A binomial truncation function proposed for the second-moment approximation of tight-binding potential and application in the ternary Ni–Hf–Ti system

Abstract

We propose a two-parameter binomial truncation function for the second-moment approximation of the tight-binding (TB-SMA) interatomic potential and illustrate in detail the procedure of constructing the potentials for binary and ternary transition metal systems. For the ternary Ni–Hf–Ti system, the lattice constants, cohesion energies, elastic constants and bulk moduli of six binary compounds, i.e. L12 Ni3Hf, NiHf3, Ni3Ti, NiTi3, Hf3Ti and HfTi3, are firstly acquired by ab initio calculations and then employed to derive the binomial-truncated TB-SMA Ni–Hf–Ti potential. Applying the ab initio derived Ni–Hf–Ti potential, the lattice constants, cohesive energy, elastic constants and bulk moduli of another six binary compounds, i.e. D03 NiHf3, NiTi3 HfTi3, and B2 NiHf, NiTi, HfTi, and two ternary compounds, i.e. C1b NiHfTi, L21 Ni2HfTi, are calculated, respectively. It is found that, for the eight binary compounds studied, the calculated lattice constants and cohesion energies are in excellent agreement with those directly acquired from ab initio calculations and that the elastic constants and bulk moduli calculated from the potential are also qualitatively consistent with the results from ab initio calculations.