Inter-element miscibility driven stabilization of ordered pseudo-binary alloy

The study addresses how to stabilize and realize ordered, anisotropic crystal structures in multicomponent alloys that are not predicted as thermodynamic ground states in conventional phase diagrams. Although numerous crystal structures are geometrically possible at a fixed composition, typically only thermodynamically stable phases such as L1₂-FePd₃ are experimentally obtained. Inspired by prior work where interstitial nitrogen altered Fe–Ni ordering by exploiting differential element affinity, the authors hypothesize that introducing a substitutional third element with specific inter-element miscibility—immiscible with Fe but miscible with Pd—can stabilize an otherwise inaccessible layered Z3 structure in Fe–Pd alloys. They target FePd₃ because selective placement of the third element could transform the isotropic L1₂ phase into a highly anisotropic layered structure, enabling significant property changes.

Prior computational and experimental studies have mapped phase stability and structural selectivity in Fe–Pd alloys, identifying L1₂-FePd₃ as the stable phase across conditions. Structural control via external extremes (size, pressure, lattice strain) and interstitial chemistry (e.g., N-induced L1₀-FeNi formation) demonstrated that element-specific affinities can drive ordering transformations. Binary phase diagrams show many elements are miscible with Pd but immiscible with Fe, suggesting a route to tailor ordering. Reports on Fe–Pd–In alloys are limited to In-rich (>20 at.%) or very In-poor (<1.2 at.%) compositions, indicating the challenge of forming intermediate-composition ternaries. This work builds on these insights to explore substitutional third-element effects (In and other group 12–14 elements) on stabilizing a Z3-ordered structure.

Synthesis strategy: A stepwise chemical route was used to create Fe–Pd–In nanoparticles (NPs) with homogeneous nanoscale mixing: (i) synthesis of ~23 nm Pd nanoparticles; (ii) alloying of In with Pd to form PdInₓ alloy NPs; (iii) growth of FeOₓ shells on PdInₓ NPs; and (iv) reductive annealing (Ar + 4% H₂) at 600 or 800 °C for 3 h to reduce FeOₓ and diffuse Fe into the Pd–In core, yielding Fe–Pd–In ternary alloy NPs. The initial composition examined was Pd/In/Fe = 63/14/23 at.% (Pd/In = 82/18; Pd/Fe = 73/27). To probe phase formation windows, Pd–In@FeOₓ NPs with Pd/Fe = 70/30 at.% and varying Pd/In were annealed at 800 °C for 3 h.

Characterization: Powder X-ray diffraction (Cu Kα) with Rietveld refinement identified crystal structures and lattice parameters. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and atomic-resolution EDX elemental mapping determined atomic ordering and In site occupancy. X-ray absorption fine structure (XAFS/EXAFS) at Fe-, Pd-, and In-K edges probed local coordination, analyzed with REX2000 and FEFF8-derived scattering functions. In situ XRD on SiO₂-coated PdIn@FeOₓ NPs tracked phase evolution and thermal stability at 800 °C. Additional experiments included sintering of PdIn@FeOₓ NPs to micrometer-scale particles, and control anneals of mixed Pd@FeOₓ NPs with separate In powder to assess the necessity of homogeneous mixing.

Property measurements: Magnetic hysteresis (VSM, −20 to 20 kOe, room temperature) compared L1₂-(Fe,In)Pd₃ and Z3-Fe(Pd,In)₃ NPs with similar Pd/Fe but different Pd/In ratios. Hydrogen storage was evaluated via pressure–composition isotherms at 30 and 60 °C.

First-principles calculations: Density functional theory (OpenMX; PBE-GGA) computed formation energies and electronic structures of L1₂- and Z3-type Fe–Pd–M systems. Conventional cells were chosen to match atom counts across structures, enabling direct energy comparisons. Calculations replaced one Fe or Pd atom with M (M = Zn, Cd, Hg, Ga, In, Tl, Ge, Sn, Pb) to model dilute substitution. Formation energies were defined relative to elemental chemical potentials. Composition-dependent stability between L1₂-(Fe₁₋ₓInₓ)Pd₃ and Z3-Fe₂(Pd₅₋ₓInₓ) was evaluated. Non-collinear calculations assessed magnetocrystalline anisotropy energies. Computational parameters included s²p²d² (Fe) and s²p²d²f¹ (Pd, M) basis sets, 500 Ry cutoff, and dense k-point meshes (Z3: 30×30×16; L1₂: 21×21×30).

