Application of a 2-beam model for improving the structure factors from precession electron diffraction intensities

Area of Science:

• Crystallography
• Materials Science
• Electron Microscopy

Background:

• Precession electron diffraction (PED) is a powerful technique for crystal structure analysis.
• Accurate interpretation of PED intensities is crucial for determining structure factor amplitudes.
• Existing models for PED intensity simulation and inversion have limitations, particularly for complex or thick crystalline samples.

Purpose of the Study:

• To develop and validate a simplified 2-beam model for simulating and inverting PED intensities.
• To assess the utility of this model for direct structure factor amplitude determination.
• To explore the applicability and limitations of the 2-beam model in conjunction with direct methods for crystal structure determination.

Main Methods:

• Simulation of PED intensities using a 2-beam dynamical diffraction model.
• Inversion of the 2-beam model to deduce structure factor amplitudes from experimental intensities.
• Application of the method to thin crystalline samples of (Ga,In)2SnO5.
• Evaluation of the model's performance with thicker samples, using MFI zeolite as a test case.

Main Results:

• The 2-beam model successfully simulates PED intensities and allows for direct inversion to obtain structure factor amplitudes with minimal prior structural knowledge.
• The approach proved effective for thin crystals (approx. < 400Å), enabling structure indications when combined with direct methods.
• The model's accuracy significantly degrades for thicker crystals, as demonstrated with the MFI zeolite data.

Conclusions:

• The 2-beam model offers a practical approach for structure factor determination from PED data of thin crystals.
• While advantageous over kinematical approximations, the 2-beam model is ultimately too simplified for general application.
• Future research should focus on developing more accurate yet user-friendly models for PED data analysis.