Mechanical behavior, specifically plastic deformation at low and high temperatures in metal alloys is governed by the motion of dislocations. 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 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's 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. This methodology has explained solid-solution softening in molybdenum (explaining a 50-year-old mystery of metallurgy), dislocation cores in aluminum and titanium, and provided a wide range of mechanical behavior predictions for magnesium alloys.
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