Re: Question
Mathematically, we know that the Fourier transform (FT) is a linear
operator, so FT{f1+f2}=FT{f1} +FT{f2}. No mangled convolution.
Nick
Brian H. Toby wrote:
> I had to think for a bit: the Fourier transform of a sum is equal to
> the sum of the terms transformed individually, so the G(r) for a
> mixture is the weighted sum of G(r) for the components.
>
> Brian
>
> On Sep 27, 2006, at 9:05 AM, Andy Fitch wrote:
>
>> We have a question about pdf analysis. If my sample is two
>> phase, so the diffraction pattern is the sum of two individual
>> patterns, what does the G(r) show? Is it just the sum of two
>> individual G(r)s or some mangled convolution between the two?
>
>
--
Dr Nicholas Armstrong
NIST-UTS Research Fellow
***
University of Technology Sydney (UTS), Australia
***
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]
***
National Institute of Standards and Technology (NIST), United States
***
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***
RE: Crystal size in GSAS
Hi If you have to use these techniques, the integral breadths are the one to use -- as Pam pointed out. Also keep in mind that the integral breadth produces a volume-weighted dimension. This is an apparent measure of the crystallite size parallel to the diffraction vector, and must be related to crystallite shape for overall crystallite dimensions to be resolved (see Langford & Louer's work on ZnO in JAC through the 80s & 90s). This also assumes that the crystallite size distribution is narrow. Enjoy!! Regards, Nick - Original Message - From: "Whitfield, Pamela" <[EMAIL PROTECTED]> Date: Friday, June 30, 2006 11:29 pm To: rietveld_l@ill.fr > Stephane > > Just one small point - strictly speaking you should be using > integral breadth rather than FWHM for size/strain analysis. > > Pam > > -Original Message- > From: Von Dreele, Robert B. [mailto:[EMAIL PROTECTED] > Sent: June 29, 2006 2:24 PM > To: rietveld_l@ill.fr > > > Stephanie, > The GSAS routine REFLIST has an option to produce a "single phase > ascii" file of reflections. One of the columns in that file is > FWHM. Alternatively there is a graphic in EXPGUI (widplt) that will > plot FWHM and its Gaussian & Lorentzian contributions as a function > of 2-theta. Bob Von Dreele > > R.B. Von Dreele > IPNS Division > Argonne National Laboratory > Argonne, IL 60439-4814 > > > > -Original Message- > From: ruggeri [mailto:[EMAIL PROTECTED] > Sent: Thursday, June 29, 2006 12:17 PM > To: rietveld_l@ill.fr > > > Hello, > I am trying also to calculate crystal size from GSAS, and I want to > find back the fwhm of all the peaks from their position: how is it > possible? Thanks > > Stéphane Ruggeri, Ph.D. > Stagiaire post-doctoral > INRS Énergie, Matériaux et Télécommunications > 1650, boul. Lionel-Boulet > Varennes (Québec) > J3X 1S2 > Téléphone/Office : (450) 929 8139 > Télécopieur/Fax : (450) 929-8198 > > -Message d'origine- > De : [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] > Envoyé : 29 juin 2006 13:31 > À : rietveld_l@ill.fr > Objet : Crystal size in GSAS > > > Hi, > > I am wondering if GSAS calculates the crystal size? If not how can > I calculate the crystal size? I am using a profile type 3 function > (psedovoight) and obtaining the GU,GV,GW values as 0,0, 1.27 E+04 > for a Pt/C phase respectively. The Chi-square fit is 2.164. > Thankyou. > regards, > > Sajeev Moorthiyedath > > > >
Re: Size Strain in GSAS
HI All, It has been shown that when incorporating a priori information, Bayesian approach is the logically the most consistent (Cox 1946), since it conserves the probabilities and all information (Jaynes 2004). Least squares is a special and limited case of Bayesian applications. There are many more mathematical proof which demonstrate this. In addition, combining Bayes' theorem and entropy function, produces the most consistent solution, from the set of solutions. That is, the solution which has the least assumptions (Boltzman demonstrated this almost 100 years ago!!). Again there are many other (general) mathematical proofs which demonstrate this. Hence, we have developed a method that ensures the information and probabilities are conserved. Moreover, it has a firm mathematical and physical basis. The use of a priori information, represents one's hypothesis, assumption and/or belief. By using Bayes' theorem, hypothesis, assumption and/or beliefs are quantified using probabilities relative to the experimental data and noise/uncertainty. Please take note of the last point! In addition, when applying Bayesian/MaxEnt model selection to size distributions, we are *not* fitting the noise/instrument or secondary effects. (I've been very care to check this. See above paragraph.) In the case of profile function fitting, I strongly suggest seeing Sivia (1996). He points how this can be done for line profile functions like Gaussian, Lorentzian (and presume Voigts). About errors in the size distributions. The size of error-bars determined from the Bayesian/MaxEnt method represent the qualtity of the data, how well the background is estimated, and