Elastic Scattering of Bloch Waves in Absorbing Crystals Containing Lattice Defects

Abstract

The differential equations of Bloch wave type which are used in transmission electron microscopy for the calculation of the diffraction contrast from lattice defects are discussed with special reference to crystals with anomalous absorption (i. e. with a complex crystal potential). anomalous absorption is included, the eigenvalue equation by which the Bloch waves are defined in the perfect reference lattice, becomes non-Hermitian. It is shown that for some particular contrast effects not only the eigenvalues but also the eigenvectors must be corrected for the imaginary part of the crystal potential. As a consequence the orthogonality of the Bloch waves is violated. The correction of the eigenvectors may result in long-range contrast tails of the images of lattice defects (intraband scattering). If, however, only the peak positions of the contrast profiles are considered, it suffices in practical cases to correct only the eigenvalues as is usually assumed for the diffraction in perfect crystals.