Angular forces and melting in bcc transition metals: A case study of molybdenum

Using multi-ion interatomic potentials derived from first-principles generalized pseudopotential theory (GPT) together with molecular-dynamics (MD) simulation, a detailed study of melting and related high-temperature solid and liquid properties in molybdenum has been performed. The energetics in such bcc transition metals are dominated by d-state interactions that give rise to both many-body angular forces and enhanced electron-thermal contributions. The angular forces are accounted for in the GPT through explicit three- and four-ion potentials, ${\mathit{v}}_3$ and ${\mathit{v}}_4$, which in the present work are applied in analytic model-GPT (MGPT) form. With the MGPT potentials, ion-thermal melting in Mo has been investigated both mechanically, by cycling up and down through the observed MD melting point at constant volume, and thermodynamically, by calculating solid and liquid free energies. In the former approach, parallel MD simulations have also been done with a corresponding effective-pair potential ${\mathit{v}}_2^{\mathrm{eff}}$ in which the angular dependence of ${\mathit{v}}_3$ and ${\mathit{v}}_4$ has been averaged. The multi-ion angular forces, which are essential to an accurate description of the bcc solid, are found to lower the dynamically observed melting point by about 1000 K. Above the melting transition, however, ${\mathit{v}}_2^{\mathrm{eff}}$ gives a reasonbly good account of the structure and thermal energy of the liquid and the accuracy of this description improves with increasing temperature.