  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.
