Based on the available data of specific heat Cv. at constant volume and the Grüneisen parameter γ of both lattice and electron contributions, we present a consistent method for simultaneously calculating the effective or synthesized Crüneisen parameter along Hugoniot, γeH, covering solid, mixed, and liquid states, and the melting temperature Tm for ε-iron. The rationality validation for this method is confirmed as compared with the experimental data, including the measured Tm and Hugoniot bulk sound velocities Cb. The calculated γeH and Tm for ε-iron at the Earth's inner-core boundary (330 GPa) are 1.58 and 5930K, respectively, which are close to the values of 1.53 and 6050K given by Anderson [J. Phys. Chem. Solids 64 (2003) 2125]. This method for determination of γeH could be, in principle, also applicable to any thermodynamic state calculations, e.g., along isothermal and isentropic paths, other than the Hugoniot locus.
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