Equation of State of Periclase and Birch's Relationship between Velocity and Density

Abstract

BASED on systematic investigation of velocity of compressional waves in isotropic aggregates of oxides and silicates at high pressure, Birch¹ observed that velocity is proportional to density for substances with similar mean atomic weight. He concluded that velocity in isotropic aggregates of oxides and silicates is a function of two principal variables—density and mean atomic weight—the variation of density for substances with the same mean atomic weight reflects differences of structure and composition. Birch also postulated that for a given substance, velocity and density may be related in much the same way when they are changed by compression, and this postulate was used in attempts to determine the density distribution in the Earth². Later, McQueen et al.³ noticed that, for similar materials, the bulk sound velocity is also proportional to density. Many of Birch's determinations of the velocity of compressional waves V_p may now be combined with Simmons's⁴ determinations of the velocity of shear waves V_s to yield the bulk sound velocity C defined as for these determinations were made in the same laboratory with almost identical samples. Nai-hsien Mao (private communication) has confirmed these findings with many more data. This relationship may be expressed as where ρ is density and a and b are constant coefficients for substances with the same mean atomic weight; both coefficients may be functions of the mean atomic weight.