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

Research output: Contribution to journalResearch articleContributedpeer-review

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-wavelength 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.

Details

Original languageEnglish
Article number48006
JournalEurophysics Letters
Volume111
Issue number4
Publication statusPublished - 7 Sept 2015
Peer-reviewedYes

External IDs

Scopus 84941588282

Keywords

Keywords

  • Phase-field crystal model, Continuum elasticity, Numerical simulation