A crystal structure can be described by an electrostatic potential function. The Fourier transforms of the function are called structure factors. To determine a crystal structure both the magnitude and phase of the structure factors are needed. Experiments which are based on kinematic diffraction only contain information about the magnitudes but not the phases – this is often called the “phase problem”. In the absence of direct measurements of phase, the phases must be deduced from magnitudes using computer-intensive statistical or other algorithms. This can require the measurement of many thousands of magnitudes and the solution may not be unique. 3-beam dynamical diffraction occurs when two sets of crystal planes satisfy their Bragg conditions simultaneously, allowing for interference between the scattered waves. Therefore, the intensities near a 3-beam orientation depend on the summation of the three structure factor phases (“triplet phase”) involved, permitting direct measurement of the triplet phase.
It has been shown that, for centrosymmetric crystals, it is possible to measure cosine triplet phase directly, by inspection, from a 3-beam convergent beam electron diffraction (CBED) pattern [1-3]. In this work, we explore the application of theoretical descriptions of 3 beam scattering [4-9] to estimate triplet phase in non-centrosymmetric crystals. We present full dynamical calculations that show that the triplet phase can be measured within 45 by inspection of the CBED pattern. We illustrate this with preliminary experiments using large angle rocking beam electron diffraction (LARBED) [10]..
Acknowledgement
The authors acknowledge the use of facilities and staff support at the Monash Centre for Electron Microscopy.