Reconstruction of Rossʹ linear-mixing model for the equation of state of deuterium Original Research Article

The linear mixing (LM) model proposed by Ross [Phys. Rev. B 58 (1998) 669] can accurately reproduce experimental Hugoniot data for shocked liquid deuterium at pressures up to 6 Mbar. Using a simple dissociation scheme, the model smoothly interpolates between (or linearly “mixes”) a molecular fluid equation of state (EOS) applicable at low pressures, and a metallic-like description valid under more extreme conditions, with the relative composition of the mixture determined by minimizing the total Helmholtz free energy of the system. Although the formulation of the LM model is straightforward, it nevertheless involves a series of nontrivial computations and results whose details are fragmented in the published literature. We present an explicit and self-contained reconstruction of the LM model, and correct minor typographical errors that appeared in the original publications. Limitations of Rossʹ approach and comparisons with popular alternate theories are also discussed, although no attempt is made to conduct a thorough survey of existing EOS models for deuterium. Listings of the Mathematica codes used to compute the principal Hugoniot curve, and equilibrium thermodynamic quantities such as the specific heat, Grüneisen coefficient, and sound speed, are provided in the appendices.