Free energy of embedded nanoclusters: Role of the configurational contributions

Diffusion and reaction processes during thermal treatment or particle irradiation can cause the formation of nanoclusters embedded in the host material. This modification often leads to the change of materials properties. Coarse-grained methods such as object kinetic Monte Carlo simulations and rate theory are well suited to simulate the nanocluster evolution on time and length scales easily accessible by experiments. However, these methods need a number of input parameters. One of the most important is the free binding energy of a monomer to a cluster which can be hardly obtained by measurements but can be provided by atomistic simulations. This quantity is calculated using the free formation energy of the clusters which consists not only of the formation energy but also of vibrational and configurational contributions. The present work is focused on the evaluation of the configurational part of the free formation energy. As characteristic examples coherent nanoclusters in bcc-Fe containing Cu and Ni are considered. First-principle data from literature are used to describe the interactions between the atoms. In a first step the most stable cluster configurations at T=0 are determined by Metropolis Monte Carlo simulations and their formation and binding energies are calculated. Second, a modified Wang-Landau Monte Carlo method is employed in order to determine the contribution of all possible geometrical configurations of nanoclusters to the free formation energy. Finally, the total and monomer free binding energies are calculated. It is shown that the configurational contributions to the free energy cannot be neglected if the cluster formation energy is relatively low. The calculation scheme applied in this work can be extended to other types of embedded nanoclusters in solids. Further investigations are required in order to estimate the vibrational contribution to the free energy and to perform a comparison with the configurational part.