## 3 Results and Discussion  
The calculations for the pure Na and Na-K eutectic alloy are carried out in the temperature ranges of 373-1673 K and 273-1573 K, respectively. The important feature of the used calculation procedure is that the mean atomic volumes are defined during its fulfillment due to conditions (28) and (30) for the pure metal and binary alloy, respectively. As a result, for both coolants we obtained the theoretical values of densities at each temperature under consideration (Figures 1 and 2). Experimental data for the density of liquid Na are taken from the most recent and complete handbooks [3; 4]. The corresponding polynomial series suggested in the former is based on the results listed in Refs. [49; 50] and is written as follows:  
\[ \begin{split}\rho(\text{g}/\text{cm}^{3})=0.89660679+0.5161343(\,T /1000)-1.8297218(\,T/1000)^{2}+2.2016247(\,T/1000)^{3}\\ -1.3975634(\,T/1000)^{4}+0.44866894(\,T/1000)^{5}-0.057963628(\,T/100 0)^{6}.\end{split}  \tag{32}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Metal**} & \multicolumn{2}{c}{**KG–GV**} & \multicolumn{2}{c}{**AH–GV**} & \multicolumn{2}{c}{**AH–TW**} & \multicolumn{2}{c}{**AH–VS**} \\ \cline{2-10}  & \(a\) (a.u.) & _r\({}_{\text{c}}\) (a.u. )_ & \(A\) (a.u. )_ & _R\({}_{\text{M}}\) (a.u. )_ & \(A\) (a.u. )_ & _R\({}_{\text{M}}\) (a.u. )_ & \(A\) (a.u. )_ & _R\({}_{\text{M}}\) (a.u. )_ \\ \hline Na & 3.242 & 0.4898 & \(-0.1752\) & 2.0730 &The polynomial series recommended in Ref. [4] is based on the results listed in Ref. [49] as follows:  
\[\rho(\mathrm{g/cm^{3}})=1015.03\ -\ 0.23393T-0.305T^{2}/100000. \tag{33}\]  
As seen in Figure 1, both experimental approximations (32) and (33) provide results very close to each other and to the calculated results for two pseudopotential models, KG-GV and AH-GV. At the same time, two other combinations between the pseudopotential and the exchange-correlation function (AH-TW and AH-VS) lead to some disagreement with experimental results which increases with the increase in the temperature. For the density of Na-K eutectic alloy (Figure 2) the same two combinations (KG-GV and AH-GV) provide better agreement with the experiment [50], but this agreement is not as excellent as in the case of the pure Na. The results obtained for the isobaric thermal expansion coefficients are presented in Figures 3 and 4. Experimental data for Na were defined using differentiations of Equations (32) and (33) by means of Equation (2). To define the experimental \(\alpha_{p}\) for the Na-K eutectic alloy we used an analogous procedure. For this aim the following linear approximation (with \(R^{2}=0.9937\)) of the density was derived as follows on the basis of experimental data [50]:  
\[\rho(\mathrm{g/cm^{3}})=0.9403361\ -\ 0.0002382T. \tag{34}\]  
Figure 3 shows that the maximal deviation of theoretical \(\alpha_{p\mathrm{Na}}\) from experiment [4] for each of the KG-GV and AH-GV combinations is 10%. Therewith, the results of the former combination agree better with experiment [4] approximately up to \(T=650\) K, while the results of the latter show better agreement beyond this temperature. The behavior of the experimental curve [3] possibly points to the fact that the derivative of Equation (32) is not sufficiently accurate. Otherwise, it can be asserted that the accuracy of the AH-TW  
Figure 1: Density of liquid Na calculated for different pseudopotential models in comparison with experimental data [3,4]. combination increases with the increase in temperature. Notably, the deviation of AH-TW results from the experiment [4] lies in the range 20-25%. Figure 3: Isobaric thermal expansion coefficient of liquid Na calculated for different pseudopotential models in comparison with experimental data [3;4]. Figure 2: Density of liquid Na–K eutectic alloy calculated for different pseudopotential models in comparison with experimental data [50].