A Markov theoretic description of stacking disordered aperiodic crystals including ice and opaline silica

TL;DR

This paper uses Markov theory to describe stacking disordered aperiodic crystals, providing analytic scattering expressions and insights into nucleation and growth processes in materials like ice and opaline silica.

Contribution

It generalizes the Markov description to aperiodic crystals, derives scattering formulas, and links stacking disorder to physical growth mechanisms.

Findings

Most stackings are irreversible when interaction range exceeds 4.

Analytic scattering cross section expressions for disordered crystals.

Connection between stacking disorder and nucleation processes in ice.

Abstract

We review the Markov theoretic description of 1D aperiodic crystals, describing the stacking-faulted crystal polytype as a special case of an aperiodic crystal. Under this description we generalise the centrosymmetric unit cell underlying a topologically centrosymmetric crystal to a reversible Markov chain underlying a reversible aperiodic crystal. We show that for the close-packed structure, almost all stackings are irreversible when the interaction reichweite is greater than 4. Moreover, we present an analytic expression of the scattering cross section of a large class of stacking disordered aperiodic crystals, lacking translational symmetry of their layers, including ice and opaline silica (opal CT). We then relate the observed stackings and their underlying reichweite to the physics of various nucleation and growth processes of disordered ice.