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arxiv: 2605.26364 · v1 · pith:UKQIQLONnew · submitted 2026-05-25 · ❄️ cond-mat.mtrl-sci

Finite Temperature Stacking Fault Stability in Random and Locally Ordered CoCrNi beyond the Harmonic Approximation

Reza Namakian , Fei Shuang , Thomas D Swinburne , Poulumi Dey , Ali Erdemir , Wei Gao This is my paper

Pith reviewed 2026-06-29 21:01 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords CoCrNistacking fault energyanharmonic effectslocal chemical orderrandom solid solutionfinite temperaturemachine learning potentialdislocation dissociation
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The pith

Anharmonic calculations show random CoCrNi stacking faults remain unstable at high temperatures while local chemical order stabilizes them.

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

The paper addresses the mismatch between negative intrinsic stacking fault energies predicted by zero-temperature DFT for random solid solution CoCrNi and the finite fault widths observed in experiments. Harmonic models had suggested that rising temperature would increase the energy and stabilize the faults, but anharmonic methods reveal the opposite behavior. In random configurations the energy decreases with temperature and stays negative through 1000 K. Locally ordered configurations keep positive energies over the full range. Molecular dynamics simulations show dislocations dissociate without bound in the random state but produce finite fault widths once local order is present.

Core claim

Unlike harmonic approximations, anharmonic calculations using the projected average force integrator show that the intrinsic stacking-fault energy of random solid solution CoCrNi decreases with temperature and remains negative, so that RSS stacking faults are not thermally stabilized at elevated temperatures; by contrast, locally chemically ordered CoCrNi maintains positive ISFE from 0 K to 1000 K, with molecular dynamics confirming unbounded dislocation dissociation in the random case and finite stacking-fault widths in the ordered case.

What carries the argument

The fully anharmonic projected average force integrator applied to temperature-dependent generalized stacking-fault free energies, driven by a near-quantum-accuracy machine learning interatomic potential.

If this is right

  • RSS stacking faults are not stabilized by temperature and therefore cannot explain experimental observations.
  • Local chemical order is required to maintain positive intrinsic stacking fault energies at finite temperature.
  • Dislocation dissociation remains unbounded in random CoCrNi but is limited once local order is introduced.
  • Harmonic approximations give the wrong temperature trend for stacking-fault stability in this alloy.
  • The degree of local ordering controls whether stacking faults are stable at operating temperatures.

Where Pith is reading between the lines

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

  • Processing routes that promote or suppress short-range order could be used to tune dislocation mobility and work-hardening rates.
  • The same anharmonic temperature dependence may appear in other medium-entropy alloys previously analyzed only with harmonic models.
  • High-temperature strength predictions for CoCrNi-based alloys should incorporate the stability shift induced by local order rather than relying on random-solution assumptions.

Load-bearing premise

The machine learning interatomic potential faithfully reproduces the anharmonic vibrational free energies and the dependence of stacking-fault energies on chemical order.

What would settle it

Direct measurement of stacking-fault widths versus temperature in CoCrNi samples prepared with controlled levels of random solid solution versus local chemical order, compared against the computed free-energy curves.

Figures

Figures reproduced from arXiv: 2605.26364 by Ali Erdemir, Fei Shuang, Poulumi Dey, Reza Namakian, Thomas D Swinburne, Wei Gao.

Figure 1
Figure 1. Figure 1: (a, b) Representative atomic configurations of (a) the 450-atom RSS supercell and (b) the 2,520-atom LCO supercell containing nanometer-sized domains. (c, d) Probability density distributions of the first-nearest-neighbor Warren-Cowley parameters calculated across the ensemble of 50 RSS and 50 LCO configurations, respectively. constructed by randomly distributing equimolar fractions of Co, Cr, and Ni. A re… view at source ↗
Figure 2
Figure 2. Figure 2: (a) HCP–FCC free energy difference. Our EAM and NNP results obtained within the harmonic approximation are compared with literature data using different magnetic and vibrational approximations: magnetic (M) or nonmagnetic (NM) calculations, and harmonic (HA) or quasi-harmonic (QHA) approxi￾mations. The shaded blue and red regions indicate the standard deviation across an ensemble of 50 unique random config… view at source ↗
Figure 3
Figure 3. Figure 3: (a) ISFE and (b) USFE calculated via the PAFI method for an ensemble of 50 configurations in both RSS and LCO states. Solid lines represent mean values, while shaded regions denote the standard deviation. (c, f) GSFE curves for two representative configurations of the RSS and LCO states, respectively. (d, e) and (g, h) Probability density functions, fitted with Gaussian distributions, illustrating the stat… view at source ↗
Figure 4
Figure 4. Figure 4: Large-scale edge dislocation simulations in CoCrNi. (a, b) 1.67-million atom supercells (9.9 × 60.2 × 30.4 nm) showing the initial RSS and LCO configurations embedding an edge dislocation. (c, d) Equilibrated edge dislocation core structures at 300 K for RSS and LCO states, respectively. Atoms are identified via ICNA and colored by local structure: HCP (red), BCC (blue), and Other (gray); FCC atoms are hid… view at source ↗
read the original abstract

Previous density functional theory (DFT) calculations for random solid solution (RSS) CoCrNi predict negative intrinsic stacking-fault energy (ISFE) at 0 K, contrary to experimental observations of finite stacking-fault widths. Two explanations have been proposed: finite-temperature stabilization of the RSS state, suggested by harmonic approximations showing increasing ISFE with temperature, and local chemical order (LCO), which shifts the ISFE to positive values at 0 K. Here, we compute temperature-dependent generalized stacking-fault free energies for RSS and LCO CoCrNi using a near-quantum-accuracy machine learning interatomic potential and the fully anharmonic projected average force integrator. Unlike harmonic approximations, our anharmonic calculations show that the RSS ISFE decreases with temperature and remains negative, indicating that RSS stacking faults are not thermally stabilized at elevated temperatures. By contrast, LCO maintains positive ISFE over 0-1000 K. Molecular dynamics simulations further confirm unbounded dislocation dissociation in RSS CoCrNi but finite stacking-fault widths in the LCO state.

