Dynamics of modulated and composite aperiodic crystals: the signature of the inner polarization in the neutron coherent inelastic scattering

TL;DR

This paper introduces the concept of inner polarization and a parameter beta to analyze the dynamical properties of modulated and composite aperiodic crystals, aiding in experimental interpretation via neutron scattering.

Contribution

It unifies the dynamical analysis of aperiodic crystals and demonstrates how beta can distinguish structure types and predict scattering intensities.

Findings

Beta distinguishes between different acoustic modes.

The ratio of dynamic to static structure factors depends on beta.

Beta helps identify whether a structure is composite or modulated.

Abstract

We compare within an unifying formalism the dynamical properties of modulated and composite aperiodic (incommensurate) crystals. We discuss the concept of inner polarization and we define an inner polarization parameter beta that distinguishes between different acoustic modes of aperiodic crystals. Although this concept has its limitations, we show that it can be used to extract valuable information from neutron coherent inelastic scattering experiments. Within certain conditions, the ratio between the dynamic and the static structure factors at various Bragg peaks depends on beta. We show how the knowledge of beta for modes of an unknown structure can be used to decide whether the structure is composite or modulated. Furthermore, the same information can be used to predict scattered intensity within unexplored regions of the reciprocal space, being thus a guide for experiments