Analysis of a tilted Sample -- take off angle

[Philipp Poeml]

Hi John and all,

I have a question here:
I have currently in my machine a flat sample, but it is tilted. By about 4-5 degrees in the x axis direction.

For some reason ( don't ask) I would like very much to analyse this sample anyway, even though it's very difficult to focus and also the take off angle must be wrong and totally different for all spectrometers.

Note that our standards are of course flat and have a 40 degrees take off angle.

Could anyone tell me the error I would impose on my results with this tilted sample?

How can I calculate or simulate this? Are there some formulary with take off angle?

Will this lead to totally wrong results or is the error small? Maybe even smaller than the other uncertainties?

Please let me know any ideas.

Thanks
Ph

[Philipp Poeml]

Ok, I take the non existing answers as a "this is a stupid idea" and/or nobody knows.

So, I might go ahead and re-embed the sample.

Cheers,
Ph

[UofO EPMA Lab]

Don't give up so easily!   

The easy way to simulate the effect is to take a composition and run it through CalcZAF with different takeoff angles. It's not exactly the same geometry as your tilted sample, but similar enough.

But before we do that, remember, you can rotate the tilted sample in the sample holder to align it so that for two opposing spectrometers, the take-off angle is close to 40 degrees.  It would be sensible to run your major elements on these two spectrometers and use the other spectrometers, which will essentially have smaller or larger take off angles but won't show the tilt effects as obviously, for trace elements.

Since x-rays with similar energies (and mass absorption coefficients) won't be affected very differently by different take off angles, let's pick a composition with a range of emission line energies, say, a sodium silicate glass. Here's the first calculation from CalcZAF at 40 degrees:

ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Fe ka  1.0123  1.0000  1.1033  1.1169  1.1450   .9636   .9727  7.1120  2.1091 126.947
   Ca ka  1.0432   .9897   .9903  1.0224  1.0078   .9826   .9230  4.0390  3.7138 310.118
   Si ka  1.4496   .9977   .9581  1.3857   .9345  1.0253   .6247  1.8390  8.1566 1785.49
   Al ka  1.5253   .9925   .9840  1.4896   .9522  1.0333   .5818  1.5600  9.6154 2059.83
   Na ka  2.2531   .9967   .9724  2.1838   .9280  1.0479   .3736  1.0730 13.9795 4105.93
   O  ka  3.8333   .9984   .8922  3.4146   .8396  1.0626   .1828   .5317 28.2114 8514.37

We'll want to watch ABSCOR values as that is the absorption correction and therefore the major player for tilted samples since we are essentially changing the absorption path length by tilting to other angles. Basically, the lower the takeoff angle, the greater the absorption path length and the greater the absorption effect.

Now, by using the Analytical | Operating Conditions menu we can try other take off angles. Here is 30 degrees:

ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Fe ka  1.0157  1.0000  1.1033  1.1207  1.1450   .9636   .9651  7.1120  2.1091 126.947
   Ca ka  1.0554   .9907   .9903  1.0354  1.0078   .9826   .9027  4.0390  3.7138 310.118
   Si ka  1.5832   .9979   .9581  1.5137   .9345  1.0253   .5565  1.8390  8.1566 1785.49
   Al ka  1.6811   .9929   .9840  1.6424   .9522  1.0333   .5107  1.5600  9.6154 2059.83
   Na ka  2.6354   .9969   .9724  2.5548   .9280  1.0479   .3048  1.0730 13.9795 4105.93
   O  ka  4.5934   .9985   .8922  4.0920   .8396  1.0626   .1392   .5317 28.2114 8514.37

And here is 50 degrees:

ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Fe ka  1.0103  1.0000  1.1033  1.1147  1.1450   .9636   .9770  7.1120  2.1091 126.947
   Ca ka  1.0363   .9890   .9903  1.0149  1.0078   .9826   .9348  4.0390  3.7138 310.118
   Si ka  1.3750   .9976   .9581  1.3142   .9345  1.0253   .6690  1.8390  8.1566 1785.49
   Al ka  1.4381   .9922   .9840  1.4041   .9522  1.0333   .6287  1.5600  9.6154 2059.83
   Na ka  2.0388   .9966   .9724  1.9758   .9280  1.0479   .4241  1.0730 13.9795 4105.93
   O  ka  3.3771   .9984   .8922  3.0080   .8396  1.0626   .2189   .5317 28.2114 8514.37


So clearly for lower energy elements, this is a significant concern, but for higher energy x-rays such as Fe ka, the effect is much smaller and might even be ignored.

[Philipp Poeml]

Thanks John, for the help.

