Evaluation of vacancy formation energy for BCC-, FCC-, and HCP-metals using density functional theory

Introduction. Vacancies are among the crystal lattice defects that have a significant effect on the structural transformations processes during thermal, chemical-thermal, thermomechanical, and other types of alloys treatment. The vacancy formation energy is one of the most important parameters used to describe diffusion processes. An effective approach to its definition is based on the use of the density functional theory (DFT). The main advantage of this method is to carry out computations without any parameters defined empirically. The purpose of the work is to estimate vacancy formation energy of BCC-, FCC- and HCP-metals widely used in mechanical engineering and to compare these findings obtained using various exchange-correlation functionals (GGA and meta-GGA). Computation procedure. The computations were carried out using the projector-augmented wave method using the GPAW code and the atomic simulation environment (ASE). The Perdew-Burke-Ernzerhof, MGGAC and rMGGAC functionals were used. The wave functions were described by plane waves within simulations. Vacancies formation energy was evaluated using supercells approach with a size 3 × 3 × 3. Computations were carried out for BCC-metals (Li, Na, K, V, Cr, Fe, Rb, Nb, Mo, Cs, Ta, W), FCC-metals (Al, Ni, Cu, Rh, Pd, Ag, Ir, Pt, Au, Pb, Co) and HCP-metals (Be, Ti, Zr, Mg, Sc, Zn, Y, Ru, Cd, Hf, Os, Co, Re). Results and discussion. A comparison of the defined vacancy formation energies indicates the validity of the following ratio of values: . The values obtained using the open source GPAW code are characterized by the same patterns as for widely spread commercially distributed program VASP. It was revealed that the use of the PBE and MGGAC functionals leads to a slight deviation relative to the experimentally determined vacancies formation energy in contrast to the computations using rMGGAC.