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

2 major / 1 minor

Summary. The manuscript computes temperature-dependent generalized stacking-fault free energies in random solid solution (RSS) and locally chemically ordered (LCO) CoCrNi using a machine-learning interatomic potential trained on DFT data together with the projected average force integrator to capture anharmonic effects. It reports that the RSS intrinsic stacking-fault energy (ISFE) decreases with temperature and remains negative up to 1000 K (contrary to prior harmonic results), while the LCO ISFE stays positive over the same range; molecular-dynamics simulations are used to confirm unbounded dislocation dissociation in RSS versus finite stacking-fault widths in LCO.

Significance. If the underlying potential faithfully reproduces the chemical-order dependence of anharmonic vibrational contributions, the work would usefully demonstrate that anharmonicity does not thermally stabilize RSS stacking faults and that local chemical order is required to reconcile zero-K DFT predictions with experiment. The explicit use of a fully anharmonic integrator and direct MD confirmation of dislocation behavior are methodological strengths that go beyond harmonic approximations.

major comments (2)
  1. [Abstract / Methods] Abstract / Methods description: the central claim that anharmonic effects cause the RSS ISFE to decrease with temperature (while LCO remains positive) rests on the ML interatomic potential correctly capturing the chemical-order dependence of anharmonic free-energy contributions. No quantitative error bars, cross-validation metrics against DFT for the finite-T generalized stacking-fault free energy, or benchmarks on thermal disorder in RSS versus LCO environments are supplied; any systematic bias in the potential could reverse the reported sign of d(ISFE)/dT.
  2. [Abstract] Abstract: the reported temperature trends lack reported uncertainties or convergence data for the projected average force integration; without these controls it is impossible to determine whether the RSS ISFE decrease is robust or within the numerical precision of the method.
minor comments (1)
  1. [Abstract] The abstract would be clearer if it briefly stated the supercell sizes and number of independent samples used for the free-energy calculations and MD runs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments highlighting the need for stronger validation of the ML potential and explicit uncertainty reporting. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Abstract / Methods] Abstract / Methods description: the central claim that anharmonic effects cause the RSS ISFE to decrease with temperature (while LCO remains positive) rests on the ML interatomic potential correctly capturing the chemical-order dependence of anharmonic free-energy contributions. No quantitative error bars, cross-validation metrics against DFT for the finite-T generalized stacking-fault free energy, or benchmarks on thermal disorder in RSS versus LCO environments are supplied; any systematic bias in the potential could reverse the reported sign of d(ISFE)/dT.

    Authors: We agree that explicit validation of the potential for anharmonic, finite-T properties in chemically disordered environments is important to support the central claim. The MLIP was trained on DFT data spanning RSS and LCO configurations, including AIMD snapshots, with force and energy errors reported in the original training paper; however, we did not include dedicated finite-T GSFE cross-validation or thermal-disorder benchmarks in this manuscript. We will add cross-validation metrics on RSS vs. LCO environments and error estimates derived from the PAFI integrator to the revised Methods section. Direct DFT finite-T GSFE benchmarks remain computationally prohibitive, but the MD dislocation results provide independent consistency checks. revision: yes

  2. Referee: [Abstract] Abstract: the reported temperature trends lack reported uncertainties or convergence data for the projected average force integration; without these controls it is impossible to determine whether the RSS ISFE decrease is robust or within the numerical precision of the method.

    Authors: We acknowledge the absence of reported uncertainties and convergence data for the PAFI calculations in the current manuscript. We will revise the abstract, results, and methods to include standard deviations from multiple independent PAFI runs, convergence tests with respect to the number of force samples, and error propagation for the temperature-dependent ISFE values. This will allow readers to assess the robustness of the reported trends. revision: yes

Circularity Check

0 steps flagged

No circularity; explicit anharmonic free-energy integration from MLIP trained on external DFT

full rationale

The derivation computes generalized stacking-fault free energies via molecular dynamics and the projected average force integrator applied to a machine-learning potential trained on independent DFT data. Reported temperature trends for RSS and LCO ISFE are direct numerical outputs of these simulations rather than algebraic reductions, fitted parameters renamed as predictions, or load-bearing self-citations. The chain is externally anchored to DFT training data and does not contain any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the transferability of a fitted ML potential to anharmonic defect energetics and on the correctness of the projected average force integrator for free-energy differences; both are domain-standard tools but introduce fitted parameters and numerical approximations not independently verified in the provided abstract.

free parameters (1)
  • ML interatomic potential parameters
    The potential is trained on DFT data; its parameters are fitted and directly control the computed free energies.
axioms (1)
  • domain assumption The projected average force integrator accurately captures fully anharmonic contributions to stacking-fault free energy
    Invoked as the method enabling the temperature-dependent results beyond harmonic approximation.

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discussion (0)

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