GARNET CRYSTAL-STRUCTURES - AN AB-INITIO PERTURBED ION STUDY

An ab initio perturbed ion (aiPI) study using X-ray diffraction data h as been carried out for pure and doped calcium aluminum silicate garne t, Ca3Al2Si3O12 (grossularite, GROS), and yttrium aluminum garnet, Y-3 -Al5O12 (YAG); crystal structures. Different clusters containing from 55 to 139 ions have been built up, using large Slater type orbitals (S TOs)to represent each atomic center. Basis sets and geometry optimizat ions have been performed with the aim of determining the relative stab ility, cell parameters, force constants, and vibrational frequencies o f radial displacements associated with the local relaxation for pure a nd doped structures. Numerical results are compared with experimental data, and the geometrical cell parameters of different structures obta ined by computer simulation are found to be similar to the experimenta l results. This comparison validates the aiPI methodology used in the theoretical characterization of the local properties of complex ionic systems. For GROS, the substitution of Cr3+ for Al3+ at the octahedral site is energetically favorable while the substitution of Cr4+ for Si 4+ at the tetrahedral site is unstable. For YAG, the substitution of C r3+ for Al3+ at octahedral or tetrahedral sites is energetically unfav orable. The differences between the ionic radii reported by Shannon an d Prewitt for the species concerned in the doping process are capable of explaining the relaxation of crystal lattice parameters for tetrahe dral sites. However, the relaxation in octahedral sites is lower than the differences in ionic radii. The doping process produces a decrease of force constant (k) values associated with the breathing fundamenta l vibrational mode for YAG garnet while an opposite effect appears in GROS. The k associated with the radial displacement in octahedral subs titution in grossularite is especially high. The bulk modulus of the p ure structures has also been theoretically calculated, GROS being less compressible than YAG.