Towards a Statistical Theory of Texture Evolution

Under standard processing conditions, many materials possess polycrystalline microstructures composed of a large number of small monocrystalline grains separated by grain boundaries. The energetics and connectivity of the grain boundaries network plays a crucial role in defining the properties of a material across a wide range of scales. A central problem in materials science is to develop technologies capable of producing arrangements of grains—textures—that provide for a desired set of material properties. One of the most challenging aspects of this problem is to understand the role of topological reconfigurations during coarsening. In this paper, we study mesoscopic behavior of a one-dimensional grain-boundary system and investigate the possibility of modeling texture evolution. We propose a stochastic framework based on the theory of continuous time random walks that may be used to model this system and compare the predictions of the corresponding evolution equations with numerical simulations of a full grain-boundary system.