We employ helium-atom scattering (HAS) and density functional theory (DFT) based on the ultrasoft pseudopotential scheme and the plane-wave basis set to investigate the strain and stress balance in nanopatterned N/Cu(001) surfaces. HAS shows that, with increasing N coverage (and decreasing stripe widths), the stress-relief-driven lateral expansion of the averaged lattice parameter within finite-sized N-containing patches reduces from 3.5% to 1.8% and that, beyond a critical exposure, the lateral expansion of the patches increases again slightly, to 2.4%. The latter implies that in this higher coverage range the compressive stress is partially relieved via another mechanism, which turns out to be nucleation of Cu-vacancy trenches. In full agreement with the above and previous experimental observations, DFT calculations show that an optimized N-induced $c$(2 × 2) structure has a net surface stress level of 4.2 N/m and such stress is effectively relieved when stripes of clean Cu(001) form along the $\langle 100\rangle$ direction or when trenchlike steps of Cu atoms form along the $\langle 110\rangle$ direction. Additionally, the calculations demonstrate that (contrary to earlier suggestions) rumpling displacements within the outermost Cu layer do not act to relieve the compressive surface stress levels and that, while clocklike displacements could relieve stress levels, such displacements are energetically unstable.

• Received 14 November 2010

DOI:https://doi.org/10.1103/PhysRevB.84.165413