Steering of a grain boundary with strain, electromagnetic field, and stochastic boundary excitation

Abstract

In a previous work [Lusk et al., J. Appl. Phys. 99, 023505 (2006)], grain boundary and triple junction motion control using a laser spot was simulated within a noninertial, two-dimensional setting. That work focused on the physical process by which these defect structures could be induced to move. The present work seeks to begin the development of a control theory for such steering operations. To this end, a model system is introduced wherein the control of grain boundaries is abstracted into a piecewise homogeneous chain of harmonic oscillators. The interface demarcates regions of differing elastic stiffness and accretes via isothermal fluctuation theory. Energy is controlled via Langevin excitation and viscous damping applied to a single boundary mass. Steering of the grain boundary is achieved via applied strain and body forces. A closed-form relationship is established which allows the time-dependent probability distribution of the interface position to be expressed in terms of temperature, strain, body force, number of masses, and one dimensionless ratio. This analytical result is used to validate the predictions of molecular dynamics and dissipative particle dynamics (DPD) simulations. The DPD simulator is then treated as a physical experiment, and interface control via both constant and time-varying actuation is explored, with time-varying trajectories calculated using the analytic expression for interface position distribution.