratio: .158527
Takeoff Angle: 35.5000, K-Ratio: .159304
Takeoff Angle: 36.0000, K-Ratio: .160069
Takeoff Angle: 36.5000, K-Ratio: .160823
Takeoff Angle: 37.0000, K-Ratio: .161566
Takeoff Angle: 37.5000, K-Ratio: .162297
Takeoff Angle: 38.0000, K-Ratio: .163017
Takeoff Angle: 38.5000, K-Ratio: .163726
Takeoff Angle: 39.0000, K-Ratio: .164424
Takeoff Angle: 39.5000, K-Ratio: .165112
Takeoff Angle: 40.0000, K-Ratio: .165788
Takeoff Angle: 40.5000, K-Ratio: .166454
Takeoff Angle: 41.0000, K-Ratio: .167110
Takeoff Angle: 41.5000, K-Ratio: .167756
Takeoff Angle: 42.0000, K-Ratio: .168391
Takeoff Angle: 42.5000, K-Ratio: .169017
Takeoff Angle: 43.0000, K-Ratio: .169632
Takeoff Angle: 43.5000, K-Ratio: .170237
Takeoff Angle: 44.0000, K-Ratio: .170833
Takeoff Angle: 44.5000, K-Ratio: .171419
Takeoff Angle: 45.0000, K-Ratio: .171996
Which has a 0.80 relative percent change per degree! That will help to nail these effective WDS k-ratios down.
Hopefully the probe will be available next weekend so I can sneak in do some quick k-ratio measurements on the WDS spectrometers, along with the EDS spectrometer!
I have data that can help with this. In my instrument, I have 4 SDD. The detector ports are nominally identical (at least the front two are identical and the back two are identical and all at the same relative height. and mounting angle) The k-ratios from a flat, polished sample normal to the beam should be identical. I have plenty of QC data that we can examine to test this. The screwball is ensuring the sample is orthogonal to the beam. I have a laser level and mirror I use to test this but it isn't as good as a microprobe. I can also intentionally tilt the sample to change the effective take-off angle.
I've attached a document describing validation procedures I use to determine such things as the optimal working distance and the alignment of the detector.
One advantage of calibrating WDS EPMA over the EDS SEM is that the EPMA stage is usually not capable of being tilted. However the EPMA stage level with respect to the beam perpendicularity still needs to be checked per your section 4.6. Observing an electron image and optical image while the stage is raised and lowered would seem to help determine this.
Another advantage of EPMA might be that using the WDS x-ray defocus is much more severe than an EDS spectrometer at least in two dimensions. The (partial) concentricity of a WDS x-ray image on a flat sample is more complicated, but maybe more sensitive?
I am interested in the digital inclinometer mentioned. What specific models do you think would be useful?
Since you have a 4 EDS SEM can you speak to how well the four detectors are aligned with respect to each other and what if anything you had to do to bring them into agreement?
Have you performed simultaneous k-ratio tests on this instrument for all 4 spectrometers? If so, what sort of agreement do you see for something like Si Ka in SiO2 and Fe2SiO4 at 25 keV?
If I model this system in CalcZAF I see this sort of variation in the k-ratios as a function of angle:
Effective K-Ratios for Primary Standard: 14 SiO2 synthetic
Secondary Standard: 263 Fe2SiO4 (synthetic fayalite)
Emission line: si ka at 25 keV
Absorption Correction Method: Phi(pz) Absorption of Armstrong/Packwood-Brown 1981 MAS
MAC File: LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Percent (absolute) k-ratio change per degree at 40 degrees: .130966
Percent (relative) k-ratio change per degree at 40 degrees: .662938
Takeoff Angle: 35.0000, K-Ratio: .189129
Takeoff Angle: 35.5000, K-Ratio: .189898
Takeoff Angle: 36.0000, K-Ratio: .190655
Takeoff Angle: 36.5000, K-Ratio: .191398
Takeoff Angle: 37.0000, K-Ratio: .192130
Takeoff Angle: 37.5000, K-Ratio: .192849
Takeoff Angle: 38.0000, K-Ratio: .193556
Takeoff Angle: 38.5000, K-Ratio: .194251
Takeoff Angle: 39.0000, K-Ratio: .194934
Takeoff Angle: 39.5000, K-Ratio: .195606
Takeoff Angle: 40.0000, K-Ratio: .196266
Takeoff Angle: 40.5000, K-Ratio: .196915
Takeoff Angle: 41.0000, K-Ratio: .197553
Takeoff Angle: 41.5000, K-Ratio: .198181
Takeoff Angle: 42.0000, K-Ratio: .198797
Takeoff Angle: 42.5000, K-Ratio: .199403
Takeoff Angle: 43.0000, K-Ratio: .199998
Takeoff Angle: 43.5000, K-Ratio: .200584
Takeoff Angle: 44.0000, K-Ratio: .201159
Takeoff Angle: 44.5000, K-Ratio: .201724
Takeoff Angle: 45.0000, K-Ratio: .202279
What is the nominal takeoff for your 4 EDS spectrometers?
