Influence of phonon and electron excitations on the free energy of defect clusters in solids: A first-principles study

摘要

Although many processes of nanostructure evolution in solids occur atelevated temperatures, basic data obtained from ground state energetics areused in the modeling of these phenomena. In order to illustrate the effect ofphonon and electron excitations on the free binding energy of defect clusters,first-principles calculations are performed for vacancy-solute pairs as well asvacancy and Cu dimers, trimers, and quadromers in bcc Fe. Based on theequilibrium atomic positions determined by the relaxation of the supercell withthe defect in the ground state under constant volume (CV) as well as zeropressure (ZP) conditions, the contribution of phonon excitations to the freebinding energy is calculated within the framework of the harmonicapproximation. The contribution of electron excitations is obtained using thecorresponding ground state data for the electronic density of states.Quasi-harmonic corrections to the ZP-based results do not yield significantchanges in the temperature range relevant for applications. At 1000 K themaximum decrease/increase of the ZP-based data for the absolute value of thefree binding energy with respect to the corresponding ground state value isfound for the vacancy-W (43%) / vacancy-Mn (35%) pair. These results clearlydemonstrate that contributions of phonon and electron excitation to the freebinding energy of the defect clusters are generally not negligible. The generalbehavior of the free binding energy of vacancy and Cu dimers, trimers andquadromers is similar to that of the vacancy-solute pairs. The results obtainedin this work are of general importance for studies on the thermodynamics andkinetics of defect clusters in solids.