# Close packed structure with finite range interaction: computational mechanics of layer pair interaction

## TL;DR

This paper models the stacking problem in layered materials using computational mechanics and an Ising model, providing a general method to analyze phase diagrams and polytypes, applicable to real materials like ZnS and Cobalt.

## Contribution

It introduces a general computational mechanics approach to analyze stacking sequences with finite range interactions, including phase diagram and polytype analysis.

## Key findings

- Phase diagram characterization of stacking arrangements
- Occurrence of higher order polytypes at phase boundaries
- Applicability to real materials like ZnS and Cobalt

## Abstract

The stacking problem is approached by computational mechanics, using an Ising next nearest neighbor model. Computational mechanics allows to treat the stacking arrangement as an information processing system in the light of a symbol generating process. A general method for solving the stochastic matrix of the random Gibbs field is presented, and then applied to the problem at hand. The corresponding phase diagram is then discussed in terms of the underlying $\epsilon$-machine, or optimal finite state machine, describing statistically the system. The occurrence of higher order polytypes at the borders of the phase diagram is also analyzed. Discussion of the applicability of the model to real system such as ZnS and Cobalt is done. The method derived is directly generalizable to any one dimensional model with finite range interaction.