Phase-and-Defect Diagrams for Polycrystalline Grain Boundary Segregation

Abstract

Defect engineering provides access to a much larger range of material properties and is particularly necessary when designing any high-defect density material such as nanocrystalline (NC) alloys. Traditionally, bulk equilibrium phases have been considered in a decoupled manner from defects, such as solute and segregated atoms, dislocations, and grain boundaries. In recent years, a push has been made to treat defects as “defect states” in a manner analogous to bulk phases so they can be analyzed alongside existing bulk equilibrium phase diagrams – a treatment I refer to here as “phase-and-defect” diagrams. Segregated grain boundaries (GBs) are one such defect phase, and recent progress has indicated that spectral information, which describes the full distribution of available atomic environments, is required to rigorously understand segregated polycrystalline grain boundaries. However, models proposed prior to this work are primarily thermodynamic isotherms, which suffer from several limitations that prevent their use in the development of phase-and-defect diagrams. Existing spectral isotherms often use scalar assumptions to address solute-solute interactions, or are not atomistically informed, and have not been constructed from analytical free energy functions. For this reason, they cannot be used to construct fully spectral phase-and-defect diagrams. Furthermore, existing databases of spectral parameters contain only dilute limit information, limiting the accessibility of spectral segregation predictions at finite concentrations. In this work, I take the following steps to address this need. First, I present a thermodynamic model that captures the spectral nature of both the segregation and solute interaction energies, and I describe an atomistic, physically motivated method to measure the full spectrum of GB solute interaction energies in a polycrystal. Then, I present the analytical framework for a spectral regular solution model of segregated polycrystals. I use this framework to derive a fully spectral free energy function and demonstrate how it can be used to develop a self-consistent phase-and-defect diagram which considers the bulk regular solution and the segregated polycrystalline defect state, and which shows significant improvement of the spectral model over traditional scalar representations. Finally, I develop an accelerated framework for predicting spectral solute-solute interactions, using a modified “bond-focused” local atomic environment (LAE) representation to construct descriptors for nearest neighbor pairs in the GB. I rigorously demonstrate its use for multiple binary alloys, and I then apply this accelerated framework to approximately 200 available embedded atom method (EAM) potentials to construct a large-scale database of spectral parameters for binary alloys beyond the dilute limit. This work makes accessible, for the first time, fully spectral segregation parameters at finite concentrations. Additionally, it provides a framework for incorporating those estimates into existing CALPHAD methodology, allowing the production of phase-and-defect diagrams for segregated polycrystals. In doing so, I hope that this work will improve the community’s ability to engineer stable nanocrystalline alloys and other defect states in the future.