Site preference of ternary alloying addition (Ti, Fe, Co and Ni) in DO$_3$ Fe$_3$Al, Co$_3$Al and Ni$_3$Al - basic compound for alnico-8 magnetic materials*

We performed first-principles calculations to investigate the site preference of ternary alloying additions in DO$_3$ Fe$_3$Al, Co$_3$Al and Ni$_3$Al alloys. In Fe$_3$Al the discussed ternary elements are found to occupy the Fe sublattice. For both Fe-rich and Al-rich compounds, the ternary elements with fewer 3$d$ electrons than Fe (Ti) prefer to occupy $\alpha$-sites of Fe sublattice and elements with larger number of 3$d$ electrons - the $\gamma$-sites. In Fe-rich regions, the small enthalpy difference of Ti occupying $\alpha$-sites of Fe and Al sublattices, the site distribution of Ti varies with concentration and temperature. A similar dependency was obtained for Ni distribution between Co and Al sublattice in Co$_3$Al. Similar to the Fe$_3$Al alloy, the ternary element prefer to occupy Co sublattice with a change of preferred sites from $\alpha$ for Ti and Fe to $\gamma$ for Ni. In the Ni-rich Ni$_3$Al the ternary elements prefer to occupy the Al sublattice, while, in the Al-rich alloy the ternary elements prefer to occupy Ni sublattice in a similar fashion. The magnetic moments of transition metals in Fe$_3$Al and Co$_3$Al are ordered ferromagnetically, whereas the Ni$_3$Al is nonmagnetic unless the Fe or Co are added as a ternary element.