UO₂ Thermochemistry

Purpose

This model computes the equilibrium stoichiometry deviation of UO₂ under the current thermo-chemical conditions, based on the Blackburn (1973) formulation. It is activated only when stoichiometry deviation modelling is enabled.

Activation

The model is executed only if the input option iStoichiometryDeviation is enabled (non-zero). If stoichiometry deviation modelling is disabled, the model returns immediately and no variables are updated.

Inputs

The model uses:

  • iStoichiometryDeviation (input option)

  • Stoichiometry deviation (sciantix variable, initial value)

  • Temperature (history variable)

  • Gap oxygen partial pressure (sciantix variable, in atm)

Model formulation

The model solves for the equilibrium stoichiometry deviation using the Blackburn formulation through a dedicated nonlinear solver solver.NewtonBlackburn(...). The parameter vector passed to the solver is:

  • initial stoichiometry deviation

  • temperature

  • gap oxygen partial pressure

Cut-off conditions

For numerical robustness and physical consistency, the equilibrium stoichiometry deviation is set to zero under either of the following conditions:

  • \(T < 1000~\mathrm{K}\), or

  • the gap oxygen partial pressure is zero.

Otherwise, the equilibrium value is obtained by solving the Blackburn equation via Newton iteration:

\[\Delta x_{\mathrm{eq}} = \mathrm{NewtonBlackburn}\left(\Delta x_0,\,T,\,p_{\mathrm{O}_2}\right)\]

Outputs

The model updates:

  • Equilibrium stoichiometry deviation

Reference

Blackburn (1973), Journal of Nuclear Materials, 46, 244–252. https://doi.org/10.1016/0022-3115(73)90038-X