As mentioned above, the microscopic mechanisms of oxygen diffusion vary as a function of stoichiometry in the actinide dioxides. A schematic view of the (simplified) possible mechanisms has been reported in Table 18. Dorado eta/.232 combining both experi­mental and theoretical approaches identified the oxygen migration as an interstitialcy mechanism.

For x < 0in MO2 _ x (hypostoichiometric dioxides), the dominant defects in urania and plutonia are the oxygen vacancies. Hence, the migration energy could

be reduced to the activation energy for oxygen vacancy migration Eact: ( V") as reported in the Table 18.

In fact, Stan eta/.150’152 have shown that the point defects in hypostoichiometric plutonia PuO2 _ x do not reduce to oxygen vacancy. They determined (from a point defect model) that five different defects are at work in PuO2 _ x and hence contribute to the formation of oxygen vacancies. According to them, the prefactor D0 (eqn [13]) can then be written as a function of (i) a stoichiometry-dependent correlation factor from Tahir-Kheli233 and (ii) the formation energy of oxygen vacancy (determined using the point defect model). The results of such a model are reported in Figure 29.

Recently Kato et а/23 have studied the oxygen diffusion in hypostoichiometric MOX, and they
concluded that the diffusion coefficient of oxygen lin­early depends upon the concentration of Pu in MOX.

For x > 0 in MO2 + x (hyperstoichiometric diox­ides), two recent studies evidenced that the oxygen interstitials are not the only contribution to oxygen diffusion. Experimental data obtained by Ruello et a/.229 in UO2 + x show the important role of the Willis clusters. Theoretical calculations based on coupled ab initio/kinetic Monte Carlo done by Andersson et a/.168 have shown also that the diinter­stitial cluster of oxygen may contribute to the oxygen diffusion for highly hyperstoichiometric UO2 + x. In fact, the diffusion of oxygen in hyperstoichio­metric dioxides is due to the diffusion of interstitial oxygen and to the (counteracting) contribution of more complex oxygen clusters. Hence, the diffusion coefficient increases with stoichiometry, reaches a maximum, and decreases as may be seen in Figure 30.

Recently, Stan et a/.153 proposed a semiempirical relation between the diffusion coefficient D and the stoichiometry for UO2 + x that includes a maximum:

D(T, x) = xDo exp ^_Y°^j exp(_0x) [14]

In this expression, D0 = 1.3 x 10-2 cm2 s_1, E0 = 1.039 eV, and в = 6.1. The last term of the product corre­sponds to the blocking effect of the complex oxygen clusters. Such a semiempirical model reproduces the experimental data fairly well (see Figure 31), up to x < 0.1. For higher values of x (0.0 < x< 0.2 from 300 up to 1800 K), Ramirez eta/.151 established a somewhat different semiempirical relation.