An accurate predictive framework for the experimental realizability of metastable polymorphs

Exploring structural degrees of freedom at fixed chemical composition appears to be a promising avenue forward in the search for new functional materials. However, not every low-energy polymorph discovered on a computer stands an equal chance at being synthesized in the laboratory. We propose a statistical mean field model of polymorph formation wherein the probability that a polymorph will be experimentally realized under near-equilibrium conditions is shown mathematically 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. We apply our model principally to elemental silicon, where dozens of theoretical metastable structures have been proposed but only a few have been realized. Our model, along with estimates of enthalpies and basin hypervolumes obtained from density functional theory relaxations of random structures, accounts for the metastable polymorphism displayed by silicon to the exclusion of a very large number of other theoretical low-energy structures. The model thus constitutes a screening procedure to drastically reduce the number of polymorphs, which need to be considered for kinetics analysis and experimental synthesis.