Pathways to self-organization: crystallization via nucleation and growth

TL;DR

This paper reviews theoretical and computational approaches to understanding crystallization as a self-organization process, focusing on nucleation, growth, and the analysis of transition mechanisms.

Contribution

It introduces methods for simulating and analyzing nucleation events, emphasizing statistical tools and rate calculations for crystallization processes.

Findings

Effective computational techniques for rare event simulation.

Methods for accurate nucleation rate calculation.

Analysis of crystallization transition mechanisms.

Abstract

Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In the initial stages of the transformation, a localized nucleus of the new phase forms in the old one due to a random fluctuation. Most of these nuclei disappear after a short time, but rarely a crystalline embryo may reach a critical size after which further growth becomes thermodynamically favorable and the entire system is converted into the new phase. In these lecture notes, we will discuss several theoretical concepts and computational methods to study crystallization. More specifically, we will address the rare event problem arising in the simulation of nucleation processes and explain how to calculate nucleation rates accurately. Particular attention is directed towards discussing statistical tools to analyze crystallization trajectories and identify the transition mechanism.