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

. 2023 May 01 ; 79 (Pt 3) : 280-294. [epub] 20230511

Status PubMed-not-MEDLINE Jazyk angličtina Země Spojené státy americké Médium print-electronic

Typ dokumentu časopisecké články

Perzistentní odkaz   https://www.medvik.cz/link/pmid37165959

Grantová podpora
18-10438S Grantová Agentura České Republiky
LM2018110 Ministerstvo Školství, Mládeže a Tělovýchovy

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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