First-principles study of Friedel oscillations normal to the low index surfaces of Al

Using the first-principles calculations within density functional theory (DFT), we have studied the behavior of Friedel oscillations near Al (1 0 0), (1 1 0), and (1 1 1) surfaces. The results show that for the most open Al (1 1 0) surface, the Friedel oscillation exhibits smaller oscillation amplitude, bigger wavelength and deeper depth of penetration compared to the oscillations of the more close-packed Al (1 1 1) and (1 0 0) surfaces. The characteristics of the Friedel oscillations of the Al surfaces are dominated by the charge density of Al 3p electrons near the Fermi level. We further calculate relaxations of the three surfaces, and find that the multilayer relaxations of the surfaces can be well explained by the Friedel oscillations qualitatively. In turn, we have shown that by altering interlayer spacing slightly the oscillation amplitude can be tuned, but the change near the surface is in contrary to the prediction based on the jellium model, indicating that the real lattice structure will plays a key role in the Friedel oscillations near the metal surface.