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arxiv: 2605.01181 · v1 · submitted 2026-05-02 · ❄️ cond-mat.mtrl-sci

Recognition: unknown

Grain boundary segregation of light elements and their effects on cohesion in ferritic steels

Han Lin Mai , Xiang-Yuan Cui , Tilmann Hickel , Simon P. Ringer , J\"org Neugebauer
Authors on Pith no claims yet

Pith reviewed 2026-05-09 15:10 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords grain boundary segregationferritic ironlight elementsdensity functional theorycohesionembrittlementsegregation energyRice-Wang model
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The pith

Calculations show boron and carbon strengthen grain boundaries in iron while helium, oxygen and sulfur weaken them.

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

The paper computes segregation energies and cohesive effects for nine light elements in ferritic iron grain boundaries using density functional theory on six model coincident site lattice boundaries. It evaluates both substitutional and interstitial sites, then ranks the elements by their impact on boundary strength at equal concentrations using bond-order and rigid interfacial models. Boron and carbon increase cohesion, hydrogen nitrogen and phosphorus mildly reduce it, and helium oxygen and sulfur act as strong embrittlers. The work also shows that common site-volume criteria miss the strongest binding sites and that relaxation can move atoms between site types, so both must be sampled. A large open dataset of these results is released for further use.

Core claim

Density functional theory calculations on six coincident site lattice grain boundaries in body-centered cubic iron show that, when compared at the same concentration, boron and carbon increase grain boundary cohesion, nitrogen phosphorus and hydrogen mildly decrease it, and helium oxygen and sulfur are strong decohesive agents. Accurate segregation spectra require sampling both interstitial and substitutional starting positions because volume-based criteria miss the deepest sites and atomic relaxations can erase site-type distinctions. Nearest-neighbor distances after relaxation control the lower threshold of segregation energies.

What carries the argument

Density functional theory sampling of substitutional and interstitial sites in six CSL grain boundary models, evaluated with bond-order analysis and the rigid Rice-Wang cohesive strength framework.

If this is right

  • Boron and carbon additions can be used to enhance grain boundary cohesion in ferritic steels.
  • Helium, oxygen, and sulfur concentrations should be minimized to avoid severe grain boundary embrittlement.
  • Both substitutional and interstitial sites must be considered when predicting light-element segregation spectra.
  • The released DFT dataset enables training of machine learning interatomic potentials for larger-scale steel simulations.

Where Pith is reading between the lines

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

  • The nearest-neighbor distance correlation after relaxation could serve as a low-cost screen for other solutes in similar metals.
  • Trends identified here may extend to other body-centered cubic metals where electronic interactions with iron dominate.
  • Multi-element co-segregation at the same boundary could shift the single-element rankings and deserves separate study.
  • Results suggest that grain boundary engineering strategies in steels for nuclear or hydrogen-service environments should prioritize these light-element effects.

Load-bearing premise

The six chosen CSL grain boundary models and the DFT settings are representative of real polycrystalline ferritic steels and capture the lowest-energy segregation states.

What would settle it

Direct experimental measurement of grain boundary fracture strength or segregation site occupancies in controlled-concentration ferritic iron samples containing boron versus sulfur or helium.

Figures

Figures reproduced from arXiv: 2605.01181 by Han Lin Mai, J\"org Neugebauer, Simon P. Ringer, Tilmann Hickel, Xiang-Yuan Cui.

Figure 1
Figure 1. Figure 1: The atomic structures of the six coincident-site-lattice model GBs investigated in this study, the (a) view at source ↗
Figure 2
Figure 2. Figure 2: The starting positions considered for interstitial sites in this study for the (a) view at source ↗
Figure 3
Figure 3. Figure 3: The segregation energies at the strongest trapping sites are plotted against the GB energies of the pure view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the distance from the grain boundary versus segregation energy for solutes in the same view at source ↗
Figure 5
Figure 5. Figure 5: Distributions of segregation energies of the unique sites (after SOAP-based duplicate removal, view at source ↗
Figure 6
Figure 6. Figure 6: The final relaxed segregation energy is plotted against the corresponding Voronoi volume of that site for view at source ↗
Figure 7
Figure 7. Figure 7: Nearest-neighbor distance vs. relaxed segregation energy comparison for solutes in the same GB: ( view at source ↗
Figure 8
Figure 8. Figure 8: Segregation engineering maps (segregation binding strength vs. GB cohesion modifier) for solutes in the view at source ↗
Figure 9
Figure 9. Figure 9: Segregation engineering maps (segregation binding strength vs. GB cohesion modifier) for solutes in the view at source ↗
Figure 10
Figure 10. Figure 10: A numerical breakdown of the types of unique, energetically favourable sites (E view at source ↗
read the original abstract

