# High-Pressure Synthesis of oP28-C3 N4 Recoverable to Ambient Conditions

Dominique Laniel, Florian Trybel, Wenju Zhou, Andrey Aslandukov, James Spender, Ferenc Tasnádi, Timofey Fedotenko, Umbertoluca Ranieri, Akun Liang, Alena Aslandukova, et al.

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Dominique Laniel, Florian Trybel, Wenju Zhou, Andrey Aslandukov, James Spender, et al. High-Pressure Synthesis of oP28-C3 N4 Recoverable to Ambient Conditions. Advanced Functional Materials, 2025, 35 (11), pp.2416892. 10.1002/adfm.202416892. hal-05099699

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# High-Pressure Synthesis of oP28-C₃N₄ Recoverable to Ambient Conditions

Dominique Laniel,* Florian Trybel,* Wenju Zhou, Andrey Aslandukov, James Spender, Ferenc Tasnádi, Timofey Fedotenko, Umbertoluca Ranieri, Akun Liang, Alena Aslandukova, Fariia I. Akbar, Yuqing Yin, Stella Chariton, Anna Pakhomova, Gaston Garbarino, Mohamed Mezouar, Michael Hanfland, Vitali Prakapenka, Igor A. Abrikosov, Leonid Dubrovinsky, and Natalia Dubrovinskaia

The thermodynamic parameter pressure is ideal for producing novel
ultraincompressible and superhard materials as it promotes the formation of
polymeric frameworks and higher atomic coordination. In this regard, carbon
and nitrogen are particularly attractive elements as they can produce extended
arrangements of strong covalent bonds. In this study, a previously unobserved
C₃N₄ polymorph, denoted as oP28-C₃N₄ (Pnnm, #58), is synthesized at pres-
sures between 73 and 104 GPa in laser-heated diamond anvil cells and found
recoverable to ambient conditions and stable in air. The crystal structure of
oP28-C₃N₄, comprised of corner-sharing CN₄ tetrahedra, is solved and refined
using synchrotron single-crystal X-ray diffraction. With a bulk modulus of 334(3)
GPa deduced from experimental data, the compound is highly incompressible.
Based on macroscopic and microscopic calculations, its hardness may achieve
47.5 or 79.7 GPa, respectively, making it a superhard material. Incompressibil-
ity of CN₄ tetrahedra in all experimentally observed C₃N₄ polymorphs is found
to be greater than that of the CC₄ and BN₄ tetrahedra forming the structures
of diamond and cubic boron nitride. Density functional theory calculations
provide further insight into the electronic, vibrational, and mechanical
properties of oP28-C₃N₄, as well as their stability relative to other C-N phases.

## 1. Introduction

Carbon nitrides are a fascinating class of materials, known to feature unique and remarkable properties. These solids can be roughly divided into two categories: 2D and 3D compounds. The former, coined as graphitic C₃N₄ solids (g-C₃N₄), dates back to the early 19th century and are among the first artificial polymers found in scientific reports.[1] However, their meteoric surge in interest can be linked to the demonstration by Wang et al.,[2] in 2009, of their applicability as metal-free visible light-active semiconductor photocatalysts.[1,3] On the other hand, 3D polymeric carbon nitrides show promising mechanical properties. These take root in the short and stiff C-N single-bond and the possibility for carbon and nitrogen to be four- and three-fold coordinated, respectively, thus forming very robust CN₄ tetrahedra.[4] The synthesis of spinel-type

D. Laniel, J. Spender, U. Ranieri, A. Liang
Centre for Science at Extreme Conditions and School of Physics and Astronomy
University of Edinburgh
Edinburgh EH9 3FD, UK
E-mail: dominique.laniel@ed.ac.uk

F. Trybel, F. Tasnádi, Y. Yin, I. A. Abrikosov, N. Dubrovinskaia
Department of Physics
Chemistry and Biology (IFM)
Linköping University
Linköping SE-581 83, Sweden
E-mail: florian trybel@liu.se

<figure><img src="image_3.png" /></figure>

ID The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adfm.202416892
© 2024 The Author(s). Advanced Functional Materials published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/adfm.202416892

W. Zhou, A. Aslandukov, Y. Yin, N. Dubrovinskaia
Material Physics and Technology at Extreme Conditions
Laboratory of Crystallography
University of Bayreuth
95440 Bayreuth, Germany

A. Aslandukov, A. Aslandukova, F. I. Akbar, L. Dubrovinsky
Bayerisches Geoinstitut
University of Bayreuth
95440 Bayreuth, Germany

T. Fedotenko
Photon Science
Deutsches Elektronen-Synchrotron
Notkestrasse 85, 22607 Hamburg, Germany
S. Chariton, V. Prakapenka
Center for Advanced Radiation Sources
University of Chicago
Chicago, Illinois 60637, USA

A. Pakhomova, G. Garbarino, M. Mezouar, M. Hanfland
The European Synchrotron Radiation Facility
Grenoble Cedex 9 38043, France
Si₃N₄,[5] Ge₃N₄,[6] and Sn₃N₄[7] in 1999 contributed to the effer-
vescence of the search for 3D polymeric C₃N₄ solids. Early 2024,
three compounds featuring sp³-hybridized carbon with a 3D ex-
tended arrangement of corner-sharing CN₄ units (tI14-C₃N₄,
hP126-C₃N₄, and tI24-CN₂) were synthesized in laser-heated dia-
mond anvil cells at pressures beyond 70 GPa.[8] With bulk mod-
uli ranging from 383(9) to 419(8) GPa and a calculated hard-
ness between 80.4 and 86.8 GPa—based on a microscopic hard-
ness model[9]—these materials all classify as ultraincompressible
and superhard. Moreover, these three solids, along with oP8-CN,
which is comprised of CCN₃ units,[10] were found to be recov-
erable to ambient conditions and stable in air.[8] These materi-
als display a wide range of multi-functionality, namely photolu-
minescence, high energy density, piezoelectricity, and non-linear
optical properties.[8]

