Contribution of Lattice Vibrations to the Thermodynamics of Vacancy Clusters in bcc-Fe

During the long operation time of nuclear reactors, vacancies and vacancy clusters (VC) may play an intermediary role in the formation of copper-rich precipitates (CRP), which are considered to be the main cause of hardening and embrittlement of Cu-bearing RPV steels since these defects act as obstacles to dislocation motion within the grains of polycrystalline bcc-Fe. The effect of irradiation on the microstructure of RPV steels and consequently on their mechanical properties is a multiscale phenomenon. The evolution of VCs over realistic time and length scales can be effectively studied by rate theory. However, many parameters used, such as the free binding energies of precipitates, are not very well known from experimental investigations. Atomic-level computer simulations can provide these data. The few previous attempts to include the effect of lattice vibrations into thermodynamics of Cu-precipitates in bcc-Fe did not lead to consistent results [1, 2].The present investigations are focused on the phonon contributions to the thermodynamics of VCs. In all calculations the Mendelev potential for bcc Fe is used [3]. Molecular dynamics simulations at different temperatures are performed in order to determine the velocity autocorrelation function which can be transformed into the vibrational density of states (VDOS). VDOS is also obtained using dynamical matrix method under harmonic approximation. This quantity is then used to calculate the contributions of lattice vibrations to the total free energy of bcc-Fe as well as to the free energy of formation and free binding energy of VCs. The vibrational contribution to the total free energy of bcc-Fe is compared with available CALPHAD data and with the values obtained using other interatomic potentials. At a temperature of 600 K the vibrational contribution to the free binding energy leads to a reduction of the absolute value of the corresponding zero-Kelvin free binding energy of the VC by about 10%.

[1] K. Yuge, A. Seko, I. Tanaka, S. R. Nishitani, Phys. Rev. B 72 (2005) 174201.
[2] K. Yuge, A. Seko, K. Kobayashi, T. Tatsuoka, S. R. Nishitani, H. Adachi, Mater. Trans. 45 (2004) 1473.
[3] M. I. Mendelev, S. Han, D. J. Srolovitz, G. Ackland, D. Y. Sun, M. Asta, Philo. Mag. 83 (2003) 3977.