Constraints on the structure and dynamics of the β-cristobalite polymorphs of SiO₂ and AlPO₄ from ³¹P, ²⁷Al and ²⁹Si NMR spectroscopy to 770 K

Abstract

Nuclear magnetic resonance spectroscopic data are presented for the cristobalite polymorphs of AlPO₄ and SiO₂ from RT to 770 K, through their respective α-β transitions. The nuclear magnetic resonance (NMR) data include chemical shifts for ³¹P, ²⁷Al, and ²⁹Si, ²⁷Al quadrupole coupling parameters, and ³¹P and ²⁷Al spin-lattice relaxation rates. Also presented are electron diffraction patterns of β-cristobalite AlPO₄ that show diffuse scattering similar to that reported previously for SiO₂. For the α-phases of both AlPO₄ and SiO₂, the chemical shifts decrease approximately linearly with increasing temperature from RT to T_c and discontinuously by -2 to -3 ppm from α to β. This result is consistent with a small, continuous increase in the mean T-O-T angle (〈θ〉) of the α-phases with increasing T and an increase of 〈θ〉 by about 4° across the α-β transition for both cristobalite and its AlPO₄ analogue. Based on the ²⁹Si chemical shifts, the mean Si-O-Si angle for β-cristobalite is 152.7±1° near T_c. For AlPO₄-cristobalite, the ²⁷Al nuclear quadrupole coupling constant (C_Q) decreases approximately linearly from 1.2 MHz at RT to 0.94 MHz near T_c (493±10 K). At the α-β transition the ²⁷Al C_Q approaches zero, in agreement with the cubic average structure observed by diffraction. The satellite transitions retain a small frequency distribution above the α-β transition from electric field gradients attributed to defects. The short-range cubic symmetry of the Al-site and non-linear Al-O-P angle support a dynamically disordered model of the β-cristobalite structure. Complete averaging of the ²⁷Al quadrupole coupling in the β-phase indicates that the lifetime of any short-range ordered domains must be shorter than about 1 μs.