Chromium Solubility

This model computes the solubility of chromium in UO₂ as a function of temperature and oxygen potential. It predicts chromium partitioning between a metallic phase (Cr) and an oxide phase (Cr₂O₃) and determines how much chromium is in solution or precipitated in each phase.

The default correlation is based on Riglet-Martial et al. (2014).

Reference

Riglet-Martial et al., J. Nucl. Mater. 447 (2014) 63–72. https://doi.org/10.1016/j.jnucmat.2013.12.021

Inputs

The model uses:

  • Temperature (history variable)

  • iChromiumSolubility (input option selecting the parameter set)

  • Fuel composition (uranium isotopes) and Fuel density (sciantix variables)

  • Chromium content (sciantix variable)

  • Burnup (sciantix variable), used in the Cr₂O₃/Cr partitioning rule

Model outline

  1. Oxygen chemical potential and oxygen pressure

    The oxygen chemical potential is evaluated for two reference equilibria (Cr₂O₃ and Cr) and converted into an effective oxygen pressure, expressed as \(\log_{10}(p_{\mathrm{O}_2})\).

  2. Chromium solubility in metal and oxide phases

    The chromium solubility correlations are evaluated in two temperature regimes (below/above a threshold temperature). The correlations are of the general form:

    \[x = 10^{\,p\,\log_{10}(p_{\mathrm{O}_2}) + V + \frac{U}{T}}\]

    where \(T\) is the temperature and \((p, V, U)\) are model coefficients. The result is converted to chromium weight percent in UO₂.

  3. Molar mass of uranium and conversion between wt% and atoms/m³

    A temperature-dependent uranium molar mass is computed from the isotopic inventory. The model converts between weight fractions and atomic concentrations to determine chromium atoms in the fuel.

  4. Phase partitioning (Cr₂O₃ fraction)

    The fraction of chromium in the oxide phase is computed from an exponential function of temperature, with an additional burnup-dependent correction applied for \(B \le 30\):

    • \(f_{\mathrm{Cr_2O_3}} = 1 - \exp(C_1(T - C_2))\)

    • A burnup-dependent shift is applied for low burnup.

  5. Solution vs precipitate

    For each phase (metallic Cr and oxide Cr₂O₃), the model compares the available chromium inventory to the solubility limit:

    • if inventory ≤ solubility → all chromium is in solution

    • otherwise → excess chromium is assigned to a precipitate reservoir

Outputs

The model updates the following sciantix variables:

  • Chromium solubility (wt% Cr in UO₂)

  • Chromia solubility (wt% Cr in UO₂ corresponding to Cr₂O₃ equilibrium)

  • Chromium solution / Chromium precipitate (atoms/m³)

  • Chromia solution / Chromia precipitate (atoms/m³)

The same quantities are also stored in the UO₂ material object (matrix properties) for later use by other models.