# Distinguishing Types of Disorder in Diffuse Scattering: A Numerical Simulation Study

A technique of growing importance in structural science is pair distribution function (PDF) analysis of total scattering. If you have a powder/polycrystalline sample, then in a conventional study you measure the diffraction pattern as a function of the scattering angle and look at the intensities of the Bragg peaks. A typical data set might look like this

A neutron diffraction pattern for PZN (PbZn1/3Nb2/3O3) measured using NPDF at LANSCE. Data axtends to higher values of Q, but these are not shown.

except that these data have been carefully normalised and corrected, and angle has been converted to scattering vector magnitude, a more general quantity.  This means that not only can the Bragg peaks be fitted, but the bit of the pattern between and under the Bragg peaks are also not just ‘background’ but also meaningful signal.  Hence all the scattering can be modelled (hence the term total scattering).

Why bother?

Well, the Bragg peaks — the narrow, sharp peaks in the signal — tell you about the average repeating unit in the structure, the unit cell.  The other stuff tells you about local order, so holds extra information.  One way to represent this information is to calculate from such a pattern the PDF, which tells of the probability of various interatomic distances.  This might look like this

The PDF of PZN, calculated using different maximum scattering vector magnitudes.

where there are three traces because the details of the PDF depend on how much of the data shown in the first picture you actually use when you transform to get the second.  Now, the useful thing here is that this picture gives information about hot the atoms are behaving on a local scale.  But how much information? I’ve been working in single crystal diffuse scattering (SCDS), which is like total scattering but because it is measured from a single crystal the data are not collapsed onto a single axis but give a full 3D plot of intensity versus scattering direction, not just scattering vector magnitude.  Hence, SCDS is the most comprehensive data you can reasonably get.

Except you often can’t.

SCDS needs a single crystal.  It needs a lot of time and trouble to get good data, and it needs a lot of detailed and bespoke analysis.  Many materials can’t be got as single crystals at all, so this limits its breadth of application.  PDF is also a tough technique to master, but it has some tools that eliminate at least the ‘bespoke’ part of analysing it, which is pretty useful, and does not need single crystals, which is even more useful.

So the question is: PDF has a lot of benefits over SCDS, but it collapses a 3D data set down into 1D; what information is lost?  What can SCDS tell us that PDF cannot, and vice-versa?

Some of this is tackled in the paper (behind a paywall, I’m sorry): D.J.Goossens and R.E.Whitfield, ‘Distinguishing Types of Disorder in Diffuse Scattering: A Numerical Simulation Study’, Metallurgical and Materials Transactions A, 45 (2014) 152-161.  DOI: 10.1007/s11661-013-1812-x

We look at the PDFs (calculated using DISCUS) from some SCDS-based models, to compare the insights the two techniques give.  We find that

PDF is indeed sensitive to all the phenomena explored, in the sense that they influence the features found in the PDF, but that the interpretation is much less immediately apparent when examining PDF data and perhaps more reliant on detailed modeling than SCDS, where qualitative analysis to isolate key features is possible. While the full 3D SCDS datasets perforce contain more information than the TS/PDF data, the PDF remains highly useful. SCDS tends to show up more subtle variations more clearly, particularly because features which are limited to small regions of reciprocal space are not lost in the averaging inherent in a powder experiment. This is particularly the case when relatively few of the total number of scatterers take part in the local ordering, as for example in para-terphenyl.

Hardly surprising, but is is nice to have some concrete examples (if not concrete, at least thickish mud).