Re: Size Strain in GSAS
Leonid, The lognormal distribution for particle size is not my modeling (unfortunately), but if you insist, let see once again your equations. D = Da + 0.25(DaDv)^0.5 and sigmaD = D(Dv/Da - 1/2)/2 For lognormal distribution first equation becomes: 2=(4/3)(1+c)**2+(1/4)sqrt[2*(1+c)**5] For c=0.05 we obtain: 2=1.87, for c=0.4, 2=3.43 The second equation becomes: sqrt(c)=[(9/8)(1+c)-1/2] For c=0.05, 0.22=0.68, for c=0.4, 0.63=1.75 Well, taking account that the world is not ideal I'm ready to accept that, then I think is time to close our discussion. Best wishes, Nicolae - Original Message - From: Leonid Solovyov [EMAIL PROTECTED] To: rietveld_l@ill.fr Sent: Sunday, April 17, 2005 2:58 PM Dear Nicolae, I will comment only upon your last statement because the limitations of your modeling are clear. Well, I don't know where from you taken these formulae but I observe that for spheres of equal radius, then zero dispersion, you have: sigma(D)=5D/4, different from zero! First of all, for spheres of equal radius and IDEAL definition of Dv and Da: sigmaD = D(Dv/Da - 1/2)/2 = D(9/8 - 1/2)/2 = 5D/16 Yes it is not zero, but the expressions I derived work only for 0.05 c 0.4 and I derived them not for IDEAL Dv and Da. If you perform WEIGHTED least-squares fitting of TCH p-V function to a profile simulated for spherical crystal and added by ~10% background level (to be closer to real Rietveld refinement) you will obtain the ratio of Dv/Da~3/4 not 9/8! This ratio is wrong but this is what we have from WEIGHTED least-squares fitting of TCH p-V to simulated data. In this case sigmaD = D(Dv/Da - 1/2)/2 = D(3/4 - 1/2)/2 = D/8, different from zero again, sorry, this world is not IDEAL. Best wishes, Leonid __ Do you Yahoo!? Plan great trips with Yahoo! Travel: Now over 17,000 guides! http://travel.yahoo.com/p-travelguide
Re: Size Strain in GSAS
Title: Message 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,gammaor something else does does not matter. Every thing we are talking about is additive meaning that the sum of what ever in 2Th space translates to the sum of what ever distributions. From the resulting distribution you are free to extract what ever parameter you choose. The idea in Nick Armstrongs work of obtaining a distribution without knowing its functional form is a powerful one. But the Baysean approach without a functional formresults in large errors bars in the distribution, seehttp://nvl.nist.gov/pub/nistpubs/jres/109/1/cnt109-1.htm What we should be looking forare cases where Voigt approximations are not possible. I have only ever seen one case where the actual Sinc type ripples are seen in a pattern. This was a pattern by Bob Cheary of gold columns. Other reports of ripples do exist in the literature (not available to me as I write). We must be careful not to include 2Th independentbumps produced by long narrow Soller slits inserted inthe axial plane that limits horizontal divergence. When sample related ripples are seen then you can throw Voigt based approximations out the window. In the case of the gold columns we fitted three Sinc functions added together. In other words the distribution wasreally a limited one. The work of Nick et al is sound and approaches the problems from a different perspective; it does not however negate the need to determine a priori information. The question that is openin my opinion is whether a priori information is more easily incorporated into a least squares process or a Bayesian Maxent approach. This discussion has reinvigoratedmy interest and like Bob, whom is now looking for an equation to approximate the log normal disribution, I will resurrectsome code myself that I did a while back which calculates profiles from a arbitrary distribution for the Sinc function. Instead I will include the equation for spherical crystallites and of course a user defined one which can be hkl dependent. 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 basedapproximations after all. all the best Alan -Original Message-From: Nicolae Popa [mailto:[EMAIL PROTECTED] Sent: Sunday, April 17, 2005 9:00 AMTo: rietveld_l@ill.frSubject: Re: Size Strain in GSAS Alan, (i) but a sum of two Lorentzians is not sharper than the sum of two pVs (Voigts)? (ii) We fitted the exact size profile caused by the lognormal distribution by a pV (for low lognormal dispersion) or by a sum of maximum 3 Lorenzians (for large lognormal dispersion). This is "cheaper" than the sum of 2 pVs.It involvesthe calculation ofmaximum 3 elementary functions with 4 independent parameters (3 breadths + 2 mixing parametersminus1 constraint =4) Sum of two pVs presumes 4 elementary function and 5 independent parameters (2 for one pV + 2 for the second one + a mixing parameter). Best wishes, Nicolae A pure peak fitting approach shows that two pVs (or two Voigts) when added with different FWHMs andintegrated 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. all the best alan
Re: Size Strain in GSAS
buna Nicolae, Not only arithmetic, I think is clear that both R and c were refined in a whole pattern least square fitting. A private program, not a popular Rietveld program because no one has inplemented the size profile caused by the lognormal distribution. not sure no one did.. we're working with that kind of profiles at least since 2000 (published in 2001 Acta Cryst A57, 204), without the need for any approximation going through Voigts or Pseudo Voigts. Using FFT and some math tricks you can compute the true profile for a distribution of crystallites almost in the same time you calculate a Voigt curve, so why the need to use any approximate function? I think this agrees with what Alan just pointed out (well 5000 profiles per second if you do not include any hkl dependent broadening that has to be calculated for each of them (and perhaps for each subcomponent)... otherwise the speed reduces.. but yes few ms for each profile is the current speed for my WPPM code, implementing all this stuff within the WPPM frame). But the most important disadvantage is the necessity to choose the exact type of size distribution. For Sample 1 (which, obviously, have certain distribution with certain R and c) you got quite different values of R and c for lognorm and gamma models, but the values of Dv and Da were nearly the same. Don't you feel that Dv and Da values contain more reliable information about R and c than those elaborate approximations described in chapter 6? Well, this is the general feature of the least square method. In the least square you must firstly to choose a parametrised model for something that you wish to fit. Do you know another posibility with the least square than to priory choose the model? Without model is only the deconvolution, and even there, if you wish a stable solution you must use a deconvolution method that requres a prior, starting model (I presume you followed the disertation of Nick Armstrong on this theme). also in this case it has ben shown possible to obtain a distribution without any prior information on its functional shape (J.Appl.Cryst (2004), 37, 629) and without taking the maxent treatment into account. I'm currently using without much problems for the analysis of nanostructured materials... advantages with respect to maxent are the speed and the fact that it can coexist with other broadening models (still not possible with maxent and still have to see a specimen where strain broadening is absent) and it's able to recover also a polydisperse distribution if it's present Just need to test it against maxent (if data would be kindly provided to do so). For the purists, just redo the calculation starting from different points and you can evaluate the error in the distribution using a MonteCarlo-like approach... As for the TCH-pV, well, it is no more than a pV with the Scherrer trend (1/cos) and the differential of Bragg's law (tan term) plugged in. This means it is ok as long as you consider a Williamson-Hall plot a good quantitative estimator for size and strain (IMHO). Mat PS I fully agree with Alan on the continuous request for Journals, but I bet the other Alan (the deus ex machina of the mailing list) should warn the members somehow... -- Matteo Leoni Department of Materials Engineering and Industrial Technologies University of Trento 38050 Mesiano (TN) ITALY
Re: Size Strain in GSAS
Nic, Thanks,it will take a while (as usual) to implement. Bob R.B. Von Dreele IPNS Division Argonne National Laboratory Argonne, IL 60439-4814 -Original Message- From: Nicolae Popa [mailto:[EMAIL PROTECTED] Sent: Sunday, April 17, 2005 1:27 AM To: rietveld_l@ill.fr Bob, A nice math. description amenable to RR exists, take a look at JAC(2002) 35, 338-346. Nice because the size profile is described by a pV (at regular lognormal dispersions) or by a sum of maximum three Lorentzians (at large lognormal dispersions - those 3% that Alan spiked about). The breadths and mixing parameters of pV or of the sum of Lorenzians are calculated analytically from the two parameters of the lognormal distribution, R and c. You realize that if approximate the instrumental and the strain profiles by Voigts, it results a sum of three Voigts for the whole profile and for a fast computation, every Voigt can be replaced by our loved TCH pV. Best wishes, Nic Nic, Well, I have been tempted from time to time to implement a log normal type distribution in on eof the profile functions. A nice math description ameanable to RR would help. Bob
Re: Size Strain in GSAS
Title: Message Alan, (i) but a sum of two Lorentzians is not sharper than the sum of two pVs (Voigts)? (ii) We fitted the exact size profile caused by the lognormal distribution by a pV (for low lognormal dispersion) or by a sum of maximum 3 Lorenzians (for large lognormal dispersion). This is "cheaper" than the sum of 2 pVs.It involvesthe calculation ofmaximum 3 elementary functions with 4 independent parameters (3 breadths + 2 mixing parametersminus1 constraint =4) Sum of two pVs presumes 4 elementary function and 5 independent parameters (2 for one pV + 2 for the second one + a mixing parameter). Best wishes, Nicolae A pure peak fitting approach shows that two pVs (or two Voigts) when added with different FWHMs andintegrated 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. all the best alan
Re: Size Strain in GSAS
Bob, A nice math. description amenable to RR exists, take a look at JAC(2002) 35, 338-346. Nice because the size profile is described by a pV (at regular lognormal dispersions) or by a sum of maximum three Lorentzians (at large lognormal dispersions - those 3% that Alan spiked about). The breadths and mixing parameters of pV or of the sum of Lorenzians are calculated analytically from the two parameters of the lognormal distribution, R and c. You realize that if approximate the instrumental and the strain profiles by Voigts, it results a sum of three Voigts for the whole profile and for a fast computation, every Voigt can be replaced by our loved TCH pV. Best wishes, Nic Nic, Well, I have been tempted from time to time to implement a log normal type distribution in on eof the profile functions. A nice math description ameanable to RR would help. Bob
Re: Size Strain in GSAS
Dear Nicolae, I will comment only upon your last statement because the limitations of your modeling are clear. Well, I don't know where from you taken these formulae but I observe that for spheres of equal radius, then zero dispersion, you have: sigma(D)=5D/4, different from zero! First of all, for spheres of equal radius and IDEAL definition of Dv and Da: sigmaD = D(Dv/Da - 1/2)/2 = D(9/8 - 1/2)/2 = 5D/16 Yes it is not zero, but the expressions I derived work only for 0.05 c 0.4 and I derived them not for IDEAL Dv and Da. If you perform WEIGHTED least-squares fitting of TCH p-V function to a profile simulated for spherical crystal and added by ~10% background level (to be closer to real Rietveld refinement) you will obtain the ratio of Dv/Da~3/4 not 9/8! This ratio is wrong but this is what we have from WEIGHTED least-squares fitting of TCH p-V to simulated data. In this case sigmaD = D(Dv/Da - 1/2)/2 = D(3/4 - 1/2)/2 = D/8, different from zero again, sorry, this world is not IDEAL. Best wishes, Leonid __ Do you Yahoo!? Plan great trips with Yahoo! Travel: Now over 17,000 guides! http://travel.yahoo.com/p-travelguide
Re: Size Strain in GSAS
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. Dear Nicolae, This arithmetic is clear, thanks, but since you did not specify this exact way of R calculation in the paper it was not evident. There are several other ways of deriving R, for instance: to calculate Dv from the inverse integral breadth and then use eq. (12) or (17) etc. Besides, you did not refine R for simulated data in chapter 6 - it was fixed. When you apply this formalism to real data you refine both R and c, they may correlate and the result of such correlation is not apparent. But the most important disadvantage is the necessity to choose the exact type of size distribution. For Sample 1 (which, obviously, have certain distribution with certain R and c) you got quite different values of R and c for lognorm and gamma models, but the values of Dv and Da were nearly the same. Don't you feel that Dv and Da values contain more reliable information about R and c than those elaborate approximations described in chapter 6? In new version of DDM (see the following message) I included some estimations of average crystallite diameter D and its dispersion sigmaD based on empirical approximations derived from fitting TCH-pV function to simulated profiles for the model of spherical crystallites with different size distribution dispersions. For simulated data (which are supplied with the DDM package) these magic expressions: D = Da + 0.25(DaDv)^0.5 and sigmaD = D(Dv/Da - 1/2)/2 allowed reproducing D and sigmaD with less than 10% deviation in the interval of relative dispersions 0.05 c 0.4 for both gamma and lognorm distributions. Of course, I don't think that these expressions are perfect and I would be glad to see better estimations. Best regards, Leonid __ Do you Yahoo!? Plan great trips with Yahoo! Travel: Now over 17,000 guides! http://travel.yahoo.com/p-travelguide
Re: Size Strain in GSAS
Title: Message
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 eta1.