Here is some data I collected a few weeks ago from my QC block which contains K412 and the necessary standards (Al2O3, SiO2, Fe, CaF2, MgO). For each material, I collected 13 spectra from each of 4 detectors. For the standards, I did a little data quality assurance and then summed the spectra (per detector) to build a standard. The standards are then fit to each unknown. The result is a set of 13 k-ratios for each characteristic line set for each element. I summarize these k-ratios by calculating mean, min, max, std and a couple other statistics and tabulate this. The results are:
40×10 DataFrame
Row │ variable det nspec mean min max std mms mps frac
│ Symbol Cat... Int64 Float64 Float64 Float64 Float64 Float64 Float64 Float64
─────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
1 │ k[Al K-L3 + 3 others, Al2O3] 0 13 0.0673782 0.0667252 0.0688065 0.000563834 0.0668143 0.067942 0.83682
2 │ k[Al K-L3 + 3 others, Al2O3] 1 13 0.0664715 0.0658443 0.0672787 0.000546057 0.0659254 0.0670175 0.821491
3 │ k[Al K-L3 + 3 others, Al2O3] 2 13 0.0671671 0.0660373 0.0684215 0.00057184 0.0665952 0.0677389 0.851369
4 │ k[Al K-L3 + 3 others, Al2O3] 3 13 0.067121 0.0662979 0.0681173 0.000524488 0.0665966 0.0676455 0.781406
5 │ k[Al K-L3 + 3 others, Al2O3] 4 13 0.0670778 0.0665836 0.0679787 0.000431807 0.066646 0.0675097 0.64374
6 │ k[Ca K-L3 + 3 others, CaF2] 0 13 0.206919 0.20563 0.208516 0.000864144 0.206055 0.207783 0.417624
7 │ k[Ca K-L3 + 3 others, CaF2] 1 13 0.200773 0.199439 0.202793 0.000951106 0.199822 0.201724 0.473721
8 │ k[Ca K-L3 + 3 others, CaF2] 2 13 0.198908 0.196795 0.201411 0.00139895 0.197509 0.200307 0.703317
9 │ k[Ca K-L3 + 3 others, CaF2] 3 13 0.201701 0.200865 0.203697 0.000876597 0.200824 0.202577 0.434603
10 │ k[Ca K-L3 + 3 others, CaF2] 4 13 0.202279 0.201183 0.204263 0.000897193 0.201381 0.203176 0.443543
11 │ k[Fe K-L3 + 1 other, Fe] 0 13 0.0664122 0.0656582 0.0671871 0.000507176 0.0659051 0.0669194 0.763678
12 │ k[Fe K-L3 + 1 other, Fe] 1 13 0.0661916 0.0657228 0.0672809 0.000469286 0.0657223 0.0666609 0.708981
13 │ k[Fe K-L3 + 1 other, Fe] 2 13 0.0665982 0.0656377 0.0676449 0.000624965 0.0659733 0.0672232 0.938411
14 │ k[Fe K-L3 + 1 other, Fe] 3 13 0.0661991 0.0657107 0.0668829 0.000332966 0.0658661 0.066532 0.502976
15 │ k[Fe K-L3 + 1 other, Fe] 4 13 0.0663986 0.065982 0.0672085 0.000358371 0.0660402 0.066757 0.539727
16 │ k[Fe K-M3 + 3 others, Fe] 0 13 0.0650205 0.0629254 0.0671526 0.00142598 0.0635945 0.0664465 2.19313
17 │ k[Fe K-M3 + 3 others, Fe] 1 13 0.0654008 0.0632611 0.0672457 0.00126211 0.0641387 0.0666629 1.9298
18 │ k[Fe K-M3 + 3 others, Fe] 2 13 0.065876 0.0621917 0.0685643 0.00178602 0.06409 0.067662 2.71118
19 │ k[Fe K-M3 + 3 others, Fe] 3 13 0.0647002 0.0622948 0.066894 0.00146527 0.063235 0.0661655 2.26471
20 │ k[Fe K-M3 + 3 others, Fe] 4 13 0.0652447 0.0633649 0.0663351 0.000881101 0.0643636 0.0661258 1.35046
21 │ k[Fe L3-M5 + 13 others, Fe] 0 13 0.03989 0.0390774 0.0411357 0.000739593 0.0391504 0.0406296 1.85408
22 │ k[Fe L3-M5 + 13 others, Fe] 1 13 0.0403173 0.0385843 0.0421022 0.00102367 0.0392937 0.041341 2.53903
23 │ k[Fe L3-M5 + 13 others, Fe] 2 13 0.0422189 0.0401851 0.0440921 0.00114563 0.0410733 0.0433645 2.71355
24 │ k[Fe L3-M5 + 13 others, Fe] 3 13 0.0413002 0.0398211 0.0428919 0.000976003 0.0403242 0.0422762 2.3632
25 │ k[Fe L3-M5 + 13 others, Fe] 4 13 0.0416638 0.0410419 0.0428226 0.000562996 0.0411008 0.0422268 1.35128
26 │ k[Mg K-L3 + 1 other, MgO] 0 13 0.144145 0.14326 0.145784 0.000778769 0.143367 0.144924 0.540266
27 │ k[Mg K-L3 + 1 other, MgO] 1 13 0.143494 0.142553 0.145288 0.000865561 0.142629 0.14436 0.603202
28 │ k[Mg K-L3 + 1 other, MgO] 2 13 0.146789 0.145792 0.147557 0.000484152 0.146304 0.147273 0.329829
