Vibrational Contribution on Nucleation Free Energy of Cu Precipitates in Fe-Cu System

Abstract

The thermal vibrational effects on the nucleation free energy of the bcc-Cu precipitates in the Fe-Cu system have been explored. Thermal expansion coefficients of bcc-Fe have been correctly predicted by the quasi-harmonic approximation, using the phonon dispersions calculated on the basis of the density functional theory. The Einstein model with a temperature-dependent bulk modulus shows free energy values almost identical to the quasi-harmonic predictions. The vibrational contribution obtained from the Einstein model is reduced to 1.6 × 10−21 J (10 meV), which is almost negligible for the free energy change of cluster nucleation.