Dear all
I have to weigh in here as someone who has been using total scattering
measurements for some while now.
I suggest that since this is a crystallography mail list I should
restrict discussion to crystals and not amorphous or nano-crystalline
materials.
What Bragg diffraction gives is the single-particle distribution
functions. Typically Rietveld refinement gives something like the mean
position of an atom. When you calculate bond lengths, you are actually
calculating the distance between mean positions.
On the other hand, PDF gives you the what it says, namely a pair
distribution function that is a histogram of instantaneous distances
between atoms, which is a fundamentally different quantity from the
mean positions between atoms.
Now if you have a simple crystal (let us say NaCl) where the atoms are
vibrating harmonically, the mean of the instantaneous distances
between atoms obtained from Rietveld, which we can write as <Na><Cl>,
is not going to differ from the distances between mean positions
obtained from a PDF analysis, which we can write as <NaCl>; in this
case you don't gain much. But, if you have a lot of disorder that is
not harmonic, then the distance between mean positions is not in any
way related to the actual instantaneous bond lengths. We saw this
clearly from our measurements of quartz. In this case, as quartz goes
through the phase transition, the distance between the mean Si and O
positions, <Si><O>, decreases a lot on heating through the phase
transition, whereas the mean instantaneous interatomic distance from
pdf, namely <SiO>, doesn't appear to change at all through the phase
transition (as you might expect). We see <SiO> > <Si><O>, as you
would expect, with the difference increasing on heating, but the
difference vanishing on cooling down to 0 K (again as you would expect).
There are many interesting cases where the local structure is not a
mere reflection of the long-range order, and for these a combination
of pdf and Rietveld is great. I would stress that we are convinced
that one should use the information contained in the Bragg peaks
explicitly as well as the information contained within the total
scattering (Bragg peaks + diffuse scattering background).
I would make a small number of additional comments:
1. Background corrections are critical, but are doable. The downside
is that to get good data you do have to measure for some hours on an
instrument like GEM at ISIS
2. You need to go to high Q. GEM lets us get to 50 Å^1. By
comparison, measuring on Cu Kalpha out to theta = 90° only gets to Q
of 8 Å^1. The requirement to go to high Q is to reduce truncation
ripples and to improve real-space resolution. Signals are weak at
higher Q, hence the need for longer counting times.
3. The ability to go to high Q means you could collect a lot of data.
The huge quantities of data this would mean in 3d from a single
crystal are unviable to work with, and hence powders are the only real
option. But just as Rietveld has shown that powders are okay for
structure, we have found that powder in total scattering are okay if
your questions are not too ambitious.
4. The pdf from total scattering is actually not the same as the
Patterson, since the Patterson is constructed only from the Bragg peaks.
5. We use Reverse Monte Carlo to analyse our data, fitting not only to
the total scattering and pdf but also to the Bragg peaks. Since Bragg
peaks have hkl indices, this enables us to recover some 3d
information. RMC ignites debate; my view is that it works.
Bottom line is that there are classes of scientific problem for which
a proper PDF analysis gives you very new insights. And it no longer
needs to be a specialist tool.
Best wishes
Martin Dove
On 13 Jun 2008, at 09:39, Favre-Nicolin Vincent wrote:
Hi,
I've only begun to look at pdf, but it seems to me that pdf is only
really
interesting if you want to model non-crystalline material (or
nano-crystalline), so that there is no long-range periodicity
(limited size,
defects on the borders, large strain, variation in composition,...),
and
therefore the F^2 calculation is not even on option. The reason I've
begun to
look at pdf is that I'm working on a sample with nano-columns that
are (at
best !) 3 or 4 nm in diameter - we're still looking for the Bragg
peaks !
From a computationnal point of view, I think it takes in practice
much more
time to compute the pdf - indeed it is N^2, but N does not even
correspond to
a single unit cell (or sub-unit if centered/centro), but the entire
object
(if nano-sized). If the pdf is computed for a truly crystalline
compound, it
can be reduced to N_asym * N_shell (atoms in the asym unit cell /
asym in the
shell of radius corresponding to the largest d you're interested in).
Vincent
--
Vincent Favre-Nicolin http://vincefn.net
Université Joseph Fourier http://www.ujf-grenoble.fr
CEA/ Institut Nanosciences & Cryogénie http://inac.cea.fr
ObjCryst & Fox http://objcryst.sourceforge.net
Martin Dove
Department of Earth Sciences
University of Cambridge
Downing Street
Cambridge CB2 3EQ
Tel: 01223 333482 (office) / 01223 711541 (home)
URL: http:://www.esc.cam.ac.uk/astaff/dove
