Statistical Mechanics of Aperiodic Order
Michael Engel (University of Michigan)

Aperiodic solids are a state of matter with long-range order but without periodicity. They typically come in two flavors: modulated phases and quasicrystals. Both where known to exist mathematically but judged <em>impossible</em> until their experimental discoveries. Prominent examples cover inorganic and organic compounds, including many minerals, in equilibrium or under extreme conditions. Recently the study of aperiodic order has been extended to soft matter and nanoscale systems.

In this presentation, I will discuss the statistical mechanics of aperiodic order and its study in computer simulation. An important theoretical tool are higher-dimensional configuration spaces to describe the complex geometry and structural rearrangements called phason modes. I will present the first occurrence of a modulated crystal [1] and an icosahedral quasicrystal [2] from the melt in classical molecular dynamics simulations, which allow direct testing of theoretical predictions. The findings elucidate the role of entropy for the formation and stabilization of aperiodic order.

[1] M. Engel, "Entropic stabilization of tunable planar modulated superstructures", PRL 106, 095504 (2011).

[2] M. Engel, P.F. Damasceno, C.L. Phillips, S.C. Glotzer, "Computational self-assembly of a one-component icosahedral quasicrystal", Nature Materials 14, 109-116 (2015).