Valence-dependent analytic bond-order potential for transition metals

Abstract

An analytic interatomic bond-order potential is derived that depends explicitly on the valence of the transition-metal element. It generalizes the second-moment Finnis-Sinclair and fourth-moment Carlsson potentials to include higher moments. We find that the sixth-moment approximation predicts not only the structural trend from hcp→ bcc→ hcp→ fcc that is observed across the nonmagnetic 4d and 5d transition-metal series, but also the different ferromagnetic moments of the bcc, fcc, and hcp phases of the 3d transition-metal iron. An analytic expression for the force is obtained and proved to converge to the Hellmann-Feynman force as higher moments are included.

Modeling Topologically Close-Packed Phases in Superalloys: Valence-Dependent Bond-Order Potentials Based on Ab-Initio Calculations

“…Similarly to our previous work on the structural trends across the transition metals [3], we determined the density of states for topologically-close packed phases within the sixth moment approximation of the analytic BOP. In particular, we used canonical nearest-neighbour bond integrals [21] ddσ : ddπ : ddδ = −6 : 4 : −1 (6) with a decay ∝ 1/R 5 and band-widths as obtained from tight-binding calculations.…”

“…The derivation of the analytic BOP is based on Chebyshev polynomials of the second kind and presented in detail in Ref. [3]. This BOP depends explicitly on the valence (i.e.…”

“…Within the bondorder potential (BOP) formalism, the tight-binding DOS is represented as an analytic expansion [3] in terms of moments µ…”

“…Atomistic modeling of tcp stability with interatomic potentials requires to go beyond the second-moment approximation to the electronic density of states by including up to at least the sixth moment [2]. We have developed an analytic bond-order potential (BOP) that systematically takes into account higher moment contributions to the density of states and depends explicitly on the valence of the transition-metal elements [3]. For the parameterization of the new BOP, we performed extensive density functional theory (DFT) calculations of elemental and binary compound phases of Ni, the technologically important alloying element Cr, and the refractory metals Mo, Re, and W. We will discuss the structural trends of the DFT calculations, compare to the predictions of the analytic BOP and report on our progress on the parameterization of the analytic BOP for the Re-W system.…”

“…In order to be able to understand the stability of tcp phases as a function of the local coordination, we require an approximation to the solution of the tight-binding model. We have presented a bond-order potential (BOP) that is an analytic expansion of the DOS in terms of moments [3]. This BOP depends explicitly on the valence of Figure 1: The Mendeleev number M, here shown for the transition metals, is a one-dimensional ordering parameter for the elements of the periodic table [7,8].…”