Polymorphism in elemental silicon: Probabilistic interpretation of the realizability of metastable structures

TL;DR

This paper introduces a probabilistic framework based on statistical mechanics and density functional theory to explain why certain silicon polymorphs are experimentally observed as metastable, while many others are not.

Contribution

It presents a novel probabilistic model that predicts the likelihood of metastable silicon structures forming under near-equilibrium conditions.

Findings

The probability depends on the energy basin hypervolume and Boltzmann weight.

The model accurately accounts for silicon's observed metastable polymorphs.

Many low-energy structures are unlikely to form despite their stability.

Abstract

With few systems of technological interest having been studied as extensively as elemental silicon, there currently exists a wide disparity between the number of predicted low-energy silicon polymorphs and those, which have been experimentally realized as metastable at ambient conditions. We put forward an explanation for this disparity wherein the likelihood of formation of a given polymorph under near-equilibrium conditions can be estimated on the basis of mean field isothermal-isobaric (N, p, T) ensemble statistics. The probability that a polymorph will be experimentally realized is shown to depend upon both the hypervolume of that structure's potential energy basin of attraction and a Boltzmann factor weight containing the polymorph's potential enthalpy per particle. Both attributes are calculated using density functional theory relaxations of randomly generated initial structures. We find that the metastable polymorphism displayed by silicon can be accounted for using this framework to the exclusion of a very large number of other low-energy structures.