Ambiguity in indexing electron diffraction patterns of R3 crystals

Area of Science:

• Crystallography
• Materials Science
• Electron Diffraction

Background:

• The R3 space group lacks specific symmetry operations.
• These missing operations can lead to the formation of 'pseudoplanes' in crystals.
• Pseudoplanes share interplanar spacing and angles with true crystallographic planes, causing ambiguity.

Purpose of the Study:

• To address the lack of uniqueness in electron diffraction (ED) patterns for crystals with R3 symmetry.
• To explain how pseudoplanes cause difficulties in analyzing crystal orientations.
• To propose a method for accurate indexing of R3 ED patterns.

Main Methods:

• Analysis of symmetry operations in the R3 space group.
• Investigation of pseudoplane formation and its effect on ED patterns.
• Comparison of atomic arrangements in pseudoplanes and original planes.
• Development of a routine for indexing R3 ED patterns.

Main Results:

• R3 symmetry can generate pseudoplanes that mimic true crystallographic planes in ED patterns.
• Differences in atomic arrangements between pseudoplanes and original planes are subtle and reflected in diffraction spot intensities.
• Standard ED pattern analysis often leads to incorrect zone axis assignments for R3 crystals.
• The proposed routine offers a systematic approach to overcome this indexing ambiguity.

Conclusions:

• The inherent symmetry of R3 space group leads to pseudoplanes, complicating ED pattern interpretation.
• Accurate indexing of R3 ED patterns is crucial for correct crystal orientation analysis.
• The developed routine provides a reliable method to resolve ambiguities in R3 ED pattern indexing.