The fresh fuel plutonium concentration and distribu­tion (homogeneous or heterogeneous microstructure) and the induced variations in the local stoichiome­try are supplementary parameters for MOX fuels. The plutonium concentration decreases with burnup whereas it increases in UO2. Therefore, the differ­ences observed in fresh fuels linked to the plutonium effect can be expected to decrease with burnup, at least for homogeneous MOX fuels. In hetero­geneous MOX, the microstructure may have an enhanced impact because of the presence of Pu-rich agglomerates in which the burnup is much higher than in the matrix. However, recent studies showed that this effect is in fact negligible.27,28

2.17.2.3.2 Microstructure

The microstructure of the fuel is linked to the pres­ence of additives and porosity, voids, and fission gas bubbles, their concentrations changing with the radial position. Other parameters concern the fuel matrix itself: the densification at the beginning of life and the grain size evolution. The effect of poros­ity and voids can be approximated by applying a factor to the matrix conductivity, determined for instance by the formula of Maxwell giving the effec­tive thermal conductivity 1eq of a medium consti­tuted by a matrix of conductivity 1m containing a small volume fraction vf of inclusions having a con­ductivity 1f (eqn [3]). This approximation is obtained only when 1m ^ If, and is therefore not usable for ceramic or metallic precipitates. Approximate formu­lae, validated for porosity in nuclear fuels, were pro­posed by Brandt and Neuer.29

l if + 2lm + 2vf(if — im) , 2(1 — vf) 3

1eq “ 1m if + 21m + Vf (1m — if) ifiC^if 1m^ + VT ^

The macroscopic cracking and fracture of the pellet are heterogeneities that cannot be taken into account for the definition of an equivalent thermal conduc­tivity because their size is not small compared to the size of the pellet. Cracking can be separated into radial and tangential, the latter decreasing the appar­ent thermal conductivity.

Extensive microstructure changes take place with the formation of the HBS starting from the periphery of the pellet for discharge burnups higher than about 40 MWd kg HM—1 or local burnups higher than about 60 MWd kg HM—1. This structure is characterized by a reduced grain size, an increase in porosity, and a depletion of fission gas from the UO2 matrix.30,31

2.17.2.3.3 Burnup

The fuel burnup reflects the proportion of fissioned atoms and is the most commonly used parameter for the interpretation of thermal conductivity degrada­tion. In principle, this parameter integrates the phe­nomena that do not depend on the irradiation conditions, that is, the concentration of nonvolatile fission products. In practice, it is often the only param­eter of the correlations and is used to account for (almost) all irradiation effects. Some particular effects exist at low burnup: the fast buildup of irradiation damage, and at high burnup: the formation ofthe HBS.