Schemes to determine the crystal potential under dynamical conditions using voltage variation

Area of Science:

• Materials Science
• Crystallography
• Condensed Matter Physics

Background:

• X-ray diffraction routinely determines charge densities and crystal structures due to weak scattering.
• Strong dynamical diffraction in high-energy electron diffraction hinders similar direct analysis.
• Dynamical diffraction involves wave propagation and crystal potential scattering, influenced by voltage-dependent relativistic effects.

Purpose of the Study:

• To develop a method for direct crystal potential determination using electron diffraction.
• To overcome limitations imposed by strong dynamical diffraction in electron scattering.
• To establish a relationship between diffracted intensities and crystal potential.

Main Methods:

• Measuring electron diffracted intensities at two different voltages.
• Analyzing the relationship between intensity differences and crystal potential.
• Utilizing first-order perturbation theory and exact calculations for validation.

Main Results:

• The difference in diffracted intensities at two voltages is directly proportional to the crystal potential.
• First-order perturbation theory calculations show negligible differences compared to exact calculations.
• A simple procedure exists to recover the crystal potential if the full complex wave function is known.

Conclusions:

• Direct determination of crystal potential from electron diffraction is feasible.
• Measuring intensity variations with voltage offers a new route to analyze crystal potentials.
• This method holds promise for detailed crystallographic studies even under dynamical diffraction conditions.