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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

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Octagonal symmetry in low-discrepancy β-manganese.

Wolfgang Hornfeck¹, Philipp Kuhn¹

¹Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany.

Acta Crystallographica. Section A, Foundations and Advances

|September 2, 2014

Summary

A novel cubic variant of beta-manganese (β-Mn) displays local octagonal symmetry. This structure is nearly optimal for minimizing geometrical discrepancy and maximizing interatomic distances, offering insights into structural chemistry.

Keywords:

cubic variant low-discrepancy octagonal symmetry β-Mn

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Area of Science:

Crystallography
Materials Science
Solid-State Chemistry

Background:

Beta-manganese (β-Mn) is a complex cubic structure.
Understanding structural variations is key to materials properties.

Purpose of the Study:

To present a low-discrepancy cubic variant of β-Mn.
To analyze its structural features and optimality.
To introduce geometrical discrepancy maps for structural analysis.

Main Methods:

Derivation of ideal structural parameters for the P4132 enantiomorph.
Calculation of geometrical star discrepancy (D(*)) and minimal interatomic distance (dmin) maps.
Comparison of actual and ideal β-Mn structure models.

Main Results:

A β-Mn variant with local octagonal symmetry along <100> axes was identified.
The 'octagonal' variant demonstrates near-optimal minimization of D(*) and maximization of dmin.
Geometrical discrepancy maps were calculated over a range of generalized β-Mn structures.

Conclusions:

The identified 'octagonal' β-Mn variant represents a near-optimal structure.
Geometrical discrepancy maps are powerful tools for structural chemistry.
This approach can predict and discriminate between structural models.