29 │ k[Mg K-L3 + 1 other, MgO] 3 13 0.146177 0.145544 0.14718 0.000507883 0.145669 0.146685 0.347444
30 │ k[Mg K-L3 + 1 other, MgO] 4 13 0.145219 0.144653 0.14651 0.00057413 0.144645 0.145793 0.395355
31 │ k[O K-L3 + 1 other, Al2O3] 0 13 0.652263 0.647599 0.661162 0.00379261 0.64847 0.656055 0.581454
32 │ k[O K-L3 + 1 other, Al2O3] 1 13 0.638632 0.633832 0.644866 0.0032374 0.635395 0.641869 0.506927
33 │ k[O K-L3 + 1 other, Al2O3] 2 13 0.645777 0.640643 0.651841 0.00294525 0.642831 0.648722 0.456079
34 │ k[O K-L3 + 1 other, Al2O3] 3 13 0.651737 0.645822 0.658638 0.00353831 0.648199 0.655275 0.542905
35 │ k[O K-L3 + 1 other, Al2O3] 4 13 0.649076 0.644075 0.655744 0.00315486 0.645921 0.652231 0.486055
36 │ k[Si K-L3 + 3 others, SiO2] 0 13 0.346675 0.345486 0.349379 0.00119801 0.345477 0.347873 0.345572
37 │ k[Si K-L3 + 3 others, SiO2] 1 13 0.34378 0.341762 0.346746 0.00149526 0.342285 0.345275 0.434947
38 │ k[Si K-L3 + 3 others, SiO2] 2 13 0.350525 0.348511 0.352958 0.00115872 0.349367 0.351684 0.330567
39 │ k[Si K-L3 + 3 others, SiO2] 3 13 0.346128 0.34396 0.349919 0.00172684 0.344401 0.347855 0.498902
40 │ k[Si K-L3 + 3 others, SiO2] 4 13 0.346853 0.345311 0.349609 0.00130634 0.345547 0.348159 0.376626
I've attached the Jupyter notebook (exported as HTML) and the results as a CSV file and plot in SVG format.
I'll leave the interpretation to JD.
This is really nice, but can we see the k-ratios for the individual spectra?
Ideally could you plot the single spectrum k-ratios for each spectrometer for each emission lines up for us? Separate graphs for Al, Ca, Si, Mg and O with 4 colors (for each spectrometer) for all the individual spectra so we can see the scatter and overlap?
Sure. The individual spectrum k-ratios are attached (CSV) as well as a plot (SVG).
Detectors 0 and 3 are to the left-front and right-front of the instrument, 1 and 2 are to the left-rear and right-rear. Detector 4 spectra represent the sum of detector 0, 1, 2 & 3 spectra.
Nominally, the elevation angle is 35 degrees. The spectra are plotted by acquisition (so all 5 represent the same electrons.)
The sample was not specially leveled before this data was collected so there is a distinct likelihood the sample was tilted by a degree or two. I don't know.
(https://smf.probesoftware.com/gallery/399_14_10_23_12_46_57.png)
Really interesting data. Thank-you for posting this.
From a quick look at things the variation from spectrometer to spectrometer seems to be on the same order or a little better as my WDS k-ratios. What was the keV for these measurements? I'm going to try some k-ratio measurements on multiple WDS spectrometers (plus an EDS spectrometer) as mentioned previously but at 25 keV and using SiO2 and Fe2SiO4 to increase the absorption correction.
Of course as you mentioned there is the question of sample tilt. Have you tried to model a plane to fit these k-ratios based on the spectrometer orientations? That is, can you fit these k-ratios to effective take off angles that approximate a sample surface place?
20 keV.
I haven't tried to model the sample tilt. I'm more inclined (no pun intended) to remeasure but use the vertical laser level (something like this https://www.amazon.com/Bosch-GPL100-30G-3-Point-Alignment-Self-Leveling/dp/B08WJQBKDB) and a mirror to test the orientation. I assume my column is vertical. A small circular mirror is placed on the surface of the stage. The laser level is hung out over the edge of the column. With the stage drawer extended, I retro reflect the laser from the surface of the sample and/or stage. The orientation is tweaked until the laser reflects back on itself.
I think you're tilting in the right direction! :)
And also maybe try with 25 keV for a larger absorption correction...
