Birch's law and polymorphic phase transformations

Abstract

Birch's law implies a unique relationship between elastic wave velocity υ and density ρ for materials of common mean atomic weight M¯ irrespective of whether density changes are due to crystallographic structure, pressure, or temperature. Velocity data are presented for materials undergoing the olivine-spinel, olivine-beta phase, quartz-rutile, pyroxene-garnet, pyroxene-ilmenite, and ilmenite-perovskite phase transformations. These data indicate that υ-ρ relationships across such polymorphic transformations are not always equivalent to υ-ρ changes caused by varying pressure, temperature, or composition at constant mean atomic weight. For the earth these data imply that previous discussions of the composition (specifically the iron content) of the upper and lower mantles based on υ-ρ systematics may have to be reevaluated.