Vibrational contribution to the thermodynamics of nanosized precipitates: vacancy-copper clusters in bcc-Fe

TL;DR

This study investigates how lattice vibrations influence the thermodynamics of nanosized vacancy-copper clusters in bcc-Fe, using a combination of simulations and phonon density of states calculations to improve understanding of defect energetics.

Contribution

It introduces a method to incorporate vibrational effects into thermodynamic models of nanosized clusters in bcc-Fe, enhancing previous approaches with phonon calculations and improved potentials.

Findings

Vibrational effects significantly impact cluster free energies.

The results align with previous empirical and first-principle data.

Vibrational contributions are integrated into analytical models for kinetic simulations.

Abstract

Within the harmonic approximation, the effects of lattice vibration on the thermodynamics of nano-sized coherent clusters in bcc-Fe consisting of vacancies and/or copper are investigated. A combination of on-lattice simulated annealing based on Metropolis Monte Carlo simulations and off-lattice relaxation by Molecular Dynamics is applied to obtain the most stable cluster configurations at T = 0 K. The most recent interatomic potential built within the framework of the embedded atom method for the Fe-Cu system is used. The vibrational part of the total free energy of defect clusters in bcc-Fe is calculated using their phonon density of states. The total free energy of pure bcc-Fe and fcc-Cu as well as the total formation free energy and the total binding free energy of the vacancy-copper clusters are determined for finite temperatures. Our results are compared with the available data from previous investigations performed using empirical many-body interatomic potentials and first-principle methods. For further applications in rate theory and object kinetic Monte Carlo simulations, the vibrational effects evaluated in the present study are included in the previously derived analytical fits based on the classical capillary model.