DFT study on the contribution of phonon and electron excitations to the free energy of embedded defect clusters

Modeling of nanostructure evolution in solids requires the knowledge of comprehensive data on the properties of point defects and defect clusters. Since most processes occur at elevated temperatures not only the energetics of the defects in the ground state but also their temperature-dependent free energy must be known. The determination of the contribution of phonon and electron excitations to the free binding energy of small embedded defect clusters is illustrated in the case of bcc-Fe. The fundamentals of the first-principles calculation method have been recently described [1]. First of all, the ground state properties of the clusters are determined under zero pressure (ZP) conditions. Second, the phonon contribution to the free energy is calculated within the harmonic approximation using the equilibrium atomic positions determined in the ground state. The application of a quasi-harmonic correction to the ZP-based data does not modify the results significantly. Therefore the obtained data are valid under zero-pressure conditions at higher temperatures than in the framework of the purely harmonic approach. These conditions are usually realized in experiments. Third, the contribution of electron excitations to the defect free energy is calculated. The electron excitations can lead to an additional deviation of the total free energy from the ground state value or can compensate the deviation caused by the phonon contribution. Depending on the examples considered the free binding energy of a defect cluster can differ significantly from the ground state value.
[1] D. Murali, M. Posselt, M. Schiwarth, Phys. Rev. B 92, 064103 (2015).