Effective Takeoff Angle Calibrations for WDS Spectrometers

[Probeman]

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://probesoftware.com/smf/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://probesoftware.com/smf/index.php?topic=369.msg1948#msg1948

These issues are discussed further in this post:

https://probesoftware.com/smf/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://probesoftware.com/smf/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:



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:



And here with the effective takeoff angle feature enabled:



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...

[John Donovan]

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://probesoftware.com/smf/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"!.

[Probeman]

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:

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:

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!

[Nicholas Ritchie]

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.

[Probeman]

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?

[Nicholas Ritchie]

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.

[Probeman]

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?

[Nicholas Ritchie]

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.

[Probeman]

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?

[Nicholas Ritchie]

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.

[Probeman]

I think you're tilting in the right direction!   

And also maybe try with 25 keV for a larger absorption correction...

[Probeman]

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:



Pretty consistent (Mn2SiO4 was the last standard run). 

Here for Si in Fe2SiO4:



Here for Co2SiO4:



and here for Ni2SiO4 (the largest absorption correction):



The line and text in red are from the effective k-ratio calculator in CalcZAF:

https://probesoftware.com/smf/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).

[Probeman]

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:



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!

[Probeman]

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://probesoftware.com/smf/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://probesoftware.com/smf/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):



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:



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:

[Probeman]

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://probesoftware.com/smf/index.php?topic=155.0

So let's go back to raw-k-ratios and plot this up, first for Mn2SiO4:



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:



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:



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!