Estimation of the free energy of charge transfer in molten UO₂

Abstract

The free energy change associated with the charge transfer reaction 2U^4-→U³⁺ + U⁵⁺ in molten UO₂ is estimated and it is argued that this will play an important role in determining the thermodynamic and transport properties of the melt. The calculations are based on the assumption that modification of its charge affects only the Coulomb interaction of a uranium ion with the other ions in the system, the short-range interactions being unchanged. It is shown that the required free energy may be expressed in terms of the average electric potential at the ion, which in turn depends on the radial distribution functions describing correlations with the other ions. The hypernetted chain approximation is used to calculate these radial distribution functions. This approximation is demonstrated to be accurate by testing it on an analogue charge-transfer reaction in molten alkali halides, for which experimental data are available. It is found that the free energy of the reaction in molten UO₂ is about 1·7 eV lower than its value in the solid at zero temperature and probably has a value of about 0·7 eV. This implies that a substantial fraction of uranium ions in the melt are in the charge states U³⁺ and U⁵⁺.