Synthesis and crystal structure of silicon pernitride SiN₂ at 140 GPa

SiN₂ was synthesized from the elements at 140 GPa in a laser-heated diamond anvil cell. Crystal-structure determination (single-crystal synchrotron X-ray data) revealed that the title compound crystallizes in the pyrite structure type (space group Pa ).

Abstract

Silicon pernitride, SiN₂, was synthesized from the elements at 140 GPa in a laser-heated diamond anvil cell. Its crystal structure was solved and refined by means of synchrotron-based single-crystal X-ray diffraction data. The title compound crystallizes in the pyrite structure type (space group Pa , No. 205). The Si atom occupies a site with multiplicity 4 (Wyckoff letter b, site symmetry . .), while the N atom is located on a site with multiplicity 8 (Wyckoff letter c, site symmetry .3.). The crystal structure of SiN₂ is comprised of slightly distorted [SiN₆] octa­hedra inter­connected with each other by sharing vertices. Crystal chemical analysis of bond lengths suggests that Si has a formal oxidation state of +IV, while nitro­gen forms pernitride anions (N—N)^4–.

1. Chemical context

Nitro­gen-rich materials have gained a lot of attention due to their diverse properties such as high hardness, incompressibility (Young et al., 2006 ▸; Bykov et al. 2019a ▸) and high energy density (Bykov et al., 2021 ▸; Wang et al., 2022 ▸). Among these, binary high-pressure nitrides of group 14 elements are of particular inter­est, as they exhibit remarkable elastic and electronic properties compared to their ambient-pressure counterparts. In particular, cubic silicon nitride γ-Si₃N₄, synthesized from the elements at about 15 GPa, is significantly more incompressible than the ambient-pressure α- and β-polymorphs (Zerr et al., 1999 ▸). Recently Niwa et al. (2017 ▸) have synthesized pernitrides of group 14 elements (SiN₂, SnN₂ and GeN₂) by using laser-heated diamond anvil cells at pressures above 60 GPa. The crystal structures of GeN₂ and SnN₂ were solved and refined against powder X-ray diffraction data. However, the weak X-ray powder pattern of SiN₂ only allowed the suggestion that SiN₂ crystallizes in the pyrite structure type, while no structure refinement was performed.

In this work, we synthesized SiN₂ from the elements at pressures of 140 GPa and examined it by means of synchrotron single-crystal X-ray diffraction in order to solve and refine its crystal structure.

2. Structural commentary

SiN₂ crystallizes in fact in the pyrite structure type in the space group Pa (No. 205). The asymmetric unit comprises two atoms, a silicon atom (multiplicity 4, Wyckoff letter b, site symmetry . .), and a nitro­gen atom (8 c, .3.). The nitro­gen atoms form N—N dimers, and consequently each of the N atoms is tetra­hedrally coordinated by three Si atoms and one N atom. The centers of the N—N dimers form an fcc sublattice, which together with the inter­penetrating fcc sublattice of Si atoms can be considered as a derivative of the rock salt structure type. Slightly distorted [SiN₆] octa­hedra [Si—N distance 6× 1.7517 (11) Å] inter­connect with each other by sharing common vertices (Fig. 1 ▸). There is a linear correlation between the nitro­gen–nitro­gen distance in dimers and the formal ionic charge and bond order of the (N₂) ^x− anion (Laniel et al., 2022 ▸). In the case of SiN₂, the refined nitro­gen–nitro­gen distance of 1.402 (8) Å indicates that the N—N bond has single-bond character. This distance is in a good agreement with N—N distances observed in other pernitrides that contain single-bonded (N—N)^4– units (Tasnádi et al., 2021 ▸). However, it is longer compared to N—N bonds in diazenides (Laniel et al., 2022 ▸; Bykov et al., 2020 ▸) and in dinitrides of trivalent metals (Niwa et al., 2014 ▸; Bykov et al., 2019b ▸). Based on the empirical formula suggested by Laniel et al. (2022 ▸) for dinitrides, FC = (BL − 1.104)/0.074, where FC is the absolute value of the formal charge on the di­nitro­gen unit and BL is the N—N bond length in Å, a clear assignment can be made. For SiN₂, the value of FC was calculated as 4.04, which is in excellent agreement with the most common oxidation state of +IV for silicon.

Figure 1.

Crystal structure of SiN₂ at 140 GPa in polyhedral representation with Si atoms in orange and N atoms in blue. Shown are [SiN₆] octa­hedra inter­connected by N atoms. Displacement ellipsoids are represented at the 75% probability level.

