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Domino phase-retrieval algorithm for structure determination using electron diffraction and high-resolution

F N Chukhovskii¹, A M Poliakov

¹Institute of Crystallography, the Russian Academy of Sciences, 117333 Moscow, Leninsky Prospect 59, Russia.

Acta Crystallographica. Section A, Foundations of Crystallography

|December 24, 2002

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This study introduces a novel direct-methods approach for atomic structure determination using electron diffraction (ED) and high-resolution transmission electron microscopy (HRTEM) data. The new "domino" algorithm successfully retrieves phases for complex structure factors, enabling accurate crystal structure solutions.

Area of Science:

Materials Science
Crystallography
Electron Microscopy

Background:

Conventional direct methods for atomic structure determination face challenges with dynamical electron diffraction (ED) data.
Dynamical effects in ED data result in complex structure factors, invalidating the positivity constraint used in kinematical methods.
Heavy atoms' contributions to high-resolution transmission electron microscopy (HRTEM) images are also affected by dynamical scattering.

Purpose of the Study:

To develop a general solution for the phase-retrieval problem in atomic structure determination using electron diffraction.
To combine dynamical ED and HRTEM data within a direct-methods framework.
To enable full-phase restoration of complex structure factors crucial for accurate structural analysis.

Main Methods:

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A novel direct-methods formalism is proposed, termed the 'domino' fashion, integrating ED and HRTEM data.
The core is a phase-retrieval algorithm specifically designed for dynamical ED and HRTEM data.
The method fuses traditional direct-method techniques with the unique characteristics of dynamical electron scattering.

Main Results:

The 'dynamical' direct-methods concept successfully utilizes both dynamical ED and HRTEM data for phase retrieval.
A numerical example using (Ga,In)2SnO5 ceramic demonstrates the method's capability for unique phase-retrieval.
The proposed domino transform algorithm effectively phases diffraction patterns, yielding accurate complex structure factors.

Conclusions:

The developed domino transform algorithm provides a valuable method for phasing diffraction patterns in electron crystallography.
This approach overcomes limitations of conventional methods when dealing with dynamical electron scattering effects.
The technique is readily applicable to experiments where both ED and HRTEM data are collected simultaneously.