The densities of compounds at high pressures and the state of the Earth's interior

Abstract

A quantum statistical method, already well developed for pure elements, has been extended to the prediction of the equation of state of compounds at extremely high pressures at absolute zero. Application of a finite-strain condition to possible constituents of the earth, found by Birch to be valid for many materials, leads to satisfactory interpolation between the existing laboratory data and the quantum predictions for these materials. The quantum calculations begin to hold at pressures of the order of 1014 dynes/cm2, pressures greatly exceeding those obtainable within the earth. The finite-strain interpolative procedure is assumed to predict the pressure-density relationships at pressures corresponding to those prevailing within the earth. From Bullen's pressure-density values for the earth, it is found that, assuming the absence of phase transitions, the base of the mantle has the same density as an olivine possessing 63 per cent Mg2SiO4. By a similar procedure, the earth's outer core cannot be pure iron, but has the same density as a mixture of 90 per cent iron and 10 per cent olivine. For the temperatures prevailing within the earth, the quantum calculations at absolute zero are not significantly altered; a latitude in the interpolative procedure is indicated at these temperatures, leading to a composition of olivine at the base of the mantle ranging between 47 and 63 per cent Mg2SiO4.