3. Synthesis and crystallization

A piece of silicon (10×10×5 µm³) was placed in the sample chamber of a BX90-type diamond anvil cell equipped with Boehler–Almax type diamonds using culets of 100 µm in diameter. The sample chamber was eventually created by laser-drilling a 50 µm hole in the Re gasket preindented to a thickness of 18 µm. Nitro­gen, loaded using the high-pressure gas-loading system of the Bavarian Geoinstitute (Kurnosov et al., 2008 ▸), served both as a pressure-transmitting medium and as a reagent. Pressure was determined by the shift of the diamond Raman band (Akahama & Kawamura, 2006 ▸). Upon compression to the target pressure of 140 GPa, the sample was heated using a focused Nd:YAG laser (λ = 1064 nm) to temperatures exceeding 2500 K. The heating duration was approximately 10 seconds. The reaction products consisted of multiple high-quality, single-crystalline domains.

4. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1 ▸. The sample was studied by means of synchrotron single-crystal X-ray diffraction (SCXD) at the beamline ID11 (ESRF, Grenoble, France) with the following beamline setup: λ = 0.28457 Å, beamsize ∼0.7×0.7 μm², Eiger CdTe 2M detector. For the SCXD measurements, samples were rotated around a vertical ω-axis in the range ±30°. The diffraction images were acquired at an angular step Δω = 0.5° and an exposure time of 5 s per frame. For analysis of the single-crystal diffraction data (indexing, data integration, frame scaling and absorption correction) we used the CrysAlis PRO software package (Rigaku OD, 2023 ▸). To calibrate an instrumental mode using CrysAlis PRO, i.e., the sample-to-detector distance, detector origin, offsets of goniometer angles, and rotation of both X-ray beam and the detector around the instrument axis, we used a single crystal of orthoenstatite [(Mg_1.93Fe_0.06)(Si_1.93,Al_0.06)O₆, space group Pbca, a = 8.8117 (2), b = 5.18320 (10), and c = 18.239 (13) Å].

Table 1. Experimental details.

Crystal data
Chemical formula	SiN2
M r	56.11
Crystal system, space group	Cubic, P a
Temperature (K)	293
a (Å)	4.1205 (5)
V (Å3)	69.96 (3)
Z	4
Radiation type	Synchrotron, λ = 0.28457 Å
μ (mm−1)	0.21
Crystal size (mm)	0.001 × 0.001 × 0.001
Data collection
Diffractometer	Customized ω-circle diffractometer
Absorption correction	Multi-scan (CrysAlis PRO; Rigaku OD, 2023 ▸)
T min, T max	0.750, 1.000
No. of measured, independent and observed [I > 2σ(I)] reflections	269, 101, 60
R int	0.049
(sin θ/λ)max (Å−1)	1.112
Refinement
R[F 2 > 2σ(F 2)], wR(F 2), S	0.071, 0.191, 1.07
No. of reflections	101
No. of parameters	6
Δρmax, Δρmin (e Å−3)	1.08, −1.15

Computer programs: CrysAlis PRO (Rigaku OD, 2023 ▸), SHELXT (Sheldrick, 2015a ▸), SHELXL (Sheldrick, 2015b ▸), VESTA (Momma & Izumi, 2011 ▸) and OLEX2 (Dolomanov et al., 2009 ▸).

Data analysis followed several steps:

1. After collecting SCXD data sets (series of ∼120 frames), a 3D peak search procedure was performed as implemented CrysAlis PRO. This search identified reflections from all crystalline phases present in the collection spot, including reaction products, initial reagents, pressure-transmitting medium, diamonds and gasket material.

2. The peak search table was processed by means of the DaFi program (Aslandukov et al., 2022 ▸), which sorts reflections into groups: if reflections fall into one group they origin­ate from one grain of the multigrain sample.

3. The reflection groups were assessed individually by indexing the reflections within the current group using built-in procedures in CrysAlis PRO. If indexing succeeded, the group was chosen for final data integration.

4. Datasets were integrated, and data was reduced following standard procedures, taking into account the shadowing of the diamond anvil cell.

