How to calculate the penetration depth and information depth for a particular incident angle in GIXRD? Thin film material is aluminum and X-ray source is Cu Kalfa.
Dear Uday Kumar ,
please go through my presentation down to the grazing incidence part:
Presentation Attenuation Length and Penetration Depth of X-rays
The relevant formulae for extreme grazing incidence are summarized at page 8.
You mainly need the density of Al (necessary for the critical angle and/or delta) and the attenuation coefficient µ (necessary for the calculation of beta).
Good luck and
best regards
G.M.
P.S : I will send you this presentation via RG messenger, because during opening the full-text via RG the attenuation coefficient µ is unfortunately not properly displayed all over the text and formulae...
Dear Gerhard Martens ,
I am very thankful to you for sharing your presentation. It is very helpful for me.
Thanks again for your kind cooperation.
With best regards
Uday Kumar
Dear Uday Kumar and Gerhard Martens
I think the answer of Gerhard Martens is one of the good answers, but the answer to this question is very difficult, I think. That is to say, if the incident X-ray does not fulfil the diffraction condition, Gerhard's answer is appropriate. But when the diffraction condition is fulfilled, then the X-rays are penetrating into very deep places and then a part of the waves will come back to the surface. This holds when the single crystal size is larger enough. This kind of diffraction should be treated by the dynamical theory of X-ray diffraction, because Uday's question is probably supposing such a sample as Si wafer measured by grazing incident X-rays. How do you think? If the sample is a perfect single crystal, and wide enough, the X-rays penetrate to the back side of the single srystal, isn't it? Or Gerhardd's answer is still hold? I have a new question.
Yours sincerely
Jun
Dear Jun Kawai ,
thanks for your thoughts onto this subject.
For particle radiation there is a phenomenon, which is known as 'channelling'.
This means, that within a single crystal at a particular direction, at which
a) no atoms will affect the beam and
b) the 'channel' has a sufficient width,
the particle beam propagates through the material with an attenuation coefficient smaller than in polycrystalline or amorphous material.
For x-rays, to my knowledge, the phenomenon is not known.
Even in the case, that the diffraction condition is 'fulfilled' as you call it, the x-rays obey the Lambert-Beer law with the same attenuation coefficient.
Diffraction condition is 'fulfilled' only means for me, that
a) coherent/elastic scatter of a small fraction of the x-rays took place, and
b) the scatter direction is just that of constructive interference of the x-rays being scattered from adjacent scatter 'points';
it is c) not attributed to a different attenuation coefficient, neither for the incoming*) beam, nor for the diffracted beam.
*) This beam (or a small part of it) does not know, whether it will be diffracted some where on his tour across the material.
Best regards
G.M.
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