Hello,
i was wondering if it is possible to calculate reasonably good estimates for Debye-Waller factors for a given crystal and temperature? Has somebody advice on how to go about this type of question or has someone perhaps even coded some script or software for this purpose?
Thanks in advance
@Thomas The objective of this work was to obtain a simpler and more accurate analytical expression to determine the Debye–Waller factor of crystals using an n-dimensional Debye approximation involving binomial coefficients and incomplete gamma functions. The results obtained were compared with the corresponding experimental and theoretical results and, the calculated values were shown to be in excellent agreement with those obtained in the experimental and other previous studies.
https://www.researchgate.net/publication/225723198_Calculation_of_the_Debye-Waller_factor_of_crystals_using_the_n-dimensional_Debye_function_involving_binomial_coefficients_and_incomplete_gamma_functions
https://www.researchgate.net/post/How_does_the_Debye-Waller_factor_affect_the_position_of_the_Bragg_peak_in_XRD
As V. Kahlenberg mentioned, it would be nice to know for what do you need it and what do you expect to solve? There are several assumptions (like the substitution pointed out) which affect the D-W factor so that one should not overstrain the original model.
Thank you all for your suggestions. V. Kahlenberg was hinting in the right direction. I want to refine T-dependent (neutron) diffraction data. The literature suggestion is appreciated. I'll check it out, though I'm afraid the empirical approach may not be sufficient. My problem is, that I am actually interested in the cation distribution. My cations have a large difference in neutron scattering length but similar mass. Perhaps, the contribution of the D-W factor may not even be that dramatic. However, in a Rietveld refinement the D-W-factors correlate with cation distribution parameters, which is a source of error I'd like to minimize. I guess, reasonable constrains on the D-W-factors would help. Also, the refinement turns out much neater, when using anisotropic D-W-factors. I lack the experience though to tell, whether or not this makes sense physically.
I guess you need to go back to the roots in order to find out what is really physically correct or "only" an acceptable fit for some experimental observation which enables a better fit. Over the years I found several structure models where the D-W factors were disbelieved since they appeared unrealistically high. Unfortunately I do not have any information about newer approaches which would improve a physical interpretation of DB factors. Good luck! (Let me know if you find something :-) )
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