generally the poor conditioning of the size distribution problem. This last point is critical. That is, the problem is ill-conditioned and explains why many possible solutions can "fit" the data. Another way to look at it is that the Bayesian/MaxEnt error-bars represent a "slice" through the probability density function in the solution space, and represent the "population" of solutions which can fit the data within the 68% probability region. However, by using the entropy function we can always be sure there exist one and only solution with a maximum entropy relative to the experimental data etc... (again see the many mathematical proofs...). With a least squares approach this is not always the case. Best Regards, Nick ps. I agree, it is inappropriate to use the email group to request Journal articles. 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: alan coelho <[EMAIL PROTECTED]> Date: Monday, April 18, 2005 7:03 pm > This is by far the best topic on this list for a long time as > opposed to > requests for Journal papers which as pointed out by someone else is > inappropriate in the first place and illegal in the second. > > > > Nicolae wrote: > > >(i) but a sum of two Lorentzians is not sharper than the sum of > two pVs > (Voigts)? > > > > This I know, it should not matter what is used as long as the > mapping of > the function to a distribution is done accurately. Whether it is > lognomal, gamma or something else does does not matter. > > > > 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 Armstrong's work of obtaining a distribution without > knowing its functional form is a powerful one. But the Baysean > approachwithout a functional form results in large errors bars in the > distribution, see > http://nvl.nist.gov/pub/nistpubs/jres/109/1/cnt109-1.htm > > > > What we should be looking for are cases where Voigt appro
Re: Size Strain In GSAS
Springer, Berlin [10] Armstrong, N. PhD Thesis, UTS, Australia Nicolae Popa 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 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 i
Re: Size Strain In GSAS
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
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: Nicolae Popa <[EMAIL PROTECTED]>
Date: Saturday, March 26, 2005 9:10 pm
> 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?
> > >
> > &
Re: Size Strain In GSAS
Hi, I pointed out that each model needs to be tested and their plausibility determined. 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 sample for both size distributions using lognormal and gamma distribution functions, 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 the greatest probability was selected. This approach takes into account the assumptions of each model, parameters, uncertainties, instrumental and noise effects etc. See Sivia (1996)Data Analysis: A Bayesian Tutorial (Oxford Science Publications). Best wishes, 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: Nicolae Popa <[EMAIL PROTECTED]> Date: Saturday, March 26, 2005 8:05 pm > 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, except where the sender expressly, and with authority, states them to be the views the University of Technology Sydney. Before opening any attachments, please check them for viruses and defects.
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 par
Size distribution from Rietveld refinement
Hi All. Regarding the RR ceria. The analysis carried out by us and discussed in Armstrong et al (2004a,b) did not assume a lognormal distribution, but tested the distribution model. The results from the Bayesian/MaxEnt methods, were free of any distribution function. Additional analysis showed that a lognormal distribution function fitted the Bayesian/MaxEnt results reasonable well. Regards, Nicholas - Original Message - From: Leonid Solovyov <[EMAIL PROTECTED]> Date: Monday, November 22, 2004 9:12 pm > Dear Rietvelders, > > Despite the heated discussion of the problem, the initial question, > which, actually, concerned the size distribution from Rietveld > refinement, seems to be unsettled. > Can we derive ANY information on the crystallite size distribution > (based on sensible assumptions) from the Thompson-Cox-Hastings > size-broadening parameters P and X normally obtained from Rietveld > refinement? > For the Ceria Size-Strain Round Robin sample the crystallite > distribution dispersion was determined from the profile analysis > assuming lognormal distribution. This suggests that the diffraction > data contained this information. Why Rietveld refinement can not be > used for this purpose? > I realize that most simple questions may be most difficult to answer, > but nevertheless... > > Regards, > Leonid > > > __ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam protection around > http://mail.yahoo.com > -- 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, except where the sender expressly, and with authority, states them to be the views the University of Technology Sydney. Before opening any attachments, please check them for viruses and defects.
