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

Hornfeck, W.; Červený, K.

doi:10.1107/S2053273323002437

Figure 5
Schematic representation of the interrelation between various maximal and non-maximal entropies (combinatorial, coordinational, configurational) and the subdivision entropy on different levels of structural hierarchy. On the Wyckoff position level of hierarchy the difference of (maximal) entropies defines the conventional non-maximal entropies (from left to right), while on the crystal structure level of hierarchy the (partially weighted) sum of entropies defines the maximal and non-maximal configurational entropy (from bottom to top). Note that the distinction between differences and sums of entropies depends on a deliberate choice of how to distribute terms on either side of the equals sign. In the scheme as presented here, the case for differences of entropies is based on the choice of collecting all maximal entropies together, while distributing collective and individual contributions on opposite sides of the equation could highlight the fact that the non-maximal entropies fulfil the same role as a subdivision complexity on the Wyckoff position level as the subdivision complexity $[H_{{\rm subdiv}}]$ does on the crystal structure level, thus highlighting the applicability of the strong additivity property on both levels of hierarchy (in this case the common weighting factors w_M or w_A can be omitted on the Wyckoff position level of hierarchy).

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ISSN: 2053-2733

Volume 79| Part 3| May 2023| Pages 280-294

https://doi.org/10.1107/S2053273323002437

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