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arxiv: 2606.09023 · v1 · pith:4EPJIV3Vnew · submitted 2026-06-08 · ❄️ cond-mat.mtrl-sci

Precipitate phase selection and grain boundary morphology in Cu-Ni-Si-Mn alloys: A machine-learning interatomic potential study

Aadil Fayaz Wani , Il-Seok Jeong , Haekwan Jeon , Jaesun Kim , SuDong Park , Eun-Ae Choi , Seung Zeon Han , Seungwu Han
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Byungki Ryu
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Pith reviewed 2026-06-27 16:07 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords Cu-Ni-Si-Mn alloysgrain boundary precipitationmachine-learning interatomic potentialNi2SiMn6Ni16Si7interface structureprecipitate morphologyG-phase
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The pith

Mn addition in Cu-Ni-Si alloys switches grain-boundary precipitates from irregular Ni2Si to continuous film-shaped Mn6Ni16Si7 by changing interface coherence.

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

The paper uses machine-learning interatomic potential calculations to trace how manganese alters precipitation at grain boundaries in copper-nickel-silicon alloys. Without Mn the stable Ni2Si phase forms coherent interfaces with copper that produce plate-like strained precipitates; after coarsening these interfaces create local repulsion and open, irregular grain-boundary structures. With Mn the G-phase Mn6Ni16Si7 forms incoherent interfaces of moderate energy that maintain continuous contact and stabilize film-like morphology. The atomic origin of this phase selection accounts for the observed shift from degraded to improved mechanical properties when manganese is added.

Core claim

Mn addition favors GB precipitation of Mn6Ni16Si7 rather than Ni2Si. The coherent interface structure between Cu and Ni2Si favors plate-like strained precipitates in the matrix; upon coarsening and stress release an out-of-phase coherent-like interface forms at GBs, generating a local repulsive region that produces surface-like open-boundary structures and irregular morphology. In contrast, Cu/Mn6Ni16Si7 interfaces remain predominantly incoherent with moderate boundary energies and no pronounced repulsive regime, thereby stabilizing continuous interfacial contact and film-shaped GB precipitation.

What carries the argument

Machine-learning interatomic potential calculations of Cu/Ni2Si and Cu/Mn6Ni16Si7 interphase boundary structures and energies

If this is right

  • Mn-free alloys exhibit irregularly-shaped Ni2Si precipitates with open-boundary-like Cu/Ni2Si interfaces.
  • Mn-added alloys exhibit film-like G-phase precipitates at grain boundaries.
  • Coherent Cu/Ni2Si interfaces drive plate-like matrix precipitates that evolve into irregular GB morphology after stress release.
  • Incoherent Cu/Mn6Ni16Si7 interfaces with moderate energies prevent repulsive regimes and maintain continuous film contact.

Where Pith is reading between the lines

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

  • The same interface-coherence criterion could be used to screen other minor-element additions for desired precipitate morphology in copper alloys.
  • Large-scale MLIP simulations of the type performed here may identify temperature or composition windows where the out-of-phase repulsive regime in Ni2Si is suppressed.
  • If the moderate-energy incoherent interfaces prove general, they could serve as a design rule for stabilizing film-like grain-boundary phases in other FCC alloy systems.

Load-bearing premise

The machine-learning interatomic potential accurately reproduces the DFT-level energetics for the interfacial bonding and microstructural configurations in these specific alloy systems, and the modeled interfaces represent the experimental grain boundary conditions.

What would settle it

High-resolution transmission electron microscopy showing that Cu/Ni2Si grain-boundary interfaces remain fully coherent without repulsive regions or open-boundary structures while Cu/Mn6Ni16Si7 interfaces exhibit high-energy coherent patches.

Figures

Figures reproduced from arXiv: 2606.09023 by Aadil Fayaz Wani, Byungki Ryu, Eun-Ae Choi, Haekwan Jeon, Il-Seok Jeong, Jaesun Kim, Seungwu Han, Seung Zeon Han, Sudong Park.

Figure 1
Figure 1. Figure 1: Atomic structure (a) Cu, (b) Ni2Si, and (c) G-phase. The crystallographic directions are shown in each structure. correspond to bulk, bulk strained, and bulk strained G-phase respectively. The interface configurations in (d) and (e) correspond to the interface structures for Cu(11̅0)/Ni2Si(100) and Cu(100)/G-phase(100), respectively [PITH_FULL_IMAGE:figures/full_fig_p027_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Formation energy evolution of Cu solid solution with different Ni, Si, and Mn solute states. The values are obtained from DFT and various MLIPs for direct comparison of energetic trends and relative accuracy [PITH_FULL_IMAGE:figures/full_fig_p028_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of (a) surface energy, (b) interface energy and (c) strain energy for Ni2Si and G-phase obtained from DFT and various MLIPs [PITH_FULL_IMAGE:figures/full_fig_p029_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of (a, d, g) energy density at smaller particle sizes, (b, e, h) total energy at smaller sizes, and (c, f, i) energy density at larger sizes of Ni2Si precipitates inside and outside the Cu matrix computed using DFT and MLIP models [PITH_FULL_IMAGE:figures/full_fig_p030_4.png] view at source ↗
read the original abstract

