(323f) An Unified Energy Landscape View of Crystal Melting

There is still an open debate on the mechanisms that drive melting in crystalline materials, and in particular, a unified treatment of numerous melting-related phenomena (e.g. melting point depression in nanoparticles, pressure-induced melting, and maximum superheating limits) is still lacking.  Under most experimental conditions, materials contain surfaces and/or a sufficient number of internal defects to allow melting to proceed without appreciable superheating at the thermodynamic melting point, i.e. the temperature at which the free energies of the liquid and solid phases are equal.   Even so, various factors can alter the apparent melting point of a crystalline material, including surface curvature, applied stress, and sample shape.

In previous computational investigations, the statistical distributions of mechanically stable structures in super-cooled liquids [[1]], glasses [[2]] and crystalline solids [[3]] were obtained by sampling the potential energy (or enthalpy) landscape of each material.  Here, we use this so-called Inherent Structure (IS) [[4]] approach to study the vibrational and configurational density-of-states of two prototypical crystalline material systems represented by empirical potentials, silicon (using the EDIP potential [[5]]) and aluminum (using an EAM potential [[6]]), and generate a unified basis for describing the melting of crystals in a variety of settings. 

We first study the homogeneous melting mechanism in surface-free samples and discuss the maximum superheating limit.  We find that the degeneracy of (configurational and vibrational) states grows exponentially with increasing energy and that the exponent directly provides an excellent estimate for the maximum superheating limit.  We then consider heterogeneously-nucleated melting in which a surface is already present.  Here, we consider three distinct cases: a semi-infinite crystal with a planar melt/crystal interface, a nanoparticle, and an infinite crystal containing an internal cavity.  Once again, melting in these systems is predicted by exponential growth in configurational and vibrational state degeneracy.  We also show that the IS theory is able to compactly (and atomically) describe how curvature affects melting.  In particular, we demonstrate that the potential energy landscape of the melt near a solid plays a significant role in setting the overall melting behavior of a material sample.