On the combinatorics of crystal structures. II. Number of Wyckoff sequences of a given subdivision complexity.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY Acta Crystallographica Section A: Foundations and Advances Pub Date : 2023-05-01 DOI:10.1107/S2053273323002437

Wolfgang Hornfeck, Kamil Červený

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Abstract

Wyckoff sequences are a way of encoding combinatorial information about crystal structures of a given symmetry. In particular, they offer an easy access to the calculation of a crystal structure's combinatorial, coordinational and configurational complexity, taking into account the individual multiplicities (combinatorial degrees of freedom) and arities (coordinational degrees of freedom) associated with each Wyckoff position. However, distinct Wyckoff sequences can yield the same total numbers of combinatorial and coordinational degrees of freedom. In this case, they share the same value for their Shannon entropy based subdivision complexity. The enumeration of Wyckoff sequences with this property is a combinatorial problem solved in this work, first in the general case of fixed subdivision complexity but non-specified Wyckoff sequence length, and second for the restricted case of Wyckoff sequences of both fixed subdivision complexity and fixed Wyckoff sequence length. The combinatorial results are accompanied by calculations of the combinatorial, coordinational, configurational and subdivision complexities, performed on Wyckoff sequences representing actual crystal structures.

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论晶体结构的组合学。2给定细分复杂度的Wyckoff序列的个数。

威科夫序列是一种对给定对称性晶体结构的组合信息进行编码的方法。特别是，考虑到与每个Wyckoff位置相关的单个多重度(组合自由度)和相似性(协调自由度)，它们提供了一个简单的方法来计算晶体结构的组合、协调和构型复杂性。然而，不同的Wyckoff序列可以产生相同的组合自由度和协调自由度的总数。在这种情况下，它们基于香农熵的细分复杂度共享相同的值。具有这一性质的Wyckoff序列的枚举是本文所要解决的一个组合问题，首先是在细分复杂度固定但Wyckoff序列长度不指定的一般情况下，其次是在细分复杂度和Wyckoff序列长度都固定的限制情况下。组合结果伴随着对代表实际晶体结构的Wyckoff序列的组合、配位、构型和细分复杂性的计算。

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来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.