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" (eta1 for old psVoigt) sample to see if a) the fit
is the same and b) the eta1 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
AMTo: rietveld_l@ill.frSubject: Re: Size Strain in
GSAS
Dear Bob,
If I understand well, you say that eta1
(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 wetried 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 AMTo: rietveld_l@ill.frSubject: 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 areat this moment.
Nicolae Popa
A word from a "provider" of a Rietveld code (please don't call
me a "programmer").
"But if
c0.4 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 AMTo:
[EMAIL PROTECTED]Cc:
rietveld_l@ill.frSubject: Re: Size Strain in
GSAS
Dear Nicolae, Maybe ya ploho
chitayu i ploho soobrazhayu, but even after yourexplanation
Re: Size Strain in GSAS
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 pVs (or two Voigts) when
added with different FWHMs
andintegrated 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
AMTo: rietveld_l@ill.frSubject: 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 eta1.
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" (eta1 for old psVoigt) sample to
see if a) the fit is the same and b) the eta1 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
AMTo: rietveld_l@ill.frSubject: Re: Size Strain in
GSAS
Dear Bob,
If I understand well, you say that eta1
(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 wetried 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 kn
Re: Size Strain in GSAS
Hi, In response to some of this post: There was a move by a bunch of us in the ICDD to hold a profile fitting round robin ( which I think would by quite useful ). But it died when we realized the prodigious level of resources that would be required to make sense of the rather large matrix of data that would arrive. But with regards to a round robin on this question: seems to me some qualified individual could simply do the work and publish a nice paper on it. Regards, Jim At 12:30 PM 4/15/2005 +0200, you wrote: urn:schemas-microsoft-com:office:office 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 eta1. 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 (eta1 for old psVoigt) sample to see if a) the fit is the same and b) the eta1 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 eta1 (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
Re: Size Strain in GSAS
Nic, Well, I have been tempted from time to time to implement a log normal type distribution in on eof the profile functions. A nice math description ameanable to RR would help. Bob From: Nicolae Popa [mailto:[EMAIL PROTECTED] Sent: Fri 4/15/2005 2:30 AM To: rietveld_l@ill.fr 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 eta1. 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 (eta1 for old psVoigt) sample to see if a) the fit is the same and b) the eta1 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 eta1 (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
Re: Size Strain in GSAS
Alan, Ah - the rocks dust model. It works well. Bob From: alan coelho [mailto:[EMAIL PROTECTED] Sent: Fri 4/15/2005 5:30 AM To: rietveld_l@ill.fr 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 eta1. 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 (eta1 for old psVoigt) sample to see if a) the fit is the same and b) the eta1 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
RE: Size Strain in GSAS
It was shown in paragraph 6 of JAC 35 (2002) 338-346 that size-broadened profiles given by both lognormal and gamma distributions can be approximated by a weighted sum of Lorentz and Gauss functions for a broad range of distribution dispersions. Besides, round robins can sometimes be long adventures... 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 __ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
Re: Size Strain in GSAS
... 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 c0.4 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
Re: Size Strain in GSAS
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)). 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 __ Do you Yahoo!? Read only the mail you want - Yahoo! Mail SpamGuard. http://promotions.yahoo.com/new_mail
Re: Size Strain in GSAS
Dear Nicolae, Maybe ya ploho chitayu i ploho soobrazhayu, but even after yourexplanation I can't see a way to calculate R from the results offitting described in chapters 6 7 of JAC 35 (2002) 338-346. From suchfitting you obtain only dispersion parameter c. Or I missed something?Anyway, being "Rietvelders" we still have to deal with TCH-pV functionand we need to extract as much as possible correct information from it.Hope we shall see more appropriate functions for microstructureanalysis 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 theargument 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 c0.4 any pV fails. Best wishes, Nicolae
RE: Size Strain in GSAS
Title: Message A word from a "provider" of a Rietveld code (please don't call me a "programmer"). "But if c0.4 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 AMTo: [EMAIL PROTECTED]Cc: rietveld_l@ill.frSubject: Re: Size Strain in GSAS Dear Nicolae, Maybe ya ploho chitayu i ploho soobrazhayu, but even after yourexplanation I can't see a way to calculate R from the results offitting described in chapters 6 7 of JAC 35 (2002) 338-346. From suchfitting you obtain only dispersion parameter c. Or I missed something?Anyway, being "Rietvelders" we still have to deal with TCH-pV functionand we need to extract as much as possible correct information from it.Hope we shall see more appropriate functions for microstructureanalysis 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 theargument 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 c0.4 any pV fails. Best wishes, Nicolae
RE: Size Strain [ In GSAS ??? ]
Hi all, Well, I thought I'd weigh in on this with a discussion of an aforementioned SRM project: We are in the final stages of preparing an SRM for determination of crystallite size from line profile analysis. Through the course of his PhD work and NIST postdoctoral position, Nick Armstrong has developed a MaxEnt / Bayesian method specifically for the certification. The method can quantify, from the quality of the raw data, the probably that a proposed model for the crystallite size distribution is the true one. Thus, the certified values of the standard will include a valid measure of their uncertainty that, in our humble opinion, would not be obtainable with alternative methods. Details, and results of the method as applied to the RR CeO2, have been published. We are working at the production of ~kg quantities of strain free CeO2 and ZnO for use as the SRM feedstock; no small challenge. We expect two outcomes: 1) The community will have a standard by which results from mortal methods may be readily tested and compared. 2) A high-intensity squabble will ensue as to whether or not we got the right answer. With regards to the latter issue: Nick and I have been approached about another round robin. Forgive me, but: round robins don't have anything to do with accuracy. They test for uniformity of measurements in the field, the major premise being that, as a result of mature methodology, a narrow distribution is expected. Note the highly successful, Rietveld, QPA, and instrument sensitivity round robins. There is, however, no mature methodology here. Indeed, only a small number of operations worldwide can perform a credible microstructure analysis, and their methods certainly differ. It is our intention to make the data collected for the certification available to the community. But with regards to model testing for the more advanced, physical model, methods (with the use of simulated, bi-model data for instance), I would suggest that more of a collaborative effort be organized. Regards, Jim James P. Cline [EMAIL PROTECTED] Ceramics Division Voice (301) 975 5793 National Institute of Standards and Technology FAX (301) 975 5334 100 Bureau Dr. stop 8520 Gaithersburg, MD 20899-8523USA
Re: Size Strain in GSAS
Title: Message 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 areat this moment. Nicolae Popa A word from a "provider" of a Rietveld code (please don't call me a "programmer"). "But if c0.4 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 AMTo: [EMAIL PROTECTED]Cc: rietveld_l@ill.frSubject: Re: Size Strain in GSAS Dear Nicolae, Maybe ya ploho chitayu i ploho soobrazhayu, but even after yourexplanation I can't see a way to calculate R from the results offitting described in chapters 6 7 of JAC 35 (2002) 338-346. From suchfitting you obtain only dispersion parameter c. Or I missed something?Anyway, being "Rietvelders" we still have to deal with TCH-pV functionand we need to extract as much as possible correct information from it.Hope we shall see more appropriate functions for microstructureanalysis 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 theargument 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 c0.4 any pV fails. Best wishes, Nicolae
RE: Size Strain in GSAS
Title: Message 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 AMTo: rietveld_l@ill.frSubject: 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 areat this moment. Nicolae Popa A word from a "provider" of a Rietveld code (please don't call me a "programmer"). "But if c0.4 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 AMTo: [EMAIL PROTECTED]Cc: rietveld_l@ill.frSubject: Re: Size Strain in GSAS Dear Nicolae, Maybe ya ploho chitayu i ploho soobrazhayu, but even after yourexplanation I can't see a way to calculate R from the results offitting described in chapters 6 7 of JAC 35 (2002) 338-346. From suchfitting you obtain only dispersion parameter c. Or I missed something?Anyway, being "Rietvelders" we still have to deal with TCH-pV functionand we need to extract as much as possible correct information from it.Hope we shall see more appropriate functions for microstructureanalysis 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 theargument 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 c0.4 any pV fails. Best wishes, Nicolae
Re: Size Strain in GSAS
Title: Message Dear Bob, If I understand well, you say that eta1 (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 wetried 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 AMTo: rietveld_l@ill.frSubject: 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 areat this moment. Nicolae Popa A word from a "provider" of a Rietveld code (please don't call me a "programmer"). "But if c0.4 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 AMTo: [EMAIL PROTECTED]Cc: rietveld_l@ill.frSubject: Re: Size Strain in GSAS Dear Nicolae, Maybe ya ploho chitayu i ploho soobrazhayu, but even after yourexplanation I can't see a way to calculate R from the results offitting described in chapters 6 7 of JAC 35 (2002) 338-346. From suchfitting you obtain only dispersion parameter c. Or I missed something?Anyway, being "Rietvelders" we still have to deal with TCH-pV functionand we need to extract as much as possible correct information from it.Hope we shall see more appropriate functions for microstructureanalysis 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 theargument 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 c0.4 any pV fails. Best wishes, Nicolae
