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.
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