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Updated: Oct 25, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Thermodynamic stability of hard sphere crystals in dimensions 3 through 10
Patrick Charbonneau1,2, Caitlin M Gish3, Robert S Hoy3
1Department of Chemistry, Duke University, Durham, NC, 27708, USA.
Abstract:
Although much is known about the metastable liquid branch of hard spheres-from low dimension d up to [Formula: see text]-its crystal counterpart remains largely unexplored for [Formula: see text]. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to [Formula: see text], and the dimensional trends suggest that crystal stability likely persists well beyond that point.
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