2.02.6.1 Self-Diffusion

The diffusion of oxygen or cations has been mainly investigated in the actinide dioxides MO2 with the fluorite structure. Usually, the diffusion coefficient D is expressed using an Arrhenius law — type equation

D = D"exK_;w 1131

where D0 is the prefactor, Emig. is an effective migra­tion energy, kB is the Boltzmann constant, and Tis the temperature. While very commonly used, the details of the diffusion are unfortunately hidden behind this equation. The prefactor depends upon hopping fre­quency and geometrical factors while the effective migration energy should be expressed as a free energy (see, e. g., Ando and Oishi217 or Howard and Lidiard218) and should include the formation energy ofthe migrat­ing defect. In pure dioxides, for example, the oxygen diffusion occurs via vacancy/interstitial migration, depending on the stoichiometry — that is, on the oxygen partial pressure (see Section 2.02.4.3.1 on defects).

In general, the diffusion depends strongly on any type of defects present in the crystal lattice. Also the grain boundaries play a major role, as they act as short­cuts for the diffusion (see Vincent-Aublant eta/.219 and Sabioni et a/.220). Thus, the reliability of the diffusion measurements is related to the control/measurement of the stoichiometry and microstructure.

Those experimental issues lead to a very large scatter of data (see, e. g., Sabioni et a/.,2 0 Belle and Berman,2 1 Sabioni et a/.22 ), and hence complemen­tary ab initio and MD calculations by Terentyev,80 Stan and Cristea,150 Stan,154 Andersson et a/.,168 Vincent-Aublant et a/.,2 9 and Kupryazhkin et a/.22 are performed to bring microscopic insights to the experiments, but with various degrees of success. The proposed models cannot generally overcome the identification of the defects responsible for the diffu­sion. This is because the types of the stable defects themselves (vacancies, interstitials, and also complex defects such as clusters; see Section 2.02.4.3.1) are far from being resolved. Hence, the diffusion coefficients as a function of stoichiometry are fitted on semi­empirical equations. Another way to circumvent this issue is to follow Siethoff.224 He has recently reexhib­ited a relation between the effective migration energies and the elastic properties in many crystallographic families, including the fluorite structures.

As many reviews have been written on the self­diffusion in actinide dioxides in the past, and as the data collected are so inconsistent to each other, we refer the reader to the review done by Belle and Berman221 for UO2, PuO2, and ThO2 for the studies done before 1984 to get the experimental data. Recently, new data have been reported, and we refer the reader to the studies by Sabioni eta/.,2 , 2 Mendez eta/.,225 Korte eta/.,226 Sali eta/.,227 Arima eta/.,228 Ruello eta/.,229 Kato eta/.230 and Garcia eta/231 and references therein. In the following, we will limit ourselves to report some semiempirical equations in known cases.