Applied Math Seminar: Lattice Green function calculations in the presence of a dislocation

Seminar | April 4 | 4-5 p.m. | 740 Evans Hall

 Dallas Trinkle, University Of Illinois at Urbana-Champaign

 Department of Mathematics

Mechanical behavior, specifically plastic deformation at low and high temperatures in metal alloys is governed by the motion of dislocations: topological line defects in a crystal. Dislocations in crystalline materials were hypothesized nearly eighty years ago, and their experimental and theoretical study has provided powerful tools for modern materials engineering. While the long-range elastic field of a dislocation is known and straight-forward to compute, many of the strongest effects of dislocations occur in the "core"–the center of the dislocation–where elasticity breaks down, and new chemical bonding environments can often make even empirical potential descriptions suspect. Hence, there is much effort to use the accuracy of modern quantum mechanical methods (like density-functional theory) to study dislocation cores accurately, as well as their interaction with other defects, such as solutes and boundaries. While there are a variety of possible coupling or "multiscale" techniques available, I will focus on flexible boundary conditions, which use the lattice Green function to couple electronic structure to an infinite harmonic bulk; this approach greatly simplifies many "hand-shaking" problems, and generally provides a computationally efficient approach. We recently developed a new numerical approach that accounts for the topology change of a dislocation. This methodology has explained solid-solution softening in molybdenum (explaining a 50-year-old mystery of metallurgy), dislocation cores in aluminum, titanium, and iron, and provided a wide range of mechanical behavior predictions for magnesium alloys, and recently the dislocation core structures for a 1/2< 110 > Ni screw dislocation and a < 110 > Ni3Al screw superdislocation.