Hard sphere crystallization gets rarer with increasing dimension

TL;DR

This paper investigates how the free energy barrier for crystallization of hard spheres increases with dimension, highlighting the role of geometrical frustration and polydispersity, and compares jamming behavior across multiple dimensions.

Contribution

It provides a microscopic analysis of fluid-crystal interfacial free energy contributions and explores how crystallization becomes rarer in higher dimensions, including the impact of polydispersity.

Findings

Crystallization barrier grows with dimension

Polydispersity prevents crystal formation in higher dimensions

Fluid stability increases with dimension, enabling jamming studies

Abstract

We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the simplex-based fluid order and the crystal [J.A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in press (2009)].