Simulation of electron diffraction patterns from partially ordered layer lattices

By extending the theoretical treatments of Cowley and Hendricks and Teller, we have shown that the diffracted wave functions from successive slabs in crystals containing planar defects are related by simple recurrence equations. Recurrence equations greatly simplify the simulation of diffraction from coherently faulted crystals. Selected-area electron diffraction patterns for zeolite beta are simulated and compared with experimental data. Results are consistent with previous observations, made by structure imaging and powder X-ray diffraction, that zeolite beta is a highly disordered intergrowth of two unfaulted end-member structures, with a probability of a stacking fault being close to 50%. The quantitative accuracy of the recursion model of electron diffraction is limited by dynamical scattering effects.