In fact, none of the X-rays we are using would be less than 3 keV, for example, U Ma 3.3 keV. So it should be similar to what Ca ka shows in your example.

Our effect will also be smaller, because the sample is not going from 40 degrees to 30 or 50, but it should be from 35 to 45 max.

I found that simulation last week in Calczaf and tried to do some simulations, but I am not sure how to use it. I will now try to reproduce your example.

I found this in the probewin.pdf:

"TakeOff=40.0
This keyword specifies the actual x-ray take-off angle of the microprobe. This value can be changed during the data acquisition process, but is generally not modified. However for modeling various experimental effects, this value can be changed from the Analytical | Operating Conditions menu item in Standard for Windows. Typically JEOL and Cameca = 40 and ARL = 52.5. The allowed takeoff range is 1 to 90 degrees. The default value is 40 degrees."

Does this "Standard for Windows" program still exist?

Edit by John: Standard for Windows is now called Standard.  But the same applies to CalcZAF.

[Philipp Poeml]

So, for a standard example, I calculated this:

40 Degrees TOA:
ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Pu mb   .9317  1.0000  1.0331   .9625  1.1733   .8805   .6993  3.9730  6.2925 500.345
   U  ma   .9304  1.0000  1.0341   .9621  1.1619   .8899   .6309  3.5520  7.0383 654.921
   Nd la  1.3864  1.0000   .9717  1.3472   .9458  1.0274   .5941  6.2080  4.0271 820.756
   Cs la  1.4907   .9996   .9778  1.4571   .9270  1.0548   .5261  5.0120  4.9880 1012.65
   Xe la  1.5733   .9996   .9843  1.5480   .9278  1.0610   .4928  4.7830  5.2268 1131.10
   O  ka  9.0504  1.0000   .6603  5.9761   .4965  1.3301   .0516   .5317 47.0190 9661.05

35 Degrees
 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Pu mb   .9259  1.0000  1.0331   .9565  1.1733   .8805   .6727  3.9730  6.2925 500.345
   U  ma   .9251  1.0000  1.0341   .9566  1.1619   .8899   .6012  3.5520  7.0383 654.921
   Nd la  1.4302  1.0000   .9717  1.3898   .9458  1.0274   .5633  6.2080  4.0271 820.756
   Cs la  1.5450   .9996   .9778  1.5102   .9270  1.0548   .4940  5.0120  4.9880 1012.65
   Xe la  1.6367   .9996   .9843  1.6104   .9278  1.0610   .4605  4.7830  5.2268 1131.10
   O  ka  9.5460  1.0000   .6603  6.3034   .4965  1.3301   .0454   .5317 47.0190 9661.05

45 Degrees
ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Pu mb   .9363  1.0000  1.0331   .9673  1.1733   .8805   .7204  3.9730  6.2925 500.345
   U  ma   .9347  1.0000  1.0341   .9665  1.1619   .8899   .6549  3.5520  7.0383 654.921
   Nd la  1.3529  1.0000   .9717  1.3146   .9458  1.0274   .6191  6.2080  4.0271 820.756
   Cs la  1.4489   .9996   .9778  1.4162   .9270  1.0548   .5527  5.0120  4.9880 1012.65
   Xe la  1.5245   .9996   .9843  1.5000   .9278  1.0610   .5198  4.7830  5.2268 1131.10
   O  ka  8.6097  1.0000   .6603  5.6852   .4965  1.3301   .0575   .5317 47.0190 9661.05

So, for U,Pu I see a variation in the ABSCOR of about +/- 0,005, but for Nd,Cs,Xe +/- 0.05. Now the question is: Is that a lot? How would I see this in the wt.% numbers?

Edit by John: The variation in the wt% would be reflected on a 1:1 basis since these matrix correction numbers are multiplicative. In other words a 1% variation in the matrix correction will produce a 1% change in the concentration, but as you point out below that is relative to the matrix correction of the standard, so it depends on both. See here for the necessary equation:

http://probesoftware.com/download/PROBEWIN.pdf#page=407

[Philipp Poeml]

Hi John,

a question on Calczaf:
I can export a past run from PfE and import it into Calczaf to play with the take off angle.

However it changes then the take off angle for both the standards and the sample.

For my case I would need to keep the standards at 40 degrees and play with the take off angle for the unknowns. Then I could simulate a measurement with a tilted sample and get a wt.% output.

Is there a way to do this?

Cheers
Philipp

[John Donovan]

For my case I would need to keep the standards at 40 degrees and play with the take off angle for the unknowns. Then I could simulate a measurement with a tilted sample and get a wt.% output.

Is there a way to do this?

Sorry no. The software assumes standards and unknown have been acquired on the same instrument.