Basin-Size Mapping: Prediction of Metastable Polymorph Synthesizability Across TaC–TaN Alloys

The sizes of the basins of attraction on the potential energy surface are helpful indicators in determining the experimental synthesizability of metastable phases. In principle, these basins can be controlled with changes in thermodynamic conditions such as composition, pressure, and surface energy. Herein, we use random structure sampling to computationally study how alloying smoothly perturbs basin of attraction sizes. The TaC_1–xN_x pseudobinary is an ideal test system given the structural and polymorphic contrast of its parent compounds and their technological relevance as epitaxial substrates for Al_1–xGa_xN. While we find limited thermodynamic stability across all computationally observed phases, random structure sampling shows a significant composition region where the rocksalt basin dominates. As such, we predict the potential for the nonequilibrium synthesis of metastable rocksalt TaC_1–xN_x alloys as substrates for Al_1–xGa_xN. At higher nitrogen concentrations, other low-energy metastable polymorphs emerge that continue to retain the hexagonal close packing suitable for III–N growth. Confidence in these trends was established through uncertainty quantification of the basin sizes and energy distributions; such analysis utilized the Beta and Dirichlet distributions. We also find (a) polymorph basin sizes can be rationalized in terms of energetic preferences for different coordination environments; and (b) basin sizes universally shrink with increasing nitrogen content, making the system more prone to amorphous growth.