An extension is proposed of the Shannon entropy‐based structural complexity measure introduced by Krivovichev, taking into account the geometric coordinational degrees of freedom a crystal structure has. This allows a discrimination to be made between crystal structures which share the same number of atoms in their reduced cells, yet differ in the number of their free parameters with respect to their fractional atomic coordinates. The strong additivity property of the Shannon entropy is used to shed light on the complexity measure of Krivovichev and how it gains complexity contributions due to single Wyckoff positions. Using the same property allows for combining the proposed coordinational complexity measure with Krivovichev's combinatorial one to give a unique quantitative descriptor of a crystal structure's configurational complexity. An additional contribution of chemical degrees of freedom is discussed, yielding an even more refined scheme of complexity measures which can be obtained from a crystal structure's description: the six C's of complexity.

中文翻译：

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关于Krivovichev复杂性度量的扩展。

考虑到晶体结构具有的几何协调自由度，对Krivovichev提出的基于Shannon熵的结构复杂性度量提出了一个扩展。这允许在其还原晶胞中共享相同数目的原子，但就其分数原子坐标而言其自由参数的数目不同的晶体结构之间进行区分。Shannon熵的强可加性用于阐明Krivovichev的复杂性度量，以及它如何由于单个Wyckoff位置而获得复杂性贡献。使用相同的属性可以将拟议的协调复杂性度量与Krivovichev的组合度量相结合，以给出晶体结构的构型复杂性的唯一定量描述符。