pith. sign in

arxiv: 2604.26560 · v1 · submitted 2026-04-29 · ❄️ cond-mat.mtrl-sci

Unraveling the symmetry of Al5C3N

Vitalii Shtender , Chin Shen Ong , Pedro Berastegui , Olivier Donzel-Gargand , Johan Cedervall , Charles Hervoches , Premek Beran , Olle Eriksson
show 1 more author
Ulf Jansson
This is my paper

Pith reviewed 2026-05-07 13:19 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords Al5C3Ncrystal structuredisordercentrosymmetricX-ray diffractionneutron diffractionDFT calculationsnanolaminate
0
0 comments X

The pith

Al5C3N adopts a disordered centrosymmetric structure in P63/mmc rather than the ordered non-centrosymmetric P63mc model previously assigned.

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

The paper re-examines the structure of the high-temperature ceramic Al5C3N, which had been described as an ordered nanolaminate with a specific stacking sequence in the non-centrosymmetric space group P63mc. Single-crystal X-ray diffraction data reject that model outright. Joint refinement of X-ray and neutron diffraction data supports a centrosymmetric space group with carbon and nitrogen disorder across two sites, producing the stacking sequence -Al2C-Al(C/N)-Al2(C/N)2-. Density functional theory calculations find this disordered centrosymmetric arrangement lower in energy by 0.2 eV per formula unit, and scanning transmission electron microscopy supplies direct structural confirmation.

Core claim

Our single-crystal X-ray diffraction analysis clearly indicates that the non-centrosymmetric space group P63mc must be rejected. From a joint refinement of single-crystal X-ray and powder neutron diffraction data, the occupancies of C and N were refined at two sites in P63/mmc resulting in the stacking sequence -Al2C-Al(C/N)-Al2(C/N)2-. Furthermore, DFT calculations show that a centrosymmetric disordered structure described in a supercell has the lowest energy, 0.2 eV per formula unit, relative to the previously reported P63mc structure. The calculated band structure shows both direct and indirect band gaps which lead to implications for the physical properties. Finally, STEM analysis gives,

What carries the argument

Combined single-crystal X-ray and powder neutron diffraction refinements that distinguish centrosymmetric from non-centrosymmetric models by refining carbon and nitrogen site occupancies, backed by supercell DFT energy comparisons.

If this is right

  • The material is predicted to possess both direct and indirect band gaps.
  • The disordered stacking alters the nanolaminate character that had been assumed for property predictions.
  • Physical properties such as thermal and electronic behavior must be re-evaluated for high-temperature ceramic applications.

Where Pith is reading between the lines

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

  • Disorder between carbon and nitrogen may occur in other members of the Al-C-N system or related layered ceramics.
  • The presence of both direct and indirect gaps suggests possible routes to tune optical response through controlled synthesis.
  • High-resolution local probes beyond average diffraction could map the actual spatial distribution of C and N atoms.

Load-bearing premise

The crystals and powders contain no significant defects, twinning, or secondary phases that could produce diffraction patterns mimicking or hiding the difference between ordered and disordered arrangements.

What would settle it

Diffraction data showing intensity statistics or systematic absences that fit only the non-centrosymmetric space group, or supercell DFT calculations placing the ordered P63mc structure below the disordered P63/mmc structure in energy.

read the original abstract

The high-temperature ceramic compound Al5C3N with promising application usage belongs to the scarcely studied Al-C-N system. It was originally reported as an ordered compound in the non-centrosymmetric space group P63mc and described as a nanolaminate with an -Al2C-AlN-Al2C2- stacking sequence. The recently reported structural disorder in the related compound Al4SiC4 led us to question this proposed structure for Al5C3N and investigate the possibility of a disordered structure in the centrosymmetric space group P63/mmc. In the present work, we employed different synthesis routes to maximize the yield and quality of the desired phase, and applied a variety of techniques to probe the Al5C3N crystal structure. Our single-crystal X-ray diffraction analysis clearly indicates that the non-centrosymmetric space group P63mc must be rejected. From a joint refinement of single-crystal X-ray and powder neutron diffraction data, the occupancies of C and N were refined at two sites in P63/mmc resulting in the stacking sequence -Al2C-Al(C/N)-Al2(C/N)2-. Furthermore, DFT calculations show that a centrosymmetric disordered structure described in a supercell has the lowest energy, 0.2 eV per formula unit, relative to the previously reported P63mc structure. The calculated band structure shows both direct and indirect band gaps which lead to implications for the physical properties. Finally, STEM analysis provides additional evidence that the crystal structure of Al5C3N is better described in the centrosymmetric space group P63/mmc.