Supplementary Material

CCDC reference: 2295150

Additional supporting information: crystallographic information; 3D view; checkCIF report

supplementary crystallographic information

Crystal data

SiN2	Synchrotron radiation, λ = 0.28457 Å
Mr = 56.11	Cell parameters from 79 reflections
Cubic, Pa3	θ = 3.4–16.4°
a = 4.1205 (5) Å	µ = 0.21 mm−1
V = 69.96 (3) Å3	T = 293 K
Z = 4	Irregular, colourless
F(000) = 112	0.001 × 0.001 × 0.001 mm
Dx = 5.327 Mg m−3

Data collection

Customized ω-circle diffractometer	101 independent reflections
Radiation source: synchrotron, ESRF, beamline ID11	60 reflections with I > 2σ(I)
Synchrotron monochromator	Rint = 0.049
Detector resolution: 5.0 pixels mm-1	θmax = 18.5°, θmin = 3.4°
ω scans	h = −4→4
Absorption correction: multi-scan (CrysAlisPro; Rigaku OD, 2023)	k = −7→8
Tmin = 0.750, Tmax = 1.000	l = −8→7
269 measured reflections

Refinement

Refinement on F2	0 restraints
Least-squares matrix: full	Primary atom site location: dual
R[F2 > 2σ(F2)] = 0.071	w = 1/[σ2(Fo2) + (0.109P)2] where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.191	(Δ/σ)max < 0.001
S = 1.07	Δρmax = 1.08 e Å−3
101 reflections	Δρmin = −1.15 e Å−3
6 parameters

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Si1	0.5000	0.5000	0.5000	0.0084 (5)
N1	0.5982 (5)	0.4018 (5)	0.9018 (5)	0.0076 (6)

Atomic displacement parameters (Ų)

	U11	U22	U33	U12	U13	U23
Si1	0.0084 (5)	0.0084 (5)	0.0084 (5)	−0.0005 (3)	−0.0005 (3)	−0.0005 (3)
N1	0.0076 (6)	0.0076 (6)	0.0076 (6)	0.0012 (8)	0.0012 (8)	−0.0012 (8)

Geometric parameters (Å, º)

Si1—N1	1.7517 (11)	Si1—N1v	1.7517 (11)
Si1—N1i	1.7517 (11)	N1—Si1vi	1.7517 (11)
Si1—N1ii	1.7517 (11)	N1—Si1vii	1.7517 (11)
Si1—N1iii	1.7517 (11)	N1—N1viii	1.402 (8)
Si1—N1iv	1.7517 (11)
N1—Si1—N1iii	86.94 (4)	N1iv—Si1—N1ii	86.94 (4)
N1iv—Si1—N1v	93.06 (4)	N1v—Si1—N1i	86.94 (4)
N1ii—Si1—N1i	93.06 (4)	N1—Si1—N1v	86.94 (4)
N1—Si1—N1iv	180.0	N1—Si1—N1i	93.06 (4)
N1iii—Si1—N1i	180.00 (14)	Si1—N1—Si1vi	112.54 (10)
N1iii—Si1—N1iv	93.06 (4)	Si1vii—N1—Si1vi	112.54 (10)
N1iii—Si1—N1v	93.06 (4)	Si1vii—N1—Si1	112.54 (10)
N1—Si1—N1ii	93.06 (4)	N1viii—N1—Si1vi	106.20 (12)
N1ii—Si1—N1v	180.0	N1viii—N1—Si1vii	106.20 (12)
N1iii—Si1—N1ii	86.94 (4)	N1viii—N1—Si1	106.20 (12)
N1iv—Si1—N1i	86.94 (4)
N1iii—Si1—N1—Si1vii	94.59 (6)	N1i—Si1—N1—Si1vii	−85.41 (6)
N1iii—Si1—N1—Si1vi	−33.8 (3)	N1ii—Si1—N1—Si1vii	7.82 (11)
N1v—Si1—N1—Si1vi	59.4 (2)	N1iii—Si1—N1—N1viii	−149.62 (10)
N1i—Si1—N1—Si1vi	146.2 (3)	N1v—Si1—N1—N1viii	−56.39 (6)
N1ii—Si1—N1—Si1vi	−120.6 (2)	N1i—Si1—N1—N1viii	30.38 (10)
N1v—Si1—N1—Si1vii	−172.18 (11)	N1ii—Si1—N1—N1viii	123.61 (6)

Symmetry codes: (i) −x+1, y+1/2, −z+3/2; (ii) −x+3/2, −y+1, z−1/2; (iii) x, −y+1/2, z−1/2; (iv) −x+1, −y+1, −z+1; (v) x−1/2, y, −z+3/2; (vi) −x+1, y−1/2, −z+3/2; (vii) −x+3/2, −y+1, z+1/2; (viii) −x+1, −y+1, −z+2.

Funding Statement

Funding for this research was provided by: Deutsche Forschungsgemeinschaft (grant No. BY112/2-1 to Maxim Bykov). A PhD scholarship for GK from the Friedrich Naumann Foundation for Freedom with funds from the Federal Ministry of Education and Research (BMBF) is gratefully acknowledged.