Second gradient vs. surface energy in the Asaro-Grinfeld instability

Abstract
This paper study an instability phenomenon that arise in epitaxial growth of single crystals with lattice mismatch. We compare a classical approach, based on the competition between the bulk and surface energies, with a non-standard one when the surface term is replaced by a term including the second gradient of the displacement field. We evidence how secontl order gradients may stabilize lower modes of corrugated boundaries, via an intrisic length scale.