Crystal-chemical complexity in natural garnets; structural constraints on chemical variability

A crystal-chemical database for natural garnets has been developed, representing common compositional and petrogenetic conditions. For most of the 281 samples, XRD single-crystal structure refinement and SEM-ion-microprobe analyses were done on the same crystal. Plots of atomic coordinates and geometrical parameters as a function of the unit-cell edge show that garnet crystal-chemistry is characterized by the presence of strong inductive effects and non-linear behaviour, the quantitative aspects of which are discussed elsewhere. There are stringent structural constraints on chemical variability due to extensive edge-sharing between adjacent polyhedra. These phenomena, which make the correct determination of reliable site populations a non-trivial task, have been investigated in detail. An automatic procedure is presented which allows the determination of reliable site-populations starting from the results of the structure refinement. It is based on multiple regression equations for the independent estimates of the amount of each cation and on their subsequent normalization according to crystal-chemical constraints.