Vacancy formation enthalpy at high pressures in tantalum

Using a mixed basis pseudopotential method, total energy calculations were performed to obtain the enthalpy of vacancy formation in Ta as a function of pressure, which is important for understanding the effects of pressure on mechanical properties. The vacancy formation enthalpy is found to increase from 2.95 eV at ambient pressures to 12.86 eV at 300 GPa, and the vacancy formation volume decreases from being 53±5% of the bulk volume per atom at ambient pressure to 20±2% at 300 GPa, for a 54-atom supercell. We also show that there is a strong correspondence between the vacancy formation enthalpy and the melting temperature in Ta. The effects of compression on mechanical properties of transition metals are not easily addressed experimentally, yet are important in modelling dynamical behaviour of materials under compressive loads. This paper addresses for the first time the pressure dependence of the enthalpy of vacancy formation in tantalum. Ta remains stable in the simple bodycentred cubic (bcc) structure over a wide pressure range [1] allowing study of the effects of compression on vacancy formation in a transition metal over a wide compression range without the complications of structural changes. High thermal, mechanical and chemical stability also makes Ta an important technological material [2]. The role of vacancies in controlling plasticity through the mobility of dislocations has not been fully explored. The vacancies allow the dislocations to overcome the interstitials and impurities by facilitating their climb to a plane normal to the glide plane by self-diffusion of atoms [3]. Moreover, dislocation glide depends upon double-kink formation [4], and though present calculations neglect vacancies in the calculation of double-kink formation energy [5], it is greatly modified by vacancies [6]. Computations of the vacancy formation enthalpy and its pressure dependence provide us with the vacancy concentration, which in turn determines the effects of vacancies on the dislocation motion. Small changes in the vacancy formation 0953-8984/03/060855+07$30.00 © 2003 IOP Publishing Ltd Printed in the UK 855 856 S Mukherjee et al enthalpy with pressure lead to large changes in vacancy concentration due to the exponential dependence of the vacancy concentration on the enthalpy. The vacancy formation enthalpy [7], Hvac, is given by Hvac = Evac(P) + P f vac, (1) where Evac is the vacancy formation energy and f vac is the vacancy formation volume at pressure P . We find the vacancy formation energy by performing total energy calculations for supercells with one atom removed, and compare the energy of the N-atom supercell with the (N − 1)-atom defective supercell. The atomic positions after the atom is removed are relaxed to minimize the total energy using analytic forces. Expressing Evac and f vac in terms of the system internal energy and volume one obtains Evac(P) = E(N − 1, P) − N − 1 N E(N, P) (2)