Rippled one-dimensionally periodic structures, commonly seen in experimental studies of the epitaxial growth and erosion of low-symmetry rectangular (110) crystal surfaces, were considered. The rippled state period (wavelength) and amplitude grew via a coarsening process that involved the motion and annihilation of the dislocations; thus disordering the perfect periodicity of these structures. Unlike ordinary dislocations in equilibrium systems, the dislocations of growing rippled states were genuine moving objects; never being at rest. The structure and dynamics of these far-from-equilibrium topological defects were here studied theoretically. Fundamental dislocation dynamics laws were derived which related the dislocation velocity to the rippled-state period. The dislocation velocity laws were then used to derive coarsening laws for the temporal evolution of the rippled-state period and the ripple-amplitude (surface roughness). For simple rippled states on (110) surfaces, a coarsening law with a 2/7 time-exponent was obtained. Under some conditions, it was found that these states could exhibit faster coarsening, with a 1/3 time-exponent. Also considered were the dislocations in the rectangular rippled surface states, for which the coarsening law had a 1/4 time-exponent. The coarsening laws that occurred at the transition from a rippled to a rhomboidal pyramid state were also considered, as well as the cross-over effects which occurred in rippled states in the proximity of this transition on (110) crystal surfaces.

Dislocation Dynamics and Surface Coarsening of Rippled States in the Epitaxial Growth and Erosion on (110) Crystal Surfaces. L.Golubović, A.Levandovsky: Physical Review E, 2008, 77[5, I], 051606