Quantitative zone-axis convergent-beam electron diffraction (CBED) studies of metals. I. Structure-factor measurements

The zone-axis CBED pattern-matching technique ZAPMATCH [Bird & Saunders (1992). Ultramicroscopy, 45, 241-251] has been applied to low-order structure-factor measurements in nickel and copper. Considerable disagreement exists between previously published results obtained with a variety of solid-state theories and experimental techniques. The nickel ZAPMATCH results confirm previous electron-diffraction critical-voltage measurements and are in excellent agreement with FLAPW (full-potential linearized augmented plane-wave) theory calculations. This is further proof of the accuracy achievable with ZAPMATCH analysis. For copper, however, while the results support the findings of previous experimental measurements, they are consistently higher than those given by a range of solid-state theories, perhaps demonstrating some limitation in the existing theory. Two extensions to the ZAPMATCH technique are also considered. First, rules are developed to determine the number of structure factors that can be refined accurately from a given CBED pattern. Second, the imaginary potential generally introduced to account for the effects of thermal diffuse scattering (TDS) is also refined. It is shown that, while the widely used Einstein model is a useful approximation, the refined values are consistently higher than the model predicts. In addition, the importance of a second-order (real) TDS correction arising from the Einstein model is investigated. Although its effects are limited in this instance, it may prove to be more significant at lower beam energies or for materials of higher atomic number.