Relaxation of curvature induced elastic stress by the Asaro-Tiller-Grinfeld instability

TL;DR

This paper demonstrates that curvature-induced elastic stress in surface crystals on spheres can be relaxed through the Asaro-Tiller-Grinfeld instability, combining numerical simulations with analytical predictions to understand the instability's characteristics.

Contribution

The study introduces a combined numerical and analytical approach to show that the ATG instability can relax curvature-induced stress in surface crystals, extending understanding of stress relaxation mechanisms.

Findings

Numerical results match analytical predictions for wave numbers of the ATG instability.

The surface phase-field crystal model effectively captures the instability dynamics.

Characteristic wave numbers vary with surface coverage and curvature-induced compression.

Abstract

A two-dimensional crystal on the surface of a sphere experiences elastic stress due to the incompatibility of the crystal axes and the curvature. A common mechanism to relax elastic stress is the Asaro-Tiller-Grinfeld (ATG) instability. With a combined numerical and analytical approach we demonstrate, that also curvature induced stress in surface crystals can be relaxed by the long wave length ATG instability. The numerical results are obtained using a surface phase-field crystal (PFC) model, from which we determine the characteristic wave numbers of the ATG instability for various surface coverages corresponding to different curvature induced compressions. The results are compared with an analytic expression for the characteristic wave number, obtained from a continuum approach which accounts for hexagonal crystals and intrinsic PFC symmetries. We find our numerical results in accordance with the analytical predictions.