Grain boundary network design

Abstract

Grain boundaries in polycrystals form a complex interconnected network of intercrystalline interfaces. The crystallographic character of individual grain boundaries and the network structure of the grain boundary ensemble have been experimentally observed to have a strong influence on many materials properties. This observation suggests that if we could control the types of grain boundaries present in a polycrystal and their spatial arrangement then it would be possible to dramatically improve the properties of polycrystalline materials and tailor them to specific engineering applications. However, there are a number of major obstacles that have, until now, precluded the realization of this opportunity: (1) methods capable of simultaneously quantifying the crystallographic and topological structure of grain boundary networks do not exist; (2) theoretical models relating grain boundary network structure to physical properties have not yet been developed; and, consequently, (3) there are no techniques to quantitatively identify grain boundary network structures that would be beneficial for a given property. In this thesis I address these obstacles by first developing a new statistical description of grain boundary network structure called the triple junction distribution function (TJDF), which encodes both crystallographic and topological information. I establish new results regarding the physical symmetries of triple junctions and find a relationship between crystallographic texture and grain boundary network structure. I then use the TJDF to develop a model for the effective diffusivity of a grain boundary network. Finally, using the relationship between texture and grain boundary network structure that I develop, I describe a method for texture-mediated grain boundary network design. This process permits the theoretical design of grain boundary networks with properties tailored to a given engineering application and is applicable to any polycrystalline material. I demonstrate the potential of this technique by application to a specific design problem involving competing design objectives for mechanical and kinetic materials properties. The result is a designed microstructure that is predicted to outperform an isotropic polycrystal by seven orders of magnitude.