The influence of size on the composition of nano-precipitates in coherent precipitation

Various experiments show that the solute content in small coherent precipitates in their early stages of growth-coarsening is significantly lower than its equilibrium value and gradually increases with the particle size until equilibrium composition is reached. In this paper, we investigate the thermodynamic stability of a mono-dispersed assembly of coherent precipitates in a finite matrix by minimizing the total free energy of the system to account for this size effect observed for nano-phases. Both interfacial energy and misfit elastic energy were taken into account and simple regular solid solutions were considered for both phases. It is found that for small sizes, precipitates with a low solute content are favoured energetically. The solute content in precipitates decreases when increasing either interfacial energy or coherency misfit. The solute concentration in nano-particles is observed to increase with size. The asymptotic composition remains under the equilibrium concentration even for small misfits. The model was confronted to atom probe tomography experiments performed in FeCr system. Predictions exhibit a composition trend with precipitate size that is in good agreement with experiments.