Size versus electronic factors in transition metal carbide and TCP phase stability

Abstract

The contributions of atomic size and electronic factors to the structural stability of transition metal carbides and topologically close-packed (TCP) phases are investigated. The hard-sphere model that has been used by Cottrell to rationalize the occurrence of the octahedral and trigonal local coordination polyhedra within the transition metal carbides is shown to have limitations in TiC since density functional theory (DFT) predicts that the second most metastable phase closest to the B1 (NaCl) ground state takes the B (BN) structure type with 5-atom local coordination polyhedra with very short Ti–C bond lengths. The importance of electronic factors in the TCP phases is demonstrated by DFT predictions that the A15, and phases are stabilized between groups VI and VII of the elemental transition metals, whereas the and Laves phases are destabilized. The origin of this difference is related to the bimodal shape parameter of the electronic density of states by using the bond-order potential expansion of the structural energy within a canonical tight-binding model. The importance of the size factor in the TCP phases is illustrated by the DFT heats of formation for the binary systems Mo–Re, Mo–Ru, Nb–Re and Nb–Ru which show that the and Laves phases become more and more stable compared to A15, and as the size factor increases from Mo–Re through to Nb–Ru.

Keywords:

• TCP phases
• transition metal carbides
• phase stability
• size factor
• electronic factors
• structural trends
• Frank–Kasper polyhedra