RE: Size Strain in GSAS
Title: Message 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" (eta1 for old psVoigt) sample to see if a) the fit is the same and b) the eta1 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 AMTo: rietveld_l@ill.frSubject: Re: Size Strain in GSAS Dear Bob, If I understand well, you say that eta1 (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 wetried 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 AMTo: rietveld_l@ill.frSubject: 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 areat this moment. Nicolae Popa A word from a "provider" of a Rietveld code (please don't call me a "programmer"). "But if c0.4 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 AMTo: [EMAIL PROTECTED]Cc: rietveld_l@ill.frSubject: Re: Size Strain in GSAS Dear Nicolae, Maybe ya ploho chitayu i ploho soobrazhayu, but even after yourexplanation I can't see a way to calculate R from the results offitting described in chapters 6 7 of JAC 35 (2002) 338-346. From suchfitting you obtain only dispersion parameter c. Or I missed something?Anyway, being "Rietvelders" we still have to deal with TCH-pV functionand we need to extract as much as possible correct information from it.Hope we shall see more appropriate functions for microstructureanalysis 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 theargument 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 code
Re: Size Strain in GSAS
8. The simple modified TCH model (triple-Voigt), used in most major Rietveld programs these days, is surprisingly flexible. It works well for most of the samples (super-Lorentzian is an example when it fails, as well as many others, but this is less frequent that onewould expect) and gives some numbers for coherent domain size and strain. If we are lucky to know more about the sample (for instance, the information is available that a lognormal size distribution, certain type of dislocations, etc., is most likely to be prevalent for majority of grains in the sample), those numbers will let us calculate real numbers that relate to the real physical parameters (say, the first moment and dispersion of the size distribution, etc.) in many cases, as discussed here previously. Good conclusion, but before deriving real numbers that relate to the real physical parameters one needs first to calibrate the pseudo-Voigt-based calculation of those numbers (Dv and Da, or L_volume and L_area in other notations)using at least simulated profiles for VARIOUS dispersions. I hope that the round robin on simulated data will be translated into reality soon. Leonid __ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
RE: Size Strain in GSAS
It was shown in paragraph 6 of JAC 35 (2002) 338-346 that size-broadened profiles given by both lognormal and gamma distributions can be approximated by a weighted sum of Lorentz and Gauss functions for a broad range of distribution dispersions. Besides, round robins can sometimes be long adventures... Davor -Original Message- From: Leonid Solovyov [mailto:[EMAIL PROTECTED] Sent: Wednesday, April 13, 2005 12:11 AM To: rietveld_l@ill.fr Subject: Re: Size Strain in GSAS 8. The simple modified TCH model (triple-Voigt), used in most major Rietveld programs these days, is surprisingly flexible. It works well for most of the samples (super-Lorentzian is an example when it fails, as well as many others, but this is less frequent that onewould expect) and gives some numbers for coherent domain size and strain. If we are lucky to know more about the sample (for instance, the information is available that a lognormal size distribution, certain type of dislocations, etc., is most likely to be prevalent for majority of grains in the sample), those numbers will let us calculate real numbers that relate to the real physical parameters (say, the first moment and dispersion of the size distribution, etc.) in many cases, as discussed here previously. Good conclusion, but before deriving real numbers that relate to the real physical parameters one needs first to calibrate the pseudo-Voigt-based calculation of those numbers (Dv and Da, or L_volume and L_area in other notations)using at least simulated profiles for VARIOUS dispersions. I hope that the round robin on simulated data will be translated into reality soon. Leonid __ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
Re: Size Strain in GSAS
I guess, this discussion has already died down but I couldn't find a moment for reply soon enough:-) As Prague was already mentioned, let me try to summarize what I think about this subject and have said there (let's hope I actually remember it:-): 1. A careful line broadening analysis (at this point in time) is better done outside Rietveld refinement 2. A physical model is better and preferred to a phenomenological model for analyzing line broadening However, because we discuss the Size-Strain analysis in Rietveld here: 3. Rietveld obviously needs some kind of line-broadening modeling in order to at least correct for sample broadening effects (especially anisotropic ones) to extract correct integrated intensities for crystal-structure refinement. Thus, any model that works is good. 4. Rietveld needs to have a line-broadening model that works for an arbitrary crystal structure (up to triclinic) and arbitrary sample (i.e. many possible sources of broadening could be present in a given sample). Therefore, a phenomenological model is the only one available at this point, as physical models are still struggling with cubic (or hexagonal) structures and a very limited spectrum of physical sources causing broadening. In conclusion: 5. I think that the work done by Nick Armstrong and others is definitely a way to go, but also a long way to go before we get to the level mentioned under 4 (I certainly won't live to see it:-). 6. I also believe that (even when 5 is fulfilled) diffraction will often need some additional information provided by complementary characterization methods (i.e. TEM, SEM,...) to completely and accurately characterize defects in a sample, as we may calculate the most probable solution but won't often be able to discriminate between other very likely solutions, that is, the most probable is very often not significantly different from other physically plausible solutions (lognormal and gamma examples already mentioned). 7. Previous point implies that trying to do too much with only diffraction data might actually be dangerous. One can find too many dead-wrong numbers in the literature using some of the physical models (for instance, dislocation densities, etc.), as a real physical cause of broadening was probably different and/or there was a strong correlation between refinable parameters that depend on the diffraction angle in a similar way. Considering the above: 8. The simple modified TCH model (triple-Voigt), used in most major Rietveld programs these days, is surprisingly flexible. It works well for most of the samples (super-Lorentzian is an example when it fails, as well as many others, but this is less frequent that one would expect) and gives some numbers for coherent domain size and strain. If we are lucky to know more about the sample (for instance, the information is available that a lognormal size distribution, certain type of dislocations, etc., is most likely to be prevalent for majority of grains in the sample), those numbers will let us calculate real numbers that relate to the real physical parameters (say, the first moment and dispersion of the size distribution, etc.) in many cases, as discussed here previously. Davor P.S: 9. The fact that a certain physical model does not yield a particular analytical function as a physically broadened profile does not mean that the function cannot successfully approximate that profile, as any such calculation includes many approximations of different kinds. There were numerous examples in literature showing that a simple Voigt function was able to approximate quite different cases. Of course, that is not true in general. -Original Message- From: Matteo Leoni [mailto:[EMAIL PROTECTED] Sent: Tuesday, March 29, 2005 4:59 AM To: rietveld_l@ill.fr Subject: RE: Size Strain In GSAS Leonid (and others) just my 2 cents to the whole story (as this is a long standing point of discussion: Davor correct me if I'm wrong, but this was also one of the key points in the latest size-strain meeting in Prague, right?) Your recipe for estimating size distribution from the parameters of a Voight-fitted profile is clear and straightforward, but I wonder have you, or someone else, tested it on, say, simulated data for the model of spherical crystallites having lognormal size distribution with various dispersions? done several times... if you start from a pattern synthesised from a lognormal and you analyse it using a post-mortem LPA method (i.e. extract a width and a shape parameter and play with them to get some microstructural information), you obtain a result which (in most cases) does not allow you to reconstruct the original data (the Fourier transform of a Voigt and that of the function describing a lognormal distribution of spherical domains are different). I would invite all people using ANY traditional line profile analysis method to do
Re: Size Strain in GSAS