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

0 major / 3 minor

Summary. The manuscript re-investigates the structure of the high-temperature ceramic Al5C3N, previously assigned to the ordered non-centrosymmetric space group P63mc with stacking -Al2C-AlN-Al2C2-. Single-crystal XRD intensity statistics and absences reject P63mc; a joint single-crystal XRD plus powder neutron refinement in P63/mmc converges on partial C/N occupancies at two sites yielding the disordered stacking sequence -Al2C-Al(C/N)-Al2(C/N)2-. DFT calculations on a supercell model of the disordered structure find it lower in energy by 0.2 eV per formula unit than the prior P63mc model, while STEM imaging supplies corroborating local-structure evidence. The calculated band structure exhibits both direct and indirect gaps.

Significance. If the revised structure holds, the work corrects the description of a scarcely studied member of the Al-C-N system and supplies a concrete energy difference plus band-gap predictions that can be tested experimentally. The central claim rests on the convergence of four independent techniques (single-crystal XRD, neutron diffraction, DFT, STEM) rather than any fitted parameter or self-referential construction, which is a methodological strength.

minor comments (3)
  1. The abstract states that occupancies were refined at two sites but does not quote the final values or their uncertainties; adding these numbers (or a table reference) would let readers immediately gauge the degree of disorder.
  2. The DFT section reports a 0.2 eV per formula unit difference but does not specify the supercell size or the explicit atomic configuration used to model the disorder; a brief description or supplementary CIF would improve reproducibility.
  3. The STEM images are cited as additional evidence; labeling the panels with the expected Al, C, and N column intensities for the disordered model would make the visual comparison more direct.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending acceptance. We appreciate the recognition that the central claim is supported by the convergence of four independent techniques rather than any single fitted parameter.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's claims rest on independent single-crystal XRD data rejecting P63mc via intensity statistics and absences, joint XRD+neutron refinement converging on partial C/N occupancies in P63/mmc, separate DFT supercell energy calculations (0.2 eV/f.u. lower for disordered model), and STEM corroboration. No self-definitional equations, no fitted parameters renamed as predictions, no load-bearing self-citations, and no ansatz or uniqueness imported from prior author work. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim depends on standard crystallographic refinement procedures and DFT relative-energy comparisons. No new free parameters are introduced beyond site occupancies refined from data, and no invented entities are postulated.

axioms (2)
  • standard math Standard assumptions of space-group symmetry and atomic site occupancy refinement in crystallography
    Invoked for joint XRD and neutron data analysis to distinguish P63mc from P63/mmc.
  • domain assumption DFT calculations provide reliable relative total energies between ordered and disordered structural models
    Used to establish the 0.2 eV/f.u. stability advantage of the supercell disordered structure.

pith-pipeline@v0.9.0 · 5626 in / 1480 out tokens · 62476 ms · 2026-05-07T13:19:33.668053+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    von Stackelberg, E

    M. von Stackelberg, E. Schnorrenberg, R. Paulus, et al., Z. Phys. Chem. A, 1935, 175, 127–139

    work page 1935

  2. [2]

    von Stackelberg and K

    M. von Stackelberg and K. F. Spiess, Z. Phys. Chem. Abt. A, Chem. Thermodyn. Kinetik, Elektrochemie, 1935, 175, 140–153

    work page 1935

  3. [3]

    G. A. Jeffrey and V. Y. Wu, Acta Cryst., 1963, 16, 559–566

    work page 1963

  4. [4]

    G. A. Jefrey and V. Y. Wu, Acta Cryst., 1966, 20, 538–547

    work page 1966

  5. [5]

    L. L. Oden and R. McCune, J. Am. Ceram. Soc., 1990, 73, 1529–1533

    work page 1990

  6. [6]

    Schneider, L

    G. Schneider, L. Gauckler, G. Petzow, et al., J. Am. Ceram. Soc., 1979, 62, 574–576

    work page 1979

  7. [7]

    M. A. Pietzka and J. C. Schuster, J. Am. Ceram. Soc., 1996, 79, 2321–2330

    work page 1996

  8. [8]

    C. A. Qiu and R. Metselaar, J. Am. Ceram. Soc., 1997, 80, 2013–2020

    work page 1997

  9. [9]

    Y. C. Mu, D. L. Yu and M. Z. Wang, Int. J. Refr. Met. & Hard Mat., 2011, 29, 639–640

    work page 2011

  10. [10]

    T. M. Gesing and W. Jeitschko, Z. Naturforsch. B, 1995, 50, 196–200

    work page 1995

  11. [11]

