Lattice dynamics and Born instability in yttrium aluminum garnet, Y₃A1₅O₁₂

Abstract

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.

The Sm:YAG primary fluorescence pressure scale

“…This implies that the Sm:YAG garnet structure becomes mechanically unstable beyond this pressure. This observation is in agreement with recent lattice dynamic calculations [ Goel et al ., ; Saunders et al ., ], which predict a mechanical instability of YAG associated with a d C 44 /d P < 1 above 108 GPa [ Goel et al ., ].…”

Electronic and elastic properties of yttrium gallium garnet under pressure from ab initio studies

“…In some cubic binary compounds, the C 44 softening can be related with a phase transition mechanism. 29 Recent studies in YAG from empirical lattice dynamic calculations 8 and from atomistic model 30 report that YAG becomes mechanically unstable around 108 GPa due to the violation of the Born stability criteria by C 44. Reported experimental energy dispersive X-ray diffraction results suggest that the longrange crystalline order of Sm-doped YAG 31 is lost beyond 100 GPa.…”

“…The high degree of complexity and the big amount of atoms in the garnet structure justify the absence of previous ab initio studies of the electronic, structural, and dynamical properties both at room and high pressures in many garnets and in particular in YGG. Most of the theoretical studies of some of most known garnets, like YAG, have been investigated by means of atomistic approach involving semi-empirical interatomic potentials with the rigid ion model (RIM), 8 and also few first-principles density functional theory (DFT) calculations for the ground-state have been performed. 7 The use of ab initio DFT simulations for the study of materials under extreme conditions is a very well established technique in the field of high pressure semiconductor physics.…”

Structural, elastic and vibrational properties of nanocrystalline lutetium gallium garnet under high pressure

“…13,14 In spite of the fact that the use of ab initio density functional theory (DFT) calculations for the study of materials under extreme conditions is a very well established technique in the field of high pressure semiconductor physics, 15 most of the theoretical studies of some of the best-known garnets, like Y 3 Al 5 O 12 , have been performed by means of an atomistic approach involving semi-empirical interatomic potentials using the rigid ion model (RIM) 14 and by first-principles density functional theory (DFT) calculations only for the groundstate. 13,14 In spite of the fact that the use of ab initio density functional theory (DFT) calculations for the study of materials under extreme conditions is a very well established technique in the field of high pressure semiconductor physics, 15 most of the theoretical studies of some of the best-known garnets, like Y 3 Al 5 O 12 , have been performed by means of an atomistic approach involving semi-empirical interatomic potentials using the rigid ion model (RIM) 14 and by first-principles density functional theory (DFT) calculations only for the groundstate.…”