Comments on the power law representation of Birch's law

The systematics of the sound velocity-density-mass patterns found in minerals and rocks have been almost universally agreed upon, although graphical representations of the data take several forms. A growing body of literature now correlates the data by means of power law expressions rather than by straight-line plots, as were first presented by Birch. A few discrepancies still remain between some mineral data and the best graphical representations of Birch's law. This paper explains the discrepancies evidenced by the high-pressure polymorphs of silica in terms of well-recognized thermodynamic formulas. It is pointed out that the simpler forms of the power law representations assume implicitly the Murnaghau equation of state. By allowing the exponent on density in the power law to be a function of density according to other equations of state, Birch's law comes much closer to predicting the sound velocities of the high-pressure phases of silica.