# Pattern X-Ray Diffraction Fitting

Assuming I have an experimental powder XRD spectra and I have a number of computational structures without any knowledge of which is correct, how can I simulate the powder XRD spectra? Once I have determined which structure is most likely, can I use the powder XRD to further refine the lattice constants of the structure?

• how to simulate powder diffraction – see mattermodeling.stackexchange.com/questions/142/… Nov 24 '20 at 22:18
• @marcin This assumes I want to simulate a powder, this is part of the process but I want to fit a powder which isn't as trivial. It seems rietveld analysis is what I am looking for but I am unsure where to start. Nov 24 '20 at 22:34

You have two different question in the same post.

how can I simulate the powder XRD spectra?

To just simulate the XRD spectra you can use this answer https://mattermodeling.stackexchange.com/a/146/24.

can I use the powder XRD to further refine the lattice constants of the structure?

The long answer: For the fitting process, or refinement, you don't need a set of starting structures. One of the successful method to obtain the crystal parameters from a powder diffraction pattern is the Rietveld method.

In this method, you only need one starting structure. Then, the software generate a theoretical pattern (as in your first question) and then the method uses a least squares approach to refine/fit the theoretical pattern to the experimental one. Here several parameters are changed. This process is repeated several times until attain convergence. In case the figure of merit (see below) be bad, you can then use another structure from your set as starting one.

The parameters that are fitted are several and can be used further to describe your structure:

• Background parameters: usually 1 to 12 parameters.
• Sample displacement: sample transparency, and zero shift corrections. (move peak position)
• Multiple peak shape parameters.
• FWHM parameters: i.e. Caglioti parameters (see section 3.1.2)
• Asymmetry parameters (FCJ parameters)
• Unit cell dimensions
• one to six parameters (a, b, c, α, β, γ), depending on the crystal family/system, for each present phase.
• Preferred orientation, and sometimes absorption, porosity, and extinction coefficients, which can be independent for each phase.
• Scale factors (for each phase)
• Positional parameters of all independent atoms in the crystal model (generally 0 to 3 per atom).
• Population parameters
• Occupation of site positions by atoms.
• Atomic displacement parameters
• Isotropic and anisotropic (temperature) parameters.

The parameters that measure the quality of the fit (figures of merit) indicating the quality of the fit are:

• Profile Residual (reliability factor)
• Weighted profile residual
• Bragg residual
• Expected profile residua
• Goodness of fit

Finally, here you can view a tutorial about Rietveld refinement using the Fullprof Suite (one of the best software for this task).

• This seems like a good answer. I do technically have two questions, but I think typically these things have to be done at the same time which is why I asked it the way I did. Nov 25 '20 at 15:14
• I am not getting your issue, sorry. When you do a Rietveld refinement, you have to start only with an initial structure, then the program will generate the corresponding theoretical pattern and then start the refinement/fitting process. After finished, you report your structure together with the figure of merits.
– Camps
Nov 25 '20 at 18:28