Hi, maybe I'm late in the discussion, but what about if we use a Rietveld ( or whole pattern fitting) refinement in order to extract data for the profile and use it to make the extraction of size and strain effects? thanks and greetings Miguel Hesiquio-Garduño Profesor Asociado C Departamento de Ciencia de Materiales Academia de Ciencias de la Ingeniería ESFM-IPN I guess, this discussion has already died down but I couldn't find a moment for reply soon enough:-) As Prague was already mentioned, let me try to summarize what I think about this subject and have said there (let's hope I actually remember it:-): 1. A careful line broadening analysis (at this point in time) is better done outside Rietveld refinement 2. A physical model is better and preferred to a phenomenological model for analyzing line broadening However, because we discuss the Size-Strain analysis in Rietveld here: 3. Rietveld obviously needs some kind of line-broadening modeling in order to at least correct for sample broadening effects (especially anisotropic ones) to extract correct integrated intensities for crystal-structure refinement. Thus, any model that works is good. 4. Rietveld needs to have a line-broadening model that works for an arbitrary crystal structure (up to triclinic) and arbitrary sample (i.e. many possible sources of broadening could be present in a given sample). Therefore, a phenomenological model is the only one available at this point, as physical models are still struggling with cubic (or hexagonal) structures and a very limited spectrum of physical sources causing broadening. In conclusion: 5. I think that the work done by Nick Armstrong and others is definitely a way to go, but also a long way to go before we get to the level mentioned under 4 (I certainly won't live to see it:-). 6. I also believe that (even when 5 is fulfilled) diffraction will often need some additional information provided by complementary characterization methods (i.e. TEM, SEM,...) to completely and accurately characterize defects in a sample, as we may calculate the most probable solution but won't often be able to discriminate between other very likely solutions, that is, the most probable is very often not significantly different from other physically plausible solutions (lognormal and gamma examples already mentioned). 7. Previous point implies that trying to do too much with only diffraction data might actually be dangerous. One can find too many dead-wrong numbers in the literature using some of the physical models (for instance, dislocation densities, etc.), as a real physical cause of broadening was probably different and/or there was a strong correlation between refinable parameters that depend on the diffraction angle in a similar way. Considering the above: 8. The simple modified TCH model (triple-Voigt), used in most major Rietveld programs these days, is surprisingly flexible. It works well for most of the samples (super-Lorentzian is an example when it fails, as well as many others, but this is less frequent that one would expect) and gives some numbers for coherent domain size and strain. If we are lucky to know more about the sample (for instance, the information is available that a lognormal size distribution, certain type of dislocations, etc., is most likely to be prevalent for majority of grains in the sample), those numbers will let us calculate real numbers that relate to the real physical parameters (say, the first moment and dispersion of the size distribution, etc.) in many cases, as discussed here previously. Davor P.S: 9. The fact that a certain physical model does not yield a particular analytical function as a physically broadened profile does not mean that the function cannot successfully approximate that profile, as any such calculation includes many approximations of different kinds. There were numerous examples in literature showing that a simple Voigt function was able to approximate quite different cases. Of course, that is not true in general. -Original Message- From: Matteo Leoni [mailto:[EMAIL PROTECTED] Sent: Tuesday, March 29, 2005 4:59 AM To: rietveld_l@ill.fr Subject: RE: Size Strain In GSAS Leonid (and others) just my 2 cents to the whole story (as this is a long standing point of discussion: Davor correct me if I'm wrong, but this was also one of the key points in the latest size-strain meeting in Prague, right?) Your recipe for estimating size distribution from the parameters of a Voight-fitted profile is clear and straightforward, but I wonder have you, or someone else, tested it on, say, simulated data for the model of spherical crystallites having lognormal size distribution with various dispersions? done several times... if you start from a pattern synthesised from a lognormal and you analyse it using a post-mortem LPA method (i.e. extract a width and a shape parameter and play
Re: Size Strain In GSAS
Hi, Long text but not fully convincing. At least concerning my questions (still posted at the bottom). I'm risking a hurry reply without reading all references (including to be published and PhD Thesis). See comments below. that likelihood term is described by a goodness of fit, say chi-square function, which improves as the models become more complex or increase in the number of parameters. The Ockham's Razor term, on the other hand, penalizes a model for the number of parameters by including the a priori distribution and uncertainties in parameter values. Hence this term offsets the influence the likelihood term may have, thereby arriving at a choice of model where the number of parameters can be justified. In this case it is possible to use a uniform prior Both, lognormal and gamma are physically based distributions, both have the same numbers of parameters, both give the same restored profile inside the noise, the same chi square (and Rw-gamma even slightly better), the prior distributions are the same (uniform?) uncertainties in parameter values are comparable, what Razor term penalizes? space (see below). The solution with the greatest entropy relative to a priori model and experimental data is the solution with the least assumptions or the solution with the most amount of randomness. Solutions with a lower entropy are solutions where specific assumptions have been made which can not be justified. For example, we apply this method to determining the modal properties of a size distribution i.e. monomodal or bimodal size distributions. Say if we assume, distribution has a bimodal features, when in reality it is a monodal distribution, this assumption will results in a solution with a lower entropy. The same is also case for the converse problem (see [3]). Moreover, we can use this method to select between different distribution models such as lognormal or gamma distributions. It means that for gamma distribution you found the entropy was lower and then this model is not justified. Significantly lower? Probably you have a measure concerning the significance of the difference between the entropies of the two models? On the other hand, why lognormal is the solution with the least assumptions? What we are trying to do with the full Bayesian/MaxEnt method (see [1])is determine a free form solution or a non-parametric solution [5],f, where the solutions is either a line profile or a distribution determine from the experimental data and knowledge of the instrumental, noise and background effects. By free formor non-parametric solution I mean a profile and/or distributions which does not assume a specific set of parameters, as defined by say a lognormal distribution or a Voigt line profile function. The a priori model, m, can be defined by a And, certainly, the free form solution has the highest entropy, anyway higher than the initial guess (lognormal). This is the optimal solution, if I understood correctly. I wonder if this optimal solution from the point of view of MaxEnt. is not one from the following solutions: w*Logn+(1-w)*Gamm. To these solutions (of infinite multiplicity) the peak profiles are indifferent. Dear All, I'm sorry for the delay in relying. I also want to pass on my thanks to Jim Cline for pointing out that wasn't around to response to some of the queries/issues. It has been interesting reading the discussion, since coming back to Sydney. I don't mean to add more fuel to the fire, but I do hope to outline/address some of the issues which have been raised, while giving a more precise outline of the Bayesian/maximum entropy (MaxEnt) method as applied to line profile analysis. By way of background information and reference, the most recent publications which present the theory and application of the Bayesian/MaxEnt to analyzing size/shape broadened (simulated and experimental) data are given in [1-4]-- see below. None of this work would be possible without the core collaborators which include: Jim Cline (NIST), Walter Kalceff (UTS), Annette Dowd (UTS) and John Bonevich (NIST) in various combinations. In summary, [1] gives a full and mathematical derivation of the Bayesian/MaxEnt method and is applied to simulated and experimental data. In [2], the application of the full Bayesian/Maxent and Markov Chain Monte Carlo (MCMC) methods to size analysis. Ref.[3] shows how Bayesian/MaxEnt/MCMC methods can be applied to distinguish monomodal and bimodal size distributions i.e Bayesian model selection. Ref [4] is another application of Bayesian model selection to distinguish between lognormal and gamma distributions which also includes full TEM data/analysis and also demonstrates how the method is sensitive to shape and microstrain effects in the line profile data. Let me first address Nicolae's queries. The application of the Bayesian/MCMC method in [2] was simply to demonstrate how the method could be used to explore the
RE: Size Strain In GSAS
Leonid, Could you, please, give a reference to a study where Dv and Da sizes were derived from the parameters of pseudo-Voight or Voight fitted to simulated profiles for various size distribution dispersions? I did something better (I hope).. at the end of the mesg you find xy data with a simulation: Ceria (Fm-3m), CuKa 0.15406 nm (delta function, i.e. no emission profile aberration)), size broadening due to a lognormal distribution of spheres only, no background, no noise, no Lorentz-Polarization, no aberrations of any kind. Peaks present in the pattern: 111 200 220 311 222 400 331 420 422 333/511 fitted but not used in the analysis as they have same d. Simulation done using WPPM, or, simply, taking the FT of the formulae proposed in Acta Cryst (2002) A58, 190-200 for the lognorm. The program used for the simulation allows fully recovery of the original parameters, starting from different initial values (self consistent check..). Analysis done using traditional peak fitting Williamson-Hall and Warren-Averbach methods, applying the formulae found e.g. on Phil Mag (1998) A77 [3], 621-640 to obtain the lognorm from the Da and Dv values (should the ref be unavailable, they can be easily calculated, or I can also provide the formulae). I can send the simulation parameters and all plots/calculations I did to the interested members (just drop me a line). Results of WH and WA seems good but the distributions they provide are completely out with respect to the true one (unless I did some mistake, but that can be easily checked). I could have attached the results file here, but I'm sure Alan (as list moderator) would haven't been quite happy about attachments. Happy calculation, for those who wants to do the analysis by themselves without knowing the result in advance! Mat - Matteo Leoni, PhD Department of Materials Engineering and Industrial Technologies University of Trento 38050 Mesiano (TN) ITALY SIMULATED DATA in xy (2theta Intensity) format. 