Parameterization of the crystal structure of garnet in terms of symmetry-adapted basis-vectors of the ideal tetrahedron and octahedron: Application to the pressure-dependence of the crystal structure of Y3Al5O12 between 0 and 126 GPa

Non-linear optimisation of the anion coordinates in garnet-structured compounds (A(3)B(2)C(3)O(12)) with space group Ia (3) over bard has been used to define a universal prototypic crystal structure in which the tetrahedral site (CO4) and the octahedral site (BO6) exhibit close to the ideal point group symmetries of (4) over bar 3m and m (3) over barm respectively. Distortions in actual garnet-structured compounds are then described in terms of condensed normal modes of the two isolated, ideal polyhedra that are consistent with the site point group symmetry within the space group Ia (3) over bard. The methodology is applied to the pressure-dependence of the crystal structure of Y3Al5O12 from 0 GPa to 126 GPa that have been determined from first-principles calculations. The structural evolution of Y3Al5O12 with pressure is dominated by changes in the (AlO4)-O-iv site which rotates and becomes significantly more regular as pressure increases. The coupled response of the octahedral site is more complex as it responds to the changes in the tetrahedral site. The evolution of the crystal structure of YAG with pressure is briefly compared to the experimentally determined pressure-dependence of the crystal structure of pyrope, Mg3Al2Si3O12.