High‐Temperature Elastic Moduli of Flux‐Grown α‐GeO₂ Single Crystal

Abstract

From high-precision Brillouin spectroscopy measurements, six elastic constants (C11, C33, C44, C66, C12, and C14) of a flux-grown GeO2 single crystal with the α-quartz-like structure are obtained in the 298-1273 K temperature range. High-temperature powder X-ray diffraction data is collected to determine the temperature dependence of the lattice parameters and the volume thermal expansion coefficients. The temperature dependence of the mass density, ρ, is evaluated and used to estimate the thermal dependence of its refractive indices (ordinary and extraordinary), according to the Lorentz-Lorenz equation. The extraction of the ambient piezoelectric stress contribution, e11, from the C'11-C11 difference gives, for the piezoelectric strain coefficient d11 , a value of 5.7(2) pC N(-1), which is more than twice that of α-quartz. As the quartz structure of α-GeO2 remains stable until melting, piezoelectric activity is observed until 1273 K.

Flux-Grown Piezoelectric Materials: Application to α-Quartz Analogues

“…The values of the flux-grown single crystal elastic stiffness constants C E IJ compared with those obtained by Brillouin or pulse-echo methods on hydrothermally-grown samples, Table 1, are in good accordance while large discrepancies exist with the computed values concerning C The room temperature experimental values of single-crystal elastic stiffness constants C E IJ at constant electric field of flux-grown α-GeO 2 in MoO 3 -based solvents were determined using Brillouin scattering, Table 2 [109]. In this work, three platelets were used, defined in the standard Cartesian coordinate system as X-plate, Y-plate and Z-plate which respectively correspond to the (100), (2)(3)(4)(5)(6)(7)(8)(9)(10) and (003) (hkl)-crystallographic planes.…”

“…The crystal elastic constants values of the MoO 3 -based flux-grown α-GeO 2 material present close similarities with most of the published C IJ data on hydrothermally-grown α-GeO 2 crystals, Table 2. Therefore, the small discrepancy, registered more especially on the C 11 and C 14 moduli, was attributed to the strong reduction of the OH concentration in the lattice of flux-grown α-GeO 2 crystals which was believed to induce a slightly stiffer behavior [109]. The presence of OH-interactions in the crystal would increase its ionic character and consequently softer its elastic behavior.…”

“…In agreement with infrared measurements [27,93], neither hydroxyl groups nor water inclusions were detected by Raman spectroscopy. Furthermore, these MoO 3 -based flux-grown α-GeO 2 samples were heated up to 1000 °C several times without presenting the well-known milky hue attributed to the release of water from hydroxyl impurities with increasing temperature [109]. Ambient polarized Raman measurements performed on flux-grown α-quartz GeO 2 single crystals along with state of the art density functional theory (DFT) based calculations were reported [93,106,107].…”

“…Powder X-ray patterns of flux-grown α-GeO 2 were registered at several temperatures from room temperature up to 1050 °C [93,109]. For each studied temperature, the whole diffraction pattern was assigned to the α-quartz phase of GeO 2 .…”

“…These flux-grown α-GeO 2 C IJ values are compared in Table 2 with recent computed [109,114,115] and experimental elastic constant data obtained from hydrothermally-grown crystals [23,24,116]. C D IJ are elastic stiffness constants at constant electric displacement i.e., not corrected from the piezoelectric effect where e 11 is the piezoelectric stress constant and ε 11 the dielectric tensor at constant strain.…”