Re: Size Strain in GSAS

[alan coelho]

Title: Message

Nicolae >To resume, I think (for example) that is better to approximate by a sum of >three Lorentzians (involving 4 profile parameters) than by a sum of two >pVs (involving 5 profile parameters).   I couldnt agree more.   >Concerning the numerical calculation of the profiles, still I'm not convinced >that is the ideal solution. You have not only the size profile to calculate, >but also at least two convolutions, with the strain and the instrumental >profiles. Moreover, what are doing the codes that use the gradient >calculated analytically?   Size distribution is a start and Leonie does seem to have worked in some of the other effects to his credit.   Whether all this actually helps in the analysis of Size/Strain does not seem to concern many - so why not experiment.   By gradient, I presume you mean the derivatives of the distribution with respect to parameters. This would require a mixture of numerical and analytical derivatives - very simpe using the chain rule. Dont see why the same cant be done in other codes.   all the best alan     -----Original Message----- From: Nicolae Popa [mailto:[EMAIL PROTECTED] Sent: Monday, April 18, 2005 3:33 PM To: rietveld_l@ill.fr Subject: Re: Size Strain in GSAS Alen, you right, as far as the profile corresponding to a given distribution is accurately described, any representation is good. Nevertheless, at comparative accuracies, it is not better to use a representation with smaller numbers of parameters? The profile parameters are functions of the parameters of distribution; in particular for the discussed distributions, lognormal, gamma, the profile parameters are functions of a unique distribution parameter "c". Further, to have a functional formula for profile to be implemented in the Rietveld programs, the dependence on "c" of  the profile parameters must be found (somehow, empirical formulae for example). Now, the number of profile parameters you have used in the primary fit becomes critical. If this number is small the dependence of everyone  on "c" is more or less smoothed. If the number of these parameters is higher than necessary, the dependence on "c" is rather "ugly" and difficult describe. To resume, I think (for example) that is better to approximate by a sum of three Lorentzians (involving 4 profile parameters) than by a sum of two pVs (involving 5 profile parameters).   Concerning the numerical calculation of the profiles, still I'm not convinced that is the ideal solution. You have not only the size profile to calculate, but also at least two convolutions, with the strain and the instrumental profiles. Moreover, what are doing the codes that use the gradient calculated analytically?   Best wishes, Nicolae     This is by far the best topic on this list for a long time as opposed to requests for Journal papers which as pointed out by someone else is inappropriate in the first place and illegal in the second.   Nicolae wrote: >(i) but a sum of two Lorentzians is not sharper than the sum of two pVs (Voigts)?   This I know, it should not matter what is used as long as the mapping of the function to a distribution is done accurately. Whether it is lognomal, gamma or something else does does not matter.   .   As a hint to those who write such code the calculation of a profile for an arbitraty distribution operates at around 5000 profiles per second as I noticed over the weekend - not much slower that a gaussian Nicolae. Maybe there's no need for a pseuod-Voigt / Lorentzian based approximations after all.     all the best Alan