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REVIEW 4 major objections 5 minor 26 references

New 3D and 2D Octacarbon C8 and isoelectronic B4N4 having peculiar mechanic and magnetic properties. First-principles identifications

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper proposes new carbon phases: a tetragonal 3D C8 nearly as incompressible as diamond, a B4N4 analog, and a 2D C8 calculated to be ferromagnetic.

desk verdict Plausible new C8/B4N4 structures with overclaimed stability and hardness; the hexagonal elastic constants are internally inconsistent and no phonon or formation-enthalpy check is provided. read the letter →

arxiv 1908.09265 v1 pith:QQSSMEAO submitted 2019-08-25 cond-mat.mtrl-sci

Samir F Matar This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords octacarboncarbonallotropeultra-hardmaterialboronnitridetwo-dimensionalferromagnetismdensityfunctionaltheorymagneto-volumeeffectspinchemistry
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes that carbon can take two new three-dimensional forms and one two-dimensional form with properties beyond those of known allotropes: a tetragonal C8 (space group P4/mmm) calculated to be cohesive and nearly as incompressible as diamond, a boron-nitride counterpart B4N4 with the same electron count, slightly lower stiffness, and a diamond-scale band gap, and a layered hexagonal C8 whose calculated ground state is ferromagnetic with a magnetization of 1.8 $\mu_\mathrm{B}$ per cell. A careful reader would care because the predictions place a carbon-only three-dimensional lattice near diamond's bulk modulus and suggest a carbon-based two-dimensional magnet that works without transition metals. The evidence comes from density functional total energies, energy-volume equations of state, elastic constants, electron-localization maps, and spin-polarized band structures; stability is asserted from positive elastic constants and favorable cohesive energies.

What carries the argument

The central machinery is plane-wave density functional theory in the generalized gradient approximation, used to relax each proposed structure, followed by three cross-checks. Birch–Murnaghan energy-volume equations of state (a standard fit used to extract elastic response) provide equilibrium volumes, bulk moduli, and the pressure derivative; finite-distortion elastic constants produce the full stiffness matrix, the Voigt bulk modulus, and the mechanical stability inequalities ($C_{11}>C_{12}$, $C_{11}C_{33}>C_{13}^2$, $(C_{11}+C_{12})C_{33}>2C_{13}^2$); and electron-localization maps visualize the covalent C–C versus ionocovalent B–N character. For 2D-C8 the decisive comparison is between non-spin-polarized and spin-polarized total energies, whose roughly 0.15 eV difference favors the ferromagnetic state; the critical pressure $P_\mathrm{C} = (B_0/B')[(V_0/V_1)^{B'}-1]$ converts the spin-polarized to non-spin-polarized volume difference into a magnetization-collapse pressure.

What would settle it

A phonon calculation of tetragonal C8 at its relaxed equilibrium volume would settle the structural claim: imaginary vibrational frequencies would show the phase is dynamically unstable, directly contradicting the stability conclusion.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that a body-centered tetragonal arrangement of eight carbon atoms—C8 in space group P4/mmm—is a cohesive, ultra-incompressible allotrope: its calculated bulk modulus is about 395 GPa, close to cubic Ia-3 C8 (413 GPa) and diamond (about 429 GPa), and its cohesive energy per atom sits between the two. Substituting boron and nitrogen pairwise for carbon gives a distorted tetragonal B4N4 with ionocovalent B–N bonding, a bulk modulus near 350 GPa, and a band gap of roughly the same magnitude as diamond's. In two dimensions, a P6/mmm C8 sheet built from two interpenetrating carbon substructures—magnetic C1 pairs and a semiconducting honeycomb C2 layer—is calculated to have a ferromagnetic ground state with 1.8 $\mu_\mathrm{B}$ per cell (0.9 $\mu_\mathrm{B}$ per C1 atom), a large volume increase upon magnetization, and a critical pressure of 12 GPa for the collapse of magnetization, behavior the paper classifies as soft ferromagnetic.

