## 3 Results
### Partial Radial Distribution Functions and Coordination Numbers  
The average distribution of F ions around Li, Na, K, and Ce ions is characterized by the functions \(g_{ij}(r)\), shown in Figure 6. It can be seen that the location of the first maximum, which reflects the most probable distance from particle \(i\) to particles \(j\) of the first coordination sphere, shifts towards larger \(r\) as the values of \(i\) change from Li to Ce. This is due to the increase in particle diameter \(i\) when moving in this direction. A more clearly formed second order in the arrangement of F ions around Li ions is due to the greater abundance of the latter compared to other positive ions, and a similar order around Ce ions is associated with their large electric charge, due to which the attracted F ions slow down diffusion. The cation-cation and anion-anion radial distribution functions for the FLiNaK+15 mol.% CeF\({}_{3}\) system at a temperature of 950 K are shown in Figure 7. As can be seen from the figure, the maxima of the peaks of the functions corresponding to different components are localized at different distances, which are determined by both the size of the ions and the concentration of the components in the melt. The functions \(g_{\mathrm{Ce-Ce}}(r)\) and \(g_{\mathrm{Li-Li}}(r)\), have the highest peak intensities, which indicates a more \"ordered\" arrangement of like ions (Ce or Li) relative to each other. If in the first case, this can be due to the large electric charge of Ce atoms and, consequently, their large inertia, created by the surrounding F ions, then in the second case, this can be explained by the small size and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Li** & **Na** & **K** & **F** & **Ce** \\ \hline \(a\), \(10^{-5}\ \mathrm{cm^{2}/s}\) & 0.0092 & 0.0107 & 0.0094 & 0.0109 & 0.00362 \\ \(b\), \(10^{-5}\ \mathrm{cm^{2}/s}\) & 5.783 & 7.309 & 6.015 & 7.147 & 2.783 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters \(a\) and \(b\) for linear Equation (6). mass of Li ions compared to other ions. The small size and mass of Li ions allows them to mix better and get stuck in the voids formed by larger ions. The temperature dependence of the calculated coordination numbers for the molten salt mixture FLiNaK+0.15 mol.% CeF\({}_{3}\) is shown in Figure 8. As can be seen from the figure, the coordination numbers for cations of the same name, as a rule, slightly decrease with increasing temperature. Moreover, a more significant decrease in \(n_{ii}\) occurs for the lightest cations, i.e. when index \(i\) is defined as Li. A decrease in \(n_{ii}\) with increasing temperature is practically not observed in the case of cation-anion pairs. Note that the F and Li ions, which have the highest representation in the molten salt under consideration, have the highest values of the coordination number \(n_{ii}\). Due to the low concentrations of Na and Ce ions in the system, the coordination numbers \(n_{ii}\) were calculated in terms of the radial distribution functions \(g_{ii}(r)\), where \(i\) = Na or Ce, have very low values that do not adequately reflect the short-range order in the 3D subsystems of Na and Ce ions. The values of \(n_{ii}\) for Na ions are also not given in [31; 32], where the structure of pure molten FLiNaK was studied. Figure 6: The partial radial distribution functions of Li–F, Na–F, K–F and Ce–F at 950 K.  
Figure 7: The partial radial distribution functions of Li–Li, Na–Na (in the insert), K–K, F–F and Ce–Ce at 950 K.  
The increase in coordination numbers in FLiNaK+15 mol.% CeF\({}_{3}\) relative to pure molten FLiNaK is shown in Figure 9. The addition of CeF\({}_{3}\) to FLiNaK primarily increases the mole fraction of fluorine from 50% to 53.2% in the molten salt. As a result, an increase in the coordination numbers of the cation-anion (LiF, NaF, and KF) and anion-anion (FF) type seems quite natural. The smallest Li cation is able to surround itself with the largest number of Li cations.