Physically Derived Rulesfor Simulating Faceted Crystal Growth using Cellular Automata

TL;DR

This paper introduces physically grounded algorithms for simulating faceted crystal growth via cellular automata, accurately capturing morphology and revealing a new transition in crystal shapes.

Contribution

It provides a rigorous physical foundation for cellular automata models of crystal growth, linking numerical methods to attachment kinetics and diffusion physics.

Findings

Successfully reproduces realistic crystal morphologies

Identifies a novel morphological transition in thin plate-like crystals

Connects cellular automata algorithms to physical diffusion and attachment processes

Abstract

We derive a set of algorithms for simulating the diffusion-limited growth of faceted crystals using local cellular automata. This technique has been shown to work well in reproducing realistic crystal morphologies, and the present work provides a more rigorous physical foundation that connects the numerical code to the physics of attachment kinetics and diffusion dynamics. We then apply these algorithms to examine a novel morphological transition in the growth of thin plate-like crystals.