A thermodynamically complete equation of two-phase (gamma, alpha) state of cerium was derived in terms of a pseudobinary solid-solution model developed by Aptekar' and Ponyatovskii. According to the model, unalloyed cerium is considered to be a substitutional solid solution whose components are represented by atoms with different electron configurations. The free energy of the individual phases (solid-solution components) is represented as a sum of three terms that describe the atomic interaction at T = 0 K, quasi-harmonic lattice vibrations, and the combined contribution of the anharmonicity and thermally excited electrons. The equation of state is shown to adequately describe the unusual behavior of cerium under the effect of static actions. In this work, calculations of the dynamic compression of cerium are performed. The calculations indicate that, up to the completion of the gamma-alpha transition, the formation of the shockwave front in cerium is impossible and compression of cerium occurs in an isentropic wave of simple compression. As the pressure increases, a multiwave configuration with the participation of isentropic and shock waves is realized in cerium. The initial state in which the shock wave is propagated changes depending on the wave intensity; i.e., the initial state "slides" along the leading isentropic wave. The shock adiabat was shown to not pass through the very complex range of metastable existence of alpha-, alpha'-, and alpha '' phases. This provides prerequisites for experimental finding the alpha-epsilon transformation which can occur in the shock wave and is not masked with the preceding alpha-alpha' and alpha'-alpha '' transformations. When assuming the absence of the alpha-epsilon transformation, the calculated coordinates of the point corresponding to the start of melting in the shock wave are p(melt) = 11.3 GPa and T-melt = 1130 K.
