Nonetheless, the type 4 profile model has built-in constraints according to the cell class -- so it is easy to use and refines with far greater stablility that the Lxx terms. My advice to non-experts is still the following:The predetermined profile functions in the present free Rietveld programmes will never be able to cover all physically relevant cases of line broadening in a physically sensible way.
If you suspect that you have some reflection classes having peak widths wider than others, try out the type 4 model -- refining the Sxx terms and then eta. If the fit improves significantly, you likely have anistotropic peak broadening. If not, you don't & go back to using the type 3 model and ignore the L tensor.
This is not only a question of having large flexibility and having many parameters available, like in the Stephens (and precursors) model. Flexibility may also mean to introduce simpler models or to impose other restrictions, which may not be introduced by fixing parameters or by linear constraints. This is e.g. the case if composition fluctuations occur in a solid solution. Such cases can also be fitted with the Stephens model, however, with too many parameters which may lead to correlations and other unwanted/unphysical results and artefacts of the refinement, e.g. anisotropy for cubic crystals (which is impossible for composition fluctuations).
Actually, the Lxx version could work for composition fluctuations with the appropriate number of parameters (if the predefined Lorentzian shape of the broadening is o.k. - I refer only to the anisotropy), if correct symmetry constraints are introduced to the different Lxx, which should be possible by linear constraints in that case. I never did that in GSAS. Actually, TOPAS (commercial, by Bruker) provides the appropriate tools to define your own profile functions in a very flexible way based on physical models if you want to do it on the 2theta scale (but not on the scale of the Fourier transform, as by LeBail1987 and Leoni/Scardi, which also have some advantages).
>The Stephens model is correct only for strain broadening -- but my experience is that it does a pretty good job fitting other types of anisotropic broadening, for example anisotropic crystallite size broadening. In >the cases where pretty good is not good enough, then it would make sense to check out the Lxx terms -- but only after trying the Type 4 model to confirm that the observed broading indeed does vary by >reflection class.
Here it really depends on what you want to do with your profile parameters..... Of course size and strain parameter can correlate considerably.
Best regards Andreas Leineweber
MPI f�r Metallforschung Heisenbergstra�e 3 70569 Stuttgart