1.80e+001 4.470421e+000 1.806000e+001 4.513074e+000 1.812000e+001 4.556395e+000 1.818000e+001 4.600401e+000 1.824000e+001 4.645108e+000 1.83e+001 4.690529e+000 1.836000e+001 4.736682e+000 1.842000e+001 4.783659e+000 1.848000e+001 4.831332e+000 1.854000e+001 4.879787e+000 1.86e+001 4.929045e+000 1.866000e+001 4.979123e+000 1.872000e+001 5.030047e+000 1.878000e+001 5.081826e+000 1.884000e+001 5.134484e+000 1.89e+001 5.188043e+000 1.896000e+001 5.242526e+000 1.902000e+001 5.297955e+000 1.908000e+001 5.354352e+000 1.914000e+001 5.411743e+000 1.92e+001 5.470151e+000 1.926000e+001 5.529602e+000 1.932000e+001 5.590123e+000 1.938000e+001 5.651740e+000 1.944000e+001 5.714484e+000 1.95e+001 5.778379e+000 1.956000e+001 5.843577e+000 1.962000e+001 5.909879e+000 1.968000e+001 5.977428e+000 1.974000e+001 6.046257e+000 1.98e+001 6.116400e+000 1.986000e+001 6.187892e+000 1.992000e+001 6.260770e+000 1.998000e+001 6.335082e+000 2.004000e+001 6.410849e+000 2.01e+001 6.488118e+000 2.016000e+001 6.566933e+000 2.022000e+001 6.647338e+000 2.028000e+001 6.729377e+000 2.034000e+001 6.813098e+000 2.04e+001 6.898548e+000 2.046000e+001 6.985779e+000 2.052000e+001 7.074842e+000 2.058000e+001 7.165793e+000 2.064000e+001 7.258687e+000 2.07e+001 7.353585e+000 2.076000e+001 7.450544e+000 2.082000e+001 7.549629e+000 2.088000e+001 7.650906e+000 2.094000e+001 7.754684e+000 2.10e+001 7.860571e+000 2.106000e+001 7.968865e+000 2.112000e+001 8.079643e+000 2.118000e+001 8.192986e+000 2.124000e+001 8.308978e+000 2.13e+001 8.427707e+000 2.136000e+001 8.549279e+000 2.142000e+001 8.673760e+000 2.148000e+001 8.801265e+000 2.154000e+001 8.931897e+000 2.16e+001 9.065765e+000 2.166000e+001 9.202984e+000 2.172000e+001 9.343672e+000 2.178000e+001 9.487954e+000 2.184000e+001 9.635962e+000 2.19e+001 9.787833e+000 2.196000e+001 9.943709e+000 2.202000e+001 1.010374e+001 2.208000e+001 1.026809e+001 2.214000e+001 1.043692e+001 2.22e+001 1.061041e+001 2.226000e+001 1.078874e+001 2.232000e+001 1.097211e+001 2.238000e+001 1.116071e+001 2.244000e+001 1.135477e+001 2.25e+001 1.155511e+001 2.256000e+001 1.176082e+001 2.262000e+001 1.197270e+001 2.268000e+001 1.219102e+001 2.274000e+001 1.241607e+001 2.28e+001 1.264814e+001 2.286000e+001 1.288756e+001 2.292000e+001 1.313466e+001 2.298000e+001 1.338978e+001 2.304000e+001 1.365333e+001 2.31e+001 1.392571e+001 2.316000e+001 1.420732e+001 2.322000e+001 1.449861e+001 2.328000e+001 1.480009e+001 2.334000e+001 1.511227e+001 2.34e+001 1.543569e+001 2.346000e+001 1.577095e+001 2.352000e+001 1.611867e+001 2.358000e+001 1.647952e+001 2.364000e+001 1.685423e+001 2.37e+001 1.724355e+001 2.376000e+001 1.764832e+001 2.382000e+001 1.806942e+001
RE: Size Strain In GSAS
Dear Matteo, Thanks for the exercise. From pseudo-Voight fitting I have got Dv=33A, Da=23A, which gives the average size D=21A and the relative dispersion c=0.28 (c = [sigmaD/D]^2). However, I suspect that the actual values you used for the simulation were D~30A and c~0.25. Do I win the F1 GP? :-) Actually, I have also played with simulated profiles for various dispersions and I am going to calibrate the calculations of Dv and Da from pseudo-Voight. Hope I will include these calibrated calculations to the next release of DDM. Cheers, Leonid P.S. As for a Ferrari powered by a John Deere tractor engine, I believe that none of us would win a F1 GP even with an original Ferrari engine. I have better recipe: take a Russian tank T-72 (which is simpler and cheaper than Ferrari), put it at the pole-position, turn the gun back and enjoy driving - F1 GP is guaranteed. __ Do you Yahoo!? Yahoo! Small Business - Try our new resources site! http://smallbusiness.yahoo.com/resources/
RE: Size Strain In GSAS
Dear Matteo, Thanks for the problem. I have used pseudo voigt function to fit the peaks and finally used the program BREADTH and obtained Dv=31 A, Da=18 A. Please send me your simulation parameters, plots/calculations. Regards, Apu /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ Apu Sarkar Research Fellow Variable Energy Cyclotron Centre Kolkata 700 064 phone: 91-33-2337-1230 (extn. 3190) Fax: 91-33-2334-6871 INDIA /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ - Original Message - From: Matteo Leoni [EMAIL PROTECTED] Date: Wednesday, March 30, 2005 4:39 pm ---BeginMessage--- Leonid, Could you, please, give a reference to a study where Dv and Da sizes were derived from the parameters of pseudo-Voight or Voight fitted to simulated profiles for various size distribution dispersions? I did something better (I hope).. at the end of the mesg you find xy data with a simulation: Ceria (Fm-3m), CuKa 0.15406 nm (delta function, i.e. no emission profile aberration)), size broadening due to a lognormal distribution of spheres only, no background, no noise, no Lorentz-Polarization, no aberrations of any kind. Peaks present in the pattern: 111 200 220 311 222 400 331 420 422 333/511 fitted but not used in the analysis as they have same d. Simulation done using WPPM, or, simply, taking the FT of the formulae proposed in Acta Cryst (2002) A58, 190-200 for the lognorm. The program used for the simulation allows fully recovery of the original parameters, starting from different initial values (self consistent check..). Analysis done using traditional peak fitting Williamson-Hall and Warren-Averbach methods, applying the formulae found e.g. on Phil Mag (1998) A77 [3], 621-640 to obtain the lognorm from the Da and Dv values (should the ref be unavailable, they can be easily calculated, or I can also provide the formulae). I can send the simulation parameters and all plots/calculations I did to the interested members (just drop me a line). Results of WH and WA seems good but the distributions they provide are completely out with respect to the true one (unless I did some mistake, but that can be easily checked). I could have attached the results file here, but I'm sure Alan (as list moderator) would haven't been quite happy about attachments. Happy calculation, for those who wants to do the analysis by themselves without knowing the result in advance! Mat - Matteo Leoni, PhD Department of Materials Engineering and Industrial Technologies University of Trento 38050 Mesiano (TN) ITALY SIMULATED DATA in xy (2theta Intensity) format. 1.80e+001 4.470421e+000 1.806000e+001 4.513074e+000 1.812000e+001 4.556395e+000 1.818000e+001 4.600401e+000 1.824000e+001 4.645108e+000 1.83e+001 4.690529e+000 1.836000e+001 4.736682e+000 1.842000e+001 4.783659e+000 1.848000e+001 4.831332e+000 1.854000e+001 4.879787e+000 1.86e+001 4.929045e+000 1.866000e+001 4.979123e+000 1.872000e+001 5.030047e+000 1.878000e+001 5.081826e+000 1.884000e+001 5.134484e+000 1.89e+001 5.188043e+000 1.896000e+001 5.242526e+000 1.902000e+001 5.297955e+000 1.908000e+001 5.354352e+000 1.914000e+001 5.411743e+000 1.92e+001 5.470151e+000 1.926000e+001 5.529602e+000 1.932000e+001 5.590123e+000 1.938000e+001 5.651740e+000 1.944000e+001 5.714484e+000 1.95e+001 5.778379e+000 1.956000e+001 5.843577e+000 1.962000e+001 5.909879e+000 1.968000e+001 5.977428e+000 1.974000e+001 6.046257e+000 1.98e+001 6.116400e+000 1.986000e+001 6.187892e+000 1.992000e+001 6.260770e+000 1.998000e+001 6.335082e+000 2.004000e+001 6.410849e+000 2.01e+001 6.488118e+000 2.016000e+001 6.566933e+000 2.022000e+001 6.647338e+000 2.028000e+001 6.729377e+000 2.034000e+001 6.813098e+000 2.04e+001 6.898548e+000 2.046000e+001 6.985779e+000 2.052000e+001 7.074842e+000 2.058000e+001 7.165793e+000 2.064000e+001 7.258687e+000 2.07e+001 7.353585e+000 2.076000e+001 7.450544e+000 2.082000e+001 7.549629e+000 2.088000e+001 7.650906e+000 2.094000e+001 7.754684e+000 2.10e+001 7.860571e+000 2.106000e+001 7.968865e+000 2.112000e+001 8.079643e+000 2.118000e+001 8.192986e+000 2.124000e+001 8.308978e+000 2.13e+001 8.427707e+000 2.136000e+001 8.549279e+000 2.142000e+001 8.673760e+000 2.148000e+001 8.801265e+000 2.154000e+001 8.931897e+000 2.16e+001 9.065765e+000 2.166000e+001 9.202984e+000 2.172000e+001 9.343672e+000 2.178000e+001 9.487954e+000 2.184000e+001 9.635962e+000 2.19e+001 9.787833e+000 2.196000e+001 9.943709e+000 2.202000e+001 1.010374e+001 2.208000e+001 1.026809e+001 2.214000e+001 1.043692e+001 2.22e+001 1.061041e+001 2.226000e+001 1.078874e+001 2.232000e+001 1.097211e+001 2.238000e+001 1.116071e+001 2.244000e+001 1.135477e+001 2.25e+001 1.155511e+001 2.256000e+001 1.176082e+001 2.262000e+001 1.197270e+001
RE: Size Strain In GSAS
Leonid (and others) just my 2 cents to the whole story (as this is a long standing point of discussion: Davor correct me if I'm wrong, but this was also one of the key points in the latest size-strain meeting in Prague, right?) Your recipe for estimating size distribution from the parameters of a Voight-fitted profile is clear and straightforward, but I wonder have you, or someone else, tested it on, say, simulated data for the model of spherical crystallites having lognormal size distribution with various dispersions? done several times... if you start from a pattern synthesised from a lognormal and you analyse it using a post-mortem LPA method (i.e. extract a width and a shape parameter and play with them to get some microstructural information), you obtain a result which (in most cases) does not allow you to reconstruct the original data (the Fourier transform of a Voigt and that of the function describing a lognormal distribution of spherical domains are different). I would invite all people using ANY traditional line profile analysis method to do always this check. Davor already pointed out cases where it works and cases where it does not: according to my experience those belonging to the first category are just a few. With a whole pattern approach and working directly with the profile arising from a distribution of domains, in most cases you're able to recostruct the original distribution without making any assumption on its functional shape (after all, most of the information to do so is contained in the whole pattern, even if it is well hidden). Concerning the Beyesian/maxent method, well, it is always a great idea, but unfortunately right now it is not mature enough to cope with a simple problem of combined instrumental, size AND strain broadening (unless something has been done in the last year). So ok it gives you the best result compatible with your hypotheses, but beware that absence of any other source of broadening should be listed among them.. and I'm not sure this is always the case! To put some water on the fire (otherwise it will burn all of us), I think the level of detail one needs on the microstructure, conditions the methods one's going to use to extract a result. No need to use highly sophisticated methods to roughly estimate a domain size (with an error up to +/- 50%) or to establish a trend within a homogeneous set of data, or also to obtain a better fit in the Rietveld method. Conversely, if a very high level of detail is sought, then I'd forget about a traditional Rietveld refinement and start approaching the problem from the microstructure point of view (after all, if one is interested in winning a F1 GP, he'd certainly not go for a Ferrari powered by a John Deere tractor engine!). cheers Mat - Matteo Leoni, PhD Department of Materials Engineering and Industrial Technologies University of Trento 38050 Mesiano (TN) ITALY
RE: Size Strain In GSAS
done several times... With a whole pattern approach and working directly with the profile arising from a distribution of domains, in most cases you're able to recostruct the original distribution without making any assumption on its functional shape (after all, most of the information to do so is contained in the whole pattern, even if it is well hidden). Dear Matteo (and others), Could you, please, give a reference to a study where Dv and Da sizes were derived from the parameters of pseudo-Voight or Voight fitted to simulated profiles for various size distribution dispersions? Thanks in advance, Leonid __ Do you Yahoo!? Yahoo! Small Business - Try our new resources site! http://smallbusiness.yahoo.com/resources/
Re: Size Strain In GSAS
