Re: Size Strain in GSAS

[alan coelho]

Title: Message

Nicolae, Nick, Bob, Leonid,   I have looked at many patterns (recorded by others) and a few cases have shown profiles that are sharper that a Lorentzian; whereby “sharper” means that the integral breadth is smaller than that for a unit area lorentzian.   To put a figure on it would be difficult but at a guess I would say < 3% of patterns fall into this category in a noticeable manner.   I have no doubt that the work of Nick Armstrong and co. is mathematically sound but  a simulated data round robin as suggested by Leonid Solovyov may be useful – and I am not generally a fan of round robins but this s different as the data is simulated.   A pure peak fitting approach shows that two pV’s (or two Voigts) when added with different FWHMs and integrated intensities but similar peak positions and eta values can almost exactly fit Pearsons II functions that are sharper that Lorentzians. This is not surprising as both profiles comprise 6 parameters.   Thus from my observations two pVs added together can fit a bimodal distributions quite easily. In fact my guess is that two pVs can fit a large range of crystallite size distributions.   Thus distinguishing whether a distribution is not monomodal is of course possible especially if the two pV approach is taken.   Attempting to determine more than that however takes some convincing as two pVs seem to fit almost anything that I have seen that is symmetric. Thus introducing more pVs seems unnecessary.   Thus yes GSAS can determine if a distribution is not monmodal if you were to fit two identical phases to the pattern except for the TCH parameters. If the Rwp drops by .1% then I wont be convinced.   Forgive me Nick but I have not yet read all of your work and I am certain that it is sound. Outside of nano particles (and maybe even inside) my reservation are that we may well be analyzing noise and second order sample and instrumental effects.   Thus to show up my naive ness can you categorically say that there are real world distributions that two pseudo Voigts cannot fit because I have not come across such a pattern.   Once you have done that then it would be time to concentrate on strain, micro strain, surface roughness and then disloactions   all the best alan     -----Original Message----- From: Nicolae Popa [mailto:[EMAIL PROTECTED] Sent: Friday, April 15, 2005 9:30 AM To: rietveld_l@ill.fr Subject: Re: Size Strain in GSAS Dear Bob,   Perhaps I was not enough clear. Let me be more explicit. It's about one sample of CeO2 (not that from round-robin) that we fitted in 4 ways.   (i)    by GSAS with TCH-pV (ii)   by another pV resulted from gamma distribution of size (iii)  by Lorentz - (the limit of any "regular" pV - eta=1)   All these 3 variants given bad fits. For example (ii): Rw=0.144, similarly the rest. (In principle if one pV works (TCH for example) any other kind of pV must work.)   (iv)  by the profile resulted from lognormal distribution of size; this time the fit was reasonably good: Rw=0.047. It resulted c=2.8, that means a "super Lorentzian" profile (I remember that the Lorentzian limit for lognormal is c~0.4 -  JAC (2002) 35, 338). Attention, this "super Lorentzian" profile is not constructed as a pV with eta>1.   Sure, such samples are rare, or, perhaps, not so rare. A Jap. group (Ida,...., Toraya, JAC (2003) 36, 1107) reported "super Lorentzian" on a sample of SiC. They found c=1.37   Best wishes, Nic Popa   Nic, This is true for the internal math but the TCH function was assembled to reproduce the true Voigt over the entire range of differing Lorentz and Gauss FWHM values so it works as if the two FWHM components are independent. As for your question, I'm not aware that anyone has actually tried to do the fit both ways on a "super Lorentzian" (eta>1 for old psVoigt) sample to see if a) the fit is the same and b) the eta>1 was an artifact. Any takers to settle this? Bob     R.B. Von Dreele IPNS Division Argonne National Laboratory Argonne, IL 60439-4814   -----Original Message----- From: Nicolae Popa [mailto:[EMAIL PROTECTED] Sent: Thursday, April 14, 2005 9:11 AM To: rietveld_l@ill.fr Subject: Re: Size Strain in GSAS Dear Bob,   If I understand well, you say that eta>1 (super Lorenzian) appeared only because eta was free parameter, but if TCH is used super Loreanzians do not occur? Nevertheless, for that curious sample of cerium oxide we tried GSAS (with TCH) and the fit was very bad. Best wishes, Nicolae   PS. By the way, TCH also forces FWHM of the Gaussian and Lorenzian components to be equal, but indeed, eta is not free and cannot be greater than 1.   Nic, I know about "super Lorentzians". Trouble is that many of those older reports were from Rietveld refinements "pre TCH" and used a formulation of the pseudo-Voigt which forced the FWHM of the Gaussian and Lorentzian components to be equal and allowed the mixing coefficient (eta) to be a free variable (n.b. it is not free in the TCH formulation). Thus, these ought to be discounted in any discussion about the occurence of super Lorentzian effects in real samples. Bob     R.B. Von Dreele IPNS Division Argonne National Laboratory Argonne, IL 60439-4814   -----Original Message----- From: Nicolae Popa [mailto:[EMAIL PROTECTED] Sent: Thursday, April 14, 2005 8:10 AM To: rietveld_l@ill.fr Subject: Re: Size Strain in GSAS   Right, is rare, but we have meet once. A cerium oxide sample from a commercial company, c=2.8. I don't know if they did deliberately, probably not, otherwise the hard work to obtain such curiosity is costly and the company risks a bankruptcy. On the other hand superlorenzian profiles were reported from a long time, only were interpreted as coming from bimodal size distributions. And third, you see, people have difficulties to extract size distribution from the Rietveld codes as they are at this moment.   Nicolae Popa   A word from a "provider" of a Rietveld code (please don't call me a "programmer"). "But if c>0.4 any pV fails" - OK, for what fraction of the universe of "real world" samples is "c">0.4? I suspect, given the general success of the TCH pseudoVoigt function, that it is exceedingly small and only occurs when one works hard to deliberately make a sample like that.     R.B. Von Dreele IPNS Division Argonne National Laboratory Argonne, IL 60439-4814   -----Original Message----- From: Nicolae Popa [mailto:[EMAIL PROTECTED] Sent: Thursday, April 14, 2005 7:14 AM To: [EMAIL PROTECTED] Cc: rietveld_l@ill.fr Subject: Re: Size Strain in GSAS >Dear Nicolae, >Maybe ya ploho chitayu i ploho soobrazhayu, but even after your >explanation I can't see a way to calculate <R> from the results of >fitting described in chapters 6 & 7 of JAC 35 (2002) 338-346. From such >fitting you obtain only dispersion parameter c. Or I missed something? >Anyway, being "Rietvelders" we still have to deal with TCH-pV function >and we need to extract as much as possible correct information from it. >Hope we shall see more appropriate functions for microstructure >analysis in popular Rietveld programs. >Cheers, >Leonid Dear Leonid,   Indeed you missed something. I presume you have the paper. Then, take a look to the formula (15a). This is the size profile for lognormal. There is the function PHI - bar of argument 2*pi*s*<R>.  Replace this function PHI - bar from (15a) by the _expression_ (21a) with the argument x=2*pi*s*<R>. You get it? So, not only "c" but also <R>.   "We are Rietvelders" means that we must be only "codes drivers", "cheffeurs des codes", "voditeli program"? Have we to accept the "Procust bed" of the Rietveld codes at a given moment? All Rietveld codes are improving in time, isn't it?   In particular for the Round_Robin sample TCH-pV works because c=0.18. (Davor explained how Dv and Da are found). But if c>0.4 any pV fails.   Best wishes,   Nicolae