## 3 Results
### Self-Diffusion of Ions  
The values of the self-diffusion coefficients of Li, Na, K, F, and Ce ions at different temperatures are presented in Table 2. In addition to the \(D\) values for the FLiNaK+CeF\({}_{3}\) system, the values of the \(D\) coefficients for pure FLiNaK calculated by us as well as those obtained from the experiment [30] are also shown here. The experimental values of \(D\) determined at temperatures not exceeding 936 K are presented at two temperatures (800 and 880 K). According to our calculations, both for pure FLiNaK and for the FLiNaK+CeF\({}_{3}\) system near the operating temperature (i.e., at \(T=950\) K) of MSR, F\({}^{-}\) ions have the highest values of the coefficient \(D\). The same result was obtained from MD ab initio calculations for pure FLiNaK in [8]. The temperature dependences of the calculated self-diffusion coefficients and their linear approximations for the FLiNaK+15 mol.% CeF\({}_{3}\) system are shown in Figure 5. For the ions forming FLiNaK, there is good agreement between the calculated and approximated dependences \(D(T)\). However, in the case of Ce ions, the calculated values of the coefficient \(D\) have a strong scatter relative to the approximating straight line. For pure FLiNaK, the \(D\) values for the F and Li ions are similar over the entire temperature range under study. This may be due to the pairing of these ions and the joint motion of such pairs. However, when CeF\({}_{3}\) is added to FLiNaK, this effect is not so noticeable due to the attraction of F ions to the trivalent Ce ions. Figure 4: Simulated and experimental densities of FLiNaK system; dash line shows the linear fit of our MD data; blue triangles show results of experiment [28], pink dots represent the simulated data obtained in the polarizable MD model [29]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(T\) (K) & **System** & **Li** & **Na** & **K** & **F** & **Ce** \\ \hline \multirow{3}{*}{800} & Pure FLiNaK & 1.82 & 1.43 & 1.45 & 1.84 & - \\  & Exp. FLiNaK & 1.43 & 1.84 & 1.66 & 1.72 & - \\  & FLiNaK+Ce & 1.57 & 1.25 & 1.50 & 1.57 & 0.113 \\ \hline \multirow{3}{*}{880} & Pure FLiNaK & 2.87 & 2.47 & 2.19 & 2.92 & - \\  & Exp. FLiNaK & 2.39 & 3.03 & 2.57 & 2.62 & - \\  & FLiNaK+Ce & 2.31 & 2.10 & 2.25 & 2.44 & 0.402 \\ \hline \multirow{3}{*}{950} & Pure FLiNaK & 3.80 & 3.37 & 2.84 & 3.87 & - \\  & Exp. FLiNaK & (3.47) & (4.36) & (3.56) & (3.57) & - \\  & FLiNaK+Ce & 2.95 & 2.85 & 2.91 & 3.20 & 0.656 \\ \hline \multirow{3}{*}{1020} & Pure FLiNaK & 4.72 & 4.27 & 3.49 & 4.81 & - \\  & Exp. FLiNaK & (4.80) & (5.48) & (4.35) & (4.34) & - \\ \cline{1-1}  & FLiNaK+Ce & 3.60 & 3.60 & 3.57 & 3.97 & 0.909 \\ \hline \hline \end{tabular}  
* The values in parentheses correspond to the extrapolation to high temperatures of the Arrhenius dependence \(D(T)\) obtained in the experiment [28].  
\end{table} 
Table 2: Self-diffusion coefficients of ions (in units of \(10^{-5}\) cm\({}^{2}\)/s) in FLiNaK and mixture FLiNaK+CeF\({}_{3}\) calculated by the Arrhenius relation from data of MD calculation and experiment [28] *. Figure 5: Self-diffusion coefficients of molten salt mixture FLiNaK+CeF\({}_{3}\) components; the linear approximation of the MD calculation of the \(D\) coefficient is presented as a solid line, and the linear approximation of the \(D_{\infty}(T)\) dependence is shown as a dashed line. Approximation dependences \(D(T)\) for Li, Na, K, F ii Ce ions are represented by an analytical expression:  
\[D=aT-b\ (10^{-5}\ \mathrm{cm^{2}/s}), \tag{6}\]  
whose parameters \(a\) and \(b\) are listed in Table 3, and temperature \(T\) is expressed in K.  
When passing from an MD system with PBC to an infinite system, a very slight increase (<2%) in the self-diffusion coefficients is observed, which are determined from the approximation dependence \(D_{\infty}(T)\) (relative to that of \(D(T)\)) for Li, Na, K, and F ions. For Ce ions, which have a much higher atomic weight, the coefficient \(D\) can increase up to 5% going to an infinite system.