The significant interest and importance of the C–N system warrants further investigations. Indeed, many more superhard C₃N₄ polymorphs, as well as CN and CN₂ solids, are predicted to be stable by recent structure search calculations.[11–13] Some compounds are anticipated to form at relatively mild pressures, such as *hP28-C₃N₄* (P31c) at 9.1 GPa,[13] *tP8-CN* (*P₄₂/m*) at 14 GPa,[11] as well as *oP28-C₃N₄* (*Pnnm*) from 47 GPa.[12] It is worth noting that calculations accurately predicted three of the four previously discovered 3D polymeric carbon nitrides, namely *oP8-CN* (*Pnnm*), *tI24-CN₂* (*I-42d*), and *tI14-C₃N₄* (*I-42m*);[8,11,13,14] with *hP126-C₃N₄* (*P6₃/m*) being an exception due to its very large unit cell.

In this study, the C–N system was investigated at pressures
from 37 to 104 GPa in laser-heated diamond anvil cells. The
previously predicted C₃N₄ polymorph *oP28-C₃N₄* (*Pnnm*)—never
experimentally observed hitherto— was found at pressures just
above 70 GPa. This new phase was characterized by single-crystal
X-ray diffraction and its structure was solved and refined. It is
found to be ultraincompressible, superhard, recoverable to am-
bient conditions, and stable in the air. Remarkably, its constitut-
ing CN₄ tetrahedra are found to be less compressible than dia-
dmond's CC₄ and cubic boron nitride's BN₄ tetrahedra. Here per-
formed density functional theory (DFT) calculations give detailed
information on the mechanical, vibrational, and electronic prop-
erties of *oP28-C₃N₄*, and provide static enthalpy convex hulls of
the C–N binary system that include all thus far pressure-formed
solids as well as a plethora of predicted phases.

**2. Results and Discussion**

Eight BX90-type diamond anvil cells (DACs)[15] were prepared and equipped with 250 or 120 µm culet diamond anvils. Three were loaded with cyanuric triazide (CTA, C₃N₁₂), three with tetra-cyanoethylene (TCNE, C₆N₄), while the two others were loaded with boron-doped diamond and N₂, as well as boron-doped diamond and CTA (Table S1, Supporting Information). One of these DACs (sample #1) was initially compressed to a pressure of 37 GPa and laser-heated. Due to the sample producing an intense flash of light, temperatures could not be accurately measured but are estimated to be above 3000 K. The heated portion of the sample visually changed, becoming transparent (Figure S1, Supporting Information). An X-ray diffraction map revealed the decomposition of CTA into molecular nitrogen and diamond. The same reaction products were observed from all samples at pres-

sures below 70 GPa (i.e., 31, 40, 41, 50, and 63 GPa) after laser-
heating (Table S1, Supporting Information). Sample #1 was then
further compressed to 59 GPa and laser-heated again, with a max-
imum measured temperature of 2600(200) K. The heated areas
again became optically transparent (Figure S1, Supporting Infor-
mation), and the pressure increased to 73 GPa. Sample mapping
with X-ray diffraction unveiled the presence of known phases,
i.e., ζ-N₂,[¹⁶] oP8-CN,[⁸,¹⁷] and CTA,[¹⁸] along with sharp diffrac-
tion spots belonging to an unknown phase. The produced crys-
tallites were found to typically be about two microns in diame-
ter or less, with some producing high-quality sharp and intense
diffraction spots. The quality of the crystal selected for the struc-
ture solution can be judged from the reciprocal space reconstruc-
tion (see Figure S2, Supporting Information for the (-1kl) slice of
the reciprocal space of an oP28-C₃N₄ single crystal at 73 GPa).
The same unknown phase was observed in samples #2, #3, #4,
and #5 at pressures of 94, 104, 87, and 85 GPa, respectively, after
laser heating (Table S1, Supporting Information). To determine
the crystal structure of the new compound, single-crystal X-ray
diffraction (SCXRD) data were collected on the best sample posi-
tions.