I messed up and forgot to acquire Si by EDS along with the WDS spectrometers, so I will try again when the instrument is free again. In the meantime here are the WDS results starting with Si Ka in Mn2SiO4 (vs. SiO2) at 25 keV:
(https://smf.probesoftware.com/gallery/1_23_10_23_9_14_37.png)
Pretty consistent (Mn2SiO4 was the last standard run).
Here for Si in Fe2SiO4:
(https://smf.probesoftware.com/gallery/1_23_10_23_9_17_11.png)
Here for Co2SiO4:
(https://smf.probesoftware.com/gallery/1_23_10_23_9_17_30.png)
and here for Ni2SiO4 (the largest absorption correction):
(https://smf.probesoftware.com/gallery/1_23_10_23_9_17_45.png)
The line and text in red are from the effective k-ratio calculator in CalcZAF:
https://smf.probesoftware.com/index.php?topic=598.msg12062#msg12062
Tentative conclusion is that spectrometers 3 and 5 (interestingly both are 2 atmosphere detectors using PET) are close to theoretical effective take off angles, while spectrometers 1, 2 and 4 (all TAP) have effective take off angles that are higher than the nominal value (40).
For example, continuing from the previous post, looking at Si Ka in Mn2SiO4 relative to SiO2 at 25 keV we obtain this output from the effective takeoff angle calculator in CalcZAF:
Effective K-Ratios for Primary Standard: 14 SiO2 synthetic
Secondary Standard: 275 Mn2SiO4 (manganese olivine) synthetic
Emission line: si ka at 25 keV
Absorption Correction Method: Phi(pz) Absorption of Armstrong/Packwood-Brown 1981 MAS
MAC File: LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Percent (absolute) k-ratio change per degree at 40 degrees: .126188
Percent (relative) k-ratio change per degree at 40 degrees: .588985
Takeoff Angle: 35.0000, K-Ratio: .206103
Takeoff Angle: 35.5000, K-Ratio: .206850
Takeoff Angle: 36.0000, K-Ratio: .207584
Takeoff Angle: 36.5000, K-Ratio: .208305
Takeoff Angle: 37.0000, K-Ratio: .209013
Takeoff Angle: 37.5000, K-Ratio: .209709
Takeoff Angle: 38.0000, K-Ratio: .210392
Takeoff Angle: 38.5000, K-Ratio: .211064
Takeoff Angle: 39.0000, K-Ratio: .211723
Takeoff Angle: 39.5000, K-Ratio: .212371
Takeoff Angle: 40.0000, K-Ratio: .213008
Takeoff Angle: 40.5000, K-Ratio: .213633
Takeoff Angle: 41.0000, K-Ratio: .214247
Takeoff Angle: 41.5000, K-Ratio: .214850
Takeoff Angle: 42.0000, K-Ratio: .215443
Takeoff Angle: 42.5000, K-Ratio: .216025
Takeoff Angle: 43.0000, K-Ratio: .216596
Takeoff Angle: 43.5000, K-Ratio: .217158
Takeoff Angle: 44.0000, K-Ratio: .217709
Takeoff Angle: 44.5000, K-Ratio: .218251
Takeoff Angle: 45.0000, K-Ratio: .218782
Again looking at the Mn2SiO4 measurements:
(https://smf.probesoftware.com/gallery/1_23_10_23_9_14_37.png)
we can see that spectrometer 2 with a measured k-ratio of 0.218 is somewhere around at a take off angle of 45 degrees! Could that be possibe?
Si Ka on a TAP Bragg crystal is at a very low sin theta with the spectrometer crystal extended all the way into the instrument...
By the way, I measured the sample tilt on this standard mount (when importing the standard coordinates using three fiducial points) and it was around 0.1 degrees, so not an issue with sample tilt!
In an effort to try and determine what is the "correct" k-ratio for a given system is (e.g., Si Ka at 25 keV in Fe2SiO4/SiO2), I note that CalcZAF now has a new feature that allows one to calculate k-ratios using the Use All Matrix Corrections" checkbox:
https://smf.probesoftware.com/index.php?topic=598.msg12175#msg12175
This will at least show how closely the different matrix corrections compare with each other.
But perhaps a more effective measure is to compare multiple standards with each other using the Evaluate application:
https://smf.probesoftware.com/index.php?topic=340.0
So, here is a comparison of the various synthetic silicate (olivine) standards first using the Armstrong absorption correction at 25 keV (check out the zero value on the Y-axis):
(https://smf.probesoftware.com/gallery/395_03_11_23_8_47_48.png)
Observe that all the silicates (with the obvious exception of HfSiO4) seem to be close to their published (assumed stoichiometric) values, which gives us some confidence in the theoretical k-ratio calculations for each of these silicates. If we compare with the PAP absorption correction we obtain this plot:
(https://smf.probesoftware.com/gallery/395_03_11_23_8_48_38.png)
Here we can see that the HfSiO4 has improved, but the accuracy of all the other silicates has gotten significantly worse. So, let's stick with the Armstrong matrix correction for now...
