Chemical bonding, elasticity, and valence force field models: A case study for $\alpha -{\mathrm{Pt}}_2\mathrm{Si}$ and PtSi

We have carried out a detailed study of the chemical bonding for two room-temperature stable platinum silicide phases, tetragonal $\alpha -{\mathrm{Pt}}_2\mathrm{Si}$ and orthorhombic PtSi. An analysis of the valence electronic charge density reveals surprising evidence of covalent three-center bonds in both silicide phases, as well as two-dimensional metallic sheets in $\alpha -{\mathrm{Pt}}_2\mathrm{Si}.$ These elements of the bonding are further analyzed by constructing valence force field models using the results from recent first principles calculations of the six (nine) independent, nonzero elastic constants of $\alpha -{\mathrm{Pt}}_2\mathrm{Si}$ (PtSi). The resulting volume-, radial-, and angular-dependent force constants provide insight into the relative strength of various bonding elements as well as the trends observed in the elastic constants themselves. The valence force field analysis yields quantitative information about the nature of the chemical bonding that is not easily discernible from the more qualitative charge density plots. More generally, this study demonstrates that the detailed variations in the elastic constants of a material contain useful information about the chemical bonds that can be extracted using valence force field models. Inversely, these models also allow for identification of specific elements of the chemical bonding with particular trends in the elastic constants, both within a given material and among a class of related materials.