Igor Lvovitch Iosilevski

Thermodynamic model of solid non-stoichiometric uranium dioxide

A new equation of state for solid UO2+x is presented, based on an extended ionic model. A thermodynamic description of the imperfect and non-stoichiometric ionic solid is obtained accounting for short- and long-ranged inter-ionic forces, as well as for formation of Frenkel defects. Both Coulomb and short-range interactions between defects are encompassed in a highly non-ideal ionic system where interactions of Frenkel defects are taken into account explicitly as short-ranged interactions of quasi-dipoles. A simplified analytical form for the free energy of the perfect anharmonic crystal was obtained and then combined with additional contributions from formation and interaction of defects. By fitting a few numerical constants, the variations of thermodynamic properties of UO2+x are predicted as functions of temperature, density and stoichiometry. The model describes the pre-melting transition into the superionic state in solid stoichiometric UO2 and predicts the behaviour of the transition line in the non-stoichiometric domain.

Equation of State of UO2

An international project supported by INTAS (International Association for Promotion of Cooperation with Scientists from the New Independent States of the former Soviet Union) was started in 1994 with the intent of constructing an equation of state (EOS) for liquid and gaseous UO2, which fully reproduces the comprehensive thermodynamic database for this compound. The new equation of state was devised for applications encompassing hypo- and hyper-stoichiometric compositions. A so-called “chemical model” was used for the theoretical description of liquid urania. This model is based on the thermodynamic perturbation theory (TPT) modified in order to account for the specific properties of the system investigated. It describes, in a unified formalism, a multicomponent mixture of chemically reactive, strongly interacting neutral and charged molecules and atoms. Comparisons of the predicted equilibrium vapor pressures with literature data provided an initial validation of the model up to temperatures of the order of 5500 K. A further, positive result is the fairly good agreement of the predicted heat capacity with experimental values, which extend up to 8000 K. A characteristic feature of non-congruentvaporization in UO2±x is the production of a very high maximum vapor pressure (Pmax∼1 GPa) as well as a substantial oxygen enrichment of the vapor phase over boiling UO2 ((O/U)max∼7). The critical point of a truly non-congruent phase transition in UO2 was also calculated. This point essentially differs from that defined for a gas–liquid phase transition in simple liquids; in particular, the equation (∂P/∂V)c∼(P/V)≠0 applies here. The predicted critical parameters are: Tc≈10120 K, Pc≈965 MPa, ρc≈2.61 g·cm−3.

Equation of state of shock compressed plasma of metals

For the example of shock compressed nickel and iron, one can see that the chemical model can provide satisfactory description of strongly coupled plasma of expanded metals. The same agreement with experimental data was achieved for copper and lead [13,14].

Phase Transition in Simplest Plasma Models

The well-known simplest plasma model One-Component Plasma (OCP) is the system of free moving charges of the same sign in the uniform compensating background of opposite sign. This model is studied carefully nowadays [1÷3]. It should be emphasized that this model is not the single one but it is the family of models in fact. The difference may be in the additional short-range interaction and in the type of statistics, but the main subject for the following discussion is the difference in the nature and the thermodynamic role of background.

Spinodal Decomposition of Metastable Melting in the Zero‐Temperature Limit

“Conventional” scenario of metastable melting in ordinary substances in the limit of zero temperature assumes that the melting curve reaches the matter zero isotherm (“cold curve”). The same is true for standard variant of one‐component plasma model on rigid compensating background in both limits: classical and “cold” quantum melting. The modified OCP on uniform, but compressible background shows the completely different scenario of the metastable melting closure. The remarkable feature of this scenario is that the liquid freezing curve terminates at liquid spinodal curve of 1st‐order liquid gas phase transition, which takes place in this type of OCP models (“spinodal decomposition”).

Anomalous Phase Diagrams in the Simplest Plasma Models

Remarkable feature of new first‐order phase transitions of gas‐liquid gas‐crystal types in combination with traditional solid‐liquid transition are under consideration in a modified one‐component plasma model (OCP) with uniform, but compressible background. Structure and parameters of this phase transition strongly depend on the value of charge number Z. Under high values of Z the model shows remarkable and completely unusual topology of phase diagram.

Thermodynamic Properties of UO2, as Predicted by the New Equation of State

This chapter contains the description of the eventually recommended equation of state for uranium oxide, called here INTAS-99-EOS, as expressed in terms of models and sub-models presented in the previous Chapters. In the frame of the chemical model approach, this equation probably represents the most comprehensive EOS of UO2±x, affordable by optimal use of the presently available theoretical tools and experimental databases. The equation is of a MIX type, as sketched in Chapter 2; the details of its structure are explained and discussed in Chapters 3 to 6. After a recapitulation of the fundamental hypotheses and a summary of the main features, this Chapter is dedicated to the presentation of an extensive set of numerical calculations and to the comparison with predictions of alternative models.

Gas-Liquid Coexistence in Uranium Dioxide

The general condition of equilibrium, i.e., the requirement of the minimum of the corresponding thermodynamic potential, (e.g., of the Gibbs free energy with respect to N, P, and T, or of the Helmholtz free energy with respect to N, V, and T taken as independent variables) includes also the phase equilibrium. If the system considered is or can be separated into two or more phases, and if the surface inter-phase contribution is negligible, the corresponding thermodynamic potential is a linear combination of the thermodynamic potentials of the single phases. For example, if only two phases exist, e.g., liquid and vapour (for definiteness under isothermal — isochoric conditions), the thermodynamic potential (Helmholtz free energy) can be expressed as:

Governing Equations and Fundamental Formulae

\mathcal{F}(T,\mathcal{V},N_1 ,...,N_M ) = \mathcal{F}^{(liq)} (T,\mathcal{V}^{(liq)} ,N_1^{(liq)} ,...,N_M^{(liq)} ) + \mathcal{F}^{(vap)} (T,\mathcal{V}^{(vap)} ,N_1^{(vap)} ,...,N_M^{(vap)} ).