Symmetrization of low-energy electron diffraction patterns

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Abstract
Using the layer-by-layer approach to low-energy electron diffraction (LEED) the authors explain how to symmetrize the beam scattering matrix for layers. The coincidence structure formed by the layers may be dense or open and may possess any of the 17 two-dimensional space group symmetries. The beams of the electron field become diffracted by the layers in a manner determined by von Laue's diffraction conditions. These conditions turn out to arrange the beams in mutually independent bundles. After establishing the transformation properties of bundles of beams under the point group part of the two-dimensional space group the authors derive a scheme for finding symmetrized combinations of interacting beams. The formalism is applied to the layer-KKR method for LEED calculation. In particular the symmetrization of the beam patterns created by three overlayer structures on surfaces of face-centred cubic crystals are described: the primitive 2*2 structure and the ( square root 2* square root 2)45 degrees structure on the (100) surface together with the ( square root 3* square root 3)30 degrees structure on the (111) surface.