Harmonic and anharmonic properties of spinel MgAl2O4
-
Isao Suzuki
,
Ichiro Ohno
Abstract
The resonant sphere technique, RST, was applied to measure the elastic moduli of spinel. Resonant frequencies of 23 modes were measured between 293 and 1167 K. Results are similar to previous measurements by two of the authors (IS and OLA) using a rectangular prism specimen in that resonant frequencies of all modes decrease with temperature, and some modes show discontinuous change of slopes near 904 K. In the present work, inversion calculations of the frequency data to obtain elastic moduli was repeated until the standard error, s, was minimized so that s = 0.16 kHz (0.012%). Elastic moduli and their probable errors in GPa are: C11 = 281.310 ± 0.014, C12 = 155.437 ± 0.013, C44 = 154.587 ± 0.007, and Cs = 62.936 ± 0.003, where density p = 3.5846 g/cm3 at 293 K. The anisotropy factor is A = C44/Cs = 2.46 and is much larger than that of other cubic crystals. Isotropic properties are: bulk moduli, KS = 197.39 ± 0.01 GPa; isothermal bulk modulus, KT = 196.20 GPa; and rigidity modulus, μ = 107.81 GPa (the Hill average).
Temperature dependence was clarified for elastic moduli in which one of shear moduli, Cs [= (C11 - C12)/2] shows a distinctive bend at Tc = 904 K. The bend in KS [ = (C11 + 2C12)/3] at Tc is less pronounced because of opposite changes of slopes for C11 and C12 at 904 K. Combining elasticity and thermal expansivity data, we evaluate anharmonic parameters, resulting in the Grüneisen parameter, γ = 1.17, and the Anderson-Grüneisen parameters, δS = 2.98 and δT = 4.72 at T = 300 K; whereas, these are parameters are 1.10, 4.46, and 6.37, respectively, at T = 1200 K. The Grüneisen parameter is about 0.1 lower on the high-temperature side of Tc compared to its value on the lowtemperature side
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Thermal expansivity of mantle relevant magnesium silicates derived from vibrational spectroscopy at high pressure
- Differential laser-interferometer for thermal expansion measurements
- New diamond anvil cells for gigahertz ultrasonic interferometry and X-ray diffraction
- Elasticity measurement of silica glass under gas pressure
- Sound velocities of wadsleyite b-(Mg0.88Fe0.12)2SiO4 to 10 GPa
- Sound velocities and elastic properties of g-Mg2SiO4 to 873 K by Brillouin spectroscopy
- Harmonic and anharmonic properties of spinel MgAl2O4
- The MD simulation of the equation of state of MgO: Application as a pressure calibration standard at high temperature and high pressure
- Ab initio structure of MgSiO3 ilmenite at high pressure
- Thermoelasticity of silicate perovskites and magnesiowüstite and its implications for the Earth’s lower mantle
- Thermodynamic functions at zero pressure and their relation to equations of state of minerals
- Accuracy of equation-of-state formulations
- Extrapolation of lower mantle properties to zero pressure: Constraints on composition and temperature
- Constraints on the P-V-T equation of state of MgSiO3 perovskite
- Structure analysis and stability field of β-iron at high P and T
- Iron phases at high pressures and temperatures: Phase transition and melting
- Calculated melting curves for phases of iron
- Grüneisen parameter of e-iron up to 300 GPa from in-situ X-ray study
- Grüneisen parameters and isothermal equations of state
Articles in the same Issue
- Thermal expansivity of mantle relevant magnesium silicates derived from vibrational spectroscopy at high pressure
- Differential laser-interferometer for thermal expansion measurements
- New diamond anvil cells for gigahertz ultrasonic interferometry and X-ray diffraction
- Elasticity measurement of silica glass under gas pressure
- Sound velocities of wadsleyite b-(Mg0.88Fe0.12)2SiO4 to 10 GPa
- Sound velocities and elastic properties of g-Mg2SiO4 to 873 K by Brillouin spectroscopy
- Harmonic and anharmonic properties of spinel MgAl2O4
- The MD simulation of the equation of state of MgO: Application as a pressure calibration standard at high temperature and high pressure
- Ab initio structure of MgSiO3 ilmenite at high pressure
- Thermoelasticity of silicate perovskites and magnesiowüstite and its implications for the Earth’s lower mantle
- Thermodynamic functions at zero pressure and their relation to equations of state of minerals
- Accuracy of equation-of-state formulations
- Extrapolation of lower mantle properties to zero pressure: Constraints on composition and temperature
- Constraints on the P-V-T equation of state of MgSiO3 perovskite
- Structure analysis and stability field of β-iron at high P and T
- Iron phases at high pressures and temperatures: Phase transition and melting
- Calculated melting curves for phases of iron
- Grüneisen parameter of e-iron up to 300 GPa from in-situ X-ray study
- Grüneisen parameters and isothermal equations of state
