Cu nanoprecipitate morphologies and interfacial energy densities in bcc Fe from density functional theory (DFT)

We use quantum mechanical ab initio simulation to inform a model which predicts the structures of coherent Cu nanoprecipitates that are thought to form in low-alloy reactor pressure vessel (RPV) steels. Using density functional theory (DFT) we calculated the interfacial energy densities of {1 0 0}, {1 1 0}, {1 1 1}, {2 1 0}, {2 1 1} and {2 2 1} orientated Fe-Cu interfaces. These energy density values were used in an optimisation model to predict low energy Cu nanoprecipitate geometries for nominal radii ranging from 1 to 5 nm. Strain states parallel to the Fe-Cu interface were calculated using an embedded atom method (EAM) potential for similarly sized Cu nanoprecipitates. Fe-Cu interfacial energy densities under equivalent strains were calculated using DFT allowing comparison with the predictions of the EAM potential. The DFT calculations revealed the lowest energy Fe-Cu interface orientation to be the {1 1 0}. Accordingly, the geometry prediction optimisations found that regardless of size the predicted Cu nanoprecipitate surface geometries were dominated by the {1 1 0} orientation. Notably, as the Cu nanoprecipitates increased in size the ratio of the surface made up of non-{1 1 0} orientations was observed to proportionally increase. This allows the nanoprecipitate to take a more spherical form so reducing its total surface area. Additionally, the Fe-Cu interface strains predicted by the EAM potential for all Cu nanoprecipitate radii are sufficiently small that they do not significantly alter the calculated interfacial energy density values. This finding suggests interfacial strain does not play a significant role in determining the morphology of Cu nanoprecipitates.