Energy Diagram Method for Bragg Reflections in Low Energy Electron Diffraction (LEED) Spectra

A point of view and a method of calculation derived from energy band theory are applied to the problem of finding energies of Bragg reflections from a given crystal. Energy curves are defined and calculated which describe the behavior of individual diffracted electron beams for a given set of beams incident on a particular face of the crystal. Intersections of these curves correspond to and identify the Bragg reflections associated with each beam. Energy diagrams and Bragg peak positions are shown for simple cubic and face-centered cubic lattices for various angles of incidence. We discuss the method in some simple cases and then solve the problem of finding Bragg reflections from the general crystal lattice with an arbitrary surface plane and arbitrary incident beams. The effect of the surface in producing well-defined diffracted beams for any incident beam and in grouping the Bragg reflections into these beams is described. Tables and formulas, which apply to any direction of incidence, are given for the Bragg reflections from the (001), (110) and (111) faces of the face-centered cubic lattice.