Towards a full retrieval of the deformation tensor F using convergent beam electron diffraction

Area of Science:

• Materials Science
• Crystallography
• Electron Microscopy

Background:

• Convergent Beam Electron Diffraction (CBED) is crucial for analyzing crystal structures.
• Accurate retrieval of local lattice parameters and rotations is essential for understanding material deformation.
• Existing methods may have limitations in determining all components of the deformation tensor.

Purpose of the Study:

• To present a novel method for retrieving local lattice parameters and rotations from off-axis CBED patterns.
• To validate the method using Bloch wave dynamical simulations.
• To assess the accuracy and completeness of determined deformation parameters.

Main Methods:

• Utilizing off-axis convergent beam electron diffraction (CBED) patterns.
• Employing a fitting algorithm based on kinematical approximations.
• Incorporating both diffracted and transmitted beams for analysis.
• Using the deformation gradient tensor (F) to represent rotation and strain.

Main Results:

• Seven out of nine parameters of the deformation gradient tensor (F) can be determined from a single observation direction with high accuracy (3 × 10⁻⁴ for normal strain).
• Unit cell volume retrieval requires the inclusion of both diffracted and transmitted beams in the fitting process.
• Combining two observation directions (approx. 20° apart) allows for the determination of all nine parameters of F.

Conclusions:

• The developed method offers a robust approach for precise characterization of local crystal lattice parameters and rotations.
• The integration of both diffracted and transmitted beams is critical for comprehensive lattice parameter determination.
• Multi-directional observation significantly enhances the completeness of deformation tensor retrieval.