Richard K Bowles | Searcharxiv

arXiv2023

Crystal Growth Rates from Molecular Liquids: The Kinetics of Entropy Loss

It has been established empirically that the rate of addition of molecules to the crystal during crystal growth from the melt is proportional to exp(-|ΔS_fus|/R) where ΔS_fus is the entropy of fusion. Here we show that this entropic slowdown arises directly from the separation of the entropy loss and energy loss processes associated with the freezing of the liquid. We present a theoretical treatment of the kinetics based on a model flat energy landscape and derive an explicit expression for the coupling magnitude in terms of the crystal-melt interfacial free energy. The implications of our work for nucleation kinetics are also discussed.

cond-mat.soft↗

arXiv2009

A Tiling Approach to Counting Inherent Structures in Hard Potential Systems

The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure corresponds to a collectively jammed configuration. This work develops a tiling based approach to counting inherent structures that constructs packings by combining sets of elementary locally jammed structures but eliminates those final packings that either, do not tile space, or are not collectively jammed, through the use of tile incompatibility rules. The resulting theory contains a number of geometric quantities, such as the number of growth sites on a tile and the number of tile compatibilities that provide insight into the number of inherent structures in certain limits. We also show that these geometric quantities become quite simple in a system of highly confined hard discs.

cond-mat.stat-mech↗