Estimation of bulk modulus and sound velocities of oxides at very high temperatures

Bulk modulus and sound velocities of oxides and silicates up to very high temperatures are estimated from experimental data on sound velocity obtainable at relatively low temperatures. Data for MgO, Al2O3, and Mg2SiO4 are used to illustrate the method. The theoretical basis for this method is the establishment of a linear dependence of the bulk modulus on temperature at elevated temperatures by use of the Mie-Gruneisen equation of state. The parameters required are the room-temperature values of the bulk modulus, density, thermal expansion, Gruneisen constant, and the measured enthalpy as a function of temperature. The variation of the shear and longitudinal velocities with temperature are determined from the calculated variation of the bulk modulus and shear modulus with temperature. The relations presented should apply to all materials likely to exist in the earth's mantle and, therefore, should provide a useful means of considering the effect of the geothermal gradient on the properties of rock-forming compounds.

[1]  M. A. Durand.  The Temperature Variation of the Elastic Moduli of NaCl, KCl and MgO , 1936 .

[2]  O. Anderson.  Conditions for a density minimum in the upper mantle , 1965 .

[3]  J. B. Wachtman,et al.  Young's Modulus of Various Refractory Materials as a Function of Temperature , 1959 .

[4]  N. Soga.  COMPARISON OF MEASURED AND PREDICTED BULK MODULI OF TANTALUM AND TUNGSTEN AT HIGH TEMPERATURES , 1966 .

[5]  F. Birch.  Elasticity and Constitution of the Earth's Interior , 1952 .

[6]  O. Anderson,et al.  Pressure Derivatives of Elastic Constants of Single‐Crystal MgO at 23° and ‐195.8°C , 1966 .

[7]  E. Stern.  Theory of the Anharmonic Properties of Solids , 1958 .

[8]  O. Anderson,et al.  High‐Temperature Elastic Properties of Polycrystalline MgO and Al2O3 , 1966 .

[9]  J. B. Wachtman,et al.  Linear Thermal Expansion of Aluminum Oxide and Thorium Oxide from 100° to 1100°K , 1962 .

[10]  J. B. Wachtman,et al.  Exponential Temperature Dependence of Young's Modulus for Several Oxides , 1961 .

[11]  O. Anderson,et al.  Derivation of Wachtman's Equation for the Temperature Dependence of the Elastic Moduli of Oxide Compounds , 1966 .

[12]  W. Lawrence,et al.  Relation of Single‐Crystal Elastic Constants to Polycrystalline Isotropic Elastic Moduli of MgO: II, Temperature Dependence , 1964 .

[13]  O. Anderson,et al.  Temperature dependence of the velocity derivatives of periclase , 1966 .

[14]  R. I. Beecroft,et al.  An experimental equation of state for sodium , 1961 .

[15]  E. H. Bogardus.  Third‐Order Elastic Constants of Ge, MgO, and Fused SiO2 , 1965 .

[16]  S. P. Marsh,et al.  On the composition of the Earth's interior , 1964 .

[17]  Naohiro Soga,et al.  Simplified Method for Calculating Elastic Moduli of Ceramic Powder from Compressibility and Debye Temperature Data , 1966 .

[18]  A. E. Ringwood,et al.  Density distribution and constitution of the mantle , 1964 .