Alloys inevitably contain interphase boundaries, whose energetics govern nucleation processes and precipitate morphology. In Cu-Ni-Si alloys, Mn addition markedly changes grain boundary (GB) precipitation behavior. While GB precipitation of stable Ni$_2$Si in Mn-free alloys is associated with degraded mechanical properties, Mn addition instead promotes film-shaped Mn$_6$Ni$_{16}$Si$_7$ (G-phase) precipitation, which is correlated improved mechanical properties. However, the atomic origin of the contrasting GB phase selection and morphology remains unclear. Here we perform machine-learning interatomic potential (MLIP) calculations to investigate the effect of interphase-boundary atomic structure on GB precipitates in Cu-Ni-Si alloys with and without Mn. The MLIP calculations reliably reproduce DFT-level energetics for interfacial bonding and microstructural configurations, and further predict that Mn addition favors GB precipitation of Mn$_6$Ni$_{16}$Si$_7$ rather than Ni$_2$Si. Experimentally, Mn-free alloys are observed to exhibit irregularly-shaped Ni$_2$Si precipitates with open-boundary-like Cu/Ni$_2$Si interfaces, whereas Mn-added alloys exhibit film-like G-phase at GBs. Large-scale atomistic interface calculations reveal that the coherent interface structure between Cu and Ni$_2$Si favors the formation of plate-like strained Ni$_2$Si precipitates in the matrix. Upon coarsening and stress release, an out-of-phase coherent-like interface can form at GBs, generating a local repulsive region that gives rise to surface-like open-boundary structures and explains the irregular morphology of GB stable Ni$_2$Si precipitates. In contrast, Cu/Mn$_6$Ni$_{16}$Si$_7$ interfaces remain predominantly incoherent with moderate boundary energies and no pronounced repulsive regime, thereby stabilizing continuous interfacial contact and explaining film-shaped GB precipitation.

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

1 major / 1 minor

Summary. The manuscript uses machine-learning interatomic potentials (MLIPs) to examine how Mn addition alters grain boundary (GB) precipitate phase selection and morphology in Cu-Ni-Si alloys. It claims that the MLIP reproduces DFT energetics and predicts Mn favors Mn6Ni16Si7 (G-phase) precipitation at GBs via incoherent interfaces of moderate energy that stabilize film-like morphologies, while Ni2Si in Mn-free alloys produces irregular GB precipitates due to coherent interfaces that develop out-of-phase repulsion and open-boundary structures upon coarsening and stress release. Experimental observations of precipitate shapes are presented as consistent with these predictions.

Significance. If the MLIP interface results hold, the work supplies an atomistic mechanism linking interface coherence, energy, and stress relaxation to the experimentally observed shift from irregular Ni2Si to film-like G-phase GB precipitation upon Mn addition. This could inform alloy design for improved mechanical properties. The large-scale simulations that distinguish coherent vs. incoherent behaviors and their morphological consequences are a positive feature.

major comments (1)
  1. [Abstract and Results (interface calculations)] Abstract and Results (interface calculations): The central claims that Mn addition selects Mn6Ni16Si7 via incoherent moderate-energy interfaces while Ni2Si produces irregular morphology via coherent out-of-phase repulsion rest on the MLIP correctly ranking and structurally distinguishing these Cu/Ni2Si and Cu/Mn6Ni16Si7 interfaces. The abstract asserts that the MLIP 'reliably reproduce[s] DFT-level energetics for interfacial bonding and microstructural configurations,' yet the text provides no quantitative validation metrics (RMSE, energy tables, or structure comparisons) specifically for the GB-relevant supercells or the coherent-to-incoherent transition. This is load-bearing for the phase-selection and morphology explanations.
minor comments (1)
  1. [Figure captions] Figure captions and text should explicitly state the supercell sizes and boundary conditions used for the large-scale interface calculations to allow reproducibility assessment.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of its potential significance. We address the single major comment below and agree that additional quantitative detail is warranted.

read point-by-point responses

  1. Referee: The central claims that Mn addition selects Mn6Ni16Si7 via incoherent moderate-energy interfaces while Ni2Si produces irregular morphology via coherent out-of-phase repulsion rest on the MLIP correctly ranking and structurally distinguishing these Cu/Ni2Si and Cu/Mn6Ni16Si7 interfaces. The abstract asserts that the MLIP 'reliably reproduce[s] DFT-level energetics for interfacial bonding and microstructural configurations,' yet the text provides no quantitative validation metrics (RMSE, energy tables, or structure comparisons) specifically for the GB-relevant supercells or the coherent-to-incoherent transition. This is load-bearing for the phase-selection and morphology explanations.

    Authors: We agree that the manuscript would be strengthened by explicit quantitative validation metrics for the specific interface supercells central to the GB precipitate analysis. While the Methods section describes the MLIP training set and overall validation against DFT for bulk phases and selected interfaces, direct RMSE values, energy tables, and structural comparisons for the coherent Cu/Ni2Si, incoherent Cu/Ni2Si, and Cu/Mn6Ni16Si7 GB-relevant models are not provided. In the revised manuscript we will add a new subsection (or supplementary table) reporting MLIP–DFT energy differences, RMSE, and relaxed structural metrics (lattice mismatch, atomic displacements) for representative supercells of each interface type, including those used to identify the out-of-phase repulsion and incoherent regimes. This addition will directly substantiate the interface ranking and coherence arguments. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent MLIP interface calculations

full rationale

The paper's central chain computes Cu/Ni2Si and Cu/G-phase interface energies and structures via MLIP (trained on DFT), then uses those computed values to rationalize observed morphologies and phase selection. These interface results are not fitted to the morphology data or defined in terms of the target conclusions; the abstract and text present them as forward predictions from the potential. No self-definitional equations, fitted-input-as-prediction steps, or load-bearing self-citations appear in the provided text. The derivation remains self-contained against external DFT benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work relies on the trained MLIP and assumptions about interface representativeness rather than new physical entities.

free parameters (1)
  • MLIP model parameters
    The interatomic potential is trained on a dataset of DFT calculations, introducing numerous fitted parameters that determine the accuracy for interfaces.
axioms (1)
  • domain assumption The selected interface models represent the relevant experimental grain boundary configurations
    Invoked when linking simulation results to observed precipitate morphologies.

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