  The first-principles calculation of contributions of phonon and electron
excitations to free formation, binding, and migration energies of defects is
illustrated in the case of bcc-Fe. First of all, the ground state properties of
the vacancy, the foreign atoms Cu, Y, Ti, Cr, Mn, Ni, V, Mo, Si, Al, Co, O, and
the O-vacancy pair are determined under constant volume (CV) as well as zero
pressure (ZP) conditions. Second, the phonon contribution to defect free
energies is calculated within the harmonic approximation using the equilibrium
atomic positions determined in the ground state under CV and ZP conditions.
Additionally, quasi-harmonic corrections are applied to the ZP-based data. A
simple transformation similar to the quasi-harmonic approach is found between
the CV- and ZP-based frequencies. Therefore, it is not necessary to calculate
these quantities and the corresponding defect free energies separately. In
contrast to ground state energetics the CV- and ZP-based defect free energies
do not become equal with increasing supercell size. Third, it was found that
the contribution of electron excitations to the defect free energy 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. Finally,
self-diffusion via the vacancy mechanism is investigated. The ratio of the
respective CV- and ZP-based results for the vacancy diffusivity is nearly equal
to the reciprocal of that for the equilibrium concentration. This behaviour
leads to almost identical CV- and ZP-based values for the self-diffusion
coefficient. Obviously, this agreement is accidental. The consideration of the
temperature dependence of the magnetization yields self-diffusion data in very
good agreement with experiments.
