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

0572605 - FZÚ 2024 RIV GB eng J - Journal Article
Hornfeck, Wolfgang - Červený, Kamil
On the combinatorics of crystal structures. II. Number of Wyckoff sequences of a given subdivision complexity.
Acta Crystallographica Section A-Foundation and Advances. Roč. 79, May (2023), s. 280-294. ISSN 2053-2733. E-ISSN 2053-2733
R&D Projects: GA MŠMT LM2018110; GA ČR(CZ) GX21-05926X
Institutional support: RVO:68378271
Keywords : Wyckoff sequences * combinatorics * Shannon entropy * structural complexity
OECD category: Condensed matter physics (including formerly solid state physics, supercond.)
Impact factor: 1.8, year: 2022
Method of publishing: Open access

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.

Permanent Link: https://hdl.handle.net/11104/0347686