Lattice dynamics and Born instability in yttrium aluminum garnet, Y3Al5O12.

We report lattice dynamics calculations of various microscopic and macroscopic vibrational and thermodynamic properties of yttrium aluminum garnet (YAG), Y3Al5O12, as a function of pressure up to 100 GPa and temperature up to 1500 K. YAG is an important solid-state laser material with several technological applications. Garnet has a complex structure with several interconnected dodecahedra, octahedra and tetrahedra. Unlike other aluminosilicate garnets, there are no distinct features to distinguish between intramolecular and intermolecular vibrations of the crystal. At ambient pressure, low energy phonons involving mainly the vibrations of yttrium atoms play a primary role in the manifestations of elastic and thermodynamic behavior. The aluminum atoms in tetrahedral and octahedral coordination are found to be dynamically distinct. Garnet's stability can be discerned from the response of its phonon frequencies to increasing pressure. The dynamics of both octahedral and tetrahedral aluminum atoms undergo radical changes under compression which have an important bearing on their high pressure and temperature properties. At 100 GPa, YAG develops a large phonon bandgap (90-110 meV) and its microscopic and macroscopic physical properties are found to be profoundly different from that at the ambient pressure phase. There are significant changes in the high pressure thermal expansion and specific heat. The mode Grüneisen parameters show significant changes in the low energy range with pressure. Our studies show that the YAG structure becomes mechanically unstable around P = 108 GPa due to the violation of the Born stability criteria. Although this does not rule out thermodynamic crossover to a lower free energy phase at lower pressure, this places an upper bound of P = 110 GPa for the mechanical stability of YAG.