Load-bearing premise

The load-bearing premise is that the proposed structures are stable because their calculated elastic constants are positive and their cohesive energies are favorable; the paper does not compute a vibrational spectrum or a formation enthalpy relative to graphite and diamond, so a dynamically unstable or thermodynamically inaccessible phase would pass its checks.

Editorial extensions

If this is right

  • If tetragonal C8 is real and synthesizable, carbon gains a new three-dimensional allotrope with a bulk modulus near 395 GPa and a cohesive energy closer to diamond than that of cubic C8, making it a candidate hard material.
  • B4N4 would offer a wide-gap (about 5 eV), hard, ionocovalent counterpart to c-BN, potentially useful where diamond-like hardness and a large electronic gap are desired together.
  • 2D-C8 would be a carbon-only two-dimensional ferromagnet whose magnetization can be switched off by 12 GPa of pressure, a rare combination of magnetism and pressure sensitivity in a light-element layer.
  • The internal separation into a metallic magnetic C1 substructure and a semiconducting honeycomb C2 substructure implies the same monolayer could carry both magnetic and semiconducting functionality.
  • The agreement between equation-of-state and elastic-constant bulk moduli supports the reported mechanical trends for all three phases.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the small energy difference between the spin-polarized and non-spin-polarized states (about 0.15 eV per cell) suggests the ferromagnetic order of 2D-C8 may be tunable by strain, doping, or gating, not only by applied pressure.
  • The two-substructure motif—a magnetic metal threaded through a semiconducting honeycomb layer—could serve as a design template for carbon-based spintronic monolayers, though transport properties and exchange coupling are not computed here.
  • If the P4/mmm motif is stable for carbon, the same isoelectronic substitution logic used to construct B4N4 could be carried to other group-IV pairs, such as silicon and phosphorus analogues, widening the search for hard or magnetic low-dimensional allotropes.
  • Because the magnetic transition is tied to a large c/a change, growing 2D-C8 on a lattice-mismatched substrate might strain the layer enough to move the ferromagnetic-to-nonmagnetic transition to pressures far below 12 GPa.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper reports first-principles DFT (VASP/GGA-PAW) calculations for new octacarbon allotropes: a tetragonal P4/mmm 3D C8, an isoelectronic distorted tetragonal B4N4, and a hexagonal P6/mmm 2D C8. The authors claim that tetragonal C8 is cohesive and has incompressibility near diamond, that B4N4 is also ultra-hard and shows a band gap comparable to diamond, and that 2D-C8 has a ferromagnetic ground state with a magnetization-collapse pressure of 12 GPa, suggesting 'soft' ferromagnetic behavior. Stability is asserted from cohesive energies, Birch-Murnaghan EOS fits, and positive elastic constants satisfying mechanical inequalities. Electronic band structures and ELF maps are used to discuss bonding and spin polarization.

Significance. If the claims were fully substantiated, the paper would contribute new potential carbon allotropes with high incompressibility and a rare example of a 2D carbon ferromagnet, with possible relevance for spintronics and hard materials. The work uses standard DFT settings, and the EOS fits appear internally consistent; the cohesive-energy table provides a useful comparison among the phases. However, the current evidence for structural stability is incomplete, the 'hardness' language overstates what bulk-modulus data can support, and an internal inconsistency in the reported elastic constants of the hexagonal phase undermines the stability argument as presented. Because the headline claims depend on these points, the paper is not yet ready for publication.