• Discovery and structure: Nanoparticles exhibiting a P4/mmm, layered Z3 structure were synthesized in the Fe–Pd–In system. The structure consists of alternating L1₀-type Pd–Fe–Pd trilayers and a Pd–In ordered monolayer along the c-axis, denoted Z3-Fe(Pd,In₁d)₃.
• Site occupancy: Atomic-resolution EDX mapping showed In atoms are excluded from Fe layers and preferentially occupy the middle Pd layer among the three Pd layers (Wyckoff 1d/1b), consistent with being surrounded by Pd neighbors.
• Composition window: Upon annealing Pd–In@FeOₓ NPs (Pd/Fe = 70/30 at.%), XRD showed that Pd/In = 89/11 at.% yielded L1₂-type; Pd/In = 85/15 and 83/17 at.% yielded Z3-type; Pd/In = 73/27 at.% produced a mixture of phases (including PdIn₂ and others), indicating a narrow In-composition window for Z3 formation. Overall ternary compositions forming Z3 were In/(Fe+Pd+In) ≈ 11–14 at.%.
• EXAFS coordination: In both L1₂ and Z3 phases, In was coordinated predominantly by ~12 Pd atoms, confirming that In substitutes away from Fe (L1₂: replaces Fe; Z3: occupies Pd 1d layer), reflecting In’s miscibility with Pd and immiscibility with Fe.
• Thermodynamic stability: In situ XRD showed that Z3 forms within 4 min at 800 °C and remains unchanged after 25 h at 800 °C, indicating thermodynamic stability below 800 °C. Z3 also formed in micrometer-scale particles produced by sintering, ruling out a pure nanosize requirement; however, homogeneous nanoscale mixing of Fe, Pd, and In precursors was crucial—inhomogeneous mixing (Pd@FeOₓ NPs plus separate In powder) did not yield Z3.
• DFT stability trends: Formation energy calculations identified L1₂-(Fe₁,In₁)Pd₃ and Z3-Fe₂(Pd₅,In₁d) as the most stable configurations within their respective structure types. The Z3 phase becomes more stable than L1₂ above a critical In fraction of In/(In+Pd) > ~8 at.% (x > 0.48 in the modeled mixing parameterization), matching experimental trends. Extending to other group 12–14 elements showed that elements immiscible with Fe but miscible with Pd (Cd, Hg, In, Tl, Pb) stabilize Z3 relative to L1₂, whereas those miscible with both Fe and Pd (Zn, Ga, Ge, Sn) do not. Experimentally, Z3-Fe(Pd,Pb) was also synthesized, corroborating the prediction.
• Magnetic properties: Both L1₂-(Fe,In)Pd₃ and Z3-Fe(Pd,In)₃ NPs are ferromagnetic with similar saturation magnetization at room temperature, but Z3 exhibits ~15× higher coercivity, behaving as a magnetically hard phase akin to L1₀ FePd. DFT non-collinear calculations attribute this to a large increase in magnetic anisotropy energy (from ~−1.38 µeV atom⁻¹ for L1₂ to ~−0.213 meV atom⁻¹ for Z3).
• Hydrogen storage and electronic structure: Despite structural motifs suggestive of Pd-rich hydrogen absorption, Z3-Fe(Pd,In)₃ showed no hydrogen-storage capacity at 30 or 60 °C. DFT density of states revealed a small number of Pd 4d holes and minimal changes near the Fermi level between Z3-Fe₂(Pd₅,In₁) and Z3-Fe₂Pd₆, indicating that modest In incorporation preserves the electronic characteristics of Z3-FePd₃ while not favoring H uptake.

The findings validate the central hypothesis that inter-element miscibility of a substitutional third element can stabilize an otherwise inaccessible ordered structure in a binary alloy. By exploiting In’s immiscibility with Fe and miscibility with Pd, the authors direct In to Pd layers in a layered Z3 framework, thereby lowering the formation energy of Z3 relative to the conventional L1₂ phase beyond a critical In fraction. This mechanism is thermodynamic, not kinetic or size-limited, and relies on homogeneous precursor mixing to access the correct ordering pathway. The concept generalizes across elements sharing the same miscibility pattern (Cd, Hg, Tl, Pb) and was experimentally confirmed for Pb. The structural transformation from isotropic L1₂ to anisotropic Z3 markedly enhances magnetocrystalline anisotropy and coercivity without significantly altering the DOS near the Fermi level, demonstrating that targeted structural stabilization via miscibility control can tune key functional properties. The work suggests that binary phase diagrams, when combined with nanoscale synthesis routes ensuring homogeneous mixing, can guide the discovery of novel ordered nanostructures without exhaustive structure searches, and that small compositional adjustments can switch stable structures and associated properties.

This work introduces and demonstrates an inter-element miscibility-driven strategy to stabilize ordered pseudo-binary alloys, exemplified by the first experimental realization of Z3-Fe(Pd,In)₃ with P4/mmm symmetry. A small In addition, selectively occupying Pd layers due to its Pd miscibility and Fe immiscibility, stabilizes the Z3 structure thermodynamically and yields significantly enhanced coercivity while preserving key electronic features of Z3-FePd₃. DFT establishes a critical In content for Z3 stabilization and predicts broader applicability to elements with similar miscibility profiles, corroborated by experimental Z3 formation in Fe–Pd–Pb. The approach opens a pathway to discover and control ordered alloy structures guided by binary phase diagrams and nanoscale synthesis. Future directions include: systematic exploration of other binary systems with suitable third-element miscibility contrasts; mapping full compositional/temperature stability fields and kinetics; extending to bulk and thin-film forms; investigating additional functional properties (e.g., catalysis, spintronic behavior) arising from Z3-type anisotropy; and incorporating multi-element co-doping to fine-tune ordering and anisotropy.

• Narrow compositional window: Z3 forms only within limited In contents; outside this range, conventional L1₂ or mixed/unwanted phases appear.
• Requirement for homogeneous mixing: Successful Z3 formation depends on nanoscale homogeneous precursor mixing; inhomogeneous routes fail to yield Z3, potentially limiting scalability.
• Structural scope in theory: DFT comparisons focused on L1₂ vs Z3; other competing structures at similar compositions were not comprehensively surveyed, and calculations are at 0 K without reaction pathway analysis.
• Thermal stability range: Demonstrated thermodynamic stability below 800 °C; behavior at higher temperatures and long-term stability in different environments were not explored.
• Hydrogen storage: Z3-Fe(Pd,In)₃ shows no H storage at 30–60 °C, limiting potential in hydride applications.