Phase and defect diagrams based on spectral grain boundary segregation: A regular solution approach

Abstract

Recent works have proposed the treatment of alloy defect states with thermodynamics analogous to phase thermodynamics, so they can be analyzed in a manner that is comparable to bulk phase diagrams. We refer to such diagrams containing both bulk phase and defect state information as “phase-and-defect diagrams.” Segregated grain boundaries (GBs) are an example of one such defect state, which enable, for example, the stabilization of nanocrystalline alloys. The recent development of spectral thermodynamic isotherms has demonstrated that a fully spectral description, which captures the complete distribution of local atomic environments in the grain boundary network, is necessary for accurate modeling of segregation behavior. To our knowledge, there is currently no spectral free energy formulation from which a phase-and-defect diagram of the segregated polycrystalline state can be produced. In this work, we present a spectral regular solution model of grain boundary segregation, from which we derive an analytical free energy function for the segregated polycrystalline state. We then use this free energy representation to construct a phase-and-defect diagram for a hypothetical alloy system, providing a framework for future efforts in developing spectral phase-and-defect diagrams.