Topological Analysis of Local Structure in Atomic Systems

This chapter describes a topological approach for automated structure analysis in atomic systems which are substantially more robust than conventional approaches, especially for high-temperature and imperfect systems. It introduces the central ideas of Voronoi analysis and considers how they can be used to characterize local structure in atomic systems. Molecular statics and Monte Carlo methods are also routinely employed in studies of large systems with atomic resolution. Physical approaches take into account physical properties of a system, such as energy and stress, in addition to atomic coordinates. Voronoi analysis traces its history to the mathematical study of crystal lattices, and in recent decades has been used to analyze many physical and biological systems. In atomic systems, small perturbations resulting from thermal noise or small strains are often unimportant for understanding crystal structure and defects. The melting of crystals is one of the most ubiquitous and also least-understood phase transformations.