The fuel thermal conductivity changes during irradi­ation as a result of fission and high operating tem­peratures; the chemical composition, lattice structure, and microstructure evolve in a complex and correlated manner. The fuel microstructure and state result from the irradiation history (transients generate cracking, shutdown periods result in autoirradiation at low tem­peratures, etc.). A complete and three-dimensional knowledge of the fuel characteristics is required for the prediction of the thermal conductivity. The num­ber of parameters is large and it is difficult to isolate and model their effects individually. Furthermore, many parameters act in a coupled manner: that is, the impact of the individual parameters is not the sum of the individual effects. Therefore, no purely theoretical model is available and semiempirical correlations are built from the interpretation of experimental results by selecting the most influential parameters, the effect of the others being implicitly included when the models are adjusted to measurement results.

Two categories of parameters can be distin­guished: first, the parameters that depend on burnup but not on irradiation conditions. The burnup is a global parameter that integrates all the effects which are proportional or related to it only, for instance, the concentration of soluble fission products or precipi­tates. Second, the parameters are those that depend on burnup and irradiation temperature history. This is the case for radiation damage, for the state of fission products that are present as isolated atoms and can precipitate, or for the distribution of volatile fission products between the states dynamically dissolved, precipitated in bubbles or pores, or released.

The proposal of a model implies a reduction in the number of parameters remaining, for instance, only the burnup or a second parameter summarizing the effect of the irradiation history, such as the irradiation temperature1 or the lattice parameter,32 assuming that these parameters describe, with sufficient preci­sion, the state of the fuel.

The general expression of the heat conduction used for irradiated fuels is similar to the one adopted for the fresh fuel (eqn [4]). It includes the lattice conduction mechanism by phonons, empirically represented by 1/(A + BT) and largely dominant up to temperatures of about 1600 K, and the high — temperature contribution attributed to the electron vacancy pair mobility, usually represented by adding an expression of the form CeDT This last contribution

cannot be accurately quantified because of the lack of measurements at high temperatures.

1

A + BT

The quantity 1/A + BT applies only to perturbations at the atomic scale, that is, the effects of soluble fission products, and to point defects (radiation point defects, nonstoichiometry, dynamically dis­solved atoms and fission gases). It is not rigorous for precipitates and porosity, as the effect of these para­meters is macroscopic and described by composite materials formulae derived from the solution of the Fourier law. In practice, this formalism is often applied, including the effect of all the parameters. Fuel variants, such as (U, Gd)O2, UO2 doped with Cr, or MOX, are modeled on the basis of UO2, with supplementary parameters describing the effect of the additive.