Light elements play an important role in influencing the macroscale properties of engineering alloys through grain boundary (GB) segregation phenomena. However, the scarcity and scattered nature of ab initio datasets for light elements in steels makes reproduction and extraction of general trends from the literature difficult. Here, we present a comprehensive ab initio evaluation of the segregation energies and cohesive effects for H, He, B, C, N, O, P, S, extensively sampling both substitutional and interstitial sites in six model coincident site lattice (CSL) ferritic iron GBs using density functional theory (DFT). Cohesive effects are evaluated in both a quantum-chemistry bond-order and rigid Rice-Wang interfacial cohesive strength framework. Our calculations indicate that, compared at the same concentration, B and C enhance GB cohesion, N, P, H are mildly detrimental, and He, O, S as powerful decohesive agents/embrittlers. Sampling both interstitial and substitutional starting positions is necessary to accurately capture segregation spectra. Commonly utilised sampling criteria such as site volumes prove insufficient for identifying deepest GB binding sites. Solutes placed in either kind of site can induce large relaxations to the same final configuration, resulting in site classification ambiguity. The nearest neighbour distance of a solute to its neighbours after relaxation is shown to be a controlling factor for the lower threshold of segregation energies at sites. The freely available DFT dataset and analysis repositories are expected to advance understanding of GB segregation behaviours of light elements in steels and serve as a resource for developing machine learning interatomic potentials.

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 DFT calculations of segregation energies for light elements H, He, B, C, N, O, P, and S at both substitutional and interstitial sites across six CSL grain boundaries in bcc Fe. Cohesive effects are quantified via quantum-chemistry bond-order analysis and the rigid Rice-Wang interfacial strength model. The central result is a ranking at fixed concentration: B and C enhance GB cohesion, N/P/H are mildly detrimental, and He/O/S act as strong decohesives/embrittlers. The work also demonstrates that volume-based site selection is inadequate, that relaxations can blur interstitial/substitutional classification, and that nearest-neighbor distance after relaxation correlates with the lower bound of segregation energies. An open DFT dataset and analysis code are provided.

Significance. If the reported trends and dataset prove robust, the paper supplies a much-needed systematic ab initio resource for light-element GB segregation in ferritic steels, where existing literature is scattered and incomplete. The emphasis on sampling ambiguities and the release of raw data directly support development of machine-learned interatomic potentials and mechanistic understanding of embrittlement, which are high-value contributions in the field.

major comments (3)
  1. [Methods] Methods section (and associated supplementary tables): the manuscript does not report the specific exchange-correlation functional, plane-wave cutoff, k-point sampling, supercell dimensions, or convergence criteria used for the segregation-energy calculations. Without these, the numerical reliability of the small energy differences that underpin the “mildly detrimental” classification for N, P, and H cannot be assessed.
  2. [GB models and site sampling] Results on GB models and site sampling (abstract and § on CSL boundaries): the ranking of cohesive effects is derived exclusively from six specific CSL boundaries with a finite set of sampled sites. No exhaustive enumeration, comparison against experimental segregation isotherms, or tests on additional (non-CSL) boundaries are presented, yet the abstract presents the ordering as generally indicative for ferritic steels. If lower-energy sites or other boundary types reverse the sign for any element, the reported classification would not generalize.
  3. [Results tables] Table of segregation energies and cohesion changes: no error bars or estimates of numerical uncertainty are attached to the reported values. Given that several elements are classified as “mildly” vs. “strongly” detrimental on the basis of differences of only a few tens of meV, the absence of uncertainty quantification weakens the quantitative ordering.
minor comments (2)
  1. [Figures and text] Figure captions and text occasionally use “site volume” without defining the precise geometric criterion employed; a short explicit definition would aid reproducibility.
  2. [Cohesion metrics] The bond-order and Rice-Wang metrics are introduced without a brief reminder of their exact definitions or the reference states used; adding one sentence would improve accessibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have identified areas where the manuscript can be strengthened. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Methods] Methods section (and associated supplementary tables): the manuscript does not report the specific exchange-correlation functional, plane-wave cutoff, k-point sampling, supercell dimensions, or convergence criteria used for the segregation-energy calculations. Without these, the numerical reliability of the small energy differences that underpin the “mildly detrimental” classification for N, P, and H cannot be assessed.

