Diffraction from reconstructed surfaces with incommensurate domain walls

The kinematic approximation method has shown that the peak intensity and the full width at half maximum (FWHM) of stepped surfaces exhibit an oscillatory behavior for changing incident energy. This paper generalizes the kinematic approximation to an (N × 1) reconstructed surface with a distribution of various types of lateral displacements at a step. A particular solution of this model we call the fixed point solution, yields a clear intuitive understanding of these oscillations as well as an exact solution for the step density of any surface. The specific examples of (5 × 1) and (2 × 1) reconstruction are examined to show the striking differences between the reconstructed surface diffraction patterns. These differences make an examination of the half-maximum (HM) intensity position a powerful tool to determine the surface structure for any incommensurate stepped surface.