The analysis of these SCXRD data enabled a structure so-
lution and refinement (Table S2, Supporting Information), re-
vealing the formation of a novel carbon nitride with a unique
crystal structure. At 73 GPa, the structure has an orthorhombic
unit cell (Pnnm space group, #58) with lattice parameters *a* =
8.644(4), *b* = 7.3913(8) and, *c* = 2.296(3) Å (*V* = 146.7(3) Å³).
This unit cell explains well the observed powder diffraction
lines, as shown in Figure S3 (Supporting Information). The
unit cell contains a total of 28 atoms, 12 carbon, and 16 nitro-
gen atoms, which are all on the 4g Wyckoff position, result-
ing in three and four crystallographically unique atoms of C
and N, respectively. Given the atomic ratio, this compound has
the C₃N₄ stoichiometry and matches the previously predicted
oP28-C₃N₄ solid.[12] Its structure (Figure 1a) features exclusively
heteroatomic C–N bonds. All carbon and nitrogen atoms are
four-fold and three-fold coordinated, respectively, forming a 3D
polymeric network of corner-sharing CN₄ tetrahedra arranged
in sets of rings (Figure 1b,c). Four three-member rings (dreier-
rings, following F. Liebau’s nomenclature[¹⁹]) are assembled in
six-member rings (sechser-rings). This pattern is well seen if the
structure is viewed along the *c*-axis (Figure 1b). The C–N bond
length ranges from 1.372(4) to 1.436(4) Å, with an average value
of 1.409(3) Å, which indicates a bond order of one.[8] This bond
length also matches values obtained from DFT calculations.[¹¹⁻¹³]
As expected, carbon atoms are all sp³-hybridized, with the average
N–C–N bond angle being 109.4(2)°. As for the nitrogen atoms,
it is interesting to see the N1 and N2 atoms forming perfectly flat
NC₃ units (Figure 1d,e) which have an average C–N–C bond an-
gle of 120.0(2)° while the N3 and N4 atoms have a corresponding
value of 108.9(2)° producing a pyramidal NC₃ unit (Figure 1f,g).
This suggests the N1 and N2 atoms are sp²-hybridized, while the
N3 and N4 are sp³-hybridized. The unexpected planar sp² geome-
try observed for the N1 and N2 atoms is likely due to steric factors
within the robust 3D polymeric network of corner-sharing CN₄
tetrahedra in oP28-C₃N₄. A similar flattening is also known in
sterically hindered amines.[20] The average C–N bond length for
sp³-hybridized N atoms is 1.423(3) Å (values between 1.413(2) and
1.436(4) Å), which is slightly longer than the average C–N bond
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Crystal structure of *oP28-C<sub>3</sub>N<sub>4</sub>* at 73 GPa, where the C and N atoms are represented by grey and blue spheres, respectively. a) Unit cell. b) 2 × 2 × 2 unit cells, with a *dreier-* and a *sechser-ring* drawn in red and green, respectively. c) A *CN*<sub>4</sub> tetrahedron. d) Top-down view of an *NC*<sub>3</sub> unit in which the N atom is either N1 or N2. e) Side-view of an *NC*<sub>3</sub> unit in which the N atom is either N1 or N2, seen to be perfectly flat. f) Top-down view of an *NC*<sub>3</sub> unit in which the N is either N3 or N4. g) Side-view of an *NC*<sub>3</sub> unit in which the N is either N3 or N4, seen to be bent. All shown distances, whether for bond length or bond angle, are the average values.</figcaption></figure>

length of 1.394(3) Å (values between 1.372(4) and 1.421(3) Å) for sp²-hybridized N atoms.

DFT calculations were performed on *oP28-C<sub>3</sub>N<sub>4</sub>*. The relaxed structure model is in excellent agreement with the experimental model at 73 GPa (Table S2, Supporting Information). Phonon band structures are found to feature no imaginary or soft modes at this pressure, indicative of the solids' dynamical stability (Figure S4, Supporting Information). It comes as a surprise that the *oP28-C<sub>3</sub>N<sub>4</sub>* compound, given its moderate number of atoms per unit cell and the large amount of theoretical work on this system,[11,12,21–23] had only been predicted by Pickard et al.[12] To shed light on this, its enthalpy was compared to that of the other synthesized as well as various predicted carbon nitrides at pressures between 0 and 150 GPa; c.f. **Figure 2** for the calculated pressure-composition diagram built up to 150 GPa from convex hulls.[24] Based on its calculated enthalpy, *oP28-C<sub>3</sub>N<sub>4</sub>* lies on the convex hull from ≈47 to 108 GPa, preceded by *hP28-C<sub>3</sub>N<sub>4</sub>* (*P31c*) from 21 GPa. Above 110 GPa, *oP28-C<sub>3</sub>N<sub>4</sub>-II* (*Pmc2*)[12] is instead found to be the most stable *C<sub>3</sub>N<sub>4</sub>* polymorph. The “II” index was added to distinguish *oP28-C<sub>3</sub>N<sub>4</sub>-II* from *oP28-C<sub>3</sub>N<sub>4</sub>* (*Pnnm*), according to the IUPAC convention. *oP28-C<sub>3</sub>N<sub>4</sub>-II* is supplanted by the experimentally synthesized *tI14-C<sub>3</sub>N<sub>4</sub>* solid at 120 GPa.

The other experimentally synthesized C₃N₄ compound, *hP126-C₃N₄*, is only ≤10 meV per atom above the hull between 50 and 130 GPa. The latter was previously found to be stabilized at high temperatures.[8] It is worth noting that the previously theoretically predicted spinel-type C₃N₄ compound[25] does not appear thermodynamically stable up to 150 GPa, a pressure at which it is 794 meV per atom above the convex hull. As for the CN and CN₂ compositions, the experimentally synthesized *oP8-CN* and *tI14-CN₂* were found stable from 18 and 53 GPa, respectively, and are the most stable forms up to the maximum calculated pressure of 150 GPa. The *tP8-CN* (*P4₂/m*) phase appears as the most stable from 14 to 18 GPa. These results are in fair agreement with previous calculations of Pickard et al.[12] for the C₃N₄ composition, and similar to those of Dong et al.[11] for the CN and the CN₂ stoichiometries.

