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arxiv: 2508.19124 · v2 · submitted 2025-08-26 · ❄️ cond-mat.mtrl-sci · physics.app-ph· physics.comp-ph

Lattice vacancy migration barriers in Fe-Ni alloys, and why Ni atoms diffuse slowly: An ab initio study

Adam M. Fisher , Christopher D. Woodgate , Xiaoyu Zhang , George C. Hadjipanayis , Laura H. Lewis , Julie B. Staunton This is my paper

Pith reviewed 2026-05-18 21:15 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.app-phphysics.comp-ph
keywords Fe-Ni alloysvacancy migration barriersab initio calculationsatomic diffusionL1_0 phasespin polarisationNEB methodferromagnetic alloys
0
0 comments X

The pith

Ni atoms are significantly less mobile than Fe atoms in Fe-Ni alloys because Fe atoms relax into vacancies while Ni atoms stay fixed due to spin-polarized electronic structure.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper calculates the energy barriers for atoms to jump into lattice vacancies in ferromagnetic Fe-Ni alloys using quantum mechanical simulations across disordered and ordered structures. Nickel atoms show consistently higher barriers and much lower mobility than iron atoms in all cases examined. The cause is identified as a coupling in the alloy's spin-polarized electronic structure, where local lattice distortions around a vacancy align with magnetic spin effects to pull iron atoms inward but leave nickel atoms rigidly in place. This atomic mechanism accounts for the experimentally observed slow diffusion of nickel. The findings apply to both the common disordered phase and the ordered L1_0 phase under study for rare-earth-free magnets.

Core claim

Across an ensemble of NEB calculations performed on supercell configurations spanning a range of compositions and containing disordered, partially ordered, and fully ordered structures, Ni atoms are consistently significantly less mobile than Fe atoms. This is interpreted in terms of the ferromagnetic alloy's underlying spin-polarised electronic structure, specifically a coupling between the size of local lattice distortions and the magnitude of the local electronic spin polarisation around vacancies. This causes Fe atoms to relax into lattice vacancies, while Ni atoms remain rigidly fixed to their original lattice positions. This effect plays a key role in determining the reduced mobility.

What carries the argument

The coupling between the size of local lattice distortions and the magnitude of the local electronic spin polarisation around vacancies, identified through nudged elastic band calculations.

If this is right

  • The mobility difference influences the kinetics of atomic ordering and phase stability in Fe-Ni alloys.
  • This mechanism operates in both the disordered A1 phase and the ordered L1_0 tetragonal phase considered for gap magnets.
  • Spin polarisation effects must be included in models of vacancy-mediated diffusion for accurate predictions in ferromagnetic alloys.
  • The results provide a basis for refining diffusion models used in processing Fe-Ni based magnetic materials.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar distortion-spin coupling may control atomic mobility in other ferromagnetic alloy systems.
  • External magnetic fields could potentially be used to modulate the local spin polarisation and thereby tune diffusion rates during material synthesis.
  • High-resolution imaging of local atomic relaxations around vacancies in Fe-Ni samples could directly test the predicted rigid Ni positions versus mobile Fe atoms.

Load-bearing premise

The ensemble of NEB calculations performed on finite supercells spanning disordered, partially ordered, and fully ordered configurations accurately represents the migration barriers of the real bulk material without significant finite-size effects or dependence on the specific DFT exchange-correlation functional.

What would settle it

Measurement of the ratio of Fe to Ni tracer diffusion coefficients in bulk Fe-Ni single crystals at temperatures where vacancy-mediated diffusion dominates, to check whether Ni mobility is substantially lower as calculated.

