Between wave and particle-the semiclassical method for interpreting high-energy electron micrographs of crystals

The concepts of “semiclassical mechanics” are applied to the propagation of an electron beam through a crystal lattice. We obtain a variety of approximate descriptions which bridge the gap between the full quantum treatment necessary at lower voltages and the purely classical analysis which becomes valid at higher voltages. These methods, which are all based on “real space”, lead to simple physical descriptions and numerically accurate formulae for phenomena which have previously only emerged after lengthy computations based on Fourier analysis: examples are the existence of “critical voltages” and “critical angles”. It is shown how the purely classical concept of “caustic” can explain features on micrographs which are usually considered as interference fringes; this bypasses the need to construct “dispersion surfaces”. Absorption from the diffracted beams, which is caused by inelastic scattering, is incorporated into the semiclassical analysis.