    V. J. Barczak, J. Am. Ceram. Soc., 1961, 44, 299–299

    work page 1961

  12. [12]

    C. S. Ong, O. Donzel-Gargand, P. Berastegui, et al., Inorg. Chem., 2024, 63, 10490–10499

    work page 2024

  13. [13]

    X. W. Xu, L. Hu, X. Yu, et al., Chinese Phys B, 2011, 20, 126201

    work page 2011

  14. [14]

    T. Liao, J. Y. Wang and Y. C. Zhou, Phys. Rev. B, 2006, 74, 174112

    work page 2006

  15. [15]

    APEX3 and SAINT

    M. APEX3 and SAINT. Bruker AXS Inc., Wisconsin, USA., 2015

    work page 2015

  16. [16]

    Petricek, L

    V. Petricek, L. Palatinus, J. Plasil, et al., Z. Krist-Cryst. Mater., 2023, 238, 271–282

    work page 2023

  17. [17]

    Rodriguez-Carvajal, IUCr News, 2001, 26, 12–19

    J. Rodriguez-Carvajal, IUCr News, 2001, 26, 12–19. 21

    work page 2001

  18. [18]

    C. R. Hubbard and R. L. Snyder, Powder Diffraction, 1988, 3, 74–77

    work page 1988

  19. [19]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, et al., J. Phys.-Condens. Mat., 2009, 21, 395502

    work page 2009

  20. [20]

    D. R. Hamann, Phys. Rev. B, 2013, 88, 085117

    work page 2013

  21. [21]

    M. J. Van Setten, M. Giantomassi, E. Bousquet, et al., Comp. Phys. Commun., 2018, 226, 39– 54

    work page 2018

  22. [22]

    Barthel, Ultramicroscopy, 2018, 193, 1–11

    J. Barthel, Ultramicroscopy, 2018, 193, 1–11

    work page 2018

  23. [23]

    Gauthier-Brunet, T

    V. Gauthier-Brunet, T. Cabioc'h, P. Chartier, et al., J. Europ. Ceram. Soc., 2009, 29, 187–194

    work page 2009

  24. [24]

    L. Tham, M. Gupta and L. Cheng, Acta Mater, 2001, 49, 3243–3253

    work page 2001

  25. [25]

    L. J. Ci, Z. Y. Ryu, N. Y. Jin-Phillipp, et al., Acta Mater, 2006, 54, 5367–5375

    work page 2006

  26. [26]

    Nýblová, P

    D. Nýblová, P. Billik, J. Noga, et al., Jom-Us, 2018, 70, 2378–2384

    work page 2018

  27. [27]

    Deffrennes, B

    G. Deffrennes, B. Gardiola, M. Allam, et al., Calphad, 2019, 66, 101648

    work page 2019

  28. [28]

    W. A. Chupka, J. Berkowitz, C. F. Giese, et al., J. Phys. Chem., 1958, 62, 611–614

    work page 1958

  29. [29]

    Plante and C

    E. Plante and C. Schreyer, J. Res. Natl. Bur. Stand., Sect. A: Phys. Chem., 1966, 70, 253

    work page 1966

  30. [30]

    J. Li, G. Zhang, D. Liu, et al., ISIJ international, 2011, 51, 870–877

    work page 2011

  31. [31]

    Inuzuka, M

    H. Inuzuka, M. Kaga, D. Urushihara, et al., J. Solid State Chem., 2010, 183, 2570–2575

    work page 2010

  32. [32]

    K. M. Ok, E. O. Chi and P. S. Halasyamani, Chemical Society Reviews, 2006, 35, 710–717

    work page 2006

  33. [33]

    S. B. Austerman and W. G. Gehman, Journal of Materials Science, 1966, 1, 249–260

    work page 1966

  34. [34]

    F. D. Meyer and H. Hillebrecht, J. Alloys Compd., 1997, 252, 98–102

    work page 1997

  35. [35]

    Huguenot, A

    A. Huguenot, A. Riot, B. Boucher, et al., Solid State Sci., 2020, 104, 106205

    work page 2020

  36. [36]

    C. Gai, J. Thyr, O. Donzel-Gargand, et al., J. Alloys Compd., 2025, 1042, 183971

    work page 2025

  37. [37]

    P. Lu, E. Romero, S. Lee, et al., Microsc Microanal, 2014, 20, 1782–1790. Supplementary information Figure SI1. SEM image of an Al5C3N crystal. Figure SI2. EDS analysis of an Al5C3N crystal. The measured oxygen content is very low and C impurities and an AlN flake are visible. Figure SI3. Bond distances in Å and tetrahedral angles calculated for the Al5C3...

    work page 2014