The determination of the elastic properties of composite materials (multiphase aggregates, polycrystals, and porous or cracked solids) from the elastic properties of the components may be approached in several ways. The problem may be treated statistically, via scattering theory, through variational principles, or by the assumption of specific geometries for the material under consideration. Each of these methods is reviewed in turn. The widely used Voigt-Reuss-Hill average can be a poor approximation for both two-phase composites and polycrystals, and its replacement by the two Hashin-Shtrikman bounds is recommended. For pore-containing or crack-containing media, specific geometry models must be considered if useful results are to be obtained. If aggregate theory is used to estimate the moduli of individual components of a composite whose bulk properties are known, the shear moduli of the component phases must be matched (within a factor of 2 or 3) for the method to be useful. Results for nonlinear composites (which allow calculation of the pressure variation of aggregate moduli) have been obtained for only a few special cases.

The Elastic Properties of Composite Materials

Elasticity of Minerals, Glasses, and Melts

The Velocity of Compressional Waves in Rocks to 10 Kilobars, Part 2

Thermal expansions of single-crystal periclase and olivine were measured by a dilatometric method in a temperature range from room-leve1 to 1000°C. The calculated thermal expansion coefficients of periclase and olivine are given in a range of temperature from -250 to 1500°C based on the Gruneisen's theory of thermal expansion. This theory involves several harmonic and anharmonic parameters. The parameters determined in this study are well related to acoustic wave velocities, pressure and temperature derivatives of bulk modulus, Gruneisen's parameter, which have been determined by other means. It is shown that the accurate thermal expansion data provide a good estimation of elastic wave velocities and other physical constants, which are important in the study of the equation of state of the deep interior of the earth.

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Thermal Expansion of Periclase and Olivine, and their Anharmonic Properties

The elastic properties of candidate mantle phases are used to test the viability of olivine-rich (pyrolitic) and CaO + Al_2O_3-rich (eclogitic) assemblages for the mantle. High temperature adiabats for each phase of interest are constructed and compared to mantle seismic properties. Both pyrolitic and eclogitic assemblages satisfy the seismic properties between ∼ 200 and 400 km. Between 400 and 670 km depth an eclogitic assemblage yields a superior match to velocities and velocity gradients. The 400 km seismic discontinuity may represent a chemical boundary between pyrolite and picritic eclogite (“piclogite”) or phase transformations in the olivine + orthopyroxene components of a piclogitic assemblage containing about 16% olivine. High velocity gradients in the transition zone may be explained by the transformation of Ca-rich cpx to majorite garnet. Seismic properties at the top of the lower mantle are consistent with pyrolite, piclogite or perovskite, implying that the 670 km discontinuity may be a chemical boundary.

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Composition of the upper mantle: Geophysical tests of two petrological models

The single‐crystal elastic constants, their temperature coefficients, and the thermal expansion coefficients of natrual nepheline, (KAlSiO4)(NaAlSiO4)3, have been measured. The longitudinal modulus c11 and the shear modulus c66 have positive temperature coefficients. Since this implies the existence of a wide range of directions with a zero temperature coefficient of the ultrasonic travel time, nepheline may be a suitable substrate for ultrasonic surface‐wave signal processing devices.

G. R. Barsch

Papers

Elastic and thermoelastic constants of nepheline