Finally note that in order to obtain accurate concentrations in the matrix correction, the duplicate Si Ka measurements from all 5 spectrometers have to be aggregated together, so this doesn't help us determine which spectrometer has "correct" k-ratios.
For reference, here are the standard numbers and names utilized in the above plots:
(https://smf.probesoftware.com/gallery/395_03_11_23_9_18_18.png)
I managed to acquire more k-ratios last weekend for Si Ka at 25 keV on all 5 WDS spectrometers, and also on our Thermo EDS system... the idea being that maybe the EDS detector, since it has no moving parts, *might* yield a more accurate k-ratio than a WDS spectrometer with a myriad of moving parts! I'll post these plots in a moment, but first lets examine the overall differences we are seeing between the various spectrometers.
By the way, using the new sample tilt calculator in Probe for EPMA (not yet described in the user forum because Aurelien and I are still testing it), in my original k-ratio measurements from a couple of weeks ago, the sample tilt was around 0.1 degrees. Last weekend I obtained a sample tilt of around 0.2 degrees, so not too bad.
So again using the Armstrong absorption correction (as described in the previous post), and calculating concentrations, so that the absorption correction is included, we can compare the differences between the various spectrometers:
St 275 Set 2 Mn2SiO4 (manganese olivine) synthetic, Results in Elemental Weight Percents
ELEM: Si Si Si Si Si Si Mn O
TYPE: ANAL ANAL ANAL ANAL ANAL ANAL SPEC SPEC
BGDS: EXP EXP LIN EXP LIN EDS
TIME: 60.00 60.00 60.00 60.00 60.00 60.00 --- ---
BEAM: 29.87 29.87 29.87 29.87 29.87 29.87 --- ---
ELEM: Si Si Si Si Si Si Mn O SUM
XRAY: (ka) (ka) (ka) (ka) (ka) (ka) () ()
262 11.720 11.734 11.405 11.862 11.355 11.760 54.406 31.688 155.929
263 11.755 11.713 11.373 11.848 11.459 11.678 54.406 31.688 155.920
264 11.788 11.706 11.232 11.851 11.496 11.633 54.406 31.688 155.800
265 11.777 11.734 11.340 11.852 11.411 11.793 54.406 31.688 156.002
266 11.779 11.724 11.341 11.894 11.383 11.765 54.406 31.688 155.980
267 11.753 11.737 11.230 12.126 11.469 11.638 54.406 31.688 156.048
268 11.773 11.715 11.409 11.839 11.412 11.538 54.406 31.688 155.781
269 11.756 11.731 11.346 11.849 11.406 11.710 54.406 31.688 155.892
AVER: 11.762 11.724 11.335 11.890 11.424 11.690 54.406 31.688 155.919
SDEV: .021 .012 .069 .097 .047 .085 .000 .000 .094
SERR: .008 .004 .025 .034 .017 .030 .000 .000
%RSD: .18 .10 .61 .82 .41 .73 .00 .00
PUBL: 13.907 13.907 13.907 13.907 13.907 13.907 54.406 31.688 100.001
%VAR: -15.42 -15.70 -18.50 -14.50 -17.85 -15.94 .00 .00
DIFF: -2.145 -2.183 -2.572 -2.017 -2.483 -2.217 .000 .000
STDS: 14 14 14 14 14 14 --- ---
The crystals utilized above were:
ELEM: si ka si ka si ka si ka si ka si ka BEAM1 BEAM2
BGD: OFF OFF OFF OFF OFF EDS
SPEC: 1 2 3 4 5 0
CRYST: TAP LTAP LPET TAP PET EDS
So it is clear that spectrometers 1, 2 and 4 (TAP) are all a bit high, while spectrometers 3 and 5 (both PET) are a little low (by about 1/2 wt%), and the EDS pretty much splits the difference! So we're talking about an ~0.5 wt% absolute difference in concentrations or around 5% relative. In other words probably worth worrying about!
Remember (note the total of ~155 wt%), the concentrations shown above (~11 wt%) are incorrect because we're looking at 6 spectrometers which have not been aggregated using the aggregate feature:
https://smf.probesoftware.com/index.php?topic=155.0
So let's go back to raw-k-ratios and plot this up, first for Mn2SiO4:
(https://smf.probesoftware.com/gallery/395_03_11_23_9_53_36.png)
Again, TAP crystals yield higher k-ratios, PET crystals lower k-ratios and the EDS (in blue circles) pretty much splits the difference, and by the way is pretty close to our theoretical k-ratio of 0.213 from the Armstrong absorption correction. OK, here are k-ratios fro Fe2SiO4:
(https://smf.probesoftware.com/gallery/395_03_11_23_9_54_01.png)
Here the WDS spectrometers again reproduce the previous relationships, but the EDS k-ratios are sort of all over the place. Nicholas Ritchie informs me that we should not be testing Si Ka k-ratios on EDS because the Si K absorption edge in the EDS detector material makes the background modeling problematic. So maybe I'll have to take a look at Mg and Al standards, unfortunately we can't see these emission lines on PET crystals...
