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

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.