Disorder, design and vibrations

Disorder and defects are often thought to be a problem to be solved in materials science - for example, the presence defects and disorder greatly reduces electrical conductivity in crystals. In this paper we examine a particular kind of disordered crystals we termed ‘procrystals’ and showed that these procrystals have properties impossible to replicate in perfectly ordered crystals.

Procrystals are solids that would look just like an ordered crystal if you didn’t pay attention to the orientation of the building units. This condition means that the connections between units have to obey strict rules. The interaction between these rules and the underlying geometry of the lattice the material can produce odd structures that have order locally, but aren’t long range ordered like a crystal. The short-range order can be detected in diffraction experiments as instead of measuring sharp spots, as seen for crystals, we see broad lines and planes.

This procrystalline order crops up everywhere, including the structures of ice, the ferroelectric material BaTiO₃ and the simple cyanide Pt(CN)₂ but also as what happens when you randomly tile a surface with dominos or rhombuses. Procrystals don’t just have intruiging structures - their ‘correlated’ disorder could be used to produce materials that can bypass the usual tradeoffs in materials. One example of this, which we look at in this paper, is the conductivity of a material, both thermal and electrical. These are key properties for thermoelectrics, materials that convert temperature gradients into electrical current and so can harness waste heat. The efficiency of a thermoelectric is proportional to the ratio of electrical conductivity over thermal conductivity and so one common strategy for improving a thermoelectric is to try to reduce the thermal conductivity. Introducing disorder into a material is one effective way of doing this, but it usually has the unwanted consequence of also reducing the electrical conductivity, and so can be counterproductive! We show, using a simple model of a procrystal, it is possible to design in disorder that would selectively reduce the thermal conductivity (technically, the broadening of the vibrational bands is localised in reciprocal space), which need to compromise the electrical conductivity.

Here is another summary on the Goodwin group website.