Atomic displacement parameters for garnets: A lattice-dynamical evaluation

Atomic displacement parameters (a.d.p.'s), together with vibrational spectra (Raman and lR) and thermodynamic functions, have been calculated for some minerals of the garnet group, such as pyrope (Mg3Al2Si3O12), grossular (Ca3Al2Si3O12), andradite (Ca3Fe2Si3O12) and almandine (Fe3Al2Si3O12) For this purpose, a rigid-ion Born-von Karman model has been applied, using empirical atomic charges and valence force fields derived from a best fit to the vibrational spectra of a group of orthosilicates and oxides. Agreement with the experimental data is good, with the only exception of pyrope and almandine: for these minerals the calculated a.d.p.'s of the Mg2+ atom in the former and of the corresponding Fe2+ atom in the latter are too low. This result confirms the unusual behaviour of these atoms, for which dynamic disorder has been claimed. However, if the values of the specific heat and entropy are considered and compared with our calculations, this situation can be best explained assuming the transition to static disorder of the Mg2+ and Fe2+ atoms to occur at low temperature.