Hornfeck Wolfgang, Kuhn Philipp
Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany.
Acta Crystallogr A Found Adv. 2014 Sep;70(Pt 5):441-7. doi: 10.1107/S2053273314009218. Epub 2014 Jul 10.
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 x(8c) = (2-\sqrt{2})\big/16 and y(12d) = 1\big/(4 \sqrt{2}) for the P4132 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 dmin are calculated over the combined structural parameter range 0 \leq x(8c) ,\lt, 1/8 and 1/8 \leq y(12d), \lt, 1/4 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 dmin. Geometrical discrepancy maps combine predictive and discriminatory powers to appear useful within a wide range of structural chemistry studies.
本文提出了一种低偏差的β-Mn立方变体，沿三个相互垂直的〈100〉轴中的任何一个轴投影时，它呈现出局部八边形对称性。对于P4132对映体，推导出理想结构参数为x(8c) = (2 - √2)/16和y(12d) = 1/(4√2)。根据新设计的几何偏差图概念，对β-Mn的实际结构模型和理想结构模型进行了比较。在广义β-Mn型结构的组合结构参数范围0≤x(8c) ＜1/8和1/8≤y(12d) ＜1/4内，计算了几何星偏差D()和最小原子间距离dmin的二维图，结果表明，β-Mn的“八边形”变体在全局最小化D()的同时，全局最大化dmin方面几乎是最优的。几何偏差图结合了预测能力和判别能力，在广泛的结构化学研究中似乎很有用。
