Pathways to self-organization: crystallization via nucleation and growth

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.

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Cited by in corpus (16)

• The Seven Deadly Sins: when computing crystal nucleation rates, the devil is in the details
• Interfacial free energy and Tolman length of curved liquid-solid interfaces from equilibrium studies
• The barrier to ice nucleation in monatomic water
• Maximum Likelihood Analysis of Reaction Coordinates during Solidification in Ni
• Identification of a Multi-Dimensional Reaction Coordinate for Crystal Nucleation in ${\text{Ni}}_3\text{Al}$
• The Gibbs free energy of homogeneous nucleation: from atomistic nuclei to the planar limit
• Optimal reaction coordinates and kinetic rates from the projected dynamics of transition paths
• Structure and Morphology of Crystalline Nuclei arising in a Crystallizing Liquid Metallic Film
• Free Energy Landscapes, Diffusion Coefficients, and Kinetic Rates from Transition Paths
• Template induced precursor formation in heterogeneous nucleation -- Controlling polymorph selection and nucleation efficiency
• Controlling crystallization: What liquid structure and dynamics reveal about crystal nucleation mechanisms
• Effect of the Composition on the Free Energy of Crystal Nucleation for CuPd Nanoalloys
• The role of local bond-order at crystallization in a simple supercooled liquid
• Persistent Homology for Structural Characterization in Disordered Systems
• A critical comparison of general-purpose collective variables for crystal nucleation
• Deep learning of committor and explainable artificial intelligence analysis for identifying reaction coordinates