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.Comment: 6 pages, 5 figure