Hi, So, to resume your statements, by using Bayesian/Max.Entr. we can distinguish between two distributions that can not be distinguished by maximum likelihood (least square)? Hard to swallow, once the restored peak profiles are the same inside the noise. What other information than the peak profile, instrumental profile and statistical noise we have that Bayes/Max.ent. can use and the least square cannot? prior distributions to be uniform - if I understand correctly you refer to the distributions of D0 and sigma of the lognormal (gamma) distribution from which the least square chooses the solution, not to the distribution itself (logn, gamm). Then, how is this prior distribution for Baye/Max.ent.? Best, Nick Popa Hi Sorry for the delay. The Bayesian results showed that the lognormal was more probable. Yes, the problem is ill-condition which why you need to use the Bayesian/Maximum entropy method. This method takes into account the ill-conditioning of the problem. The idea being it determines the most probable solutions from the set of solutions. This solution can be shown to be the most consistent solution or the solution with the least assumptions given the experimental data, noise, instrument effects etc (see Skilling Bryan 1983; Skilling 1990; Sivia 1996). This is the role of entropy function. There are many mathemaitcal proofs for this (see Jaynes' recent book). The Bayesian analysis maps out the solution/model spaces. Also the least squares solution is simple a special case of a class of deconvolution problems. This s well established result. It is not the least ill-posed, since it assumes the prior distributions to be uniform (in a Bayesian case. See Sivia and reference therein). In fact it's likely to be the worst solution since it assumes a most ignorant state knowledge (ie. uniform proir) and doesn't always take into consideration the surrounding information. Moreover, it doesn't account for the underlying physics/mathematics, that the probability distributions/line profiles are positive additive distributions (Skilling 1990; Sivia 1996). Best wishes, Nick Dr Nicholas Armstrong Hi, once again, Fine, I'm sure you did. And what is the most plausible, lognormal or gamma? From the tests specific for least square (pattern fitting) they are equallyplausible. And take a combination of the type w*Log+(1- w)*Gam, that will be equally plausible. On the other hand, why should believe that the Baesian deconvolution (or any other sophisticated deconvolution method that can imagine) give the answermuch precisely? Both, the least square and deconvolution are ill-posed problems, but the least square is less ill-posed than the deconvolution. At least that say the manuals for statistical mathematics. Best wishes, Nicolae Popa Hi, I pointed out that each model needs to be tested and their plausibilitydetermined. This can be achieved by employing Bayesian analysis, which takes into account the diffraction data and underlying physics. I have carried out exactly same analysis for the round robin CeO2 samplefor both size distributions using lognormal and gamma distributionfunctions, and similarly for dislocations: screw, edge and mixed. The plausibility of each model was quantified using Bayesian analysis, where the probability of each model was determined, from which the model with thegreatest probability was selected. This approach takes into account the assumptions of each model, parameters, uncertainties, instrumental andnoise effects etc. See Sivia (1996)Data Analysis: A Bayesian Tutorial(Oxford Science Publications). Best wishes, Nick Dr Nicholas Armstrong Hi, But the diffraction alone cannot determine uniquely the physical model. An example at hand: the CeO2 pattern from round-robin can be equally well described by two different size distributions, lognormal and gamma and by any linear combinations of these two distributions. Is the situation different with the strain profile caused by different types of dislocations,possible mixed? Best wishes, Nicolae Popa Best approach is to develop physical models for the line profile broadening and test them for their plausibility i.e. model selection. Good luck. Best Regards, Nick Dr Nicholas Armstrong -- UTS CRICOS Provider Code: 00099F DISCLAIMER: This email message and any accompanying attachments may contain confidential information. If you are not the intended recipient, do not read, use, disseminate, distribute or copy this message or attachments.If you have received this message in error, please notify the sender immediately and delete this message. Any views expressed in this message are those of the individual sender,
RE: Size Strain In GSAS
Give me 10 min. -Original Message- From: Davor Balzar [mailto:[EMAIL PROTECTED] Sent: Monday, March 28, 2005 4:45 PM To: rietveld_l@ill.fr Dear Leonid: Yes, but on real data: Journal of Applied Crystallography 35 (2002) 338-346 (the paper is available from the Web site below). Two examples are reported; in the second, the Voigt approximation failed due to an extremely broad size distribution (or bimodal distribution). However, Voigt size-broadened profile should work for most real-world samples. The paper shows that either pseudo-Voigt or Voigt are good approximations for both (moderately broad) lognormal and (any physical) gamma size distribution of spherical crystallites. Davor Davor Balzar Department of Physics Astronomy University of Denver 2112 E Wesley Ave Denver, CO 80208 Phone: 303-871-2137 Fax: 303-871-4405 Web: www.du.edu/~balzar -Original Message- From: Leonid Solovyov [mailto:[EMAIL PROTECTED] Sent: Sunday, March 27, 2005 12:49 AM To: rietveld_l@ill.fr Subject: RE: Size Strain In GSAS On Friday 03/25 Davor Balzar wrote: Paragraph 3.3 of the article that you mentioned explains how were size and strain values calculated. One can even obtain size distribution by following the procedure that was posted to this mailing list several months ago; Dear Davor, Your recipe for estimating size distribution from the parameters of a Voight-fitted profile is clear and straightforward, but I wonder have you, or someone else, tested it on, say, simulated data for the model of spherical crystallites having lognormal size distribution with various dispersions? Best regards, Leonid __ Do you Yahoo!? Make Yahoo! your home page http://www.yahoo.com/r/hs
Re: Size Strain In GSAS
Hi, Nick Armstrong has advised me he will in non-email-land for a week or so. I'm sure he'll resume this discussion when he returns... Jim At 03:45 PM 3/28/2005 +0400, you wrote: Hi, So, to resume your statements, by using Bayesian/Max.Entr. we can distinguish between two distributions that can not be distinguished by maximum likelihood (least square)? Hard to swallow, once the restored peak profiles are the same inside the noise. What other information than the peak profile, instrumental profile and statistical noise we have that Bayes/Max.ent. can use and the least square cannot? prior distributions to be uniform - if I understand correctly you refer to the distributions of D0 and sigma of the lognormal (gamma) distribution from which the least square chooses the solution, not to the distribution itself (logn, gamm). Then, how is this prior distribution for Baye/Max.ent.? Best, Nick Popa Hi Sorry for the delay. The Bayesian results showed that the lognormal was more probable. Yes, the problem is ill-condition which why you need to use the Bayesian/Maximum entropy method. This method takes into account the ill-conditioning of the problem. The idea being it determines the most probable solutions from the set of solutions. This solution can be shown to be the most consistent solution or the solution with the least assumptions given the experimental data, noise, instrument effects etc (see Skilling Bryan 1983; Skilling 1990; Sivia 1996). This is the role of entropy function. There are many mathemaitcal proofs for this (see Jaynes' recent book). The Bayesian analysis maps out the solution/model spaces. Also the least squares solution is simple a special case of a class of deconvolution problems. This s well established result. It is not the least ill-posed, since it assumes the prior distributions to be uniform (in a Bayesian case. See Sivia and reference therein). In fact it's likely to be the worst solution since it assumes a most ignorant state knowledge (ie. uniform proir) and doesn't always take into consideration the surrounding information. Moreover, it doesn't account for the underlying physics/mathematics, that the probability distributions/line profiles are positive additive distributions (Skilling 1990; Sivia 1996). Best wishes, Nick Dr Nicholas Armstrong snip James P. Cline [EMAIL PROTECTED] Ceramics Division Voice (301) 975 5793 National Institute of Standards and Technology FAX (301) 975 5334 100 Bureau Dr. stop 8520 Gaithersburg, MD 20899-8523USA
RE: Size Strain In GSAS
Dear Apu All Firstly, GSAS wasn't designed for line profile analysis. More importantly, the line profiles resulting from the from nanocrystallites and dislocations, generally do not have the functional form described by functions, such as Voigt. I will also go as far as to say that there is no physical basis for these line profile functions for quantifying the microstructure of a sample, in terms of shape/size distribution of crystallites, and spatial distributions/type/density of dislocations. For example, the line profile arising from a lognormal distribution of spherical crystallites doesn't have the form of Voigt or Lorentzian or Gaussian line profile functions (i.e. see Scardi Leoni (2001), Acta Cryst., A52, 605-613.). Moreover, while Krivoglaz Ryaboshapka (1963) (Fiz. metal., metalloved., 15(1),18-31) showed that Gaussian line profiles can arise from a crystallite containing screw dislocations, it resulted in the strain energy diverging as the crystallite increased. This was only resolved by Wilkens (1970a,b,c) and Krivoglaz et al. (1983). These two latter cases produced general expressions for the Fourier coefficients/line profile which depended on the characteristics/density of the dislocations. Best approach is to develop physical models for the line profile broadening and test them for their plausibility i.e. model selection. Good luck. Best Regards, Nick Dr Nicholas Armstrong NIST-UTS Research Fellow *** (in Australia) UTS, Department of Applied Physics *** University of Technology,Sydney* Location: Bld 1,Level 12,Rm1217 P.O Box 123* Ph:(+61-2) 9514-2203 Broadway NSW 2007 * Fax: (+61-2) 9514-2219 Australia * E-mail:[EMAIL PROTECTED] *** (in USA) NIST, Ceramics Division *** National Institute of Standards and Technology * Fax: (+1-301) 975-5334 100 Bureau Dr. stop 8520 * Gaithersburg, MD 20899-8523USA * *** - Original Message - From: Davor Balzar [EMAIL PROTECTED] Date: Friday, March 25, 2005 7:05 pm Hi Apu: As everybody pointed out, there are better ways (for now) to do the size/strain analysis, but GSAS can also be used if observed, size- broadenedand strain-broadened profiles can all be approximated with Voigt functions. Paragraph 3.3 of the article that you mentioned explains how were size and strain values calculated. One can even obtain size distribution by followingthe procedure