RE: Size distribution from Rietveld refinement
Thank you, Davor! Despite several HOWEVERs in your message it clarifies the situation. Best wishes, Leonid __ Do you Yahoo!? Meet the all-new My Yahoo! - Try it today! http://my.yahoo.com
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
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: Leonid Solovyov [mailto:[EMAIL PROTECTED]
> Sent: Monday, November 22, 2004 3:12 AM
> To: [EMAIL PROTECTED]
> Subject: Size distribution from Rietveld refinement
>
> 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
pseudosymmetry
Dear all, the Rietveld refinement of pseudosymmetric structures can cause some artefacts. Does someone know some literature, where these artefacts are explained in detail? Especially problems of the Rietveld refinement of pseudosymmetric sodalites (pseudo centered structures, pseudo cubic structures, significant deviation of bond length (...)) are welcome. Further I am interested in your opinion about the "Distance Least Squares Procedure" to avoid these artefacts. Thank you in advance Friedrich -- ++ + Friedrich W. Karauemail: [EMAIL PROTECTED] + + LMU - Muenchen Tel.: (+49) (0)89 - 2180-77449 + + Butenandtstraße 5-13, Haus D mobil: 0179 6647667 + + 81377 Muenchen Fax: (+49) (0)89 - 2180-77440 + ++
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:Re: Bond angle and bond length
Thanks to Daniel and Maria for helping. I could calculate bond angles and bond distances. Krushna
Re: rietveld refinement
>Going back to Leonid's question, well the answer is easy: check the >premises... the assumptions behind the use of the TCH function are >not >compatible with he presence of a lognormal distribution of domains. But the TCH function gave ALMOST PERFECT fit for the Size-Strain Round Robin profiles. Where do we loose information applying THC in Rietveld refinement? In this "ALMOST"? Or, maybe, the distribution dispersion was erroneously determined in the SSRR and, actually, this information can not be unambiguously derived solely from diffraction? Leonid __ Do you Yahoo!? Meet the all-new My Yahoo! - Try it today! http://my.yahoo.com
Re: rietveld refinement
just my 2 cents... > Could I be so stupid to say that such kind of works, including mine, are > nothing? following Nicolae, I should also add to the list myself as well as most people participating to the four editions of the size-strain conference/meeting/workshop and all participants to Davor's size-strain round-robin. I bet people should spend more time in the library... this is the point. This is also a self criticism as I'm not the best library addict (though, online resources has simplified life enormously)... We should not try to use line profile analysis methods as a black box: it is easy to obtain numbers from measured data (with a proper software a computer can do it automatically), but then it is in the ability of the scientist to attach them a proper physical meaning. What it is difficult (perhaps impossible?) is willing and pretending to do it in the general case as we're dealing with something that has no precise rules (domain size, shape and their distributions are not properties of the materials, nor they can be easily predicted in advance). Some simple cases have been studied and some references already posted by several people in here, and in most of them the agreement between diffraction and alternative techniques is quite good: just in few cases, though, enough information is available to interpret the strain broadening fully in terms of physical defects present in the material, or to model the size term using a more or less complex distribution of (iso-shape) domains. But also in those cases the result is the one compatible with the model assumptions and does not pretend to be "God's truth". So welcome the round robin on a more complex sample to test the maturity of the algorithms (they should be even tested on simpler examples, as concluded on the latest size-strain conference, but that's another story..), but beware that without any a priori info (or with a wrong one!), a vast set of odd results can be obtained. As a comparison, it would be like pretending to do a search match, a structure solution or, even worse, a Rietveld refinement on a material for which we don't know any chemical information... Going back to Leonid's question, well the answer is easy: check the premises... the assumptions behind the use of the TCH function are not compatible with he presence of a lognormal distribution of domains. It can be proven mathematically that the Fourier coefficients for a profile describing a lognormal distribution of domains have a hook at low Fourier number, hook that cannot be reproduced by any whatsoever voigtian or voigtian-like curve. This is a common problem in the use of Voigt and voigt-like curves in describing the peak profiles from nanocrystalline powders and is also the main source of the "superlorentzian" peak tails (they are a trick to get rid of the physical information contained in the profile ;) we are a bit masochist, aren't we?) Best regards Mat -- Matteo Leoni Department of Materials Engineering and Industrial Technologies University of Trento 38050 Mesiano (TN) ITALY Tel +39 0461 882416e-mail: [EMAIL PROTECTED] Fax +39 0461 881977Web: www.matteoleoni.ing.unitn.it
Size distribution from Rietveld refinement
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
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
At least the anisotropic formalism by Popa (J. Appl. Cryst. (1998) 31, 176-180) has been used for anisotropic shape refinements using the MAUD Rietveld codes, on textured samples: Thin Solid Films 450, 2004, 216-221. daniel A 11:12 AM 11/22/04 +0300, vous avez écrit : > > 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 A Quantitative Texture Analysis Internet Course: http://qta.ecole.ensicaen.fr/ The Crystallographic Open Database: http://www.crystallography.net Daniel Chateigner Professeur Co-Editor Journal of Applied Crystallography CRISMAT-ENSICAEN, UMR CNRS n° 6508 Bd. Maréchal Juin, 14050 Caen FRANCE Tel prof: 33 (0) 231452611 Fax: 33 (0) 231951600 http://www.ecole.ensicaen.fr/~chateign/danielc/
Re: rietveld refinement
> > 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