    Authors: We agree that these computational parameters are essential for evaluating the reliability of the reported energy differences. We will revise the Methods section to explicitly state the exchange-correlation functional, plane-wave cutoff, k-point sampling scheme and density, supercell dimensions for each CSL grain boundary model, and the convergence criteria for energy and atomic forces. The supplementary tables will be updated with the same information. This addition will directly address the concern regarding the numerical precision of the small energy values used in the element classifications. revision: yes

  2. Referee: [GB models and site sampling] Results on GB models and site sampling (abstract and § on CSL boundaries): the ranking of cohesive effects is derived exclusively from six specific CSL boundaries with a finite set of sampled sites. No exhaustive enumeration, comparison against experimental segregation isotherms, or tests on additional (non-CSL) boundaries are presented, yet the abstract presents the ordering as generally indicative for ferritic steels. If lower-energy sites or other boundary types reverse the sign for any element, the reported classification would not generalize.

    Authors: We accept that the abstract should be qualified to avoid implying broader generality than the calculations support. We will revise the abstract to state that the reported ranking of cohesive effects applies to the six CSL grain boundaries studied. We will add a dedicated paragraph in the Discussion section that explicitly notes the limitations of the chosen CSL models and finite site sampling, references the computational impracticality of exhaustive enumeration, and discusses how other boundary types might alter trends. We will also incorporate qualitative comparisons to available experimental segregation data from the literature for the elements considered. These changes will clarify the scope without requiring new calculations. revision: partial

  3. Referee: [Results tables] Table of segregation energies and cohesion changes: no error bars or estimates of numerical uncertainty are attached to the reported values. Given that several elements are classified as “mildly” vs. “strongly” detrimental on the basis of differences of only a few tens of meV, the absence of uncertainty quantification weakens the quantitative ordering.

    Authors: We agree that uncertainty estimates are needed to support the distinctions drawn between mildly and strongly detrimental elements. We will perform additional convergence tests and include numerical uncertainty estimates (derived from variations with respect to cutoff and k-point density) in the revised tables and text. Error bars or ranges will be added to the segregation energy and cohesion change values, and the discussion of element classifications will be updated to reflect these uncertainties. This will strengthen the quantitative aspects of the results. revision: yes

Circularity Check

0 steps flagged

No circularity: direct DFT outputs with independent computational chain

full rationale

The paper's central results—segregation energies, site preferences, and cohesion changes for H/He/B/C/N/O/P/S—are obtained as direct numerical outputs from DFT structural relaxations performed on six fixed CSL GB supercells. No equations or procedures fit a parameter to a subset of the computed data and then rename that parameter as a 'prediction' of a related quantity within the same dataset. No self-citation supplies a uniqueness theorem, ansatz, or load-bearing premise that the present calculations rely upon; the Rice-Wang and bond-order metrics are standard external frameworks applied to the relaxed structures. The observation that nearest-neighbor distance correlates with the lower bound of segregation energies is an empirical post-processing finding, not a definitional reduction. The representativeness of the six CSL models for polycrystalline steels is an external-validity assumption, not a circularity internal to the derivation. The reported element ranking therefore follows from independent first-principles computations rather than from any self-referential construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard DFT approximations and the representativeness of the chosen CSL boundaries; no new entities are postulated and no free parameters are fitted to the target segregation results.

axioms (1)
  • domain assumption Density functional theory with typical exchange-correlation functionals yields reliable relative segregation energies and cohesive strength trends for light elements in iron.
    Invoked implicitly throughout the computational evaluation; standard in the field but known to have limitations for some magnetic and defect properties.

pith-pipeline@v0.9.0 · 5596 in / 1253 out tokens · 48939 ms · 2026-05-09T15:10:42.741290+00:00 · methodology

discussion (0)

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Reference graph

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