## 2 Methods
### Diffusion Coefficient  
In [PERSON] et al. [30; 31], the diffusion coefficient consists of the intrinsic diffusion in the absence of irradiation, and the thermal and athermal diffusion produced by irradiation can be derived. Owing to the irradiation-induced resolution of intragranular bubbles, the diffusion coefficient combined with [PERSON]'s theory is revised as follows [24]:  
\[D=\frac{D_{1+2+3}}{1+g/b^{\prime}} \tag{1}\]  
\[D_{1+2+3}=D_{1}+D_{2}+D_{3} \tag{2}\]  
\[g=D_{1+2+3}/L^{2} \tag{3}\]  
\[D=\frac{1}{1/(D_{1+2+3})+1/(L^{2}b^{\prime})} \tag{4}\]  
\[D_{1}=D_{01}\exp\left(\frac{-T_{01}}{T_{K}}\right) \tag{5}\]  
\[D_{2}=D_{02}\exp\left(\frac{-T_{02}}{T_{K}}\right)\sqrt{\frac{P^{\prime}}{20}} \tag{6}\]  
\[D_{3}=D_{03}\frac{P^{\prime}}{20} \tag{7}\]  
Part of the parameters are accessed from reference [30; 31; 32], where \(D\) is diffusion coefficient; \(D_{1+2+3}\) is sum of the intrinsic, thermal, and athermal diffusion coefficients; \(g\) is probability of fission spikes trapping atoms within intragranular bubbles [27]; \(b^{\prime}\) is probability of the resolution of these atoms by fission spikes; \(D_{1}\) is intrinsic diffusion coefficient; \(D_{2}\) is thermal diffusion coefficient; \(D_{3}\) is athermal diffusion coefficient; \(D_{3}\) is athermal diffusion coefficient; \(L\) is mean free path between two bubbles; \(D_{01}\), \(D_{02}\), and \(D_{03}\) are diffusion constants; \(T_{K}\) is the local temperature; \(T_{01}\) and \(T_{02}\) are the parameters of the diffusion coefficient calculation; and \(P^{\prime}\) is linear heat generation rate (LHGR). The parameters of these equations are given as: \(D_{01}\) = 3.9 \(\times\) 10\({}^{-6}\) m\({}^{2}\)/s, \(T_{01}\) = 45,275 K, \(D_{02}\) = 1.77 \(\times\) 10\({}^{-15}\) m\({}^{2}\)/s, \(T_{02}\) = 13,800 K, \(D_{03}\) = 4 \(\times\) 10\({}^{-21}\) m\({}^{2}\)/s, \(L^{2}b^{\prime}\) = 10\({}^{-15}\) m\({}^{2}\)/s.  
Intrinsic diffusion represents the motion of clusters of gas atoms. Compared with low temperatures, the phenomenon of intrinsic diffusion is more easily observed at high temperatures. Gas atoms diffuse towards grain boundaries and accumulate on the grain boundaries. When the number of gas atoms saturates the grain boundaries and the temperature exceeds the incubation threshold, gas atoms begin to diffuse from the grain boundary towards the outside under the temperature gradient. This is the process of thermal diffusion. Athermal diffusion dominates at low temperatures. Recoil is the primary mechanism by which gas atoms move, resulting from collision between these atoms. This phenomenon leads to a slower saturation.  
The above diffusion coefficients vary with temperature and are calculated and presented in Figure 1. This figure indicates that fission gas diffusion is affected by intrinsic diffusion, thermal diffusion, and athermal diffusion. In particular, intrinsic diffusion is one of the most influential items for the diffusion coefficient. Furthermore, the range of variation with temperature is the largest among all the diffusion coefficients. Withoutconsidering the athermal fission gas release, the value of the athermal diffusion coefficient is constant. Figure 1 shows a summary of the previous models and experimental results. Comparing Figure 1a,b, the diffusion coefficient in our model is within a reasonable range compared with the other models and experimental results. In addition, the diffusion coefficient of different fuels is compared, such as UO\({}_{2}\), MOX, and UN. Although the results of UO\({}_{2}\) are greater than other fuels, there is a difference between its diffusion coefficient in the calculations and measurements due to different methods being used. For example, [PERSON] and [PERSON] used \(D=32,887\times 10^{-53,527/T}\) to calculate the diffusion coefficient. Different temperature and burnup ranges were selected.