Large dataset test of Birch's law for sound propagation at high pressure

Abstract

Birch's law, prescribing a linear dependence of elastic wave speed on the density in a given material, is an important tool in understanding the composition and thermodynamic conditions of the planetary interior. However, data from direct measurements of elastic wave speed usually have too much of scatter to permit a precise test of this law. Here, we use data from experimental measurements as well as ab initio density-functional-theory based calculations existing in the literature, supplemented by our own data of the latter type for elemental solids, for such a test. Using many such datasets, we show that, although Birch's law is satisfied fairly well in all the cases, the product of elastic wave speed and one-third power of density satisfies linear dependence on density consistently and more accurately than the speed alone. This opens the possibility of more reliable extrapolation of low density velocity data to the higher densities—the primary application of Birch's law.