Studies of irradiated fuels provide important data on the thermodynamics and chemistry of the fission products at high bumup. Generally, four distinct groups of fission products are observed in irradiated nuclear fuel [85, 125]:

(a) oxides dissolved in the matrix: Sr, Zr, Nb, Y, La, Ce, Pr, Nd, Pm, Sm;

(b) metallic precipitates: Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sb, Te;

(c) oxide precipitates: Ba, Zr, Nb, Mo, (Rb, Cs, Te);

(d) gases and other volatile elements, e. g.: Kr, Xe, Br, I.

As discussed earlier, the performance of a nuclear fuel is highly dependent on its physicochemical properties, especially their variation with temperature. One such property is thermal expansion of the fuel which affects the size of the gap between the fuel outer surface and cladding inner surface. The difference between the coefficients of thermal expansion of the fuel and the cladding determines whether the initial fuel-cladding gap closes or opens when the fuel element is brought to power [1]. If the initial gap is small and the fuel expands more than the cladding, the two come into contact. The resulting pressure at the interface is known as the contact or interfacial pressure. On the other hand, if the cladding expands more than the fuel and the gap is enlarged, heat conduction through the fuel-cladding gap will be low and the fuel temperature will be high because of the thermal resistance of the fuel-cladding gap. If interaction occurs, then differential thermal expansion between the fuel and cladding affects the magnitude of stresses in the cladding and fuel. This will be accounted for by including a thermal expansion strain component in the total strain of the fuel in each of three coordinate direc­tions [1,2, 4—6]. Fuel melting and excessive thermal expansion of the fuel pellet can occur at high enthalpy levels. The sudden expansion of the pellet can fail the cladding and resulting in molten fuel dispersion that can damage the pressure boundary. Dimensional changes are also affected by the processes such as sin­tering, bloating, or irradiation-induced changes such as swelling or densification [6]. For cubic crystals, such as ThO2, UO2, and ThO2-UO2 solid solutions, the

expansion or contraction is same in all directions. As long as phase changes do not occur, the dimensional changes are reversible [12].

The pellet-cladding mechanical interaction (PCMI) failures that occurred in the CABRI test reactor (France) and in the NSRR test reactor (Japan) were mainly due to rapid fuel thermal expansion because most of the energy remained in the fuel pellet during the extremely small time scale of the reactivity pulse [67]. With the same amount of energy deposition, thoria fuel will have a higher fuel temperature due to the lower heat capacity [12]. However, this high temperature does not necessarily lead to a larger thermal expansion because of the lower thermal expansion coefficient of thoria fuel. Results have shown that ThO2-UO2 fuel will have better performance than UO2 fuel under Reactivity Initiated Accident (RIA) event conditions due to its lower thermal expansion and flatter power distribution in the fuel pellet [67].

Thermal dilation property of a material has correspondence to lowering in its density with temperature increase. The relative lowering in the density expressed in Eq. (3), leads to the following expression of the density ratio:

P/Po = {1 + [1 -(1 + (AL/Lo)3/(1 + (AL/Lo)3]} (17)

By Eq. (17), the density ratio can be evaluated from the linear dilation (AL/Lo). Conversely, the relative dilation (AL/L0) can be determined using the following relation (see Appendix 1 for details) if density change is known,

(AL/Lo) « (Po/p)033-1 (18)

The dilation property in a crystalline solid provides a measure of the extent of defect growth with temperature rise. The thermal expansion AL/L0 of a crystalline solid as per Eshelby theorem [12] can be written as:

AL/Lo = Aa/ao + 0.33 AN/No, (19)

where a0 is the lattice parameter at the reference temperature, Aa = aT-a0, N0 is the number of occupied lattice sites at ambient temperature, and AN is the number of Schottky defects. The quantity becomes significant only at temperatures >0.6 Tm. By determining both AL/L0 and Aa/a0 on the same specimen, it is possible to evaluate the energy of formation of Schottky defects. If, however, the thermally generated defects are of the Frenkel type, then thermal expansion will be same whether measured by XRD or by bulk measurements. The concentration of thermally generated Schottky defects in a cubic crystal can be determined from the above equation [12].