As shown in Figure 2, all predicted phases above 55 GPa were experimentally observed, with the exception of the *oP28-C<sub>3</sub>N<sub>4</sub>-II*. However, this can potentially be explained given its very small pressure stability domain (i.e., 108 to 113 GPa) and the absence of temperature contributions in the DFT calculations. Indeed, temperature is hypothesized to play an important role in the stability range of each phase and is expected to be the main cause of

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Composition-pressure diagram for the binary C—N system. The data used to build the bars are from convex hulls obtained from DFT calculations performed at up to 150 GPa.[24] An uncertainty of ≈5 GPa is attributed to the convex hull calculations—and thereby the here-shown phase boundaries—due to the functional choice. Experimental synthesis data points are represented by colored circles and were obtained from the measurements presented here and in Laniel et al.[8] The experimental data points on *oP8-CN* below 70 GPa are from Stavrou et al.[10]</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Pressure dependence of the structural parameters of *oP28-C*₃*N*₄. a) Unit cell volume. b) Average volume of the *CN*₄ tetrahedra. c) Normalized tetrahedra volume for *oP28-C*₃*N*₄ *tI*14-*C*₃*N*₄, *hP*126-*C*₃*N*₄, *tI*24-*CN*₂ as well as diamond[28] and c-BN[29] with respect to pressure. In all graphs, a second-order Birch-Murnaghan equation of state was fit to the *oP28-C*₃*N*₄ experimental data while a third-order Birch-Murnaghan equation of state was employed to fit the DFT data. The full and empty symbols were obtained upon sample compression and decompression, respectively.</figcaption></figure>

the discrepancies between theory and experiments that are high-
lighted in Figure 2. This is exemplified by the case of *hP*126-*C*₃*N*₄,
which at no pressure is on the convex hull in with static enthalpy
calculations, but was previously shown to be favorable against
*tI*14-*C*₃*N*₄ at high temperature.[8]

The oP28-C3N4 solid was progressively decompressed, with additional single-crystal data collected at 62, 35, 17, 4 GPa, and ambient pressure (Tables S4–S8, Supporting Information). oP28-C3N4 was found recoverable to ambient conditions and stable in air over a prolonged period of time; demonstrated by the analysis of the single-crystal and powder data obtained after the DAC’s opening (Figures S5 and S6, Table S8, Supporting Information). An X-ray diffraction intensity map, shown in Figure S7 (Supporting Information), shows the small size of the recovered crystallites. At ambient conditions, the lattice parameters were found to be *a* = 9.1296(8), *b* = 7.851(4), and *c* = 2.400(3) Å (*V* = 172.0(2) Å³). While the overall structural arrangement of the CN₄ units constituting oP28-C₃N₄ remains the same, i.e., producing four *dreier*-rings assembled in *sechser*-rings, the interatomic distances increased compared to those at 73 GPa. Indeed, the average C–N single bond length is 1.468(6) Å at ambient pressure, compared to 1.409(3) Å at 73 GPa. Each atom’s hybridization was maintained at ambient pressure, i.e., the C, N3, and N4 atoms being sp³-hybridized (average N–C–N and C–N–C angles of 109.4(4)° and of 110.5(4)°, respectively) and the N1 and N2 atoms being sp²-hybridized (average C–N–C angle of 120.0(4)°). The variation of the different bond lengths and

bond angles with pressure is shown in Figure S8 (Supporting Information). The average C–N bond length decreasing by only ≈5% between ambient pressure and 104 GPa is a testament to the extreme incompressibility of this covalent single bond. Moreover, the distortion index, quadratic elongation, and bond angle variation of the CN₄ units—as defined and readily calculated in the VESTA software[26]— do not show any meaningful difference between ambient pressure and 73 GPa, demonstrating a lack of anisotropic deformation as a function of pressure.

From the pressure-volume data collected upon the decom-
pression of *oP28-C*₃*N*₄, its bulk modulus could be extracted us-
ing a second-order Birch-Murnaghan equation of state (BM2,
see **Figure 3**).[27] A value of *K*₀ = 334(3) GPa was obtained
for the bulk modulus, with the *V*₀ parameter set to the exper-
imentally measured value of 172.0 Å³. These values are quite
close to those obtained from DFT calculations, i.e., *V*₀ = 173.2
Å³, *K*₀ = 323 GPa, and *K*₀' = 3.8 from a third-order Birch-
Murnaghan equation of state fit (BM3), and *V*₀ = 173.4 Å³ and
*K*₀ = 315 GPa from a BM2 fit. As such, *oP28-C*₃*N*₄ has the lowest
incompressibility among the synthesized C₃N₄ polymorphs,[8]
and has a bulk modulus roughly 100 GPa lower than diamond’s
(446(1) GPa).[28]

The volume of the CN₄ tetrahedra in oP28-C₃N₄ as a func-
tion of pressure was extracted from both experimental as well
as DFT-relaxed structures, along with those in tI14-C₃N₄, hP126-
C₃N₄, and tI24-CN₂ (Figure 3) obtained from DFT calculations.
The procedure to do so is described in the Experimental section.
<table><caption>**Table 1.** Volume, bulk modulus, and pressure derivative of the bulk modulus for the CN₄, CC₄, and BN₄ tetrahedra in the three C₃N₄ polymorphs and *t*I24-CN₂, diamond, and c-BN, respectively. The values were obtained by fitting the pressure-volume data using either a second-order (*K*₀' fixed to 4) or a third-order (*K*₀' refined) Birch-Murnaghan equation of state. The experimental values for diamond[28] and c-BN[29] were obtained from the literature. As both diamond and c-BN solely have atoms on Wyckoff positions with fixed atomic coordinates, the bulk modulus (and its pressure derivative) of their constituting tetrahedra is the same as that of their bulk solid.</caption><thead><tr><th></th><th>V<sub>0</sub> [Å<sup>3</sup>]</th><th>K<sub>0</sub> [GPa]</th><th>K'<sub>0</sub></th></tr></thead><tbody><tr><td>oP28-C<sub>3</sub>N<sub>4</sub> (exp)</td><td>1.615(2)*</td><td>475(5)</td><td>4*</td></tr><tr><td>oP28-C<sub>3</sub>N<sub>4</sub> (calc)</td><td>1.61</td><td>480.3</td><td>4*</td></tr><tr><td>oP28-C<sub>3</sub>N<sub>4</sub> (calc)</td><td>1.62</td><td>446.8</td><td>4.6</td></tr><tr><td>t*I14-C<sub>3</sub>N<sub>4</sub> (calc)</td><td>1.65</td><td>442.2</td><td>4.5</td></tr><tr><td>hP126-C<sub>3</sub>N<sub>4</sub> (calc)</td><td>1.61</td><td>441.7</td><td>4.2</td></tr><tr><td>t*I24-CN<sub>2</sub> (calc)</td><td>1.65</td><td>401.6</td><td>4.0</td></tr><tr><td>Diamond (exp[28])</td><td>1.891*</td><td>446(1)</td><td>3.0(1)</td></tr><tr><td>Diamond (calc)</td><td>1.89</td><td>439.6</td><td>3.6</td></tr><tr><td>c-BN (exp[29])</td><td>1.969*</td><td>395(2)</td><td>3.62(5)</td></tr><tr><td>c-BN (calc)</td><td>1.98</td><td>377.6</td><td>3.61</td></tr></tbody></table>

