... > > Yes, profiles can be approximated, but the question is not in > approximating profiles. The primary topic of the discussion is "Size > Strain in GSAS". GSAS and most other Rietveld refinement programs use > TCH-pV profile function which provides the simplest and more or less > correct way for separating microstructural and instrumental broadening > contributions. Unfortunately, the microstructural parameters such as Dv > and Da sizes derived (classically) from TCH-pV deviate significantly > from reality for narrow and broad dispersions. That's why the > TCH-pV-based calculations of Dv, Da or average crystallite diameter > need to be modified and calibrated on, at least, simulated data for > various dispersions. > The formalisms presented in chapters 6 and 7 of JAC 35 (2002) 338-346 > are more complex and they don't give a clear way for separating > microstructural from instrumental effects and, besides, for estimating > the values of Dv, Da or <R>. > > Leonid >
Dear Leonid, It is not exact what you say, ty ploho cital. 6 & 7 from JAC 35 (2002) 338-346 gives the size profile - formulae (15a) combined with (21,22) or (20a) combined with (23,24). If you look carefully, these profiles are approximated by pseudo-Voigt or sums of 2 or 3 Lorentzians. These profiles depends of 2 parameters, <R> and c, that are refinable and, once refined, both Dv and Da can be calculated (formulae (12,13) or (17,18)). NOW, if approximate the instrumental function by Voigt, that is possible in very many cases (or sums of Voigts to account for asymmetry for example) and also the strain effect by Gaussian or even Voigt, the resulted profile will be a Voigt (or sum of Voigt), that is used as profile in the whole pattern fitting, this profile including in principle all broadening effects (isotropic). You are claiming that it is not TCH-pseudoVoigt. Right, it is not, and can not be, in general, because for c>0.4 the size profile is no more pseudo-Voigt. The size profile given in that paper cover a much wider range of "c" (for lognormal distribution), including superlorentzians. On the other hand is a trivial matter for a programmer to include this profile in any whole pattern fitting code (Rietveld included). (We did that in a "private" whole pattern fitting program). But certainly not, if the programmer wish to use exclusively TCH and nothing else. Why? I don't know. Note that TCH is an empirical profile that reasonably approximate a Voigt function (not the tails) that contains an empirical constraint: that FWHH of Lorenz and Gauss components are equal one to another and equal with that of the whole psudoVoigt. Best wishes, Nicolae Popa
