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
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----- 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 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] [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 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
> > > > /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
> > >
> > >
> > >
> >
>
>
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