Texture mediated grain boundary network design in two dimensions

Abstract

While materials design in the context of texture dependent properties is well developed, theoretical tools for microstructure design in the context of grain boundary sensitive properties have not yet been established. In the present work, we present an invertible relationship between texture and grain boundary network structure for the case of spatially uncorrelated twodimensional textures. By exploiting this connection, we develop mathematical tools that permit the rigorous optimization of grain boundary network structure. Using a specific multi-objective materials design case study involving elastic, plastic and kinetic properties, we illustrate the utility of this texture mediated approach to grain boundary network design. We obtain a microstructure that minimizes grain boundary network diffusivity while simultaneously improving yield strength by an amount equal to half of the theoretically possible range. The theoretical tools developed here could complement experimental grain boundary engineering efforts to help accelerate the discovery of materials with improved performance.

Towards achieving ultrahigh thermal stability of fine-grained alumina fibers via segregation-induced ordered superstructures

“…Many properties of engineered materials are closely related to grain boundary structure and morphology 1 . Grain boundary design plays a crucial role in materials development and has been an effective way to improve the stability of nanomaterials over the past decades [2][3][4][5][6][7] . Fine-crystal nanomaterials are known to have a strong tendency to coarsen at high temperatures 8,9 , which dramatically limits their applications in the high-temperature domain.…”

Texture mediated grain boundary network design in three dimensions

“…For example, all textures that differ only by a rotation, r, e.g. f (q) and f (qr), will yield the same TJDF (this also implies that, given a TJDF, it is only possible to recover the corresponding ODF modulo a rotation operation) [39]. However, under the assumption that grain orientations are spatially uncorrelated we obtain the mapping M (1) H → M (3) H , for which every ODF maps to only one TJDF.…”

“…A formula for this mapping, developed in the context of the Fourier basis, was given in [6]. In the Dirac basis, this mapping takes a particularly simple form and is given by [39]:…”

“…Crystallographic symmetry induces equivalence relations on orientations according to q ∼ qc i ∀ c i ∈ C . We denote the set of all such equivalence relations by C. In addition to crystallographic symmetry there are distinct triple junction symmetries as described in [6,39], which induce triple junction equivalence relations. The set of all triple junc-tion equivalence relations was given explicitly by Eq.…”