that was posted to this mailing list several months ago; see below. Best wishes, Davor Davor Balzar Department of Physics Astronomy University of Denver 2112 E Wesley Ave Denver, CO 80208 Phone: 303-871-2137 Fax: 303-871-4405 Web: www.du.edu/~balzar National Institute of Standards and Technology (NIST) Division 853 Boulder, CO 80305 Phone: 303-497-3006 Fax: 303-497-5030 Web: www.boulder.nist.gov/div853/balzar -Original Message- From: Davor Balzar [EMAIL PROTECTED] Sent: Monday, November 22, 2004 3:58 PM To: rietveld_l@ill.fr Subject: RE: Size distribution from Rietveld refinement Yes, one can determine size distribution parameters by using Rietveld refinement. In particular, the lognormal size distribution is defined by two parameters (say, the average radius and the distribution dispersion, see, for instance, (2) and (3) of JAC 37 (2004) 911, SSRR for short here, or other references therein). It was first shown by Krill Birringer that both volume-weighted (Dv) and area-weighted (Da) domain size (that are normally evaluated in a diffraction experiment) can be related to the average radius and dispersion of the lognormal distribution; one obtains something like (5) in the paper SSRR. Therefore, if one can evaluate both Dv and Da by Rietveld refinement, it would be possible to determine the parameters of the size distribution, as two independent parameters are required to define the lognormal or similar types of bell-shaped distributions. Note here that a different distribution can be used, which will change the relationship between Dv Da and the parameters of the distribution (for the gamma distribution, see JAC 35 (2002) 338, for the equations equivalent to (5) in SSRR). The value that is normally evaluated through the Rietveld
Re: Size Strain In GSAS
Dear Apu, I know I will start up a good debate here, but size-strain analysis with GSAS is a non-sense. The program was not written with that purpose in mind and in fact it does not contains the instrumental aberration part of the broadening that is necessary for such computation. Indeed it is possible to get at end some size-strain data, but quite hard as you have to do all correction later and out of the program. So it is like using GSAS for peak fitting, so better to use a peak fitting dedicated program. Best wishes, Luca Lutterotti On Mar 25, 2005, at 7:15, [EMAIL PROTECTED] wrote: Dear All, I am trying to perform Rietveld refinement on a very simple system using GSAS. I have obtained a reasonable fit except the peak widths. I want to use the size and strain refinement option in GSAS to make the fit well. Please tell me how to use the SIZE STRAIN refinement option in GSAS. P.S. I am using the EXPGUI. Thanks in advace. Regards, Apu /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ Apu Sarkar Research Fellow Variable Energy Cyclotron Centre Kolkata 700 064 phone: 91-33-2337-1230 (extn. 3190) Fax: 91-33-2334-6871 INDIA /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
Re: Size Strain In GSAS
Dear Prof. Lutterotti, I was also aware of the fact that GSAS is not made for Size Strain analysis. I got interested to use the Size strain refinement feature of GSAS only after going through the article : Size-strain line broadening analysis of the ceria round-robin sample by Prof. D. Balzar et. al. Journal of Applied Crys. 37(2004)911-924. In that round robin results they have reported the size strain obtained from GSAS. I my case also when I am trying with GSAS, the diffraction pattern is fitting well except the peak braodening. I think this brodening is due to small domain size effect. I that case how will I obatin a good fit with GSAS. Thanking you. Best Regards, Apu /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ Apu Sarkar Research Fellow Variable Energy Cyclotron Centre Kolkata 700 064 phone: 91-33-2337-1230 (extn. 3190) Fax: 91-33-2334-6871 INDIA /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ - Original Message - From: Luca Lutterotti [EMAIL PROTECTED] Date: Friday, March 25, 2005 3:31 pm Dear Apu, I know I will start up a good debate here, but size-strain analysis with GSAS is a non-sense. The program was not written with that purpose in mind and in fact it does not contains the instrumental aberration part of the broadening that is necessary for such computation. Indeed it is possible to get at end some size-strain data, but quite hard as you have to do all correction later and out of the program. So it is like using GSAS for peak fitting, so better to use a peak fitting dedicated program. Best wishes, Luca Lutterotti On Mar 25, 2005, at 7:15, [EMAIL PROTECTED] wrote: Dear All, I am trying to perform Rietveld refinement on a very simple system using GSAS. I have obtained a reasonable fit except the peak widths. I want to use the size and strain refinement option in GSAS to make the fit well. Please tell me how to use the SIZE STRAIN refinement option in GSAS. P.S. I am using the EXPGUI. Thanks in advace. Regards, Apu /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ Apu Sarkar Research Fellow Variable Energy Cyclotron Centre Kolkata 700 064 phone: 91-33-2337-1230 (extn. 3190) Fax: 91-33-2334-6871 INDIA /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
Re: Size Strain In GSAS
Dear all, I think the statement that one cannot do line-profile analysis using GSAS is too strong. In principle it is possible to do some size strain analysis using GSAS, if the instrumental profile is e.g. sufficiently described previously by the Thompson-Cox-Hastings (TCH) profile function (includes measuring corresponding data on a suitable standard). I think, even involvement of the Finger asymmetry correction does not introduce systematic errors. Then the increase in the tantheta and 1/costheta related Gaussian and Lorentzian line width components of the TCH description upon Rietveld refinement on the basis of diffraction data exhibiting physical line broadening can in principle be associated with microstrain- and size-related quantities. This can also be extended by involving anisotropic size and microstrain models. Thus, on this level of line broadening analysis, everything neccessary is contained in GSAS. Of course, something like microstrain and size distributions cannot be obtained using GSAS. Of course there are problems: 0. Microstrain broadening must be proportional to tan(theta). This is not neccessarily the case. There mustn't be further line broadening contributions like stacking faults, complicating the situation. 1. If both size and strain contributions are present, one most be aware of the correlation between the tantheta and 1/costheta dependent compontents. 2. One has to be aware to which average values of the size and microstrain distributions the increases of the line width parameters can be associated with. This requires for GSAS a close analysis of the GSAS manual (how are the line-width paramerters defined!) and line broadening literature, how such pseudo-Voigt line width parameters can be related with averages microstructure parameters. Thus it is not made easy for the user to extract something like that from the line width parameters. But perhaps it is better that way, because consequently the user is forced to to deal himself with the required theory, rather than just refining a parameter called size and one called microstrain, believing in the results and publish the values Definitely there are much better procedures to analyse size and microstrain than by GSAS. So, going to the problem of Apu: If the instrumental profile is well described before using TCH, refinement of (only) LX (and perhaps P) gives you quantities whiuch you should be able to relate to size related quantities upon reading the GSAS manual and some line broadening literature. Best regards Andreas Leineweber Dear Prof. Lutterotti, I was also aware of the fact that GSAS is not made for Size Strain analysis. I got interested to use the Size strain refinement feature of GSAS only after going through the article : Size-strain line broadening analysis of the ceria round-robin sample by Prof. D. Balzar et. al. Journal of Applied Crys. 37(2004)911-924. In that round robin results they have reported the size strain obtained from GSAS. I my case also when I am trying with GSAS, the diffraction pattern is fitting well except the peak braodening. I think this brodening is due to small domain size effect. I that case how will I obatin a good fit with GSAS. Thanking you. Best Regards, Apu /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ Apu Sarkar Research Fellow Variable Energy Cyclotron Centre Kolkata 700 064 phone: 91-33-2337-1230 (extn. 3190) Fax: 91-33-2334-6871 INDIA /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ - Original Message - From: Luca Lutterotti [EMAIL PROTECTED] Date: Friday, March 25, 2005 3:31 pm Dear Apu, I know I will start up a good debate here, but size-strain analysis with GSAS is a non-sense. The program was not written with that purpose in mind and in fact it does not contains the instrumental aberration part of the broadening that is necessary for such computation. Indeed it is possible to get at end some size-strain data, but quite hard as you have to do all correction later and out of the program. So it is like using GSAS for peak fitting, so better to use a peak fitting dedicated program. Best wishes, Luca Lutterotti On Mar 25, 2005, at 7:15, [EMAIL PROTECTED] wrote: Dear All, I am trying to perform Rietveld refinement on a very simple system using GSAS. I have obtained a reasonable fit except the peak widths. I want to use the size and strain refinement option in GSAS to make the fit well. Please tell me how to use the SIZE STRAIN refinement option in GSAS. P.S. I am using the EXPGUI. Thanks in advace. Regards, Apu /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ Apu Sarkar Research Fellow Variable Energy Cyclotron Centre Kolkata 700 064
Re: Size Strain In GSAS
