In an XRD experiment, the incident X-ray beam (usually Cu K-alpha, Mo K-alpha and etc.) falls on a single crystal and, while a small portion of it gets diffracted, forming the spot pattern, most of it gets absorbed by the sample, leading to atomic transitions. These transitions will generate characteristic x-rays from the sample atoms, leaving the sample in almost all directions. As x-rays can penetrate tens of microns into the sample (depending on the elements of the sample, of course) then would it be possible that these characteristic x-rays originating from the elements of the sample be diffracted by the atomic planes of the remaining sample volume and contribute to the diffraction pattern? I would think that the phases of these x-rays will vary but this also applies to the x-rays coming from the tube (keeping in mind that the ideal explanation of diffraction considers the incident beam to consist of the same phase incident plane waves). Perhaps such an effect is possible but too small and is negligible, still I wanted to put the question out there for comments. Thanks.
Dear Burc,
you are right, fluorescence x-ray photons arising in the sample will undergo diffraction in the sample too. But as you pointed out the directions of these photons are arbitrary into the full 4pi space and only a very tiny amount will have directions which fit the Bragg law leading to diffraction peaks. You won’t really ‘see’ that contribution because a) fluorescence is a very lossy phenomenon and b) diffraction is also a very lossy one.
Furthermore distinct peaks demand for well defined collimated primary radiation, even in the case of single crystals.
In consequence you will see the fluorescence as additional background and part of that having undergone diffraction is very, very small.
With resect to your phase argument: it is not known to me that the phase of the fluorescence is in any way connected to the phase of the exciting radiation. Furthermore for example the Cu k alpha radiation is not able to excite Cu k-alpha radiation. Also from this example you see that you will not have coherent effects.
Some thoughts:
I don't fully agree with this sentence: "most of it gets absorbed by the sample, leading to atomic transitions". It depends on the crystal transmittance and on the diffraction geometry, of course, but in many cases (e.g single crystal XRD, PXRD in transmission geometry) most of it actually goes straight unabsorbed and undiffracted. (I sort of remember something like 1 out of 106 photons is diffracted).
Fluorescence indeed occurs, in all directions, and is visible as background.
However, what you describe sounds like a complex dynamical scattering picture, which I would say yes is generally too weak to be appreciated...
In addition to the intensity and coherence problems you have to take into consider the problem of trying to get interference among non monochromatic and non parallel waves... I don't know if diffraction is even geometrically allowed in such cases.
Dear Dr. Martens,
Thank you for your response. Regarding the relation between the phase of the secondary characteristic rays and the incident ray, I meant that the incident ray, in the quantum mechanical picture, consists of collimated photons whose phases probably do not match and yet we get the XRD pattern as close to an ideal one as it can be. The phases of the photons generated as a result of characteristic radiation process will also be different. This is what I meant. I also am not aware of any relation between the incoming beam phase and that of the characteristic rays originating from the sample.
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