We propose an extended Finnis-Sinclair (FS) potential by extending the repulsive term into a sextic polynomial for enhancing the repulsive interaction and adding a quartic term to describe the electronic density function. It turns out that for bcc metals the proposed potential not only overcomes the 'soft' behaviour of the original FS potential, but also performs better than the modified FS one by Ackland et al, and that for fcc metals the proposed potential is able to reproduce the lattice constants, cohesive energies, elastic constant, vacancy formation energies, equations of state, pressure-volume relationships, melting points and melting heats. Moreover, for some fcc-bcc systems, e.g. the Agrefractory metal systems, the lattice constants, cohesive energies and elastic constants of some alloys are reproduced by the proposed potential and are quite compatible with those directly determined by ab initio calculations.

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We propose a two-parameter binomial truncation function for the secondmoment 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. L1 2 Ni 3 Hf, NiHf 3 , Ni 3 Ti, NiTi 3 , Hf 3 Ti and HfTi 3 , are firstly acquired by ab initio calculations and then employed to derive the binomialtruncated 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. D0 3 NiHf 3 , NiTi 3 HfTi 3 , and B2 NiHf, NiTi, HfTi, and two ternary compounds, i.e. C1 b NiHfTi, L2 1 Ni 2 HfTi, 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.

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