On the unique evaluation of local lattice parameters by convergent-beam electron diffraction

Abstract

Abstract We summarize some practical aspects of using convergent-beam electron diffraction (CBED) patterns for determination of three-dimensional lattice parameters in crystalline materials. Owing to the insensitivities of certain lattice spacings to changes in lattice parameters, and to measurement errors imposed by finite higher-order hue zone (HOLZ) linewidths, most CBED patterns can be simulated by a number of different lattice parameter combinations. Unique combinations are found by fitting several patterns obtained from the same area. In cases where a unique set of all six parameters cannot be found, semiquantitative information about elastic stress and strain states can still be extracted. The number of obtainable lattice parameters is affected by the symmetry of the pattern and by the specific HOLZ reflections which are present, for a given accelerating voltage. Symmetry-breaking distortions in patterns from nominally orthorhombic systems can often be attributed to deviations in lattice angles as small as 0·01-0·02° away from 90°, even if such angular distortions are not expected from knowledge of the material's bulk behaviour. The correct simulation of CBED patterns further requires consideration of foil thinning artefacts on HOLZ line positions. We show that an intelligent choice of zone axis can provide useful information even from difficult sample geometries.