On the breakdown of Friedel's law in electron backscattering channelling patterns

Abstract

The theory for electron channelling patterns has been investigated. Calculations based on existing intensity expressions have been found inadequate for explaining recently observed deviations from Friedel's law. This is found to be the case even if the calculations are based on the full non-Hermitian eigenvalue matrix. The theory has hence been reinvestigated and a new intensity expression has been derived which includes the inter Bloch-wave coupling terms and is valid for non-centrosymmetric polyatomic crystals. The expression explains the observed asymmetries for GaSb which make it possible to determine unambiguously the correct non-centrosymmetric point group for this crystal. It is further found that the same effects in GaAs should be very weak in accordance with the non-observed deviation from Friedel's law in this case.

Many-beam dynamical simulation of electron backscatter diffraction patterns

“…A large number of the investigations were driven by the need to understand the diffraction contrast of lattice defects [14,15]. Many-beam effects in ECP have been studied before by Marthinsen [16][17][18]. Further simulations were done by Rossouw [8] using a dependent Bloch wave model and Dudarev [19] using an inhomogeneous transport equation approach for the inelastically scattered electrons.…”

Point-group sensitive orientation mapping of non-centrosymmetric crystals

“…4 The key information for EBSD is provided by Kikuchi diffraction patterns, 5 which, due to pronounced dynamical diffraction effects, are intrinsically sensitive to the pointgroup symmetry of a crystal. 6,7 Because of the increased information content which is provided by dynamical electron diffraction in EBSD Kikuchi patterns, the detailed simulation and analysis of the respective effects is becoming more and more important. 8 Typical applications include EBSD-based lattice strain analysis, 9 EBSD image segmentation, 10,11 and the analysis of orientation relationships in phase transformations.…”

Calculating anisotropic piezoelectric properties from texture data using the MTEX open source package

“…To distinguish the right-handed and lefthanded forms of enantiomorphic crystals additional information, such as dynamical scattering revealing a violation of Friedel's law (e.g. Goodman & Johnston 1977;Goodman & Secomb 1977;Bunge & Esling 1985;Marthinsen & Høier 1988), is required. Alternatively gyration, also called optical activity, can be used in optically transparent crystals (e.g.…”