Abstract

The Kanzaki forces are the standard way of representing point defects in the elastic continuum. They are the forces that would have to be applied on a perfect, defect-free crystalline lattice to generate the topology of the point defect. By computing these forces in atomistic lattices, one obtains a true multiscale representation of the defect.

In this talk, I generalise the concept of Kanzaki forces to all other crystalline defects. I will discuss how the resulting Kanzaki force fields are to be computed for any general defect, including dislocations, grain and twin boundaries, or cracks.

I will then focus on crystallographic dislocations. I will show that the Kanzaki force field of a dislocation consists of two separate components: a Volterra contribution associated with the disregistry that characterises the dislocation, and a core contribution associated with the specific topology of the dislocation core.

I will then show how to use each of these components to model the dislocation core in the elastic continuum. Unlike other regularisation procedures like the Peierls-Nabarro model, the resulting models are topologically true to the dislocation core, and energetically accurate up to the harmonic approximation.

Finally, I will discuss how the Kanzaki force field can be employed to study dislocation mobility using lattice dynamics, and I will highlight several lattice instabilities that arise when screw and edge dislocations are driven at high speeds.