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Overview

In crystallography, we usually make the assumption that the crystal can be considered as an array of identical unit cells. This then reduces the 'solution' of the crystal structure to the determination of the unit cell contents. BUT in many real materials, the unit cells are not all the same. Take the relaxor ferroelectric materials, such as PZN (PbZn1/3Nb2/3O3). Now, the unit cell does not have three sites (or a multiple of 3) to put the Nb and Zn atoms on -- so they cannot go into the unit cell in the ratio 1:2. In other words, the chemical average composition is not reflected in the local structure. The average unit cell never occurs -- the structure you get from conventional crystallography is an average across local configurations, but itself never actually occurs!

This means that the average structure you get from conventional diffraction (that is, from analysis of the Bragg peaks) cannot tell you what the real local strictures occurring in the crystal look like. And since it is these local structures that really reflect the crystal chemistry, you really need this local structure information if you are to work out how the structures (and material properties) arise out of the composition.

This idea of local structure, on the scale of nanometres, applies to many crystalline materials, from molecular crystals (such as those of pharmaceuticals like Ibuprofen) through hard ceramic materials (like superconductors and PZN) through to metals and ionic solids. Extreme case of disorder are glassy materials and liquids -- but we tend to look at crystalline materials exhibiting short-range order (SRO, another term for local ordering) as a sort of modulation on the long-range ordering (LRO) that gives rise to the Bragg peaks in a diffraction pattern.

Much of this work is done in collaboration with Prof. T.R.Welberry of ANU (Erdös number =3).

We've developed some software to tackle these sorts of problems.

Web version of a lecture on diffuse scattering and disorder, presented at ANSTO/AINSE/IAEA Summer School, Dec 2007. This was output from PowerPoint, so it may not view well.



Research Projects

Disorder in Molecular Materials: Molecular crystals, particularly organic molecular crystals, have been a major component of our work on diffuse scattering and short-range order. Because the average structure is an average, in some cases it cannot tell you a lot about the various configurations that really occur in the crystal. Many populations of local configurations may have the same average. Since these local configurations tell you how the molecules 'talk' to each other, being able to gain insight into this population gives you information about how molecules behave in the crystalline state. An example is the phenomenon of polymorphism -- when one molecule can form several different crystal structures. The crystal structure is a result of the interaction between molecules, and as such diffuse scattering can act as a probe of why polymorphism occurs. This is relevant in pharmaceuticals and many other classes of materials.

Project Details: This project entails growing crystals, collecting X-ray or neutron scattering data at ANU and at a national and international laboratories, using custom-made computer code to analyse the data, and in some cases writing code to tackle novel problems. Systems of interest include pharmaceuticals, systems undergoing phase transitions (see below) and molecules showing internal flexibility and polymorphism.

Diffraction Patterns; BenzilAn example study: Benzil, C14H10O2, has been the subject of considerable study. To the left are shown the complex and strong diffuse scattering patterns measured with laboratory X-rays -- all of this scattering is ignored when doing conventional crystallography! In the case of benzil, there is only one type of molecule and it only has one type of orientation -- all the diffuse scattering is due to correlations in the thermal flexing and twisting of adjacent molecules. These correlations are of short range, so can be thought of as short-range displacement correlations or if you prefer as sort of localised phonons. There is no 'disorder' at all, in one sense, yet there is a lot of short-range order due to the correlated thermal motion, which tells you about how the molecules are interacting and which interactions control the crystal properties.

The lower three pictures were calculated from a model of the short-range correlation structure in the crystal. The agreement is pretty good! For more details have a look at:

D.J.Goossens, T.R.Welberry, A.P. Heerdegen and M.J. Gutmann, 'Simultaneous Fitting of X-ray and Neutron Diffuse Scattering Data', Acta Crystallographica A A63 (2007) 30-35
and references therein.

A look at the web version of a lecture on diffuse dscattering and disorder presented at ANSTO/AINSE/IAEA Summer School, Dec 2007 outlines some aspects of the subject. Similarly, the studies of two materials are (a little bit tersely) outlined in this set of slides. References for these two pieces of work are:

L.H.Thomas, T.R.Welberry, D.J.Goossens, A.P.Heerdegen, M.J.Gutmann, S.J.Teat, C.C.Wilson, P.L.Lee and J.M.Cole, 'Disorder in Pentachloronitrobenzene, C6Cl5NO2: A Diffuse Scattering Study', Acta Crystallogr. B63 (2007) 663-673.

D.J.Goossens, A.P.Heerdegen, T.R.Welberry and A.G.Beasley,'The Molecular Conformation of Ibuprofen, C13H18O2, Through X-ray Diffuse Scattering', International Journal of Pharmaceutics 343 (2007) 59-68.


Diffuse Scattering and Phase Transitions is a good combination. A structural phase transition (of higher than first order) involves correlations with length scales which diverge with (for example) cooling, such that they go from being short-range correlations above the critical temperature, TC to being long-ranged below. Because diffuse scattering can see short-range correlations, it can be used to study the evolution of one phase into another, as the correlation lengths diverge. By measuring multiple diffuse scattering patterns at a range of temperatures above (but close to) TC, can see see just what aspects of the short-range order are driving the transitions, and which structural components are simply 'following suit'. To give a simple example, if the order goes long range in one direction, say along chains of molecules, then that allows the weaker interactions in the other directions to compound, so that (in this example) the long-range order will set in within the chains but also between the chains -- yet it is the ordering along the chains which is really crucial in driving the transition.

Project Details: A key focus of this work is the development of experimental processes as well as sample preparation and data analysis. Since we need large amounts of data collected at a range of temperatures, a synchrotron experiments are the major tool. We have made initial studies on the phase transition in para-terphenyl, and have been able to see the diffuse scattering collapse into new Bragg peaks as the correlation lengths of the short-range order diverge, and have also been able too see the anisotropy in the divergence -- how the correlation lengths are much longer in certain crystallographic directions than in others. These are the sorts of results we are looking for.

Para-terphenylAn example study is the neutron diffuse scattering from para-terphenyl, C18H14. The figure to the right shows the hk0 plane, showing how the diffuse features are very oval in shape, indicating that the correlations in the short-range order are much stronger in some direction than in others; yet below TC, the Bragg peaks that appear where the diffuse scattering used to be indicate long range order has set in in all directions simultaneously. Some of this information can be inferred from Bragg scattering if a range of assumptions about modelling the atomic displacement parameters are made, but observation of the diffuse scattering is more direct and less ambiguous.

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