Retrieval of the projected potential by inversion from the scattering matrix in electron-crystal scattering

Area of Science:

• Materials Science
• Solid State Physics
• Crystallography

Background:

• High-energy transmission electron diffraction (HETED) is a powerful technique for probing crystal structures.
• The scattering matrix (S) contains crucial information about electron-crystal interactions.
• Retrieving the unique crystal potential from the scattering matrix is essential for accurate structural analysis.

Purpose of the Study:

• To discuss the retrieval of a unique crystal potential from the scattering matrix (S) in high-energy transmission electron diffraction.
• To investigate the sufficiency of single-orientation data for determining all elements of the S matrix.
• To present an algorithm for extracting crystal potential from measured S matrix data.

Main Methods:

• Analysis of scattering matrix (S) properties in high-energy transmission electron diffraction.
• Investigation of data requirements for complete S matrix determination, including tilted incident beam measurements.
• Development and application of an algorithm for crystal potential extraction from S matrix data at single energy and thickness.
• Consideration of the thin crystal limit and simulation of data for validation.

Main Results:

• Data from a single orientation is generally insufficient to determine all elements of the scattering matrix (S).
• Additional measurements using a tilted incident beam are required for the complete determination of the S matrix.
• An algorithm is presented for extracting crystal potential from the S matrix.
• The limiting case of thin crystals is analyzed.

Conclusions:

• Complete determination of the scattering matrix (S) and subsequent retrieval of crystal potential necessitate multi-orientation or tilted beam measurements.
• The presented algorithm offers a method for crystal potential extraction under specific conditions.
• The study highlights the importance of data acquisition strategies in electron diffraction for accurate material characterization.