THE CRYSTALLOGRAPHY OF DISORDER

To my eye, the real beauty of crystallography is its universality. Grow a crystal of something – be it a protein or a superconductor or an antibiotic – and the same basic approach can be used to determine its structure. It is humbling to think that every crystal structure we will ever solve is described by the 230 space groups enumerated by Federov and Schönflies in the late 19th century.

But what happens when a material simply isn’t crystalline?

The truth is: structure determination becomes extraordinarily difficult as soon as crystallinity is lost. Our methods are so dependent on the periodic order found in crystals that it is easy to forget that this particular form of matter might actually be the exception rather than the rule. (As flagged by one of my very favourite papers — this stunningly insightful study of polyhedral packings by Sharon Glotzer and her talented team).

My personal view is that the problem starts with our language for describing non-crystalline materials. Think of how precisely we can describe the structure of rocksalt, to take an easy but illustrative example: Fm-3m, with a = 5.64 Å, and Na and Cl atoms on 4a and 4b positions. By contrast, nearly every phrasing we have to describe non-crystalline materials tells us what they’re not, rather than what they are: non-crystalline, a-morphous, dis-ordered, defective (Latin simply for “failed”, as I learned recently). What the community has known for some time now – even if we might not have the language yet to say it precisely – is that some types of disorder are more ordered than others.

In a review written with David Keen at ISIS, we argue that certain types of correlated disorder share the features that have made crystallography itself such a powerful technique. By this we mean two things. First, the same types of disordered state recur across entirely different fields; for example, the packing of proteins, the orientations of spins in magnets, and the distribution of charge in solid materials might all adopt the same aperiodic patterns. Symmetry still seems to play a key role, even if these structures will never be properly described by any one of the 230 space groups mentioned above. Second, this structural mapping is preserved in diffraction experiments. So not only do well-defined disordered states seem to exist, but we are in principle sensitive to their particular type of disorder using the same crystallographic techniques we use to study periodic systems.

How exciting it would be if we could characterise disordered matter in the same way we study the structures of crystals today! Exciting, not only because structure is always of interest to us as chemists (and, presumably, to biologists and physicists as well). But also because there’s an emerging sense — at least in the field of functional materials — that disorder often accompanies the most unconventional and ultimately useful materials properties. To take one (perhaps laboured) example: can it be accidental that superconductivity in the various high-Tc systems — now thought to be mediated by spin correlations — emerges from a magnetically disordered state? Or, more straightforwardly, that high-performance thermoelectrics require dynamic disorder in order to reduce their thermal conductivity?

One way or the other, our thesis is simple: understanding the structures of disordered materials is now the most important challenge in structural science, and the basic principles of crystallography — even if they must be applied in new and unconventional ways — may yet provide the mechanism for developing this understanding.

The crystallography of correlated disorder
D A Keen and A L Goodwin
Nature 521, 303-309 (2015)