Free energy of a⟨110⟩dumbbell interstitial defect in bcc Fe: Harmonic and anharmonic contributions

Abstract

The stability of interstitial defect and dislocation structures in bcc Fe as a function of temperature is believed to play a crucial role in determining defect evolution under irradiation conditions. The vibrational properties of defects constitute one contribution to the corresponding energetics and much work has been done within the harmonic approximation to determine the vibrational formation free energy and formation entropy of such defects. Defects can however exhibit strong local strain fields that break the cubic symmetry of the bcc lattice leading to large anharmonicities and a breakdown of the harmonic approximation as an accurate means to calculate vibrational thermodynamic quantities. Moreover, if defect diffusion is active at a time scale comparable to an atomic vibration, strong anharmonicities will always be present at any finite temperature. The current work investigates the vibrational free energy and entropy of the $⟨110⟩$ self-interstitial dumbbell defect in bcc Fe using both harmonic and anharmonic free-energy calculation methods for a range of modern empirical potentials. It is found that depending on the empirical potential and for temperatures where diffusion is limited, the harmonic approximation is justified especially for empirical potentials that have been fitted to third-order elastic constants. The unique applicability range of such calculations for bcc Fe is also discussed given that with rising temperature spin fluctuations become increasingly important ultimately leading to a softening of the 110 shear modulus and to the $\ensuremath{\alpha}\text{-bcc}/\ensuremath{\gamma}\text{-bcc}$ structural phase transformation.