Eugene Solomonovich Yakub

Molecular dynamics simulation of premelting and melting phase transitions in stoichiometric uranium dioxide

Results of molecular dynamics (MD) simulation of UO2 in a wide temperature range are presented and discussed. A new approach to the calibration of a partly ionic Busing-Ida-type model is proposed. A potential parameter set is obtained reproducing the experimental density of solid UO2 in a wide range of temperatures. A conventional simulation of the high-temperature stoichiometric UO2 on large MD cells, based on a novel fast method of computation of Coulomb forces, reveals characteristic features of a premelting lambda transition at a temperature near to that experimentally observed (T(lambda)=2670 K). A strong deviation from the Arrhenius behavior of the oxygen self-diffusion coefficient was found in the vicinity of the transition point. Predictions for liquid UO2, based on the same potential parameter set, are in good agreement with existing experimental data and theoretical calculations.

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.

Absolute Helmholtz free energy of highly anharmonic crystals: theory vs Monte Carlo.

We discuss the problem of the quantitative theoretical prediction of the absolute free energy for classical highly anharmonic solids. Helmholtz free energy of the Lennard-Jones (LJ) crystal is calculated accurately while accounting for both the anharmonicity of atomic vibrations and the pair and triple correlations in displacements of the atoms from their lattice sites. The comparison with most precise computer simulation data on sublimation and melting lines revealed that theoretical predictions are in excellent agreement with Monte Carlo simulation data in the whole range of temperatures and densities studied.

Highly Compressed Molecular Hydrogen Near the Melting Line

We studied the radial and angular molecular distribution functions of dense solid hydrogen within non-empirical atom-atom potential (AAP) approximation. Lines of translational and orientational melting were located in the Monte Carlo computer simulation and compared with experiment. Significance of the non-central short-range part of intermolecular repulsion and of molecular non-rigidity in the description of translational and orientational phase transitions in dense condensed hydrogen was demonstrated.

Short-Range Intermolecular Interaction and Phase Transitions with Rearrangement of Chemical Bonds in Solid Nitrogen

We present a simple model describing the short–range interaction between two nitrogen molecules. The possibility of its application to the prediction of phase transitions in solid nitrogen is discussed.

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)} ).