Mutual correlations of complexity indices of the crystal structure for the series of mercury-containing minerals

Daria A. Banaru, Sergey M. Aksenov, Alexander M. Banaru, Artem R. Oganov
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Abstract

The correlations of values of the crystal structure complexity indices were calculated using the major modern approaches (10 indices in total), in particular, those, proposed by Krivovichev, Oganov, the concept of implicit hierarchical depth, as well as, for the comparison, the measure of regularity of (r, R)-system introduced by Blatov. To find the correlations, a series of 33 mercury-containing mineral structures with a non-repeating system of crystallographic positions occupied by atoms without any partial occupancy was used. It was shown that almost all pairs of complexity indices are statistically significantly (p < 0.05) positively or negatively correlated. The discriminating power of the indices for the set of structures was calculated. It is discussed that all the indices can be used to assess the complexity for any series of the crystal structures, but each of them has its particular advantages and limitations.
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含汞矿物系列晶体结构复杂性指数的相互关系
利用主要的现代方法(共 10 种指数)计算了晶体结构复杂性指数值的相关性,特别是克里沃维切夫和奥加诺夫提出的指数、隐含层次深度概念,以及布拉托夫提出的(r, R)系统规则性测量方法进行比较。为了找到相关性,我们使用了一系列 33 个含汞矿物结构,这些结构中原子占据的晶体学位置系统不重复,没有任何部分占据。结果表明,几乎所有成对的复杂性指数在统计学上都有显著的正相关或负相关(p < 0.05)。计算了这些指数对一组结构的判别能力。结果表明,所有指数都可用于评估任何系列晶体结构的复杂性,但每个指数都有其特定的优势和局限性。
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