# The Vacancy Formation Energy in the Quasi-Harmonic Approximation from First Principles Calculations

## DOI:

https://doi.org/10.20535/1810-0546.2015.2.91237## Keywords:

Density functional theory, Vacancy formation energy, First principles, Quasi-harmonic approximation## Abstract

**Background.** This work is related to the theoretical calculation of the vacancy formation energy in the context of finding an answer to two unsolved questions. Firstly, there is no single answer to the question of calculations accuracy of the vacancy formation energy. Secondly, the existing phenomenological theories tacitly assume that the vacancy formation energy and entropy of vacancy formation do not depend on temperature.

**Objective.** The aim of the study was to investigate the effect of temperature factor on the free energy of vacancy formation and its components in a number of metals within the quasi-harmonic approximation.

**Methods.** The vacancy formation energy and entropy in FCC Al, Ag, and Pd are determined as a function of temperature using ab initio methods within a quasi-harmonic approximation.

**Results.** It was shown, that the vacancy formation energy substantially increases with temperature in all cases, which is related to the thermal lattice expansion. Such increase of the vacancy formation energy is compensated by the vibrational vacancy formation entropy contribution. The latter appears to be strongly increasing with temperature in the case of Mo.

**Conclusions.**However, a thermodynamic analysis shows that such increase of vacancy formation energy in the process of calculation is largely underestimated. The latter is compensated by contribution from vibrating entropy of vacancy formation and strongly increases with temperature. Such underestimation is related to certain problems in quasi-harmonic approximation.

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