Grain boundary structure-property model inference using polycrystals: The underdetermined case

Abstract Historically, attempts to correlate grain boundary (GB) structure and properties have relied on experimental measurements and computational calculations performed on bicrystals. While the resulting data can be precise, it is usually severely limited in quantity due to the cost and/or computational expense of sampling the full 5D GB character space. As a result, existing data is concentrated around highly-symmetric sub-regions. In contrast, polycrystals are ubiquitous, inexpensive, and contain a broad range of GB characters. However, extracting GB properties from the effective properties of polycrystals requires the solution of an inverse problem. In this work, we present a Bayesian framework, that we call GB property localization, to address both of these challenges by facilitating the inference of GB structure-property models from indirect polycrystal measurements and severely limited data (i.e. when the system is strongly underdetermined). The method naturally provides uncertainty quantification for the resulting inferences. We present the results of validation tests using 1DOF and 3DOF structure-property models for GB diffusivity in 2D (or columnar) microstructures, and we investigate the influence of the number of observations and the number of grains in a polycrystal on the inference quality. We identify a transition in the preferred type of data as a function of the number of observations: when data is abundant bicrystals lead to more accurate inferences; however when data is severely limited, polycrystals may provide more accurate results.