Theory of Low-Energy Electron Diffraction II. Cellular Method for Complex Monolayers and Multilayers

The method of calculating the intensities of waves in low-energy electron diffraction (LEED) whidi was applied in Part I to monatomic layers is generalized and applied to complex monolayers and multilayers. Using the "muffin-tin" model, whidi is widely used in the band theory of metals, the wave function is expanded in spherical harmonics on the surfaces of the set of atomic spheres whidi build a two-dimensional unit of the structure. The expansion coefficients are determined from the condition that the wave function should satisfy the integral equation of the problem on each of the surfaces of the atomic spheres. The method is interpreted physically in terms of the multiple scattering by the system of atoms. Corresponding to the expansion of the wave function on the atomic spheres the waves falling on and scattered by the atoms are decomposed into "partial waves". In this picture the theory is shown to be essentially equivalent to the dynamical theory of Ewald and also to the LEED theory of McRae. The pseudokinematical theory of Hoerni is derived if the multiple scattering is completely neglected. The method can be modified, particularly for higher electron energies, to the form which introduces the "scattering matrix" of atomic layers and finally to the form whidi makes use of Bloch functions and thus becomes equivalent to the usual dynamical theory of X-ray and electron diffraction.