Re: rietveld refinement
Hi, At the moment there is development of a NIST Nanocrystallite Size Standard Reference Material (SRM1979). Jim Cline and I are working on this SRM. It will include two materials: (1) CeO2 with spherical crystallite shape and size distribution in the ~20nm size range (isotropic shape); (2) ZnO with cylindrical or hexagonal prismatic crystallite shape with height in the, H~60-80nm and diameter, D~20-30nm range (anisotropic shape). This outlined in introduction of Armstrong et al (2004b) chapt.8, in "Diffraction analysis of the microstructure of materials", Springer-Verlag, pp.187--227. In both cases the Bayesian/MaxEnt method will be used to determine the *physical* size distribution and shape. For example in the case of (1), the method tests the model for a spherical crystallite shape, while also testing various size distribution models i.e lognormal, gamma etc. For this case a lognormal size distribution has found to be the appropriate distribution. In the case of (2) the distributions are for H and D, respectively, while testing different shape models can also be carried out. This presently being developed. The Bayesian/MaxEnt method is a general formulation which tests the underlying assumption of various models and determines the most probable size distribution and crystallite shape. There is lots of working/development going on!! Regards, Nicholas - Original Message - From: Nicolae Popa <[EMAIL PROTECTED]> Date: Monday, November 22, 2004 7:12 pm > > > > > It is also true that no development has been done for anisotropy. > Not yet! > > > > Well, if all previous works about trying to take account of > size/strain> anisotropy in the Rietveld method are nothing yet, > this allows to > > close the discussion. Let us wait for really serious developments to > > come. > > You not correctly understood me (I would like to believe that not > ill-disposed). > I said that no development for size anisotropy has been done including > "physical" size distributions (like lognormal, etc.) as were done > for the > isotropic case. > For example: Langford, Louer & Scardi, JAC (2000) 33, 964-974 and > Popa & > Balzar JAC (2002) 35, 338-346. > Concerning previous (phenomenological) works trying to take account of > strain/size anisotropy in the Rietveld method, I have myself a > contribution:"The (hkl) dependence of diffraction-line broadening > caused by strain and > size for all Laue groups in Rietveld refinement, N. C. Popa, J. > Appl. Cryst. > (1998) 31, 176-180." > Could I be so stupid to say that such kind of works, including > mine, are > nothing? > > Best wishes, > Nicolae Popa > > > > > > -- 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, except where the sender expressly, and with authority, states them to be the views the University of Technology Sydney. Before opening any attachments, please check them for viruses and defects.
Re: rietveld refinement
Hi, With regards to size/shape/distribution analysis of line profiles, the papers by Armstrong et al. (2004a,b,c) discusses a Bayesian/Maximum Entropy method, that determines these quantities from the line profile data. This can also resolve bimodal distributions from line profile data. This method tests models for shape/size distribution and modal properties using Bayesian analysis. The maximum entropy components is a generalisation of the approach presented in A. Le Bail and D. Lou?r. J. Appl. Cryst. (1978). 11, 50-55. It preserves the positivity of the distribution, determines the most probable distribution give the line profile data, instrument profile and statistical noise. Recent publications can be found at the following: http://nvl.nist.gov/pub/nistpubs/jres/109/1/cnt109-1.htm; Armstrong et al (2004b) chapt.8, in "Diffraction analysis of the microstructure of materials", Springer-Verlag, pp.187--227; WA5 Armstrong et al. (2004c), http://www.aip.org.au/wagga2004/. Regards,Nicholas Dr Nicholas Armstrong Department of Applied Physics University of Technology Sydney PO Box 123 Broadway NSW 2007 Ph: (+61-2) 9514-2203 Fax: (+61-2) 9514-2219 E-mail: [EMAIL PROTECTED] - Original Message - From: Armel Le Bail <[EMAIL PROTECTED]> Date: Sunday, November 21, 2004 11:10 pm > > It is also true that no development has been done for anisotropy. > Not yet! > > Well, if all previous works about trying to take account of > size/strainanisotropy in the Rietveld method are nothing yet, this > allows to > close the discussion. Let us wait for really serious developments to > come. > > Armel > > > > -- 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, except where the sender expressly, and with authority, states them to be the views the University of Technology Sydney. Before opening any attachments, please check them for viruses and defects.
