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Octagonal symmetry in low‐discrepancy β‐manganese
Author(s) -
Hornfeck Wolfgang,
Kuhn Philipp
Publication year - 2014
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273314009218
Subject(s) - ideal (ethics) , symmetry (geometry) , perpendicular , manganese , icosahedral symmetry , projection (relational algebra) , range (aeronautics) , combinatorics , physics , geometry , crystallography , star (game theory) , mathematics , materials science , mathematical analysis , chemistry , algorithm , philosophy , epistemology , metallurgy , composite material
A low‐discrepancy cubic variant of β‐Mn is presented exhibiting local octagonal symmetry upon projection along any of the three mutually perpendicular 〈100〉 axes. Ideal structural parameters are derived to be and for the P 4 1 32 enantiomorph. A comparison of the actual and ideal structure models of β‐Mn is made in terms of the newly devised concept of geometrical discrepancy maps. Two‐dimensional maps of both the geometrical star discrepancy D * and the minimal interatomic distance d min are calculated over the combined structural parameter range and of generalized β‐Mn type structures, showing that the `octagonal' variant of β‐Mn is almost optimal in terms of globally minimizing D * while at the same time globally maximizing d min . Geometrical discrepancy maps combine predictive and discriminatory powers to appear useful within a wide range of structural chemistry studies.