A Birch-Murnaghan fit to the experimental data (BM2) and to the DFT-obtained data (BM3) was performed to determine their bulk modulus. The CN₄ tetrahedron's bulk modulus in *oP28-C₃N₄* was found to be 475(5) GPa based on the experimental data, closely matching the DFT value of 480.3 GPa obtained from the BM2 fit, and a value of 446.8 GPa (*K*₀' = 4.6) for the BM3 fit. As seen in **Table 1**, when comparing BM3 values calculated from the DFT data, very similar values are found for the *t*I14-C₃N₄ (*K*₀ = 442.2 GPa; *K*₀' = 4.5) and the *h*P126-C₃N₄ (*K*₀ = 441.7 GPa; *K*₀' = 4.2) polymorphs. The mild differences, particularly in *K*₀', underlie the role of the environment of each CN₄ unit, and therefore the electronic density distribution, which in turn influences the compounds' compression mechanisms. Strengthening this interpretation is that the obtained bulk modulus for the CN₄ tetrahedra in *t*I24-CN₂—in which each CN₄ tetrahedron is corner-sharing with three others, while the fourth corners are linked together through one N-N single-bonded dimer—has a significantly lower value of 401.6 GPa (*K*₀' = 4.0). Interestingly, a comparison with the analogously DFT calculated values for CC₄ and BN₄ tetrahedra constituting diamond and cubic boron nitride (c-BN) shows CN₄ units in all three C₃N₄ polymorphs to be less compressible (Table 1 and Figure 3).

The greater compressibility of the *oP28-C₃N₄* compound itself (*K*₀ = 334(3) GPa) compared to its constituting CN₄ tetrahedra (*K*₀ = 475(5) GPa) is interesting to note. While a complete analysis of the deformation mechanism of the *oP28-C₃N₄* solid is beyond the scope of this work, it is natural to expect that the larger void spaces in the structure, i.e., the *sechser*-rings, are shrinking in volume as a function of pressure at a rate greater than the network itself, likely through the tilting of the CN₄ units with respect to one another.

Further DFT calculations were performed on *oP28-C₃N₄* at 0 GPa. **Table 2** summarizes the calculated mechanical and optical properties, and compares them to those of other recently

synthesized and recovered carbon nitrides. As shown in Figure S4 (Supporting Information), the phonon density of states of *oP28-C₃N₄* does not feature any imaginary modes at 0 GPa. *oP28-C₃N₄* has a calculated hardness of 47.5 and 79.7 GPa, according to macroscopic[30] and microscopic[9] hardness models, respectively. While still qualifying as superhard, these values are lower than those of previously synthesized 3D polymeric C—N solids.[8] It has a fracture toughness of 5.2 MPa m¹/², on par with c-BN[31] and higher than that of *oP8-CN*, but lower than those of *t*I14-C₃N₄, *h*P126-C₃N₄ and *t*I24-CN₂. The calculated elastic constants of *oP28-C₃N₄* are shown in **Table S9** (Supporting Information). Its electronic density of states, computed using the Heyd-Scuseria-Ernzerhof hybrid functional (HSE), shows an indirect bandgap of 4.97 eV and a direct bandgap of 5.0 eV at the Γ point, as well as flat bands near the Fermi energy (Figure S9, Supporting Information, c.f. Experimental Section for calculation parameters), similarly to other synthesized C₃N₄ polymorphs.[8] As previously highlighted,[8] this suggests promising possibilities when coupled with chemical doping. Indeed, low hole doping could lead to a van Hove singularity in the density of states. In turn, this can result in charge density waves, itinerant magnetism, and even superconductivity,[32,33] as demonstrated for *t*I14-C₃N₄.[34] *oP28-C₃N₄* is also expected to have a high energy density of 4.86 kJ g⁻¹, very similar to that of other C₃N₄ polymorphs as well as above that of TNT (4.18 kJ g⁻¹) but below that of RDX (5.40 kJ g⁻¹).[35]

