The Voigt-Reuss-Hill (VRH) Approximation and the Elastic Moduli of Polycrystalline ZnO, TiO2 (Rutile), and α-Al2O3
- 1 May 1968
- journal article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 39 (6) , 2777-2782
- https://doi.org/10.1063/1.1656672
Abstract
The Voigt‐Reuss‐Hill (VRH) approximation, a useful scheme by which one calculates isotropic polycrystalline elastic moduli in terms of the anisotropic single‐crystal elastic constants, is shown to be accurately applicable for ZnO, TiO2 (rutile), and α‐Al2O3, which are the simplest examples of oxide materials with the hexagonal, tetragonal, and trigonal symmetries, respectively. An experimental proof is established by measuring isotropic elastic moduli on dense‐formed polycrystalline specimens. The recommended values of the polycrystalline isotropic elastic moduli of these oxides at room temperature are as follows: for ZnO, G=4.56(±0.04) and E=12.35(±0.09); for TiO2, G=11.15(±0.09) and E=28.42(±0.14); and for α‐Al2O3, G=16.35(±0.12) and E=40.39(±0.31), where G and E are the isotropic shear and Young's moduli, respectively, and they are in units of 1011 dyn/cm2.This publication has 9 references indexed in Scilit:
- Anomalous Behavior of the Shear-Sound Velocity under Pressure for Polycrystalline ZnOJournal of Applied Physics, 1967
- The Voigt-Reuss-Hill Approximation and Elastic Moduli of Polycrystalline MgO, CaF2, β-ZnS, ZnSe, and CdTeJournal of Applied Physics, 1967
- Pressure Derivatives of the Sound Velocities of Polycrystalline AluminaJournal of the American Ceramic Society, 1966
- Variations of the Ultrasonic Pulse-Superposition Method for Increasing the Sensitivity of Delay-Time MeasurementsThe Journal of the Acoustical Society of America, 1965
- Mechanical Properties of Pure, Dense Aluminum Oxide as a Function of Temperature and Grain SizeJournal of the American Ceramic Society, 1964
- A simplified method for calculating the debye temperature from elastic constantsJournal of Physics and Chemistry of Solids, 1963
- The velocity of compressional waves in rocks to 10 kilobars: 2.Journal of Geophysical Research, 1961
- Young's Modulus of Various Refractory Materials as a Function of TemperatureJournal of the American Ceramic Society, 1959
- The Elastic Behaviour of a Crystalline AggregateProceedings of the Physical Society. Section A, 1952