Automated lattice parameter measurement from HOLZ lines and their use for the measurement of oxygen content in YBa₂Cu₃O_7-δ from nanometer-sized region

An algorithm is described which automatically adjusts values of lattice parameters or high voltage for best fit to the high-order Laue zone (HOLZ) lines in experimental convergent-beam electron diffraction (CBED) patterns for both cubic and non-cubic cell. The HOLZ line pattern is characterized by the distances between HOLZ line intersections. A standard definition of chi square is used to measure the goodness of fit. A general equation for HOLZ line positions based on the kinematic approximation is described. The effects of multiple scattering to the HOLZ line positions are discussed based on perturbation theory, the two-beam approximation, and on the Bethe potential. It is found that by avoiding the zone axis center the multiple scattering effects can be significantly minimized and accuracy in the lattice parameters increased. As an example, we have applied the method with dynamic corrections to lattice parameter measurement in YBa₂Cu₃O_7-δ from an area about 20 A diameter, using a field emission electron gun. We find a = 3.8252±0.001 A and b = 3.8968±0.0006 A in one of the two measurements. The ratio of the a and b axes gives the oxygen deficiency δ to be about 0.1.