Modeling the Morphology of Polymorphic Manganese Sulfide Nanocrystals

Many physical and chemical properties of nanocrystals are closely tied to their geometries. At thermodynamic equilibrium, the morphology of nanocrystals can be approximated by applying the Gibbs-Wulff theorem to construct the so-called “Wulff shape,” whose set of surfaces minimizes the surface energy at constant volume. Although the equilibrium morphology of elemental systems is understood, that of binary compounds is less explored.

In this talk, I will describe our analysis of the Wulff shapes of three experimentally synthesizable polymorphs of manganese sulfide (MnS) in a vacuum. We used density functional theory to calculate the surface energy of various facets ranging from low to high Miller index. First, I will show that the r²SCAN functional without van der Waals correction accurately reproduces experimental lattice constants and standard enthalpies of several materials and reactions relevant to synthesizing MnS. Second, when considering only the low-index facets, I will show that the Wulff shape of rock salt MnS (RS-MnS) nanocrystals is cubic in sulfur-poor environments and octahedral in sulfur-rich environments. Third, I will show that, contrary to the conventional belief that high-index facets have higher surface energy, several high-index low-energy surfaces are predicted to compose the equilibrium morphology of RS-MnS nanocrystals. Thus, when including the contributions of high-index facets, the Wulff shape of RS-MnS nanocrystals in sulfur-rich environments is trapezohedral.