[GSAS-II] GSAS-II size and microstrain model selection

[Toby, Brian H.]

Let me repeat Bob’s answer here for the entire mailing list and add a few more comments of my own.

Kasa,
Depending on how the sample is prepared, the usual dominant broadening effect is from mustrain broadening not crystallite size. Highest resolution data (i.e. synchrotron diffractometer data) is best at distinguishing them and a wide scan is essential as well. The uniaxial models must be aligned along the principal axis of the space group. Laboratory data can usually only do mustrain broadening; there is (usually) insufficient resolution to do meaningful size broadening. The model with the best fit is usually the best one. Unusual samples are, well, unusual.
Bob

For those who are new to this, crystallite size and microstrain are differentiated by the Q dependence of the peak broadening, with delta-Q and delta-Q/Q being constant for each, respectively. One can only tell the difference if one has discernible peaks over a wide Q range. Further, peak shape parameters can interact with the background parameters. Also, one cannot get reliable sample broadening values if one refines the instrumental broadening parameters and the sample parameters together.

In practice, except for high-resolution data (typically synchrotron & neutron) one will only be able to refine either crystallite size or microstrain, but not both. Which one to choose? Try each and see what fits the data better, but note that if microstrain gets small or crystallite size gets large then the term has no effect and is not needed.

The presence of anisotropic broadening is hard to spot by eye, so I am usually tempted to try the more complex models just before deciding that I am “done”* to see if the fit improves. If so, I keep it and if not I go back to the isotropic model. Likewise, the LGmix parameter is very unlikely to improve things and leaving it fixed at 1 is usually the best bet, but if the peak fit does not look too good by eye, I might experiment with varying that to see if I get improvement and if not, I go back to leaving it fixed at 1.

Because people tend to fit with both microstrain and crystallite size broadening and because there can be some interaction between the balance between the amount of Lorentzian character in the peaks and where the background level is set, there can be many different parameter sets that give about the same fit quality. This is why if one refines microstrain and crystallite size together and then increases the complexity of the model for one of the two, one can see a large change in the other parameter. That is an indication that the model is overfit (has more parameters than the data support).

HTH,
Brian

* Note Peter Stephen’s famous comment about never being done.

On Jan 18, 2023, at 11:16 PM, kasa belachew via GSAS-II <gsas-ii at aps.anl.gov<mailto:gsas-ii at aps.anl.gov>> wrote:

GSAS-II computes the crystallite sizes (  10-6 m) in three different (isotropic, uniaxial and ellipsoidal) and Microstrains in terms of the amount of lattice spread, unitless fraction of Δd/d (or equivalently ΔQ/Q) times 106 (isotropic, uniaxial and generalized) arrangement.
But, my question here is,
1. What is the criteria to select the model for my material?
2. Can we use all models for one material?
Thanks
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