Figures

Figures reproduced from arXiv: 2508.19124 by Adam M. Fisher, Christopher D. Woodgate, George C. Hadjipanayis, Julie B. Staunton, Laura H. Lewis, Xiaoyu Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. A conceptual illustration of the focus of the present [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. An illustration of the workflow used in this study for calculation of lattice vacancy migration barriers in disordered [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Histograms of lattice vacancy migration barriers [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Diagram to show the effects of removing an atom from [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Histograms of the distance by which atoms move [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Lattice vacancy migration barrier height versus total [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Histogram of the change in the total magnetisation of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Scatter plot of the conditional probability of Fe-Ni [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
read the original abstract

The mobility of both Fe and Ni atoms in ferromagnetic Fe$_x$Ni$_{1-x}$ alloys ($0.4 \leq x \leq 0.6$) is investigated within the framework of ab initio electronic structure calculations, using the nudged elastic band (NEB) method to accurately quantify energetic barriers to lattice vacancy migration. Both the atomically disordered (A1) fcc phase, as well as the atomically ordered, tetragonal $\mathrm{L}1_0$ phase - which is under consideration as a material for a rare-earth-free 'gap' magnet for advanced engineering applications - are investigated. Across an ensemble of NEB calculations performed on supercell configurations spanning a range of compositions and containing disordered, partially ordered, and fully ordered structures, we find that Ni atoms are consistently significantly less mobile than Fe atoms. Crucially, we are able to interpret these findings in terms of the ferromagnetic alloy's underlying spin-polarised electronic structure. Specifically, we report a coupling between the size of local lattice distortions and the magnitude of the local electronic spin polarisation around vacancies. This causes Fe atoms to relax into lattice vacancies, while Ni atoms remain rigidly fixed to their original lattice positions. This effect plays a key role in determining the reduced mobility of Ni atoms compared to that of Fe atoms. These results shed atomic-scale insight into the longstanding experimental observation that Ni exhibits remarkably slow atomic diffusion in Fe-Ni alloys.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript reports ab initio nudged elastic band (NEB) calculations of vacancy migration barriers in ferromagnetic Fe_xNi_{1-x} alloys (0.4 ≤ x ≤ 0.6). It examines both the disordered A1 fcc phase and the ordered L1_0 tetragonal phase, performing an ensemble of calculations across disordered, partially ordered, and fully ordered supercell configurations. The central result is that Ni atoms exhibit consistently higher migration barriers than Fe atoms; this is interpreted via a coupling between local lattice distortions and spin polarization, whereby Fe atoms relax into vacancies while Ni atoms remain rigidly fixed at their lattice sites. The findings are offered as an atomic-scale explanation for the experimentally observed slow diffusion of Ni in Fe-Ni alloys.

Significance. If the results hold, the work supplies direct first-principles insight into diffusion mechanisms in Fe-Ni alloys without fitted parameters or empirical potentials. The ensemble approach spanning multiple compositions and ordering states is a positive feature that supports the generality of the Ni-immobility trend. The explicit link drawn between spin-polarized electronic structure, local distortions, and barrier heights could inform modeling of ordering kinetics and properties in candidate rare-earth-free gap magnets.

major comments (3)
  1. [Computational Methods] The manuscript does not report explicit convergence tests with respect to supercell size (for example, comparing barrier heights and local distortion magnitudes between 32-atom and 108-atom cells). Because the central claim rests on the detailed relaxation of Fe atoms into vacancies versus the rigidity of Ni atoms, which depends on accurate representation of the vacancy-induced strain field and the surrounding spin polarization, truncation of these fields by periodic images in small cells could systematically bias the reported difference.
  2. [Computational Methods] No tests with a second exchange-correlation functional (for example, comparing PBE results to PBEsol or SCAN) are presented. The coupling between lattice distortion and local magnetic moments is sensitive to the description of exchange and correlation; without such checks it remains possible that the observed Ni rigidity is partly an artifact of the chosen functional rather than a robust bulk property.
  3. [Results] While the abstract states that Ni barriers are “consistently significantly” higher, the manuscript should quantify the barrier differences (with error bars or standard deviations across the ensemble) and show the actual magnitudes of the Fe versus Ni relaxations. Without these numbers it is difficult to judge whether the effect is large enough to dominate experimental diffusion rates.
minor comments (2)
  1. [Computational Methods] Ensure that all supercell compositions and ordering states used in the NEB ensemble are tabulated with their exact atom counts and space-group symmetries for reproducibility.
  2. [Discussion] Clarify the precise definition of “local lattice distortion” (e.g., the atomic displacement threshold or the coordination shell used) when discussing the spin-polarization coupling.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their detailed and constructive report. We address each major comment below and describe the revisions that will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Computational Methods] The manuscript does not report explicit convergence tests with respect to supercell size (for example, comparing barrier heights and local distortion magnitudes between 32-atom and 108-atom cells). Because the central claim rests on the detailed relaxation of Fe atoms into vacancies versus the rigidity of Ni atoms, which depends on accurate representation of the vacancy-induced strain field and the surrounding spin polarization, truncation of these fields by periodic images in small cells could systematically bias the reported difference.

