Author Topic: plotting PAP phi-rho-z  (Read 238 times)

John Donovan

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Re: plotting PAP phi-rho-z
« Reply #15 on: May 13, 2018, 08:35:30 pm »
Edit:  Fluoresence due to the continuum emitted by the substrate (or overlying material) can also contribute to phi(rho*z) within the thin layer of interest, and this (depending on beam energy) could be more significant for Zn Ka than for the Ka lines of elements of lower atomic number.  I believe that this is what Armstrong is hinting at near the bottom of p. 278 in EPQ, where he states, "...phi(rho*z) equations probably inadvertently incorporate some correction for continuum fluorescence."  Heinrich also makes brief mention of this effect in section 10.2.1 of "Electron Beam X-ray Microanalysis."

Thanks for the explanation.  This makes perfect sense.
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John Donovan

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Re: plotting PAP phi-rho-z
« Reply #16 on: May 14, 2018, 08:42:47 pm »
This is an excellent addition to CalcZAF. We will use it at Lehigh 2018.
Inspection of the equations used for the prz curve do show that it is a function of composition via the backscatter fraction and overvoltage parameters, and those are weighted by concentration; so yes, the curves are specific to the composition. As well the emitted curve clearly depends on the mac of the matrix material, again weighted by concentration.

My understanding is that the monte carlo simulation is superior for determining the lateral and vertical limits of electron scattering compared to the prz algorithm which is based on a small number of tracer experiments and via curve fitting generalized to all compositions. That is, the MC calculation is truly composition specific.

One problem with defining the depth of the analytical volume is that it is a cumulative distribution function. Is the depth the limit of electron scattering at zero residual energy, or the 99.99% limit of characteristic X-ray production, or emission. These are all quite different. There are cumulative plots in the older versions of Goldstein that allow you to quote the resolution at a specific percentage of total. The contoured energy deposition plot of Casino is very nice in outlining the volume from which a given X-ray energy can be generated.

Hi Paul,
That's a good idea.  We should be able to output a table of the % emitted volume vs. depth for each x-ray. 

Give us a few days to think about it.
john
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Ben Buse

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Re: plotting PAP phi-rho-z
« Reply #17 on: May 15, 2018, 06:06:40 am »
This looks really good, I look forward to trying it. I didn't realise how complex it was when I asked, thank you John, Brian and Paul for all your hard work and the useful discussion here regarding them

Ben

John Donovan

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Re: plotting PAP phi-rho-z
« Reply #18 on: May 16, 2018, 09:19:01 am »
One problem with defining the depth of the analytical volume is that it is a cumulative distribution function. Is the depth the limit of electron scattering at zero residual energy, or the 99.99% limit of characteristic X-ray production, or emission. These are all quite different. There are cumulative plots in the older versions of Goldstein that allow you to quote the resolution at a specific percentage of total. The contoured energy deposition plot of Casino is very nice in outlining the volume from which a given X-ray energy can be generated.

Hi Paul,
The latest CalcZAF (and PFE) update (v. 12.3.4) now outputs the 60, 80, 90, 95 and 99% area depths for the emitted x-rays.  Here is a table for Fe2SiO4 where I adjusted the keVs (using the Combined Conditions button dialog in CalcZAF) to give similar emitted intensities depths for the 99% emission volumes for Fe, Si and O:

Fe2SiO4, sample 1, Emitted intensity area vs. depth for 60, 80, 90, 95 and 99% areas:
   Fe ka    Mass Depth  Micron Depth, TO = 40, keV = 16, d = 4.39
     60%     0.1711894      0.389953
     80%     0.2519391     0.5738931
     90%     0.3197691     0.7284034
     95%     0.3779091     0.8608409
     99%     0.4909591      1.118358

   Si ka    Mass Depth  Micron Depth, TO = 40, keV = 15, d = 4.39
     60%      0.160497     0.3655969
     80%     0.2426119     0.5526467
     90%     0.3097965     0.7056869
     95%     0.3695162     0.8417225
     99%      0.492688      1.122296

   O  ka    Mass Depth  Micron Depth, TO = 40, keV = 17, d = 4.39
     60%     0.1483749     0.3379839
     80%     0.2275082      0.518242
     90%     0.3016956     0.6872336
     95%     0.3659912     0.8336929
     99%     0.4995283      1.137878

And here is the prz plot output for a "combined condition" sample in CalcZAF:

« Last Edit: May 16, 2018, 09:29:14 am by John Donovan »
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Paul Carpenter

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Re: plotting PAP phi-rho-z
« Reply #19 on: May 16, 2018, 11:28:07 am »
John,
Yes, this is very nice to have and we will use it at Lehigh Microscopy School for the "Quantitative X-ray Microanalysis: Problem Solving using EDS and WDS Techniques" course.

Cheers,
Paul
Paul Carpenter
Washington University St. Louis

John Donovan

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Re: plotting PAP phi-rho-z
« Reply #20 on: May 20, 2018, 06:22:34 pm »
I made a small tweak to the prz table output to the log window.  So just as the prz absorption model info is output to the plot:



The same info is now output to the log window as seen here:

Fe2SiO4, sample 1, Emitted intensity area vs. depth for 60, 80, 90, 95 and 99% areas:
ZAF or Phi-Rho-Z Calculations
LINEMU   Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Phi(pz) Absorption of Pouchou and Pichoir-Full (Original)

   Fe ka    Mass Depth  Micron Depth, TO = 40, keV = 15, d = 5
     60%     0.1563522     0.3127044
     80%     0.2387924     0.4775849
     90%     0.3070188     0.6140377
     95%     0.3610314     0.7220629
     99%     0.4463145     0.8926289

   Si ka    Mass Depth  Micron Depth, TO = 40, keV = 15, d = 5
     60%     0.1648737     0.3297475
     80%     0.2456282     0.4912564
     90%     0.3162884     0.6325768
     95%      0.380219     0.7604381
     99%     0.4878917     0.9757833

   O  ka    Mass Depth  Micron Depth, TO = 40, keV = 15, d = 5
     60%     0.1348381     0.2696762
     80%     0.2039859     0.4079717
     90%     0.2662188     0.5324376
     95%      0.321537      0.643074
     99%     0.4356308     0.8712616
John J. Donovan, Pres. 
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