An algorithm for refinement of lattice parameters using CBED patterns

A new algorithm for calculation of lattice parameters from convergent beam electron diffraction (CBED) patterns has been developed. Like most of the previous approaches to the problem, it is an optimization procedure matching geometric elements of high order Laue zone (HOLZ) lines in experimental patterns to corresponding elements of kinematically simulated patterns. The procedure uses an original objective function based directly on the underlying algebraic equation of the HOLZ lines. Although the new approach requires crystal orientation parameters to be fitted alongside the strain components, it is easier to implement than methods used previously. It is also straightforward to apply to strain determination from multiple patterns. Numerical tests on dynamically simulated patterns show that in the case of one or two patterns, the new procedure gives results that are more reliable than the established method based on HOLZ line intersections. As an example application, the aa and cc parameters of a TiAl alloy are determined.