## 4 Results and Discussion
### Local Atomic Relaxations  
As mentioned above, the quite large size mismatch of the alloy components in the Fe-V system causes that the effect of local atomic relaxations might not be negligible in contrast to the other studied systems (Fe-Cr, Re-W and Co-Cr) (see Table 1). In order to account for these effects we introduced a new parameter in our model, namely \(J_{\alpha}^{(relax)}\), which we calculated for each sublattice in the Fe\({}_{0.5}\)V  
Figure 4: The Cr site occupancies of the (A, B, C, D, E) sublattices in the Co-Cr system _versus_ the Cr composition, \(x_{Cr}\), at fixed \(T\) = 1,500 K. The full symbols denote the calculated results, the empty symbols represent the experimental site occupancies (error bars are less than 0.5%) [29]. \(\sigma\)-phase (assuming the experimental lattice parameters \(V\) = 0.37074 nm\({}^{3}\) and \(c/a\) = 0.517) and list them in Table 3. As can be seen, the local lattice relaxations change the effective on-site interactions only moderately and consequently the corresponding site occupancies will be hardly affected. Therefore one might expect that the effect of local atomic relaxations in binary \(\sigma\)-phases near the equiatomic composition is negligible for all binary systems, for which the component size mismatch is less than that in the Fe-V system. Site Occupancies (\(x_{V}=0.50\))  
Let us start from the equiatomic composition \(x_{V}=0.50\) and consider a possible increase in volume from \(V_{exp}\) = 0.37074 nm\({}^{3}\) to the high temperature value \(V\) = 0.38319 nm\({}^{3}\) due to thermal expansion. The calculated effective on-site interactions and corresponding local magnetic moments of Fe and V atoms are given in Table 4 at three different temperatures. Using the \(J_{\alpha}^{(1)}\) parameters and the corresponding Fe and V magnetic moments (obtained at \(T\) = 1,000 K), we calculated the distribution of the V atoms among the five \(\sigma\)-phase sublattices in the \begin{table}
\begin{tabular}{l c c c c c c} \hline  & **T (K)** & **A** & **B** & **C** & **D** & **E** \\ \hline \(J_{\alpha}^{(1)}\) (mRy/cell) & 500 & 25.406 & \(-\)7.125 & 1.031 & 21.000 & 0.0 \\  & 1,000 & 24.750 & \(-\)7.594 & 0.656 & 20.344 & 0.0 \\  & 1,500 & 24.094 & \(-\)7.781 & 0.375 & 19.875 & 0.0 \\ \(\mu_{\alpha}^{Fe}(\mu_{B})\) & 500 & 0.841 & 1.768 & 1.445 & 1.089 & 0.895 \\  & 1,000 & 1.047 & 1.790 & 1.518 & 1.240 & 1.079 \\  & 1,500 & 1.169 & 1.804 & 1.571 & 1.334 & 1.187 \\ \(\mu_{\alpha}^{V}(\mu_{B})\) & 500 & 0.091 & 0.119 & 0.108 & 0.098 & 0.091 \\  & 1,000 & 0.170 & 0.217 & 0.200 & 0.183 & 0.171 \\  & 1,500 & 0.240 & 0.303 & 0.280 & 0.257 & 0.242 \\ \hline \end{tabular}
\end{table} 
Table 4: On-site parameters \(J_{\alpha}^{(1)}\) (mRy/cell) and local magnetic moments of Fe and V atom \(\mu_{\alpha}^{Fe}\) and \(\mu_{\alpha}^{V}\) calculated for the lattice parameters \(V\) = 0.38319 nm\({}^{3}\) and \(c/a\) = 0.517 within the DLM-LSF model at three different temperatures \(T\) = 500, 1,000 and 1,500 K. \begin{table}
\begin{tabular}{l c c c c c} \hline  & **A** & **B** & **C** & **D** & **E** \\ \hline \(J_{\alpha}^{(1)}\) (mRy/cell) & 24.750 & -7.594 & 0.656 & 20.344 & 0.0 \\ \(J_{\alpha}^{(1)}+J_{\alpha}^{(relax)}\) (mRy/cell) & 22.594 & -7.219 & 0.656 & 18.656 & 0.0 \\ \hline \end{tabular}
\end{table} 
Table 3: On-site interaction parameters \(J_{\alpha}^{(1)}\) (mRy/cell) calculated for the Fe\({}_{0.5}\)V\({}_{0.5}\) alloy with/without taking into account local lattice relaxations \(J_{\alpha}^{(relax)}\) for the experimental lattice parameters \(V\) = 0.37074 nm\({}^{3}\) and \(c/a\) = 0.517 within the DLM-LSF model at \(T\) = 1,000 K.  
Fe\({}_{0.5}\)V\({}_{0.5}\) alloy with respect to temperature and alloy composition (see Figure 5). The results obtained at high temperatures agree reasonably well with the experimental values measured for an alloy composition \(x_{V}=0.48\). At the low temperature we find that for example the C sublattice is equally occupied by both alloy components.