Two-Phase (γ,α) Equation of State for Cerium and Features of its Dynamic Compression

Abstract

The unusual thermodynamic properties of cerium result from features in the narrow 4f-zone whose electrons are subdivided into localized and delocalized subsystems. In this paper the model of pseudo-binary solid solutions allowing for two different electronic states is applied to construct the thermodynamically complete two-phase equation of state for cerium. The parameters of the model were fitted to describe the thermodynamic data obtained in the static experiments with high-purity cerium. This equation of state was used to analyze wave structures realized under dynamic compression with regard to the equilibrium (γ,α) phase transition.Cerium possesses a great variety of unusual properties among which are the presence of a critical point on the line of the isomorphic (γ-α)-transition and also the anomalous behavior of elastic and thermal properties in its neighborhood. Furthermore, the phase diagram of cerium, which contains a great number of phases, is characterized by considerable complexity and inconsistency.Investigations into the phase diagram and properties of cerium in the high-pressure region were pursued under static [1-12] and dynamic [13][14][15] compression conditions. In this paper the dynamic compression of Ce is considered with the use of a thermodynamically complete two-phase equation of state (EOS) for the γ-and α-phases. As the basis for the formulation of the equation of state, the model of pseudobinary solid solutions, developed by Aptekar and Ponyatovsky [16], is applied for the description of anomalous behavior of Ce in the neighborhood of the (γ-α)-transformation. In the model, cerium is presented as a solid substitution solution composed of Ce atoms in various electronic states. According to present views, a difference in the electronic states of the α-and γ-phases is in various screening levels of spins of localized 4f electrons (Kondo volume-collapse model), or in localization (γ-phase) and delocalization (α-phase) of 4f electrons (Mott transition). But for the semi-empirical model, the refinement of electronic states is of little significance; their energy closeness is a decisive factor.The specific (per mole) thermodynamic Gibbs potential for the mixture of two kinds of cerium atoms being in sites of the fcc lattice is written in the form [16], G

Investigation of phase transformations in iron and cerium using a polyvinylidene fluoride pressure gauge

“…With a further rise in pressure, a two-wave configuration consisting of a head wave of isentropic compression followed by a shock wave occurs in cerium. In [14], it is also noted that an α-ε phase transformation (IV-V in Fig. 4) is possible in the pressure range of 6-10 GPa.…”

“…As the loading intensity is increased, the pressure at the point of connection decreases. Apparently, exactly this was meant by the authors of the model of [14], who noted that the initial state over which the shock wave propagates varies with the shock loading intensity -the initial state slides along the head isentropic wave.…”

“…The free parameters of the model are chosen so as to give the best fit to the experimental data on the thermodynamic properties of high-purity cerium under static conditions. This equation of state was used in [14] to analyze the possible wave structures arising from the dynamic compression of cerium with allowance for the phase γ-α transformation. It is shown that in the pressure range up to the completion of the γ-α transition, cerium is compressed isentropically without shock wave formation.…”

“…In this model, nonalloyed cerium is treated as a solid substitution solution composed of atoms with different electron configurations. Using the model of [9], El'kin et al [14] constructed a thermodynamically complete two-phase equation of cerium for the description of its dynamic compression. The free parameters of the model are chosen so as to give the best fit to the experimental data on the thermodynamic properties of high-purity cerium under static conditions.…”

Predictions from the equation of state of cerium yield interesting insights into experimental results

“…It has been known that cerium as a result of the low pressure phase transition dynamically shows a two wave character indicative of the y-a phase transition [4]. One of the co-authors here presented the framework for a multi-phase equation of state that characterized the region between the y and the a phases [5,6] based on some early thermodynamic work of Aptekar and Ponyatovskiy [7,8].…”