Further, the thermal dilation property is used in the evaluation of thermal stress in solid. In general, the total strain (s) in a body is the sum of the mechanical strain (sM), and the thermal strain (sT) [1],

s = sM + sT

or, s = r/E + a • AT

where E is the Young’s modulus and r is the stress. In Eq. (21), it is assumed that both the elastic modulus, E, and the coefficient of thermal expansion, a, do not vary with temperature. The stresses due to change in temperature or due to tem­perature gradient are termed as thermal stresses, rthermai and can be expressed as:

Г thermal = a • E • AT. (22)

UO2 and ThO2 have the same isometric structure, and the ionic radii of 8-fold coordinated U4+ and Th4+ are similar (1.14 and 1.19 nm, respectively) [68]. Yamashita et al. [69] made the comparison for the linear thermal expansion coeffi­cient (a) of actinide dioxides, using their measured values and literature ones at room temperature and at high temperature (1,200 K). They found that at room temperature the a values were almost the same of about 8.5 x 10-6 K-1, but at high temperatures the a values increased with increasing atomic numbers from 10.2 x ThO2 to 13.2 x 10-6 K-1 for BkO2 [69, 70]. The thermal expansion coefficients of ThO2, UO2, and PuO2 reported in the literature are shown in Table 7.

Lattice parameters of ThO2, UO2, and PuO2 reported by various authors at room temperature are shown in Table 8.

It is well known that the lattice parameter (a) of nonstoichiometric UO2+x diminishes with increasing excess oxygen content (x) and that the relation between a and x at room temperature is given as [12]

a (pm) = 547.05 — 9.4 (x) (23)

Values of linear thermal expansion (LTE) at temperature T can be calculated by the relation

LTE(T) (%) = (ат — a0) x 100/a0, (24)

where, aT is the lattice parameter at temperature T and a0 is that at the reference temperature 293 K. The unit cell parameters could be determined as a function of temperature for ThO2, UO2, and PuO2 with help of high temperature X-ray

diffractometer. Lattice parameters were measured with an accuracy of ±0.5 pm and are shown in Fig. 6.

Because of their technical importance as nuclear fuel, thermal expansions of ThO2, UO2 and PuO2 have been intensively studied using various techniques (see Table 9). These data were compiled and assessed by Touloukian et al. [61]. They presented the recommended equations of the linear thermal expansion for ThO2 and PuO2 and the provisional equation for UO2. Taylor [71], also, compiled and analyzed thermal expansion data and presented regression equations of lattice parameter as a function of temperature for these actinide dioxides.

Table 9 List of the authors worked on thermal expansion measurement on (Th1-yUy)O2 system

and year of publications

Year Authors Remarks

Review based on first principles ThO2 based SIMFUEL

ThO2 containing 17.9, 41.7 and 52.01 % of SmOi.5 in the temperature range 298-2,000 K ThO2-4 % UO2, ThO2-10 % UO2 ThO2-20 % UO2 Review paper

ThO2-Nd2O3 phase with general compositions Th1-xNdxO2_x/2 (Th, Ce, Zr)O2

ThO2, Th0.96Ce0.04O2, Th0.92Ce0.08O2 Review paper

(Th0.45U0.55)O2, (Th0.87U0.13)O2 ^d (Th0.09U0.91)O2 ThO2 and ThO2-2 wt% UO2 Review paper

High temperature XRD on ThO2 and (Th0.8U0.2)O2 ThO2 and (Th0.8U0.2)O2 with 20 wt% Ln2O3.

Review paper Review paper

ThO2 having 99.99 % purity Review paper

ThO2-10.09 % UO2 and ThO2-20.02 mol% UO2 in temperature range 293-2,273 K (U, Th)O2 where U: Th = 1:10, 293-1,273 K <1,173 K

ThO2-50.05 % UO2 in temperature range 293-1,173 K (Th0.936U0.064)O2, <1,073 K