On the combinatorics of crystal structures. II. Number of Wyckoff sequences of a given subdivision complexity
Status PubMed-not-MEDLINE Jazyk angličtina Země Spojené státy americké Médium print-electronic
Typ dokumentu časopisecké články
Grantová podpora
18-10438S
Grantová Agentura České Republiky
LM2018110
Ministerstvo Školství, Mládeže a Tělovýchovy
PubMed
37165959
PubMed Central
PMC10178003
DOI
10.1107/s2053273323002437
PII: S2053273323002437
Knihovny.cz E-zdroje
- Klíčová slova
- Shannon entropy, Wyckoff sequences, combinatorics, structural complexity,
- Publikační typ
- časopisecké články MeSH
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.
FZU Institute of Physics of the Czech Academy of Sciences Na Slovance 1999 2 182 00 Prague 8 Czechia
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