## 3. Conclusion

This high-pressure investigation of the C—N system using a variety of laser-heated carbon-nitrogen precursors characterized by synchrotron single-crystal X-ray diffraction, led to the synthesis of the previously unobserved carbon nitride, *oP28-C₃N₄*, in a pressure range of 73 to 104 GPa. It is a fifth 3D polymeric C—N compound and a third C₃N₄ polymorph. Below the threshold pressure of 73 GPa, despite many attempts, no C—N compounds were found to form. Including all relevant synthesized and predicted C—N solids, it was demonstrated that *oP28-C₃N₄* lies on the static enthalpy convex hull between ≈50 and 110 GPa. Remarkably, *oP28-C₃N₄* could be recovered down to ambient conditions and remains stable in air. It is an ultraincompressible solid with a bulk modulus of 334(3) GPa and a calculated hardness of 47.5 and 79.7 GPa, based on macroscopic and microscopic hardness models, respectively. In both cases, it qualifies as a superhard material. The pressure dependence of the volume of the C₃N₄ tetrahedra in *oP28-C₃N₄* provides evidence of their incompressibility, with an experimental bulk modulus of 475(5) GPa. This makes them less compressible than the tetrahedral building blocks of diamond and cubic boron nitride. The appeal of binary carbide nitride materials provides further impetus for the development of novel approaches to produce high-pressure stabilized materials at near ambient pressures through alternative methods that are compatible with industrial syntheses. At the other end of the pressure spectrum, investigating the C—N system at significantly higher pressures than currently done would be of interest for the potential synthesis of the sought-after spinel-type C₃N₄ compound featuring a six-fold coordinated carbon atom.[40]

<footnote>a) * represents a value that was fixed.</footnote>
<table><caption>**Table 2.** Experimental and calculated physical properties for *oP28-C3N4* and other carbon nitrides, c-BN, and diamond. Hardness was calculated using the model presented by Lyakhov and Oganov[9] (microscopic) and Chen et al.[30] (macroscopic). The band gaps were calculated with the HSE functional at ambient pressure conditions (HSE geometry for *oP28-C3N4* and values based on PBE-relaxed geometries from[8] for the other C-N compounds). Fracture toughness (*K*<sub>IC</sub>) was calculated from the elastic constants following the approach presented by Mazhnik et al.[36] References are provided for all values obtained from the literature. Parts of this table were reproduced from a previous study.[8] All experimental bulk modulus values for the carbon nitrides were obtained from a BM2 equation of state fit, while all other data is from a BM3 equation of state fit.</caption><thead><tr><th rowspan="2"></th><th colspan="2">K<sub>0</sub> [GPa]</th><th rowspan="2">Microscopic hardness [GPa]</th><th rowspan="2">Macroscopic hardness [GPa]</th><th rowspan="2">Bandgap [eV] d: direct, i: indirect</th><th rowspan="2">K<sub>IC</sub> [MPa m<sup>1/2</sup>]</th></tr><tr><th>Exp.</th><th>Calc.</th></tr></thead><tbody><tr><td>c-BN</td><td>395(2)<sup>[29]</sup></td><td>377.6</td><td>63.2<sup>[37]</sup></td><td>63.1-68.3<sup>[30]</sup></td><td>6.1 (i)<sup>[38]</sup></td><td>5.0<sup>[31]</sup></td></tr><tr><td>Diamond</td><td>446(1)<sup>[28]</sup></td><td>439.6</td><td>89.2<sup>[11]</sup></td><td>92.9<sup>[30]</sup></td><td>5.48 (j)<sup>[39]</sup></td><td>5.3-6.7<sup>[31]</sup></td></tr><tr><td>oP8-CN</td><td>365(9)</td><td>344.6</td><td>78.0</td><td>53.4</td><td>5.3 (i)</td><td>4.3</td></tr><tr><td>tI24-CN<sub>2</sub></td><td>419(8)</td><td>401.8</td><td>86.8</td><td>50.0</td><td>5.4 (i)</td><td>7.2</td></tr><tr><td>tI14-C<sub>3</sub>N<sub>4</sub></td><td>383(9)</td><td>377.2</td><td>80.4</td><td>52.9</td><td>4.3 (d)</td><td>6.1</td></tr><tr><td>hP126-C<sub>3</sub>N<sub>4</sub></td><td>417(6)</td><td>383.0</td><td>80.8</td><td>49.9</td><td>4.4 (d)</td><td>6.7</td></tr><tr><td>oP28-C<sub>3</sub>N<sub>4</sub></td><td>334(3)</td><td>323</td><td>79.7</td><td>47.5</td><td>4.97(i) (5.0 (d))</td><td>5.2</td></tr></tbody></table>

## 4. Experimental Section

**Sample Preparation:** Eight BX90-type diamond anvil cells (DACs)[15] were equipped with 250 or 120 µm diamond anvil culets. Three DACs were loaded solely with cyanuric triazide (CTA, C<sub>3</sub>N<sub>12</sub>). Another three contained tetracyanoethylene (TCNE, C<sub>6</sub>N<sub>4</sub>, 98% purity, purchased from Thermo Scientific Chemicals). The two other cells were loaded with boron-doped diamond (BDD) and N<sub>2</sub>, as well as BDD and CTA (Table S1, Supporting Information). CTA was prepared according to the literature procedure,[41] i.e., via metathesis by refluxing a 50 ml acetone solution of cyanuric chloride (C<sub>3</sub>Cl<sub>3</sub>N<sub>3</sub>, 0.5 mmol, 0.0915 g) and a suspension of sodium azide (NaN<sub>3</sub>, 1.5 mmol, 0.0975 g) for 48 h. After quickly cooling the mixture to ambient temperature, the solution was filtered to remove white solids which consisted of sodium chloride and a minimal amount of unreacted sodium azide. Crystallization was carried out by the slow evaporation of the mother liquor at room temperature over a period of 24 h, yielding transparent crystals of CTA. Chemical integrity and purity were verified using Raman spectroscopy. (Note: cyanuric triazide was an extremely shock-sensitive energetic material and, consequently, should be handled with extreme caution and with appropriate protection in small quantities only.)

