## 4 Results and Discussion
### Local Atomic Relaxations
Using the WIEN2k code we also calculated the equilibrium atomic distribution at \(T\) = 0 K. In contrast to the Fe\({}_{0.5}\)Cr\({}_{0.5}\) alloy (see Figure 3), the E sublattice of the Fe\({}_{0.5}\)V\({}_{0.5}\)\(\sigma\)-phase has a partial site occupancy by V atoms. There are 7 V + 1 Fe atoms in the E sublattice, while the C sublattice has an equal occupancy by both alloy components, _i.e._, 4 V + 4 Fe atoms. Thus the atomic site occupancies estimated within our model at low temperatures are found in good agreement with the ground state equilibrium distribution obtained at \(T\) = 0 K by the WIEN2k code. **Figure 5.** The V site occupancies of the (A, B, C, D, E) sublattices _versus_ the V composition, \(x_{V}\), at fixed \(T\) = 1,000 K. The full symbols denote the calculated results, the empty symbols represent the available experimental data (error bars within the symbol sizes) [28,32]. \(J_{\alpha}^{(1)}\) and \(\mu_{\alpha}^{(Fe,V)}\) are obtained for Fe\({}_{0.5}\)V\({}_{0.5}\) at \(T\) = 1,000 K.  
Site Occupancies (\(x_{V}=0.40,0.60\))  
Let us now consider the atomic site distribution in the Fe-V \(\sigma\)-phase with respect to the alloy composition, \(x_{V}\) (see Figure 5). The predicted site occupancies as function of the alloy composition reproduce well the experimental values for the C and E sublattices, while they differ in slope for the B and (A, D) sublattices. Due to the large size mismatch between the Fe and V atoms, the lattice parameters of the Fe-V \(\sigma\)-phase should depend significantly on the alloy composition. According to experimental measurements [27] an increase of the vanadium content by 10% from the equiatomic composition, Fe\({}_{0.5}\)V\({}_{0.5}\), linearly increases the volume of the unit cell from 0.37074 nm\({}^{3}\) (for \(x_{V}=0.5\)) to 0.37634 nm\({}^{3}\) (for \(x_{V}=0.6\)), while the \(c/a\) values decrease from 0.517 to 0.516, respectively. On the other hand, with a decrease of the vanadium content by 10% to \(x_{V}=0.4\), the volume and \(c/a\) ratio change to 0.36514 nm\({}^{3}\) and 0.518, correspondingly. Assuming a linear dependence, one can extrapolate the expanded volumes as \(V\) = 0.37747 nm\({}^{3}\) for \(x_{V}=0.4\) and \(V\) = 0.38892 nm\({}^{3}\) for \(x_{V}=0.6\). The optimization of the \(c/a\) ratio in the Fe-V \(\sigma\)-phase within the EMTO-CPA method is not really reliable due to the large size mismatch of the Fe and V atoms. Therefore, we stay at a constant \(c/a\) ratio, but keep in mind that the site occupancies might vary due to a change of \(c/a\), as has been discussed for the Fe-Cr \(\sigma\)-phase. The corresponding effective interactions \(J_{\alpha}^{(1)}\) and magnetic moments \(\mu_{\alpha}^{(Fe,V)}\) obtained for \(x_{V}=0.40\) and \(x_{V}=0.60\) are given in Table 5. One can see that for \(x_{V}=0.40\) all four effective interactions are different (smaller in absolute values) from those obtained for \(x_{V}=0.50\), while for \(x_{V}=0.60\) only the changes for the B and C sublattices are remarkable. Nevertheless, when we compare the site occupancies for the parameters obtained for \(x_{V}=0.40\) and \(x_{V}=0.60\) with those predicted from the parameters obtained for \(x_{V}=0.50\), only small differences can be observed. The corresponding values of the site occupancies calculated at \(T\) = 1,000 K are given in Table 6. As can be seen only the B, C and E site occupancies change noticeably (those, which have predominant occupancy by V atoms) for \(x_{V}=0.40\), while for \(x_{V}=0.60\) all values are nearly the same. For \(x_{V}=0.40\) the C and E sublattices now have almost an equal occupation in accord with the experimental data (see Figure 5). The occupancy of the B site is a bit smaller, but still higher than the corresponding experimental value. This discrepancy could be due to several reasons: additional structural variations with respect to the alloy composition, temperature expansion, or local atomic relaxations.