The Role of Carbon Depletion in the Morphology of Transition Metal Carbide Crystals

In this paper, we utilize density functional theory to explore the role of carbon depletion on crystal morphology in group IVB and VB transition metal carbides (TMCs). The surface energies of low-index planes ({100}, {110}, and {111}) with varying surface and bulk carbon concentration are calculated. A Python program is created to determine the crystal morphology according to Wulff construction. Our results indicate that the TMC crystal morphology can be significantly altered by the local carbon source amount. Specifically, a low carbon concentration in the processing environment favors growth of metal-terminated {111} surfaces, and the crystals appear as truncated octahedrons or octahedrons; a high concentration of carbon encourages {100} growth, which leads to cubic or truncated cubic crystals.