Application of Direct Methods to Dynamical Electron Diffraction Data for Solving Bulk Crystal Structures

Abstract

The crystal structures of two previously unknown bulk phases in the Ga–In–Sn–O system have recently been solved using direct methods applied to electron diffraction intensities. In both cases, phasing of dynamical diffraction intensities clearly indicated the positions of O atoms in the crystal structures. It is shown here that a correlation between the dynamical diffraction amplitudes and the Fourier components of |1 − ψ(r)| enables direct methods using dynamical intensities to restore structural information present in |1 − ψ(r)|. Both the presence of atom-like peaks in |1 − ψ(r)| as well as the emphasis of light atoms are explained using electron channeling theory. Similar results can be expected for any structure consisting of well resolved atomic columns parallel to the zone-axis direction for which data are recorded. With (Ga, In)2SnO5 as a model structure, it is shown that the combination of strongly dynamical electron diffraction with direct methods is a powerful technique for detecting light-atom positions in bulk inorganic crystal structures without the need to grow single crystals.