Reconciliation of two-dimensional (‘cross-grating’) and three-dimensional phenomena in electron diffraction and resolution of other anomalies on the basis of Bragg reflexions from single crystal lamellae suffering radially progressive shear strain

An intricate repetitive fringe pattern, due to the loss of electrons by diffraction from a crystal lamella, was explained earlier in terms of a crystal model in a state of progressive shear strain in which the primitive translations of successive net-planes changed progressively through the thickness of the layer. The electron diffraction pattern to be expected from this three-dimensional model is now shown theoretically to be identical geometrically with the diffraction pattern from the two-dimensional array of atoms in a single constituent net-plane comprising a cross-grating, so that the model offers also a simple explanation of two-dimensional (‘cross-grating’) diffraction effects in terms of conventional theory for diffraction from three-dimensional crystals. Normal size diffraction rings would not arise from an assembly of the model crystals, but closely similar rings would appear following the law nλ = d sin 2 θ , as distinct from the Bragg law nλ = 2 d sin θ , when, for example, the beam was normal to the shear plane and parallel to the reflecting planes prior to the incidence of strain. While such near-normal rings could fail to appear for certain potentially reflecting planes, ‘extra’ rings would appear and could be arranged in families comprising ‘bands’. These bands would have a ‘head’ on an apparently normal ring and a ‘tail’ on an ‘extra’ ring. Comparison of the model with other published data in electron diffraction suggests that it is compatible with a recently published observation of excessive d 111 / d 200 and d 111 / d 220 spacing ratios in biological work, with early work showing ‘extra’ rings and ‘bands’ from electro-deposited metal films, with ‘extra’ rings from metal foils and with small beam deviations down to zero corresponding to infinite spacings. The model, based directly on effects observed experimentally, and now shown to be supported by previously published work, needs to be examined theoretically from the point of view of stability and in connexion with both Frank and van der Merwe’s theory of orientation calling for pseudomorphic monolayers and Finch and Quarrell’s work which led to the concept of basal plane pseudomorphism.