We present the calculated structural parameters for the above mentioned garnets as a function of applied pressure in the range from 0 to 100 GPa. The calculated equations of state are further used to derive the bulk modulus and its pressure derivative by fitting the data with the Birch-Murnaghan equation of state. The calculated values of lattice constants and bulk moduli at ambient conditions typically agree with the experimental data (where available) to within 0.5% and 5%, respectively. The accuracy of quantum mechanical calculations is shown to be sufficiently high to reproduce known trends in bulk moduli, which is important as the difference between various garnets is of the order of 5-10% only.
Currently, the highest pressure achieved in experimental studies is 33 GPa (7). The results of the calculations therefore allow us to obtain changes in the structural details to significantly higher pressures, thereby simplifying a crystal-chemical analysis of the compression mechanism. Specifically, we will present a comparative analysis of the bond-length distortion, edge-length distortion and angular distortions of three garnets investigated, thereby pointing out differences and similarities in the behaviour of this family of compounds.
The data obtained for the different compounds are further analysed to find a correlation between the physical properties and the incorporated cations. While this has been phenomenologically derived on the basis of qualitative crystal-chemical considerations, the quantum mechanical calculations allow a quantification of the influence of cation size, charge distribution, etc.