major comments (4)
  1. [§3.5] For a hexagonal lattice in Voigt notation the elastic stiffness constants must satisfy C66 = (C11 - C12)/2. The reported 2D-C8 values (C11=477, C12=117, C66=13 GPa) violate this identity, since (477 - 117)/2 = 180 GPa, not 13 GPa. This inconsistency directly affects the section's conclusion that the positive elastic constants establish mechanical stability, and it must be corrected or explained.
  2. [§3.4 and Abstract] The paper repeatedly equates hardness with the bulk modulus B0 obtained from EOS fits. Hardness is a distinct mechanical property, typically correlated with shear modulus and plastic deformation resistance, not bulk modulus alone. No shear modulus, Vickers hardness, or other hardness indicator is computed, so the statement that tetragonal C8 has 'hardness close to diamond' is not supported by the presented data and should be rephrased in terms of incompressibility or supplemented with actual hardness estimates.
  3. [§3.2 and §3.5] Structural stability is inferred from cohesive energies and from positive elastic constants satisfying three inequalities. These conditions are necessary but not sufficient: a structure can pass them while still possessing imaginary phonon modes or being thermodynamically inaccessible. The manuscript presents no phonon dispersion calculation and no formation enthalpy relative to graphite or diamond. The cohesive energies in Table 2 are referenced to isolated atoms and do not establish relative phase stability. Without these checks, the proposed structures cannot be considered established local minima on the Born-Oppenheimer surface.
  4. [§3.1.2 and Fig. 4] The ferromagnetic ground state of 2D-C8 rests on a total-energy difference of about 0.15–0.2 eV per cell between spin-polarized and non-spin-polarized states. This energy difference is within the typical accuracy of GGA for magnetic ordering energies, so the identification is fragile without a more robust treatment (e.g., a Hubbard U, hybrid functional, or systematic antiferromagnetic ordering search). The AFM calculation, described only as assigning opposite spins to various atoms, is too briefly documented to serve as a decisive check.
minor comments (5)
  1. [Abstract and Table 1] The text calls cubic C8 (Ia-3) 'experimentally identified,' but reference [12] is a theoretical prediction; please correct the wording and the citation in Table 1, which currently points to reference [4].
  2. [§3.4] The critical-pressure formula is typeset incorrectly; it should read P_C = (B0/B')[(V0/V1)^B' - 1].
  3. [§3.4 and Fig. 3] The text cites B0=416 GPa for C8 Ia-3, but the EOS fit in Fig. 3 gives B0=413 GPa; please unify the values.
  4. [§2] The convergence criterion for forces is given as '0.02 eV/Å^3'; force convergence should be in units of eV/Å.
  5. [Fig. 4 caption] The caption is garbled ('...with a magnetization of 1.8states diamond...') and should be rewritten.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the computed properties are obtained from self-contained DFT calculations with external benchmarks, and the self-citations are contextual rather than load-bearing.

full rationale

The paper's central claims—tetragonal C8 and B4N4 as ultra-hard 3D phases, and 2D-C8 as a soft ferromagnet—are derived from first-principles DFT total energies, Birch equation-of-state fits, elastic constants from strain-stress relations, and electronic band structures. None of these outputs is used as an input to define the structures or to construct the properties. The bulk moduli are obtained independently from EOS fits and from Voigt averages of elastic constants, and the two routes are cross-checked against each other and against diamond and c-BN as external benchmarks; this is a validation, not a circular reduction. The critical pressure PC = 12 GPa for the 2D-C8 magnetization collapse is computed from the fitted Birch EOS parameters (B0, B′, V0, V1) using the quoted Birch relationship, so it is a derived consequence of the energy-volume calculations rather than a fitted target. The self-citations, e.g. refs. [21], [24], and [25], are used to justify methodological context, compare with prior computed values, or cite previously identified magnetic instabilities in related systems; they do not supply the load-bearing stability or property results, and no uniqueness theorem or prior result is invoked to force the present conclusions. The absence of phonon calculations and formation enthalpies is a completeness or correctness risk, not a circularity: the stability claim is weaker than asserted, but it is not true by construction. Therefore no circular step is exhibited, and the appropriate score is 0.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

All properties rest on DFT-GGA. The assumptions are the accuracy of GGA for carbon energetics and magnetism, the use of the Birch EOS to extrapolate bulk moduli, and the treatment of elastic stability as sufficient for structural stability. No new physical entities are introduced; the new structures are crystal lattices, not additional forces or particles.

