Relaxation of curvature-induced elastic stress by the Asaro-Tiller-Grinfeld instability
1 Institute of Scientific Computing, Technische Universität Dresden - Dresden, Germany
2 cfAED, Technische Universität Dresden - Dresden, Germany
Received: 21 May 2015
Accepted: 19 August 2015
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.
PACS: 81.10.Aj – Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation / 83.10.Rs – Computer simulation of molecular and particle dynamics / 68.08.De – Liquid-solid interface structure: measurements and simulations
© EPLA, 2015