Strong temperature dependence of the first pressure derivative of isothermal bulk modulus at zero pressure

The first pressure derivative of isothermal bulk modulus at zero pressure (K'_0T) is a key equation of state (EOS) parameter. Its variation with temperature is poorly constrained and may influence the inference of composition and temperature of the deep Earth. In the present study, molecular dynamics simulations are performed to derive the K'_0T of MgO from 300 to 3000 K using directly the definition of K'_0T and without relying on any EOS. The most important finding of the present study is that K'_0T depends strongly on temperature. The cross derivative ∂ ²K_0T/∂P∂T is found to be 5.1 ± 1.61 x 10^-4 K^-1 at 300 K, passing to 9.9 ± 2.7 x 10^-4 K^-1 at 1600 K, and reaches 15.1 ± 3.8 x 10^-4 K^-1 at 3000 K. The value at 300 K agrees with 3.9 ± 1.0 x 10^-4 K^-1 of Isaak (1993) within the uncertainty. The experimental adiabatic cross derivative of Chen et al. (1998), which is 2.7 ± 1.1 X 10^-3 K^-1 and often considered too high, is not far from our value of 1.1 ± 0.3 X 10^-3 K^-1 at 1600 K when the experimental and calculation uncertainties are considered. The obtained K_0T are further compared with those from EOS fittings to infer the valid temperature domains of several commonly used EOSs. With this knowledge, the consistency of zero-pressure isothermal bulk modulus (K_0T) from different experimental techniques (direct resonance measurements and fitting isothermal P-V data by an EOS) is demonstrated.