The lattice parameters of actinide oxides are usually measured in glove boxes because of radioactivity and chemical hazards. In fact, the radioactive decay may drastically modify the cell parameters with

characteristic time of months (see measurements on (Pu, Am)O2 by Jankowiak et a/.,62 on CmO2 in the review by Konings,43 and on sesquioxides by Baybarz et a/.63). Indeed, point defects (caused by irradiation or simply because of off-stoichiometry) may also induce expansion or contraction of the lattices.

The thermal expansion of the cell usually occurs when increasing the temperature, and it is usually measured starting at room temperature. Because of experimental difficulties — already mentioned — for measuring properties (and thus thermal expansion coefficients) in actinides, some ab initio and/or molec­ular dynamics (MD) calculations are nowadays done. In the framework of MD calculations, the evolution of the cell parameter can easily be followed as a function of temperature (see the calculations by Arima et a/.64 on UO2 and PuO2, and by Uchida et a/.65 on AmO2). The method is slightly different when ab initio calculations are performed (see, e. g., the work of Minamoto et a/.66 on PuO2). One cur­rently calculates the phonon spectra, estimates the free energy as a function of temperature by means of quasiharmonic approximation, and then extracts the linear thermal expansion. Such procedure may also be based on experimental data assuming some hypothesis and simplifications on the phonon spectra (see, e. g., Sobolev and coworkers67-69).

2.02.3.1 Actinide Dioxides

2.02.3.1.1 Stoichiometric dioxides

The actinide dioxides exhibit a fluorite or CaF2 struc­ture (Figure 10). Each metal atom is surrounded by eight nearest neighbor O atoms. Each O atom is sur­rounded by a tetrahedron of four equivalent M atoms. The cell parameters are reported in Table 2. They are

In fact, the recommended values77 for UO2 are as follows:

For 273K < T < 923K: a(T) = a273(9.9 7 3 x 10-1 + 9.082 x 10-6T — 2.705 x 10-10T2 + 4.391 x 10-13T3) [4]

For 923K < T < 3120K: a(T)

= a273(9.96 72 x 10-1 + 1.179 x 10-5T — 2.429 x 10-9T2 + 1.219 x 10-12T3) [5]

indeed (almost) linearly dependent upon the ionic radius of the actinide cations (see Figure 11). It is noteworthy that the cell parameters reported may be significantly affected by self-irradiation, as men­tioned, for example, in CmO2 by Konings43 based on measurements by Mosley.70

A first review of the linear thermal expansion of stoichiometric actinide dioxides has been done by Fahey et al.75 in the 1970s. This has been updated by Taylor76 in the 1980s and later by Yamashita etal.71 and Konings43 in the 1990s. In the simple case of cubic crystals (such as actinide dioxides; see below), the evolution of the cell parameter as a function of temperature is fitted using a polynomial expression up to the third (sometimes fourth) degree as follows:

a(T)=b0 + hT + Ьг T2 + b3 T3 [3]

Selected values ofthe parameters obtained are shown in Table 2. Overall, the values reported for the b1 parameters are of the same order of magnitude.

Sobolev and coworkers67-69 recently proposed an alternative approach for determining the thermal expansion of actinide dioxides from experimental data. It is based on the evaluation (from experiments) of the specific heat CV from the phonon spectra at the expense of some approximations. The thermal expan­sion aP is then deduced using the following relation:

Ус Cv (V, T) Bt (V, T)V

The thermal expansion coefficient aP depends upon the bulk modulus BT, the heat capacity CV and the Griineisen parameter gG. The results obtained by Sobolev (see figures in Sobolev and coworkers67-69) reproduce quite well the available experimental data and allow the extrapolation to temperatures higher than the measurements.