Statistical dynamical direct methods. I. The effective kinematical approximation

Area of Science:

• Crystallography
• Materials Science
• Physics

Background:

• The kinematical approximation is generally considered inadequate for transmission electron diffraction.
• Recent successes in atomic structure determination using direct methods challenge this notion.

Purpose of the Study:

• To investigate the discrepancy between the poor theoretical applicability of the kinematical approximation and its practical success in electron diffraction.
• To elucidate the underlying reasons for the effectiveness of direct methods in determining atomic structures.

Main Methods:

• Analysis of phase distribution properties in electron diffraction.
• Exploitation of prior work on anomalous scattering effects in direct methods.
• Numerical calculations to support theoretical findings.

Main Results:

• The summation operator(0) distribution of reflection phases remains effectively kinematical, with a narrow distribution, even for thicker samples.
• This narrow phase distribution validates the use of direct methods and structural refinements.
• Large unit-cell structures with random atomic positions exhibit an effective statistical kinematical approximation.

Conclusions:

• The success of direct methods in electron diffraction is not a mirage but is rooted in the effectively kinematical nature of phase distributions.
• Positivity constraints and heavy atom dominance are not strictly required for these methods to be valid.
• The findings reconcile theoretical limitations with experimental successes in atomic structure determination.