Correlation between structural parameters of garnet and garnet-like structures

Statistical analysis of structural parameters of garnet and garnet-like structures retrieved from the Inorganic Crystal Structure Database has revealed strong correlations between them. The degree of correlation depends on doping site and garnet type. Structural parameters are not equally sensitive to changes imposed by doping. The strongest correlation exists between the unit-cell parameter and the doping-ion radius. In the case of doping at the dodecahedral sites, the most sensitive parameter is the shortest dodecahedral distance. Principal component analysis (PCA) clearly shows that the first component explains most of the variation of structural data. It has a geometric basis and correlates with the effective radii of the doping ion. Partial correlation helps to identify the strongest relations between pairs of variables when the influence of other structural variables on them is controlled. It appears that in some cases partial correlation has a different sign when compared with the results of the standard correlation technique.