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-Gardu�o
Profesor Asociado C
Departamento de Ciencia de Materiales
Academia de Ciencias de la Ingenier�a
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: [email protected]
>> 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 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
>>
>