The pressure inside of the sample chambers was measured using the first-order Raman mode of diamond[42] and verified using the calibrated diffraction lines of the rhenium gasket.[43] Laser heating was performed with double-sided Nd:YAG lasers (λ = 1064 nm) at the laboratory at the Bayerisches Geoinstitut (BGI),[44] at the P02.2 beamline of the Deutsches Elektronen-Synchrotron (DESY) as well as at the GSECARS beamline of the Advance Photon Source (APS) using CTA as the laser absorber, as previously done in the literature.[18] When measured, temperatures have an accuracy of ±200 K, determined using the thermoemission produced by the laser-heated samples.[44]

**Synchrotron Experiments:** The X-ray diffraction studies were done at the ID27 (λ = 0.3738 Å) and ID15b (λ = 0.4099 Å) beamlines of the Extreme Brilliant Source European Synchrotron Radiation Facility (EBS-ESRF), at the P02.2 beamline (λ = 0.2910 Å) of DESY as well as at the GSECARS beamline (λ = 0.2952 Å) of the APS. To determine the position of the polycrystalline samples on which the single-crystal X-ray diffraction (SCXRD) acquisition was obtained, a full X-ray diffraction mapping of the pressure chambers was achieved. The sample positions displaying the most and the strongest single-crystal reflections belonging to the phase of interest were chosen for the collection of single-crystal data, collected in step-scans of 0.5° from -38° to +38°. The CrysAlisPro software[45] was utilized for the single crystal data analysis. The analysis procedure includes the peak search, the removal of the diamond anvils' and other "parasitic" signal contributions, finding reflections belonging to a unique single crystal (achieved using DAFi[46]), the unit cell determination, and the data integration. The crystal structures were then solved and refined using the

OLEX2 and JANA2006 software.[47] OLEX2 was employed to obtain a preliminary structural model and JANA2006 to cull parasitic reflections (e.g., diamonds, other single-crystals) and obtain a final structural model. The SCXRD data acquisition and analysis procedure was previously developed and described in detail.[48] Recently, this method was also successfully employed by other independent research groups.[49–51] The powder X-ray diffraction data was analysed using Dioptas,[52] and Le Bail refinements performed with the FullProf software.[53]

**Computational Details:** Kohn-Sham density functional theory (DFT) based electronic structure calculations were performed with the QUANTUM ESPRESSO package[54–56] using the projector augmented wave method.[57] The generalized gradient approximation by Perdew—Burke–Ernzerhof (PBE) for exchange and correlation was employed[58] with the corresponding potential files: for C and N the 1s electrons were treated as scalar-relativistic core states. Van der Waals corrections following the approach by Grimme et al. were used as implemented in Quantum Espresso.[59] Convergence tests with a threshold of 1 meV per atom in energy, and 1 meV Å<sup>-1</sup> per atom for forces, led to an 8 × 8 × 24 Monkhorst-Pack[60] k-point grid with a cutoff for the wave-function expansion of 100 Ry for all phases.

Variable cell relaxations (lattice parameters and atomic positions) were performed on all experimental structures to optimize the atomic coordinates and the cell vectors until the total forces were smaller than 10<sup>-4</sup> eV Å<sup>-1</sup> per atom and the deviation from the experimental pressure was below 0.1 GPa. Equation of state (EOS) calculations were performed via variable-cell structural relaxations in 10 GPa steps up to 150 GPa. Phonon dispersion relations were calculated with Phonopy[61] in a 2 × 2 × 4 supercell with respectively adjusted k-points.

The energy released from the reaction C<sub>3</sub>N<sub>4</sub> → 3 C + 2 N<sub>2</sub> at 300 K and 0 GPa for *oP28-C3N4* was estimated from the calculated harmonic phonons. The enthalpy and entropy of N<sub>2</sub> were derived from thermochemical tables,[62] as suggested by Zhang et al.[63] Carbon was assumed in the graphite phase at ambient conditions.

Two phenomenological models were used to estimate the hardness of *oP28-C3N4*: a microscopic model developed by Lyakhov and Oganov et al.[9] and a so-called macroscopic model introduced by Chen et al.[30] For the microscopic model, the chemical valences of C and N atoms and the covalent radii values have been taken from those defined in the US-PEX code.[64] For the macroscopic model, the polycrystalline bulk (K) and shear (G) moduli were calculated. To obtain these, the anisotropic single-crystal elastic stiffness constants C<sub>ij</sub> (see Table S9, Supporting Information) were calculated at 0 GPa, and the Hill approximation was applied. The energy-strain relationship and a finite difference method with (±) 1% and (±) 2% strain was employed, where the total energies were calculated with Quantum Espresso with the numerical parameters given above.
Fracture toughness was estimated using the approach from Mazhnik et al. (2019).[36]

Static enthalpy convex hull calculations were performed employing variable cell relaxations for all structures between 0 and 150 GPa. Each relaxation was followed by self-consistent field (scf) calculations at the relaxed volumes in order to ensure sufficient convergence. Pressure convergence was additionally checked against the final scf calculations. In order to obtain comparable enthalpies, a cutoff of 100 Ry for the plane wave expansion as well as a k-point density 0.02*2π Å⁻¹ was used for all phases. D3 van der Waals (vdW) corrections were included for all calculations. The convex hulls were plotted using a modified version of the phase diagram implementation within the pymatgen (Python Materials Genomics) package,[65,66] which was adapted in order to plot several convex hulls at varying pressure and obtain combined labels for each composition. For the convex hulls, oP28-C₃N₄ was compared with a range of structures from Laniel et al.,[8] Pickard et al.,[12] Dong et al.,[11] Guo et al.[13] along with recalculated structures from the Materials Project database[67] and other references.[75] Phases were included in the convex hull calculation as long as they remained in their initial symmetry during relaxation. Table S10 (Supporting Information) contains the phases extracted from previous calculation papers as well as those from the Materials Project database, along with their names as they were reported there. The endpoints of the convex hull, namely graphite, diamond, c-N₂, z-N₂, and cg-N, were explicitly calculated with the same k-point density and energy cutoff as the C-N phases. Comparing the structures calculated in Pickard et al.[12] to those calculated here at 0 GPa and 100 GPa, a systematic shift of ≈4 to ≈10 GPa, respectively, was found, which can be attributed to the difference in the chosen potential and DFT parameters. Pickard et al.[12] used PBEsol while PBE+D3 vdW was used in this work. However, a particularly good agreement for PBE+D3 vdW was found for the full pressure range for all C-N phases, as discussed in the previous work.[8] Pickard et al.[12] used the phase transition of graphite to diamond as a benchmark, which was better described by PBEsol in their tests.

