Consecutive transitions between regular and periodic nanostructures induced by ion bombardment on the Cu(110) surface have been studied as a function of the sputtering parameters (primary ion energy, substrate temperature, and ion flux). The morphologies can vary from the well-known ripple patterns oriented along the two main symmetry directions of the fcc(110) substrate, to mounded structures, and include the far from equilibrium rhomboidal pyramid motif recently observed on the Rh(110) surface. The dependence of the nanostructure facet slope and lateral separation from ion energy allows us to identify a morphological regime accessed for low ion energy, below 500 eV, corresponding to the formation of rhomboidal pyramids. The dependence from the ion flux and substrate temperature bears strong similarities with a growth experiment, and is determined by the relaxation of isolated adatom and/or vacancy clusters created in the topmost surface layer by an ion impact. The selection of preferential step orientation and slopes follows from a delicate balance between the diffusion currents along the two main diffusion channels, the <$(1) over bar $ > and the < 001 >.
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