We will consider interactions between defects of the same type and of different types, which lead to collective behavior on the mesoscale.

Boundaries have an overarching role in the determination of material properties and the materials literature is abundant with strategies for controlling their formation and stability.  For example, thermomechanical processing paths for many classes of metallic materials are designed to introduce a high density of dislocations that subsequently reorganize to produce low angle boundaries, special boundaries (e.g., twins) or fine, recrystallized grains.  The grain size of minerals is an important parameter that controls mantle circulation.

For example, experiments have shown that the ringwoodite to bridgmanite phase transition involves recrystallization, and the grain size of bridgmanite systematically increases with increasing duration and time. This implies that the small grain size in subducted slabs may significantly reduce their creep strength, which could cause slab stagnation in the shallow lower mantle.  Additive manufacturing of metals provides a recent example where a better predictive capability for the collective behavior of dislocations and formation of low angle boundaries could narrow the prohibitively large design space for the print process parameters and alloy design for printability. 

In layer-by-layer laser powder bed printing, thermomechanical fluctuations result in the buildup of high densities of geometrically necessary dislocations, which cluster into low angle cell configurations that also accommodate the cellular solidification process.  While the evolution process is poorly understood, it is apparent that these defect evolution processes can produce strengths that substantially exceed those achieved along conventional processing paths.

From a materials characterization point of view, the deviations in lattice periodicity create local changes in the electrostatic lattice potential which, in turn, gives rise to local changes in the diffraction conditions for electrons, x-rays, and neutrons. Transmission electron microscopy (TEM) has been by far the most common observation tool for the study of defects; in fact, proof for the existence of dislocations and stacking faults was obtained only a few years after the TEM was introduced commercially.

While the early defect image simulation approaches were limited to basic configurations (i.e., straight, parallel dislocations) and the two-beam diffraction case, recent years have seen the introduction of computational techniques for arbitrary defect configurations using medium and low angle annular dark field imaging, techniques that eliminate regular diffraction contrast such as bend contours, and enhance image contrast due to lattice defects, leading to superior spatial resolution and image clarity.  While the current implementations of defect image simulations all make use of analytical expressions for displacement fields, one of our focus areas will be the incorporation of other forms of displacement fields generated by the modeling described below, for instance displacement fields extracted from phase field, finite element, or molecular dynamics simulations.