Lattice-dynamical evaluation of atomic displacement parameters of minerals and its implications; the example of diopside

Abstract

A Born-von Karman rigid-ion, lattice-dynamical model has been applied to diopside with the use of empirical potentials derived by fitting the vibrational frequencies of a group of nesosilicates and oxides (including quartz). The Raman and infrared spectra are satisfactorily interpreted by these calculations; there is also good agreement with anisotropic atomic displacement parameters (ADPs) derived from accurate crystal-structure refinement at various temperatures. The agreement with theoretical and experimental data of independent origin confirms the physical meaning of both experimental and calculated ADPs; consequently, the correlation tensors between the displacement of different atoms, which can be evaluated in this way and cannot be obtained from Bragg diffraction measurements, are also reliable, thereby allowing bond-length correction for libration in the most general case. As for other oxides and silicates, the zero-point motion contribution amounts to about 35% of the total at room temperature. Hirshfeld's rigid-bond test applied to the SiO. groups is in agreement with our calculations. The values of thermodynamic functions such as the specific heat and entropy at different temperatures are also satisfactorily reproduced, although a rigid-ion model has been used and the empirical potentials were not specifically fitted to the properties of the substance under study: For this purpose, a simple treatment of anharmonic expansion is proposed. Therefore, the possibility of transferring empirical potentials to widely different groups of minerals and that of developing a routine application to derive accurate values for various properties of pure minerals at various temperatures, starting only from crystal data, are confirmed.