Actinides, rare earths, and transition metals can form mixed oxides with UO2 or (U, Pu)O2. Examples of these elements are the fission products Zr, Ce, Nd, Ba, La, Pr, Sr, Sm, Y, Rb, Te, Pu, Np.12 Their solubil­ity limits determined for binary systems are never reached in the case of irradiated fuel, and these ele­ments can be completely or partially dissolved in the
fuel matrix. When such solid solutions are formed, these atoms act as phonon scattering centers as a result of the differences in bonding potential, ionic radii, or mass between the impurities and the sub­stituted atoms (U or Pu). The total scattering coeffi­cient can be evaluated from the differences in atomic mass and ionic radii13 and from the Griineisen con­stant, which represents the strain generated in the lattice by the difference in ionic radius and is usually treated as an empirical parameter obtained from experimental data.14-17

2.17.2.2.1 Volatiles and fission gases

Insoluble or volatile fission products (Kr, Xe, Cs, Te, I, etc.) are partially dispersed as interstitials and induce static displacements of host lattice atoms U or Pu from their mean lattice sites. In that case, their effect can be interpreted with the same equa­tions as for the dissolved fission products. The fission gas, thermodynamically insoluble in the matrix, is initially injected into the lattice and may precipitate into bubbles. Since collisions with fission fragment recoil cascades tend to re-inject gas into the lattice, for temperatures below about 1100 K, a fraction of the gas is kept in dynamical solution. At higher tempera­tures, most of the gas precipitates into bubbles or pores or can be released from the pellet. The simul­taneous mechanisms of gas diffusion, precipitation, and release can be described by reaction-rate
equations18 to calculate the partitioning of the gas in the different states starting from a number of kinetic (gas creation rate, diffusion coefficient, and resolu­tion rate) and structural (grain size, radii, and con­centrations of the bubbles) parameters. The entire irradiation history of the sample and, when labora­tory annealing is involved, the applied temperature program, have to be considered.