Asymptotic behavior of relaxation and reconstruction near crystalline surfaces

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Abstract
It is shown that the asymptotic behavior of multilayer relaxation and reconstruction can be related to the bulk phonon dispersion relation in the complex wave-number plane. The conditions for the existence of oscillatory damped relaxation are derived. The method predicts in a simple and efficient way the period and decay constant of oscillatory relaxation. Three examples [Ni(110), Al(110), and Fe(111)] are worked out in detail where an accurate analytical form is obtained in terms of one or two disposable parameters. It is suggested that such analytical forms could be used in the extraction of multilayer relaxation from low-energy electron diffraction (LEED) data.