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Stress balance in nano-patterned N/Cu(001) surfaces

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 nano-patterned 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\times2) 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 <100> direction or when trench-like steps of Cu atoms form along the <110> 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 clock-like displacements could relieve stress levels, such displacements are energetically unstable.