Long-range empirical potential for the bcc structured transition metals

A long-range empirical potential is developed for bcc transition metals in the present study and successfully applied to Fe, Mo, W, V, Nb, and Ta. It is found that the lattice constants, cohesive energies, elastic constants, vacancy formation energies, structural stabilities, and surface energies derived from the present model match well with the experimental values or ab initio calculations. More importantly, the energies and forces represented by the present model can smoothly go to zero at cutoff radius, thus completely avoiding the unphysical behaviors to emerge in simulations.

Figure 1

Total energy and its first derivative as a function of lattice constant calculated from the FS potential (Ref. 1) and EAM potential (Ref. 2) for bcc Ta.

Figure 2

Total energy $\left(E_{\mathrm{total}}\right)$, repulsive term $\left(E^{\mathrm{R}}\right)$, $n$-body term $\left(E^{\mathrm{B}}\right)$, and the first derivative of total energy as a function of lattice constant for bcc Ta.

Figure 3

The relationships of pressure vs relative volume obtained from the present model and experiments, respectively, for Fe, Mo, W, V, Nb, and Ta. The solid curves are from the present model, and the scattered points are from experiments. For each curve, the value of the cross point with the vertical axis is zero. The experimental values are from Refs. 23, 24, 25, 26.