A comparative study of Keane's and Stacey's equations of state

We present a comparative study of Keane's and Stacey's equations of state (EOS), which are based on the variations of K′ with pressure. It is found that higher derivative properties, such as the pressure derivatives of the isothermal bulk modulus K, viz. K″=d2K/dP2 and K‴=d3K/dP3 calculated from the two equations, differ appreciably from each other. In the limit of infinite pressure, KK″ and K2K‴ both tend to zero, but the ratio K2K‴/KK″ remains finite for both the EOS. This property has been used to prove that the second volume derivative of the Grüneisen parameter γ, represented by λ, remains finite (λ→λ∞) in the limit of infinite pressure, a result consistent with thermodynamics of solids. Values of λ∞ for the lower mantle and the core of the Earth have been obtained using the generalized free-volume formula with the help of Keane's and Stacey's equations. The expressions for λ∞ based on the two EOS differ substantially from each other.