Actual mechanism of diffraction

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Brownml2
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Actual mechanism of diffraction

Post by Brownml2 » 22 Feb 2017, 17:25

Salutations

One topic in crystallography that I've found a surprising dearth of information on is what the fundamental interaction behind the interaction of the x-ray and atom. Pretty much every book just treats them as classical waves instead of explaining the quantum mechanics behind it. By this I don't mean that interference that leads to diffraction (I think I get that, since that is pretty much classical mechanics), but what actually happens when the x-ray interacts with the electron cloud.

The only description I've found so far is in Glusker, Lewis and Rossi that talks about "When X rays hit an atom, the rapidly oscillating electric field of the radiation sets the electrons of the atom into oscillation about their nuclei. This oscillation has the same frequency as that of the incident radiation. The result is that the electron acts as an oscillating dipole that serves as a source of secondary radiation with the frequency of the incident beam." and goes on to note that this is coherent scattering and there is no wavelength shift.

Which doesn't make a ton of sense, isn't oscillating about the nuclei an old pre-quantum explanation of orbitals? Is this saying that this is similar to Florescence/Phosphorescence where the photo is absorbed, then reemitted? That is what most of the other grad students I've talked to have assumed, but if that was the case I'd expect a Stoke's shift, the direction of emitted radiation to be random, and I don't see why you'd get a 180 degree phase shift. On the other hand, at these energy scales, a Stoke's shift of a few nm might be negligible. Also, if you are pushing an electron way off into orbit, I could see it being a lot less stable and remitting the photon before the atoms have a chance vibrate, as they do in Florescence/Phosphorescence. On the other hand, you'd be knocking a lot of electrons into outer space with the amount of energy an X-Ray packs, so I'd be supervised that in long exposure runs you don't ever trigger reactions, though again, I could justify that in that you do, but since the number of x-rays is small compared to the number of molecules in the crystal you don't notice.

The other explanation which makes less sense is that you are actually sloshing electrons around within their orbitals, with the same frequency as the x-ray. That makes total sense, you see things like that when talking about optical properties. (Actually, this book talks about that in the refraction section). However, I'm not clear how this would lead to a second x-ray, and where the energy to generate that photon would come from, if you aren't first exciting an electron into a higher orbital; wouldn't you need to steal that energy from the original x-ray in some manner, and since it has the same frequency as the original x-ray, you'd need the same energy, which sure sounds to me like the original x-ray was absorbed and reemitted.

Thanks for any clarification with this. Is there some reason that most xrd textbooks don't open with then? When I pick up a Raman/IR textbook (ie Nakamoto, Hariis and Bertolucci, Cotton) or an NMR textbook (Drago) they always start with a quantum mechanical description of what is going on, even if they mostly use classical analogies. Whereas just about every diffraction textbook is very much focused on the classical wave theory version of things.

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oleg
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Re: Actual mechanism of diffraction

Post by oleg » 23 Feb 2017, 10:48


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johnewarren
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Re: Actual mechanism of diffraction

Post by johnewarren » 23 Feb 2017, 10:55

I think the best bet is to move away from actual diffraction texts and look at physics or original publications:
http://journals.iucr.org/a/issues/1969/ ... a06427.pdf
Acta Cryst. (1969). A25, 103-108
https://doi.org/10.1107/S0567739469000155Cited by 33
Introduction to the dynamical theory of X-ray diffraction
P. P. Ewald
The general features, terminology, and method of the dynamical theory of X-ray diffraction are discussed, stressing the analogy with the general theory of small oscillations of a mechanical system.


http://journals.iucr.org/a/issues/2014/ ... sc5066.pdf
A new theory for X-ray diffraction
Paul F. Fewstera*

aPANalytical Research Centre, Sussex Innovation Centre, Falmer, Brighton, East Sussex BN1 9SB, UK
*Correspondence e-mail: paul.fewster@panalytical.com
(Received 1 August 2013; accepted 16 January 2014; online 27 March 2014)

This article proposes a new theory of X-ray scattering that has particular relevance to powder diffraction. The underlying concept of this theory is that the scattering from a crystal or crystallite is distributed throughout space: this leads to the effect that enhanced scatter can be observed at the `Bragg position' even if the `Bragg condition' is not satisfied. The scatter from a single crystal or crystallite, in any fixed orientation, has the fascinating property of contributing simultaneously to many `Bragg positions'. It also explains why diffraction peaks are obtained from samples with very few crystallites, which cannot be explained with the conventional theory. The intensity ratios for an Si powder sample are predicted with greater accuracy and the temperature factors are more realistic. Another consequence is that this new theory predicts a reliability in the intensity measurements which agrees much more closely with experimental observations compared to conventional theory that is based on `Bragg-type' scatter. The role of dynamical effects (extinction etc.) is discussed and how they are suppressed with diffuse scattering. An alternative explanation for the Lorentz factor is presented that is more general and based on the capture volume in diffraction space. This theory, when applied to the scattering from powders, will evaluate the full scattering profile, including peak widths and the `background'. The theory should provide an increased understanding of the reliability of powder diffraction measurements, and may also have wider implications for the analysis of powder diffraction data, by increasing the accuracy of intensities predicted from structural models.

http://journals.iucr.org/a/issues/1998/ ... sc0020.pdf
Acta Cryst. (1998). A54, 806-819
https://doi.org/10.1107/S0108767398011271
Diffraction Physics
A. Authier and C. Malgrange
The main theories of diffraction are briefly described and their more important results compared. The limitations of the geometrical theory are discussed and the concept of extinction introduced. The main features of the diffraction by a perfect crystal are briefly reviewed: total reflection and Darwin width associated with the Bragg gap, standing waves, anomalous absorption, ray tracing, plane-wave and spherical-wave Pendellösung, polarization properties. Real crystals are seldom perfect. They may be nearly perfect with small strains and/or individual lattice defects faults or they may be highly deformed with large strains and a high density of defects. The diffraction by the former is handled using extensions of the dynamical theory of diffraction by perfect crystals using ray tracing. The results are analytical in the case of a constant strain gradient and are otherwise described by simulations which can be compared to the experimental results. The latter case is more difficult but can be approached by more sophisticated theories such as that of Takagi and Taupin.

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