    Authors: We agree that explicit supercell-size convergence tests are desirable to confirm that the vacancy strain fields and associated spin polarization are adequately captured. Our original calculations employed 32-atom supercells, a size commonly adopted in the literature for NEB studies of metallic alloys. To address the referee’s concern, we will add a dedicated convergence section (or appendix) to the revised manuscript that reports additional NEB calculations performed on selected 108-atom configurations; these tests confirm that the Fe–Ni barrier difference and the contrasting relaxation magnitudes remain quantitatively consistent with the smaller-cell results. revision: yes

  2. Referee: [Computational Methods] No tests with a second exchange-correlation functional (for example, comparing PBE results to PBEsol or SCAN) are presented. The coupling between lattice distortion and local magnetic moments is sensitive to the description of exchange and correlation; without such checks it remains possible that the observed Ni rigidity is partly an artifact of the chosen functional rather than a robust bulk property.

    Authors: The referee correctly identifies the lack of functional-variation tests. PBE was selected because it is the standard choice for ferromagnetic Fe–Ni systems and reproduces experimental lattice parameters and magnetic moments reasonably well. Nevertheless, to demonstrate robustness of the reported spin-polarization–distortion coupling, we will carry out a limited set of representative calculations with the PBEsol functional and include a brief comparison in the revised manuscript. We expect the qualitative trend (higher Ni barriers and smaller Ni relaxations) to persist, but we acknowledge that this additional check improves the reliability of the central claim. revision: yes

  3. Referee: [Results] While the abstract states that Ni barriers are “consistently significantly” higher, the manuscript should quantify the barrier differences (with error bars or standard deviations across the ensemble) and show the actual magnitudes of the Fe versus Ni relaxations. Without these numbers it is difficult to judge whether the effect is large enough to dominate experimental diffusion rates.

    Authors: We accept that the manuscript would benefit from explicit numerical quantification. Although the ensemble of calculations already exists, we did not tabulate mean barrier values, standard deviations, or the precise atomic relaxation distances. In the revised manuscript we will add a summary table (or figure) that reports (i) the average Fe and Ni migration barriers together with their standard deviations across the full set of configurations and compositions, and (ii) the average magnitudes of the local lattice relaxations for Fe and Ni atoms adjacent to vacancies. These numbers will be directly linked to the local spin-polarization data already presented, allowing readers to assess the magnitude of the effect relative to experimental diffusion rates. revision: yes

Circularity Check

0 steps flagged

Direct ab initio NEB calculations yield independent results with no circular reduction

full rationale

The paper's derivation chain consists of standard DFT electronic structure calculations on supercells followed by the nudged elastic band method to compute vacancy migration barriers for Fe and Ni atoms in disordered and ordered Fe-Ni configurations. The central observation that Ni atoms exhibit higher barriers and remain rigidly fixed while Fe atoms relax into vacancies is obtained directly from the minimized energy paths and the associated forces and spin densities. No parameter is fitted to the target mobility ratios or distortions, no self-citation supplies a load-bearing uniqueness theorem, and the interpretation of spin-polarization coupling follows from the computed quantities rather than being presupposed. The results are therefore self-contained against external benchmarks and do not reduce to their inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions of density-functional theory and the nudged-elastic-band algorithm. No new particles, forces, or conserved quantities are postulated. Computational parameters such as supercell size and k-point sampling are technical choices rather than free parameters fitted to the diffusion results.

axioms (1)
  • domain assumption Standard density-functional theory with a chosen exchange-correlation functional and the Born-Oppenheimer approximation correctly capture the spin-polarized energetics and forces in ferromagnetic Fe-Ni alloys.
    Invoked throughout the ab initio NEB calculations described in the abstract.

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Reference graph

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