Anyway, continuing with Ni2SiO4 we obtain a similar plot to the Mn2SiO4:
(https://smf.probesoftware.com/gallery/395_03_11_23_9_54_19.png)
Again, TAP crystals high, PET crystals low and EDS in the middle. My take? Perhaps the most effective use of our EDS detectors, is to calibrate the effective takeoff angles on our WDS spectrometers! :D :D :D
In the previous post above I tried to test the effective takeoff angle using Si Ka at 25 keV (to obtain a large absorption correction) in SiO2 and various silicates as seen here in Ni2SiO4:
(https://smf.probesoftware.com/gallery/395_03_11_23_9_54_19.png)
Note that the Si Ka k-ratios on all three TAP crystals (at a low sin theta) seem to plot higher, possibly indicating a smaller effective take off angle. While Si Ka k-ratios on the PET crystals (at high sin thetas) all seem to plot lower, possibly indicating a higher effective take off angle.
So I thought we should attempt to characterize these k-ratio on our TAP crystals using an emission line with a large absorption correction and a high sin theta position on TAP. Looking at our standards I decided to try F Ka in CaF2 and BaF2 and you will remember the problems I documented that I had with the changes in peak shape as described in this post:
https://smf.probesoftware.com/index.php?topic=536.msg12187#msg12187
Fortunately, in Probe for EPMA, the k-ratios are automatically corrected for APF effects, so let's forge ahead and see how these APF corrected k-ratios compare to modeled k-ratios as seen here:
(https://smf.probesoftware.com/gallery/395_14_11_23_9_18_02.png)
So one could argue that the measured k-ratios are slightly higher than the Armstrong and XPP models, but pretty much agree with PAP, but at least a bit ambiguous at best.
So I'm going to try again using the Mg Ka line instead on TAP next time I can get on the instrument, but in the meantime it might be worth looking at the PET crystals at low and high sin thetas, e.g., Ti Ka and Si Ka.
Since we had some difficulty attempting to measure our F Ka k-ratios on TAP crystals, I decided to look at all 5 PET crystals on my instrument, using both Si Ka for high sin thetas and Ti ka for lower sin thetas.
As you may remember from previous posts this was a typical trend that we saw for Si Ka on both TAP and PET crystals:
(https://smf.probesoftware.com/gallery/395_18_11_23_8_15_27.png)
What we saw above was that for Si ka on PET (high sin thetas) we observed k-ratios falling below the expected k-ratio models (and the EDS k-ratios), while for Si Ka on TAP (at low sin thetas) we saw k-ratios that were above the predicted k-ratios (and the EDS k-ratios). But will these trends hold up for all PET crystals?
This time we tuned up Si Ka on all 5 PET crystals and EDS, but utilized a different mount than before so I was more limited in what materials I could utilize. Here are Si Ka k-ratios at 25 keV on labradorite and SiO2:
(https://smf.probesoftware.com/gallery/395_18_11_23_8_16_12.png)
Again we are able to reproduce the seemingly lower k-ratios for Si Ka on these PET crystals.
Unfortunately the EDS spectrometer gave very scattered results, probably due to the difficulty that Nicholas Ritchie mentioned regarding the fitting of the Si absorption edge from the EDS detector material. Steve Seddio is looking at these spectra to see if we can improve the modeling of the continuum to get more consistent results.
We can also see this more ambiguous data for Mg2SiO4:
(https://smf.probesoftware.com/gallery/395_18_11_23_8_16_36.png)
And for the other silicate I measured, PbSiO3, the models are very spread out, though here the EDS data was quite consistent (which makes me wonder if the issue with Si is more related to the Mg and Al peaks in the other materials), so it is included in this plot:
(https://smf.probesoftware.com/gallery/395_18_11_23_8_16_55.png)
And if we do trust the EDS k-ratio data to be more representative of a 40 degrees take off angle, then again we see all 5 PET crystals yielding k-ratios lower then we should expect. As for not using Si Ka, it would be nice to use another emission line at a high sin theta on PET but that leaves us with Ka emissions from P, S, Cl and Ar for which stable materials are not so readily available... maybe I will try GaP and InP next time...
Next we'll look at Ti Ka on all 5 PET crystals.
Continuing with simultaneous k-ratios on our 5 PET crystals (and EDS) we measure Ti Ka in SrTiO3 as a secondary standard and TiO2 as a primary standard at 25 keV:
(https://smf.probesoftware.com/gallery/395_19_11_23_8_34_22.png)
Clearly the models are not much help here, but if we assume that the EDS k-ratios are more representative of an effective take off angle of 40 degrees, we can see that (unlike the Si Ka k-ratios measured at high sin thetas which appeared to be lower than expected), we seem to have Ti ka WDS k-ratios (except for spectrometer 4) higher than the EDS, perhaps indicating a lower effective take off angle at lower sin thetas.
