First-principles determination of low-temperature order and ground states of Fe-Ni, Fe-Pd, and Fe-Pt

While the binary $\text{Fe-}X$ $\left(X=\text{Ni},\text{Pd},\text{Pt}\right)$ alloys are among the most widely applied bimetallics, open questions remain regarding whether and which of their compounds are stable at low $T$. Based on density-functional theory and first-principles cluster expansions that are “filtered” against structural and magnetic bistabilities, we assess all three systems. We (i) review the stability of the known phases; (ii) predict phases unstable with respect to bcc-fcc mixtures but stable if restricted to fcc; and, (iii) remarkably, predict previously unknown stable phases. This pinpoints where more definitive low-$T$ experiments should find new stable compounds.

Figure 1

(Color online) Total energy of the ferromagnetic ${\text{Fe}}_3\text{Ni}$ (100) SL upon varying the $c/a$ ratio and the net magnetic moment (spin polarization). All the internal degrees of freedom are relaxed for each point. The minima are strictly tetragonal (labeled as fct and bct) but referred to as bcc and fcc for simplicity throughout the text.

Figure 2

(Color online) Viewgraphs: calculated formation energies of ground-state structures for Fe-Ni, Fe-Pt, and Fe-Pd. Triangles (red) and circles (black) denote bcc- and fcc-based structures, respectively. Filled (open) symbols and solid (dotted) lines designate globally stable (fcc- or bcc-restricted) structures and convex hulls, respectively. Long-dashed lines connect the pure elemental solids in high-spin fcc and bcc structures, as labeled. Table: comparison of existing experimental and present theoretical assessments of both global low-$T$ phase stability (single structures and two-phase fields) and low-$T$ expectations based on an underlying fcc lattice only.

Figure 3

(Color online) Ground-state structures of $\text{Fe-}X$ (dark green: $X=\text{Ni},\text{Pd},\text{Pt}$ atoms; light red: Fe) in this work and earlier assessments (cf. Fig. 2). Note that based on $c/a$ ratio, we distinguish between crystallographically equivalent polymorphs [e.g., the fcc-based $Z1$ and the “(100) bct SL”].