All-electron first-principles investigations of the energetics of vicinal Cu surfaces

Abstract

Using first-principles calculations we studied the energetics (surface energy, step energy, stability with respect to faceting) of the low- and high-Miller-index (vicinal) Cu surfaces, namely, the (111), (100), (110), (311), (331), (210), (211), (511), (221), (711), (320), (553), (410), (911), and (332) surfaces. Our calculations are based on density-functional theory employing the all-electron full-potential linearized augmented plane-wave (FLAPW) method. We found that the unrelaxed vicinal Cu surfaces between (100) and (111) are unstable relative to faceting at $0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, while fully relaxed vicinal surfaces between (100) and (111) are stable relative to faceting, which is in agreement with the observed stability of vicinal Cu surfaces at room temperature. Thus atomic relaxations play an important role in the stability of the vicinal Cu surfaces. Using the surface energies of Cu(111), Cu(100), and Cu(110) and employing the effective pair-potential model, which takes into account only the changes in the coordination of the surface atoms, the surface energies of the vicinal Cu surfaces can be calculated with errors smaller than 1.0% compared with the calculated FLAPW surface energies. This result is due to the almost perfect linear scaling of the surface energies of the $\mathrm{Cu}(hkl)$ surfaces as a function of the total number of broken nearest-neighbor bonds. Furthermore, we calculate step-step interactions as a function of terrace widths and step energies of isolated steps.