Dear Apu, difficult to say without seeing the pattern with your actual fitting. Broadening with small domain size is normally more easy to fit. It could be you didn't use the proper function or refines all necessary parameters, or there is an anisotropic broadening or faulting. Every sample/analysis has his own story. Try to put a picture of the fitting somewhere on the web and post here a link to the picture as attachments are not permitted in the list. This would be better as everyone can see it and give you some suggestions. Luca On Mar 25, 2005, at 12:00, [EMAIL PROTECTED] wrote: Dear Prof. Lutterotti, I was also aware of the fact that GSAS is not made for Size Strain analysis. I got interested to use the Size strain refinement feature of GSAS only after going through the article : Size-strain line broadening analysis of the ceria round-robin sample by Prof. D. Balzar et. al. Journal of Applied Crys. 37(2004)911-924. In that round robin results they have reported the size strain obtained from GSAS. I my case also when I am trying with GSAS, the diffraction pattern is fitting well except the peak braodening. I think this brodening is due to small domain size effect. I that case how will I obatin a good fit with GSAS. Thanking you. Best Regards, Apu /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ Apu Sarkar Research Fellow Variable Energy Cyclotron Centre Kolkata 700 064 phone: 91-33-2337-1230 (extn. 3190) Fax: 91-33-2334-6871 INDIA /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ - Original Message - From: Luca Lutterotti [EMAIL PROTECTED] Date: Friday, March 25, 2005 3:31 pm Dear Apu, I know I will start up a good debate here, but size-strain analysis with GSAS is a non-sense. The program was not written with that purpose in mind and in fact it does not contains the instrumental aberration part of the broadening that is necessary for such computation. Indeed it is possible to get at end some size-strain data, but quite hard as you have to do all correction later and out of the program. So it is like using GSAS for peak fitting, so better to use a peak fitting dedicated program. Best wishes, Luca Lutterotti On Mar 25, 2005, at 7:15, [EMAIL PROTECTED] wrote: Dear All, I am trying to perform Rietveld refinement on a very simple system using GSAS. I have obtained a reasonable fit except the peak widths. I want to use the size and strain refinement option in GSAS to make the fit well. Please tell me how to use the SIZE STRAIN refinement option in GSAS. P.S. I am using the EXPGUI. Thanks in advace. Regards, Apu /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ Apu Sarkar Research Fellow Variable Energy Cyclotron Centre Kolkata 700 064 phone: 91-33-2337-1230 (extn. 3190) Fax: 91-33-2334-6871 INDIA /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
Re: Size Strain In GSAS
Hi, I wrote an article [ that appeared in Dean Smith's book ] some time back that describes how to use SRM 660a, LaB6, and the TCH function of GSAS for characterization of the IPF, and then refine the only the microstructure specific terms for an estimation of the size and strain in subsequent analyses. The approach has its limitations for sure, but it is accessible with a small effort. Regards, Jim At 02:10 PM 3/25/2005 +0100, you wrote: Dear Andreas, I didn't said it cannot be done. Only that was not made for and so it is not easy as using other tools. In principle every diffraction fitting program can be used for size-strain. Few questions: have you ever tried to do such analysis with GSAS the right way using the instrumental profile correction? Did you use only GSAS for that or you had to use other external tools/computations? (this to get a feeling about your statement: Thus, on this level of line broadening analysis, everything necessary is contained in GSAS; may be level should be clarified). I would like to know what there is inside GSAS for crystallite size and microstrain analysis in particular. Best regards, Luca Lutterotti On Mar 25, 2005, at 12:55, Andreas Leineweber wrote: Dear all, I think the statement that one cannot do line-profile analysis using GSAS is too strong. In principle it is possible to do some size strain analysis using GSAS, if the instrumental profile is e.g. sufficiently described previously by the Thompson-Cox-Hastings (TCH) profile function (includes measuring corresponding data on a suitable standard). I think, even involvement of the Finger asymmetry correction does not introduce systematic errors. Then the increase in the tantheta and 1/costheta related Gaussian and Lorentzian line width components of the TCH description upon Rietveld refinement on the basis of diffraction data exhibiting physical line broadening can in principle be associated with microstrain- and size-related quantities. This can also be extended by involving anisotropic size and microstrain models. Thus, on this level of line broadening analysis, everything neccessary is contained in GSAS. Of course, something like microstrain and size distributions cannot be obtained using GSAS. Of course there are problems: 0. Microstrain broadening must be proportional to tan(theta). This is not neccessarily the case. There mustn't be further line broadening contributions like stacking faults, complicating the situation. 1. If both size and strain contributions are present, one most be aware of the correlation between the tantheta and 1/costheta dependent compontents. 2. One has to be aware to which average values of the size and microstrain distributions the increases of the line width parameters can be associated with. This requires for GSAS a close analysis of the GSAS manual (how are the line-width paramerters defined!) and line broadening literature, how such pseudo-Voigt line width parameters can be related with averages microstructure parameters. Thus it is not made easy for the user to extract something like that from the line width parameters. But perhaps it is better that way, because consequently the user is forced to to deal himself with the required theory, rather than just refining a parameter called size and one called microstrain, believing in the results and publish the values Definitely there are much better procedures to analyse size and microstrain than by GSAS. So, going to the problem of Apu: If the instrumental profile is well described before using TCH, refinement of (only) LX (and perhaps P) gives you quantities whiuch you should be able to relate to size related quantities upon reading the GSAS manual and some line broadening literature. Best regards Andreas Leineweber Dear Prof. Lutterotti, I was also aware of the fact that GSAS is not made for Size Strain analysis. I got interested to use the Size strain refinement feature of GSAS only after going through the article : Size-strain line broadening analysis of the ceria round-robin sample by Prof. D. Balzar et. al. Journal of Applied Crys. 37(2004)911-924. In that round robin results they have reported the size strain obtained from GSAS. I my case also when I am trying with GSAS, the diffraction pattern is fitting well except the peak braodening. I think this brodening is due to small domain size effect. I that case how will I obatin a good fit with GSAS. Thanking you. Best Regards, Apu /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ Apu Sarkar Research Fellow Variable Energy Cyclotron Centre Kolkata 700 064 phone: 91-33-2337-1230 (extn. 3190) Fax: 91-33-2334-6871 INDIA /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ - Original Message - From: Luca Lutterotti [EMAIL PROTECTED] Date: Friday, March 25, 2005 3:31 pm Dear Apu, I know I will start up a good debate here, but size-strain analysis with GSAS is a non-sense
RE: Size Strain In GSAS
Hi Apu: As everybody pointed out, there are better ways (for now) to do the size/strain analysis, but GSAS can also be used if observed, size-broadened and strain-broadened profiles can all be approximated with Voigt functions. Paragraph 3.3 of the article that you mentioned explains how were size and strain values calculated. One can even obtain size distribution by following the procedure that was posted to this mailing list several months ago; see below. Best wishes, Davor Davor Balzar Department of Physics Astronomy University of Denver 2112 E Wesley Ave Denver, CO 80208 Phone: 303-871-2137 Fax: 303-871-4405 Web: www.du.edu/~balzar National Institute of Standards and Technology (NIST) Division 853 Boulder, CO 80305 Phone: 303-497-3006 Fax: 303-497-5030 Web: www.boulder.nist.gov/div853/balzar -Original Message- From: Davor Balzar [mailto:[EMAIL PROTECTED] Sent: Monday, November 22, 2004 3:58 PM To: rietveld_l@ill.fr Subject: RE: Size distribution from Rietveld refinement Yes, one can determine size distribution parameters by using Rietveld refinement. In particular, the lognormal size distribution is defined by two parameters (say, the average radius and the distribution dispersion, see, for instance, (2) and (3) of JAC 37 (2004) 911, SSRR for short here, or other references therein). It was first shown by Krill Birringer that both volume-weighted (Dv) and area-weighted (Da) domain size (that are normally evaluated in a diffraction experiment) can be related to the average radius and dispersion of the lognormal distribution; one obtains something like (5) in the paper SSRR. Therefore, if one can evaluate both Dv and Da by Rietveld refinement, it would be possible to determine the parameters of the size distribution, as two independent parameters are required to define the lognormal or similar types of bell-shaped distributions. Note here that a different distribution can be used, which will change the relationship between Dv Da and the parameters of the distribution (for the gamma distribution, see JAC 35 (2002) 338, for the equations equivalent to (5) in SSRR). The value that is normally evaluated through the Rietveld refinement is Dv, as the refinable parameters in the Thompson-Cox-Hastings (TCH) model are based on the integral-breadth methods. This means that one would have to use (9) and (15)-(18) in SSRR, to obtain Dv, which depends on both P and X parameters. As the TCH model implicitly assumes Voigt functions for both size and strain-broadened profiles (double-Voigt model), Da can be also calculated, but from X only, as it depends only on the Lorentzian size-broadened integral breadth, Da=1/(2betaL) (this and other consequences of a double-Voigt model were shown/discussed in JAC 26 (1993) 97). HOWEVER, as pointed out by others in previous messages, this assumes that (i) Both observed and physically broadened profiles are Voigt functions, which is implicit to the TCH model; (ii) Size distribution is lognormal, gamma, or whatever we assume it to be. On the former, it is easy to see if observed profiles can't be successfully fit (super-Lorentzian peak shapes, for instance), which means that the TCH peak shape cannot be used. However, an assumption that physically broadened profiles (size and strain) are also Voigt function is more difficult to prove; if not and one uses the equations described above, a systematic error will be introduced. On the latter, a good fit in Rietveld means only that a lognormal or other assumed distribution is one POSSIBLE approximation of the real size distribution in the sample. However, this equally applies to all the other parameters obtained through the Rietveld refinement and is not a special deficiency of this model. Second, even if one obtains more information about the actual size distribution via TEM, SEM, etc., sometimes it is very difficult to discern between different bell-shaped size distributions, especially if the size distribution is narrow. Davor -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Sent: Friday, March 25, 2005 4:01 AM To: rietveld_l@ill.fr Subject: Re: Size Strain In GSAS Dear Prof. Lutterotti, I was also aware of the fact that GSAS is not made for Size Strain analysis. I got interested to use the Size strain refinement feature of GSAS only after going through the article : Size-strain line broadening analysis of the ceria round-robin sample by Prof. D. Balzar et. al. Journal of Applied Crys. 37(2004)911-924. In that round robin results they have reported the size strain obtained from GSAS. I my case also when I am trying with GSAS, the diffraction pattern is fitting well except the peak braodening. I
