Valence-dependent bond-order potentials for modeling Ni-based superalloys

The creep properties of Ni-based superalloys degrade with time due to precipitation of topologically close-packed (tcp) phases. We have compiled a structure map of the occurrence of tcp phases for binary transition-metal (TM) compounds from experimental databases. The structure map highlights the well-known role of the average d-band filling for the stability of tcp phases. Atomistic modelling of tcp stability requires extending the second-moment approximation to the electronic density of states (DOS) by including up to at least the sixth moment. We have developed an analytic bond-order potential (BOP) that systematically takes into account higher moment contributions to the DOS and depends explicitly on the valence of the TM elements. By including up to sixth-moment terms the analytic BOP is able to reproduce the structural trend across the non-magnetic 4d and 5d TM series. For the parameterization of the new BOP, we performed extensive density functional theory (DFT) calculations of the elemental and binary compound phases of Ni, the technologically important alloying element Cr, and the refractory metals Mo, Re, and W. In particular, we investigated the tcp phases A15, C14, C15, C36, μ, σ, and χ for the Ni-Cr, Re-W, Mo-Re, and Mo-W binary systems. We discuss the structural trends of the DFT calculations and compare to the predictions of the analytic BOP within the canonical d-band model