Close packed structure dynamics with finite range interaction: computational mechanics with individual layer interaction

TL;DR

This paper analyzes the dynamics of close packed structures using a finite range interaction Hamiltonian within computational mechanics, comparing it to the Ising model and discussing disorder and polytype diversity.

Contribution

It introduces a simplified Hamiltonian model for polytype generation, avoiding unphysical spin assignments, and demonstrates it predicts a broader set of polytypes than previous models.

Findings

The Ahmad and Khan model predicts more polytypes.

Disorder and structure are analyzed via entropy measures.

The model is simpler and more comprehensive than previous approaches.

Abstract

This is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. A Hamiltonian introduced by Ahmad avoids the unphysical assignment of interaction terms to fictitious entities given by spins in the Hagg coding of the stacking arrangement. In this paper an analysis of polytype generation and disorder in close packed structure is made for such Hamiltonian. Results are compared with a previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed. The competing effects of disorder and structure, as given by entropy density and excess entropy, respectively, is discussed. It is argued that the Ahmad and Khan model is simpler and predicts a larger set of polytypes than previous treatments.