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

0572605 - FZÚ 2024 RIV GB eng J - Článek v odborném periodiku
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
Grant CEP: GA MŠMT LM2018110; GA ČR(CZ) GX21-05926X
Institucionální podpora: RVO:68378271
Klíčová slova: Wyckoff sequences * combinatorics * Shannon entropy * structural complexity
Obor OECD: Condensed matter physics (including formerly solid state physics, supercond.)
Impakt faktor: 1.8, rok: 2022
Způsob publikování: 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.

Trvalý link: https://hdl.handle.net/11104/0347686