Dislocation dynamics on deformable surfaces

TL;DR

This paper introduces a comprehensive theoretical framework for dislocation dynamics on deformable surfaces, revealing how surface curvature influences defect motion and interactions using an extended amplitude-phase-field crystal model.

Contribution

It extends the APFC model to curved geometries and derives a general dislocation velocity expression applicable to deformed surfaces.

Findings

Surface curvature induces self-propulsion of defects.

Deformations alter glide directions and defect interactions.

Surface geometry significantly affects defect dynamics.

Abstract

We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a general kinematic expression for dislocation velocity directly from the complex-amplitude evolution equations, which is also applicable to deformed surfaces through curvature-modified differential operators. From numerical simulations, we show that even small out-of-plane deformations reshape the phenomenology of defect motion through curvature-induced self-propulsion, modified glide directions, and non-classical defect-defect interactions. Our results show how surface geometry profoundly influences defect dynamics and establish the surface-APFC model as a powerful framework for predicting and interpreting curvature-defect coupling across a wide range of systems, from stiff but deformable layers to soft matter surfaces and membranes that retain crystalline order.