As the unit cell volume of the synthesized compounds could be refined very accurately from the single-crystal XRD data, agreement with the experimental data was considered as the most important benchmark to assess the validity of the calculations. The best match was obtained with PBE+D3 vdW, then used for all later calculations. Further analysis of the physical reason for this improved description through the inclusion of vdW corrections will be discussed elsewhere. Given the difference in the results obtained with the different functionals, it was estimated that the convex hull calculations have an uncertainty of ≈5 GPa. The uncertainty with respect to the experimental data from Laniel et al.[8] and for oP28-C₃N₄ (this work) was significantly smaller, c.f. Figure 2 in the main manuscript.

Convex hull plots for compositions CN, C₃N₄, and CN₂ between 0 and 150 GPa were uploaded to a web server which can be accessed through the information provided in reference.[24] For improved readability of these convex hulls, solely calculated phases within 300 meV per atom above the convex hull were shown.

Additional band structure and electronic density of state calculations were performed with the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional[69] using the FHI-aims code[70–75] due to the significantly more efficient implementation of hybrid functionals. HSE provides a higher accuracy for the calculated electronic bandgap given the known shortcomings of PBE. To ensure agreement between the two codes, an EOS calculation for oP28-C₃N₄ was performed with FHI-aims using PBE+D3 vdW and the same k-point settings as used in Quantum Espresso. An excellent agreement between both codes was found. In FHI-aims HSE calculations, the tight basis set for C and N, the standard HSE parameters, and 10 × 4 × 10 k-points (increased number along x-direction) were used in order to sufficiently resolve the band curvature along the Γ → X direction containing the indirect and direct bandgap. Structures were fully relaxed with the HSE functional with only minor changes compared to PBE+D3 vdW.

To analyze the compressibility of the CN₄ tetrahedron, the volumes of the tetrahedron in various compounds were obtained by first calculating the vectors from the unit cell's origin to each four sets of atoms forming the vertices of each given tetrahedron, yielding the vectors (Å, Ā, Ă, Ă, Ă). From

these, the vectors (ā = Ā − Ă, Ă = Ă − Ă, Ă = Ă − Ă, Ă = Ă − Ă) were constructed, which were used to calculate the tetrahedron's volume via:

$$V = \frac{1}{6} \left| \det \begin{pmatrix} a_x & a_y & a_z \\ b_x & b_y & b_z \\ c_x & c_y & c_z \end{pmatrix} \right| \quad (1)$$

The average tetrahedron volume was then calculated for each structure and a Birch-Murnaghan equation of state fitted to the volume-pressure data, as described in the main text. It was ensured that the volumes were correctly calculated by comparing them to the tetrahedra volume obtained from VESTA and by verifying that the same compressibility was obtained for bulk diamond and c-BN as for their constituting tetrahedra. Indeed, in diamond and c-BN, as all atoms occupy special crystallography positions with no degree of freedom, their tetrahedra must have the same compressibility as the bulk solids.

Further details of the crystal structure investigation(s) may be obtained from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen (Germany), quoting the depository number CSD-2383008 through CSD-2383013.

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

## Acknowledgements

The authors acknowledge the European Synchrotron Radiation Facility (ESRF), the Advanced Photon Source (APS), and the Deutsches Elektronen-Synchrotron (DESY) for the provision of beamtime at the ID27 and ID15b, GSECARS and P02.2 beamlines, respectively. D.L. and U.R. thank the UKRI Future Leaders Fellowship (MR/V025724/1) for financial support. N.D. and L.D. thank the Deutsche Forschungsgemeinschaft (DFG; projects LA 4916/1-1, DU 945–15/1, DU 393–9/2, and DU 393–13/1) for financial support. N.D., I.A.A., and Fl.T. acknowledge support from the Knut and Alice Wallenberg Foundation (Wallenberg Scholar grant no. KAW-2018.0194) and the Swedish government's Strategic Research Area in Materials Science on Functional Materials at Linköping University (faculty grant SFO-Mat-LiU 2009-00971). Fl.T. acknowledges furthermore support through ERC Grant (UNMASCCH-HP, 101117758). I.A.A. acknowledges support by the Swedish Research Council (VR) Grant No. 2023–05358. Computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS), partially funded by the Swedish Research Council through grant agreement no. 2022–06725. The authors further acknowledge NAISS for providing access to the LUMI supercomputer, owned by the EuroHPC Joint Undertaking and hosted by CSC (Finland) and the LUMI consortium. For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manuscript version arising from this submission.

## Conflict of Interest

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.

## Keywords

carbon nitrides, high-pressure high-temperature synthesis, laser-heated diamond anvil cells, single-crystal X-ray diffraction, superhardness, ultraincompressible
Received: September 10, 2024
Revised: November 29, 2024
Published online: December 13, 2024

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