A single-volume approach for vacancy formation thermodynamics calculations

¹ Materials Center Leoben Forschung GmbH (MCL) - Roseggerstraße 12, A-8700 Leoben, Austria
² University of Graz, Institute of Physics, NAWI Graz - Universitätsplatz 5, A-8010 Graz, Austria
³ Metal Physics Department, National Technical University of Ukraine “Kyiv Polytechnic Institute” Kyiv 03056, Ukraine
⁴ Centre for Materials Science and Nanotechnology, University of Oslo - P. O. Box 1048 Blindern, NO-0316 Oslo, Norway
⁵ Department of Materials Science and Engineering, KTH Royal Institute of Technology SE-100 44 Stockholm, Sweden
⁶ Institute of Quantum Materials Science - Ekaterinburg 620107, Russia
⁷ Magnitogorsk State Technical University - Magnitogorsk 455000, Russia

Received: 17 June 2016
Accepted: 25 October 2016

Abstract

The vacancy formation Gibbs free energy, enthalpy and entropy in fcc Al, Ag, Pd, Cu, and bcc Mo are determined by first-principles calculations using the quasi-harmonic approximation to account for vibrational contributions. We show that the Gibbs free energy can be determined with sufficient accuracy in a single-volume approach using the fixed equilibrium volume of the defect-free supercell. Although the partial contributions to the Gibbs free energy, namely, the formation enthalpy and entropy exhibit substantial errors when obtained directly in this approach, they can be computed from the Gibbs free energy using the proper thermodynamic relations. Compared to experimental data, the temperature dependence of the vacancy formation Gibbs free energy is accounted for at low temperatures, while it overestimates the measurements at high temperature, which is attributed to the neglect of anharmonic effects.