The Symmetry of Three-Beam Scattering Equations: Inversion of Three-Beam Diffraction Patterns from Centrosymmetric Crystals

摘要: It is shown that for a centrosymmetric crystal, and within the range of validity three-beam approximation, phases as well magnitudes three structure amplitudes can be measured uniquely directly from geometry intensity distributions in discs convergent-beam diffraction pattern. In fact, solution given terms distances on further inversion independent thickness. Three proofs are given, each illustrating different aspect physical processes involved. first, fundamental symmetry process to special unitary group order Gell-Mann representation used construct sub-algebras, which explicit written. SU(3) have particular significance crystallography, namely, it lowest with symmetries analysed yield structural phase. The second longer method involves projection scattering matrix into spaces eigenvectors. Unlike first method, this makes use basis; however, not necessary calculate explicitly either eigenvectors or eigenvalues. third based Bloch-wave expansion, shows system characterized by lines, ruled one dispersion surfaces, all information embodied these lines. Although theory scalar developed here electron diffraction, apply equally right circular component wave function X-rays. Some brief remarks made practicability preliminary experiments indicate phase easiest parameters measure.