We see a similar results using RbTiOPO4 a a secondary standard:
(https://smf.probesoftware.com/gallery/395_19_11_23_8_34_40.png)
Again, except for spectrometer 4, the k-ratios are higher than the EDS, perhaps indicating a lower effective take off angle at these lower sin thetas on PET. Also again, the models are somewhat ambiguous.
Next I will try P Ka at 25 keV on GaP and InP to see if we can obtain more reliable results for Si ka with EDS at high sin thetas on PET...
Modeling these effective takeoff angles in the new modeling feature in CalZAF:
we see these trends for Ti Ka at 25 KeV:
Effective K-Ratios for Primary Standard: 22 TiO2 synthetic
Secondary Standard: 1023 RbTiOPO4
Emission line: ti ka at 25 keV
Absorption Correction Method: Phi(pz) Absorption of Armstrong/Packwood-Brown 1981 MAS
MAC File: LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Absolute k-ratio change per degree at 40 degrees: .000642
Percent (relative) k-ratio change per degree at 40 degrees: .211949
Takeoff Angle: 35.0000, K-Ratio: .298486
Takeoff Angle: 35.5000, K-Ratio: .298900
Takeoff Angle: 36.0000, K-Ratio: .299303
Takeoff Angle: 36.5000, K-Ratio: .299695
Takeoff Angle: 37.0000, K-Ratio: .300076
Takeoff Angle: 37.5000, K-Ratio: .300447
Takeoff Angle: 38.0000, K-Ratio: .300808
Takeoff Angle: 38.5000, K-Ratio: .301159
Takeoff Angle: 39.0000, K-Ratio: .301502
Takeoff Angle: 39.5000, K-Ratio: .301835
Takeoff Angle: 40.0000, K-Ratio: .302160
Takeoff Angle: 40.5000, K-Ratio: .302477
Takeoff Angle: 41.0000, K-Ratio: .302785
Takeoff Angle: 41.5000, K-Ratio: .303086
Takeoff Angle: 42.0000, K-Ratio: .303379
Takeoff Angle: 42.5000, K-Ratio: .303665
Takeoff Angle: 43.0000, K-Ratio: .303944
Takeoff Angle: 43.5000, K-Ratio: .304216
Takeoff Angle: 44.0000, K-Ratio: .304481
Takeoff Angle: 44.5000, K-Ratio: .304740
Takeoff Angle: 45.0000, K-Ratio: .304992
The range in our RbTiOPO4/TiO2 k-ratio plot covers roughly +/- 5 degrees in effective take off angle!
Could my spectrometers really be out that much? Have you tested your spectrometers? What range of k-ratios do you see?
Quote from: Probeman on November 18, 2023, 08:35:27 AM
Since we had some difficulty attempting to measure our F Ka k-ratios on TAP crystals, I decided to look at all 5 PET crystals on my instrument, using both Si Ka for high sin thetas and Ti ka for lower sin thetas.
As you may remember from previous posts this was a typical trend that we saw for Si Ka on both TAP and PET crystals:
(https://smf.probesoftware.com/gallery/395_18_11_23_8_15_27.png)
What we saw above was that for Si ka on PET (high sin thetas) we observed k-ratios falling below the expected k-ratio models (and the EDS k-ratios), while for Si Ka on TAP (at low sin thetas) we saw k-ratios that were above the predicted k-ratios (and the EDS k-ratios). But will these trends hold up for all PET crystals?
So here are results from some Mg Ka on TAP k-ratio measurements I did a week ago. Unlike the measurements on Si Ka quoted above, this time the EDS agreed quite well with the WDS, except for spectometer 4! And yes, I am being super careful in adjusting the PHA and stage tilt/focus!
Here is Mg2SiO4:
(https://smf.probesoftware.com/gallery/395_04_12_23_9_20_51.png)
Diopside:
(https://smf.probesoftware.com/gallery/395_04_12_23_9_21_08.png)
SRM K-411:
(https://smf.probesoftware.com/gallery/395_04_12_23_9_21_24.png)
and SRM K-412:
(https://smf.probesoftware.com/gallery/395_04_12_23_9_21_40.png)
So what the heck is going on here? Yes, some of these k-ratios appear to be a little high compared to the models as we saw before...
I guess next I'm going to try some replicate measurements on Si ka on TAP and also PET and see if I can at least reproduce the earlier measurements. Right now I don't see any compelling trends...
