Ab initio theory of phase stability and structural selectivity in Fe-Pd alloys

In Fe-Pd alloys, the competing geometric (fcc versus bcc) and magnetic tendencies result in rich phase stability and ordering physics. Here, we study these alloys via a first principles mixed-basis cluster expansion (CE) approach. Highly accurate fcc and bcc CEs are iteratively and self-consistently constructed using a genetic algorithm, based on the first principles results for $\ensuremath{\sim}$100 ordered structures. The structural and magnetic ``filters'' are introduced to determine whether a fully relaxed structure is of fcc/bcc and high-/low-spin types. All structures satisfying the Lifshitz condition for stability in extended phase diagram regions are included as inputs to our CEs. We find that in a wide composition range (with more than 1/3 atomic content of Fe), an fcc-constrained alloy has a single stable ordered compound, L${1}_{0}$ FePd. However, L${1}_{0}$ is higher in energy than the phase-separated mixture of bcc Fe and fcc-FePd${}_{2}$ ($\ensuremath{\beta}$2 structure) at low temperatures. In the Pd-rich composition range, we find several fcc $\ensuremath{\beta}2$-like ground states: FePd${}_{2}$ ($\ensuremath{\beta}2$), Fe${}_{3}$Pd${}_{9}$, Fe${}_{2}$Pd${}_{7}$, FePd${}_{5}$, Fe${}_{2}$Pd${}_{13}$, and FePd${}_{8}$, yet we do not find FePd${}_{3}$ with the the experimentally observed L1${}_{2}$ structure. Fcc Monte Carlo simulations show a transformation from any of the attempted $\ensuremath{\beta}2$-like ground states directly into a disordered alloy. We suggest that the phonon and/or spin excitation contributions to the free energy are responsible for the observed stability of L1${}_{2}$ at higher temperatures, and likely lead to a $\ensuremath{\beta}2\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}$L${1}_{2}$ transition. Finally, we present here a complete characterization of all the fcc and bcc Lifshitz structures, i.e., the structures with ordering vectors exclusively at high-symmetry $k$ points.