free parameters (1)
  • Birch EOS fitted parameters (B0, B') = B0: 395 C8 P4/mmm, 350 B4N4, 140 SP 2D, 156 NSP 2D, 429 diamond, 413 Ia-3; B': 3.6 to 4.6
    These coefficients come from fitting the third-order Birch EOS to the DFT energy-volume curves and determine the reported hardness proxy (B0) and the critical pressure PC=12 GPa.
assumptions (4)
  • domain assumption GGA-DFT accurately describes total energies, elastic constants, and magnetic moments of carbon and BN phases.
    Invoked in Section 2; all quantitative claims use VASP PAW with GGA.
  • standard math Third-order Birch-Murnaghan EOS adequately represents the energy-volume data and yields reliable B0 and B'.
    Used in Section 3.4 to extract B0 and B', and to compute PC.
  • ad hoc to paper Positive elastic constants satisfying the stated inequalities establish structural stability.
    Section 3.5 uses only Cij and Voigt stability rules; no phonon or thermodynamic baseline is computed.
  • domain assumption Bulk modulus is a meaningful proxy for hardness.
    The abstract and Section 3.4 equate B0 with hardness, but hardness is a different property.

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Cite this review

Pith. "Pith review of New 3D and 2D Octacarbon C8 and isoelectronic B4N4 having peculiar mechanic and magnetic properties. First-principles identifications." pith.science (2026). https://pith.science/paper/QQSSMEAO

@misc{pith2026190809265,
  author       = {Pith},
  title        = {Pith review of: New 3D and 2D Octacarbon C8 and isoelectronic B4N4 having peculiar mechanic and magnetic properties. First-principles identifications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QQSSMEAO}},
  note         = {Machine review of arXiv:1908.09265}
}
read the original abstract

Cohesive energies, energy-volume equations of states EOS, electron localization ELF maps, elastic constants, and band structures are reported for original octacarbon C8 three dimensional 3D and two-dimensional 2D chemical systems based on density functional theory calculations. Specifically, tetragonal C8 is identified cohesive with hardness close to experimentally identified cubic Ia-3 C8; both exhibiting comparable hardness to diamond. Also, isoelectronic and isostructural B4N4 is calculated with a slightly lower hardness due to the ionocovalent B-N bonding and a bandgap with the same magnitude as Diamond. 2D-C8 on the other side is proposed with interpenetrating two carbon hexagonal substructures, identified from energy calculations as stable in a ferromagnetic ground state. Critical pressure for the collapse of magnetization PC=12 GPa let assign a soft ferromagnetic behavior alike Invar alloys. Electronic band structures analyses identify specific bands differentiating magnetic carbon substructure (C1) from nonmagnetic semi-conducting honeycomb-like C26 layers. These observations let propose spin chemistry perspectives once such multilayered carbon 2D compounds are grown as stand-alone or on selected substrates as thin or thick films

Figures

Figures reproduced from arXiv: 1908.09265 by the authors.

Figure 1
Figure 1. Crystal structures of the carbon systems (and BN) under consideration: a) Diamond; b) C8 I-a3 ; c) C8 P4/mmm ; d) B4N4 distorted P4/mmm; e) Magnetic 2D-C8 P6/mmm. Remarkable distances in Å are shown. N.B. Drawings were produced by VESTA ref. K. Momma and F. Izumi, "VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data," J. Appl. Crystallogr., 44, 1272-1276 (2011) [PITH_FULL_IMAGE:fi… view at source ↗
Figure 3
Figure 3. Electronic band structures of 3D title compounds [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Electronic band structures of 2D C8 (C12C26) in magnetic configuration, highlighting semi￾conducting behavior within C26 substructure and spin polarization within C12 bands with a magnetization of 1.8states diamond and the 3D octacarbon phases [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗

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