Diffuse scattering from quasicrystals

Abstract

A theory of both thermal and quenched diffuse scattering from incommensurate crystals and quasicrystals is developed. We explore, in particular, the effects of strain fluctuations due to phasons which have dropped out of equilibrium at high temperatures, providing a source of quenched, spatially varying disorder. The theory leads to anisotropic peak shapes, in analogy with Huang scattering in ordinary crystals. In contrast to Huang scattering, the peak shapes vary greatly along a given direction in reciprocal space. Analysis of peak shapes can be used to infer information about phason elastic constants. We illustrate the theory with explicit computations using icosahedral quasicrystal elastic constants taken from recent density-functional calculations.