Signatures of emerging order in complex structures via local structural analysis

The emergence of crystalline order in assemblies with complex structures, such as Frank–Kasper phases and clathrates, is poorly described by existing theories of particle-by-particle attachment of a fluid to a crystal bulk. Molecular dynamics simulations of self-assembling, idealized particles performed using multi-well, isotropic pair potentials, allow us to explore this question more comprehensively by simulating the growth of structures with varying complexities and coordination numbers [1]. We study this fluid-to-crystal phase transition using two complementary techniques: coordination number analysis coupled with a machine-learning based order parameter [2] that uses spherical harmonics to describe and classify particles by their local environment, and can distinguish crystalline sites of the same coordination number by their differing local geometries. By tracking the how identical particles transition from their less well-defined liquid environment to their distinct “role” (Wyckoff position) within the bulk crystal, we study how the evolution of a particle’s local structure gives way to global crystalline order, which in turn enables us to extract general growth principles across structure types. These insights can guide in the design and assembly of materials with desired structures and functionalities in soft matter systems.

[1] J. Dshemuchadse, P. F. Damasceno, C. L. Phillips, M. Engel, S. C. Glotzer., Proc. Natl. Acad. Sci. USA 118 (21), e2024034118 (2021).

[2] M. Spellings, S. C. Glotzer, AIChE J. 64 (6), 2198–2206 (2018).