Ab-initio grain boundary thermodynamics beyond the dilute limit

Ab-initio calculations are frequently used to compute segregation energies and to investigate the segregation behavior of alloying elements in metals. But the segregation is considered mostly in the dilute limit, without considering interactions between solute atoms. Therefore, a formulation of the grain boundary Gibbs free energy within the compound energy formalism is proposed, which allows to analyze the segregation beyond the dilute limit and to establish a link between DFT segregation energies, the grain boundary energy and the expected excess. The segregation of Ti in bcc bulk is studied and we perform density functional theory calculations to obtain endmember energies. For a complete description of energetics, we train a moment tensor potential to parameterize the model. The segregation of Ti in bcc W bulk is studied and the symmetrical Σ3[110](1̄11) grain boundary is studied in detail. Our results show that the bulk and grain boundary thermodynamics need to be considered simultaneously when calculating the segregation beyond the dilute limit. The segregation of Ti changes from an anti-segregation to a segregation behavior with increasing Ti content. Although an increased Ti content reduces the grain boundary energy, the grain boundary is still higher in energy than the bulk and no thermodynamic stabilization of nanocrystalline W-Ti is expected. The results are compared to different models from literature.