Previously I tried to test the effective takeoff angles on PET and TAP crystals for Si Ka. For example here for Mg2SiO4 and SiO2:
(https://smf.probesoftware.com/gallery/395_09_12_23_9_13_03.png)
We note that the k-ratios on the PET crystals seemed to be a little low compared to the TAP crystals with the EDS k-ratios pretty much in the middle. So (finally) I decided we should test the reproducibility of these k-ratios by making a new set of measurements:
(https://smf.probesoftware.com/gallery/395_09_12_23_8_49_42.png)
And yes, they are roughly reproducible, so that is a good thing. But more concerning is when we examine different compounds, for example one of the NIST glasses, SRM K-411:
(https://smf.probesoftware.com/gallery/395_09_12_23_9_17_11.png)
OK, well the PET k-ratios are again lower than the TAP k-ratios, but our EDS k-ratios are lower than all. What is going on here?
So let's take a look at SRM K-412:
(https://smf.probesoftware.com/gallery/395_09_12_23_9_23_08.png)
Well, forget about the WDS k-ratios, now the "wheels have come off" on our EDS k-ratios"!
There's something not quite right about the net intensities we are obtaining from our EDS software. Which is a bummer because I was hoping that we could utilize the EDS k-ratios to "calibrate" the effective take off angles on our WDS spectrometers, but maybe not. What is the problem with our EDS? Well, working with Nicholas Ritchie, Steve Seddio and Gareth Seward we think we have some possible ideas but it's complicated... more to come.
But the broader point is: have you checked your WDS and EDS detectors by running simultaneous k-ratios on all of them? I'd be interested in what others find on their instrument.
After having difficulty obtaining accurate net intensities from the Thermo Pather Portal API, see here for details:
https://smf.probesoftware.com/index.php?topic=1592.0
I decided to model the k-ratios in Penempa, first using 100K seconds, but the precision was not good enough so I ran again this time for about 100 hours each and got a precision of +/- 0.00148 on the k-ratio:
(https://smf.probesoftware.com/gallery/395_23_01_24_9_52_32.png)
Not only does it pretty much "split the difference" between the Armstrong and PAP models but it also agrees well with the EDS.
Maybe this is the way forward to calibrate our WDS effective take off angles?
After chatting with Nicholas Ritchie yesterday regarding the need for intra and inter laboratory k-ratio consensus, it occurs to me that it sure would be nice if we had some absolute k-ratio targets for specific compounds, as shown by the PENEPMA k-ratio in the plot above.
I mean it's great to obtain intra laboratory k-ratio consensus where all your spectrometers yield statistically similar k-ratios, and even better if each spectrometer could produce statistically similar k-ratios using multiple Bragg orders over the range of each spectrometer:
https://smf.probesoftware.com/index.php?topic=1811.msg13878#msg13878
And of course the ultimate goal is to see statistically similar k-ratio measurements produced between labs on a global basis, but maybe we might also have some absolute k-ratio targets?
Just for kicks I've started creating a spreadsheet with several compounds using high precision (200K seconds) modeling in PENEPMA that might be suitable for these sorts of spectrometer calibrations, for example MgO, Al2O3 and MgAl2O4 at various beam energies.
Thing is, in looking at the output from the PENEPMA GUI I noticed that only the unknown intensity variance was being output, so the folks over at Probe Software fixed that in the latest version. Interestingly when combining the variances from the quotient of two independent variables it's a bit more complicated that just adding the variances when performing a net intensity calculation (subtraction):
(https://smf.probesoftware.com/gallery/395_30_01_26_8_53_23.png)
So the code for this is here:
Function Penepma08BatchExtractKratiosVariance(sIntensity As Single, uIntensity As Single, sIntensity_var As Single, uIntensity_var As Single) As Single
' Calculate the variance of a k-ratio (quotient)
ierror = False
On Error GoTo Penepma08BatchExtractKratiosVarianceError
Dim qMeans As Single
Dim uRelVar As Single, sRelVar As Single
Dim cRelVar As Single, fVar As Single
Penepma08BatchExtractKratiosVariance! = 0#
' Calculate quotient of the means
qMeans! = uIntensity! / sIntensity!
' Calculte relative variances
uRelVar! = (uIntensity_var! * uIntensity_var!) / (uIntensity! * uIntensity!)
sRelVar! = (sIntensity_var! * sIntensity_var!) / (sIntensity! * sIntensity!)
' Calculate combined relative variance
cRelVar! = uRelVar! + sRelVar!
' Calculate final variance
fVar! = cRelVar! * (qMeans! * qMeans!)
' Calculate standard deviation of k-ratio (quotient)
Penepma08BatchExtractKratiosVariance! = Sqr(fVar!)
Exit Function
' Errors
Penepma08BatchExtractKratiosVarianceError:
MsgBox Error$, vbOKOnly + vbCritical, "Penepma08BatchExtractKratiosVariance"
Close #Temp2FileNumber%
ierror = True
Exit Function
End Function
And I had Grok check it for me so I think it's good. Anyway, just to be clear, we're talking about the output from this button in the Standard app PENEPMA GUI Batch Mode dialog:
(https://smf.probesoftware.com/gallery/395_30_01_26_9_10_38.png)
Here's the new PENEPMA k-ratio spreadsheet output as seen in Excel:
(https://smf.probesoftware.com/gallery/395_30_01_26_8_53_43.png)