just my two cents.. even if I'm aware that times are not yet mature for a
comparison of this type.
There is lot of enthusiasm behind the use of the PDF approach and the
number of symposia in conferences, as well as the number of talks on the
subject is increasing day after day... the true question is: if we're
given the same dataset (experimental data I mean), what can we get out of
the two approaches? And what's the advantage of one versus the other?
The furher question is: PDF or total scattering? The two things IMHO are
different, even if there is a general (unjustified) belief that they're
the same, cause in the PDF approach "the whole information in the pattern
in used". Well, you can do total pattern analysis without using a PDF
approach (I do it weekly): you just need the right tools!
This said, with lab data forget about PDF... perhaps with a silver or a
tungsten tube you can get futher in reciprocal space but... other methods
are the winners here! You can do a Debye analysis, no problem in that, but
in that case you fit on the data and not on the PDF (the PDF is an
intermediate byproduct).
With synchrotron data: a pattern employed to obtain the PDF should be of
such a quality that it can be easily used also as is in a Rietveld (or
alternative) approach. What's different there:
- in order to fit the background, the PDF approach considers features
ignored by most (if not all) Rietveld people (proper account for
background allows Bragg+dffuse scattering to be considered)
This is a problem of the Rietveld approach where a peak is any bell-shaped
function and background is a well behaving polynomial.
This is a weakness that can be easily accounted for!
- the PDF approach suffers of truncation problems (check any published PDF
and you'll see the ringing...). The higher the ringing, the higher the
indetermination in the positions and intensity of maxima (other reason
for the need of high q data). We know we have access to synchrotrons or
neutrons but that's not "routine work" for everyone!
- the Rietveld approach is not suited for problems showing <3D periodicity.
You can account for that in simple cases by reducing the symmetry of the
problem and considering the streaking effects as Bragg effects showing
anisotropic broadening (fcc/hcp, bcc/orthorhombic cases can be easily
worked out). Also in this case, alternatives exist to deal with
problems where structure and microstructure interplay, fully considering
Bragg and diffuse scattering even with lab data (DIFFaX+ is one of them)
without transforming the data into PDF. The Rietveld method is not
thought to solve all crystallographic problems!
For sure if you have a PDF then you can visually see the effect that in
the diffraction pattern can be well hidden!
- microstructural effects.. well that's interesting: Rietveld is usually
rough there (exceptions exists where a WPPM approach has been attached
some structural information, or where proper microstructural models
have been imported into the Rietveld). The PDF approach isstill
lacking here and this is where things will come out in the next future
much more can be added here but in the end my opinion is that there is no
winner and for sure I won't leave reciprocal space methods to fully jump
on the train of real space ones. On the other hand I still keep an eye on
real space methods as, for their inner nature, are more intuitive as they
are directly related to the object we like to study: after all, atoms are
positioned in real space
There is a loser, though: anyone using those approaches as black
boxes (believing they work cause they spite out some result). I'd go for
the best of the two worlds (direct / reciprocal) when data quality allows
for that, and in any case for the most suited to my need (I'd not use
Rietveld when I have some structure/microstructure interplay, or use the
PDF when I have nanocrystalline materials). And I'd use both and compare
the results when I can do it!
Not having a unit cell for liquids and amorphous materials does present a
conceptual problem, which seems to need the Debye formula, see eg:
http://srs.dl.ac.uk/arch/dalai/Formula.html
It seems that function is mainly used for small angle scattering, where the q
range is too small to make a pdf. The distance histogram method mentioned
there also looks interesting for computational speeds.
I'd skip the amorphous/liquids case. And I do not agree on the last
sentence, but that's another story. Skipping the true small angle
region, the Debye approach allows modelling the whole powder diffraction
pattern up to any q value....
The Debye approach is somewhat intermediate: instead of massaging the data
to get the PDF out, you work bottom up, building a diffraction pattern via
the true PDF (not an RDF) calculated from a real space object.
Yes, there are several tricks to get it fast (histogram and distance
binning/harvesting are among them, but there are several
others). Again, focus on the problem: the narrower the peaks, the bigger
the domains. Just guess the number of distances to be calculated for a
domain of the order e.g. of 100nm. The number is large and you would need
them all (together with their multiplicities) in order to calculate the
pattern. You cannot use tricks: if you have defects you need to consider
all distances (ok, well Monte Carlo can help there...)
.. and we are simply skipping problems related to shape, size
distribution, surfaces, texture, etc... cause the problem increases in
computational demand. Application for now (in the powder diffraction
world) is limited to the case of "well behaving" nano-sized powders
The ideal solution: smart use of both worlds. If maths and physics
agree on the data (reciprocal space) you can stop there. If there is
still something missing, go for the real space methods. And check if the
two are consistent cause in most cases it can be done with the right
tools!
M
PS I am getting some of the other responses while I am writing.. so some
info can be already outdated :oD
In any case I see 3 players: pattern, PDF, structure
The known choices are (if I'm not wrong):
- get pattern from structure, compare pattern -> Rietveld
- get pattern from random structure, compare pattern -> "Rietveld class"
- get PDF from pattern, get PDF from structure, compare PDFs -> PDF refine
- get PDF from pattern, guess structure from PDF -> PDF solve
- get PDF from structure/microstructure, get pattern from PDF, compare
pattern -> Debye
with the condition that Rietveld is based on 3D periodicity, the PDF
approach is not forced to!
sounds reasonable?
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Matteo Leoni, PhD
Department of Materials Engineering
and Industrial Technologies
University of Trento
38100 Mesiano (TN)
Italy
Tel +39 0461 882416 e-mail: [EMAIL PROTECTED]
Fax +39 0461 881977
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