Thermodynamic modelling of the uranium-tellurium system. Estimation of the uncertainties by a Bayesian approach.
Résumé
Under irradiation, the formation of fission products in the (U,Pu)O2 fuel with time has a
substantial effect on its chemistry. In particular, migration of the most volatile fission products (Cs,
Te, I, Mo) from the center to the periphery of the fuel pellet is induced by the large radial thermal
gradient. To predict the thermodynamic properties of the irradiated fuel, thermodynamic modeling
of the complex multi-component (Cs-I-Te-Mo) (U-Pu) O system is performed using the CALPHAD
method. In this work, the thermodynamic assessment of the U Te sub-system is performed. The
literature review reveals a lack of experimental data as well as scattering and inconsistency of some
of the data. In particular, no thermodynamic data exist on the liquid. From this review, input
thermodynamic and phase diagram data are carefully selected. The Gibbs energy functions are then
adjusted by fitting these data. An overall good agreement is obtained with all the selected data
except for the enthalpy of formation for UTe which is underestimated by 13% by our model. This
could be due to an inconsistency between the enthalpy of formation and vapor pressure data. In
a second step, the uncertainties on the thermodynamic parameters and their propagation on the
calculated thermodynamic and phase diagram data are estimated using a Bayesian approach. The
analysis shows that there are too many parameters (22) for too few data points (120 points). The
uncertainties are thus large on some of the calculated data. Moreover the inconsistency of some
of the data and the lack of thermodynamic data for the liquid makes the model uncertain. New
experimental data such as heat capacity, enthalpy of formation for the compounds, and chemical
potentials or activities for the liquid phase would improve the reliability of our model. Measurements
of phase diagram data in the U UTe2 region are also required. However this work provides the
first detailed uncertainty analysis of the U Te CALPHAD model. Moreover our approach, contrary
to other Bayesian methods, provides an analytical posterior probability distribution and analytical
credible intervals for the calculated thermodynamic quantities. It also speeds up the simulation of
the uncertainty estimations on the phase diagram