Ceramic silicon nitride (Si₃N₄) has a broad range of applications (cutting tools, antifriction bearings and etch masks in microelectronics) in various industries because of its superior properties such as excellent mechanical strength, high thermal stability and relatively low mass density.^[1–4] Studying the influence of pressure on the structural stability and possible phase transition of β-Si₃N₄ will provide us with insight into its potential applications under extreme conditions. The two known polymorphs of silicon nitride are α-Si₃N₄ and β-Si₃N₄. Both have a hexagonal lattice with different stacking sequences of the layered atoms perpendicular to the c-axis. A third cubic form (c-Si₃N₄) with a spinel structure has been found recently and studied at pressures above 15 GPa and temperatures over 2000 K.^[5–11] This phase, c-Si₃N₄, is expected to be a hard material. In 2016, Nishiyama et al. reported the synthesis of the hardest transparent spinel ceramic, i.e., polycrystalline cubic silicon nitride (c-Si₃N₄). It is believed to be the third-hardest material after diamond and cubic boron nitride (cBN).^[12–14] So it is of great importance to study the high-pressure behavior of silicon nitride.

In 2001, Zerr et al. found the fourth form of Si₃N₄ (labeled the δ phase) by energy dispersive x-ray diffraction (EDXD) measurements, which were derived from a pressure-induced phase transition of the β-Si₃N₄ at 42.6 GPa.^[15] However, the obtained data (only one pattern) was not enough to determine the structure of δ-Si₃N₄.^[15] After that, although some people predicted the structure of the δ-Si₃N₄ (Table 1),^[16,17] the structure of the δ-Si₃N₄ has not been determined yet. According to the crystallographic data predicted in some literatures, we also spent a lot of time refining the structure of δ-Si₃N₄. However, the identify the structure of δ-Si₃N₄ has not yet been identified. We believe that high-quality x-ray diffraction (XRD) patterns and more measurements are necessary to identify the structure of δ-Si₃N₄. In 2011, Xu et al. reported that the β-Si₃N₄ transforms to the δ-Si₃N₄ at about 34.0 GPa, while there was no visible δ-Si₃N₄ peaks at 34.0 GPa.^[16] In addition, many researchers have devoted their studies to the compressibility and bulk modulus of β-Si₃N₄ based on first-principles calculations. Xu et al. reported the bulk modulus of β-Si₃N₄, K₀ = 241 GPa.^[17] Kuwabara et al. obtained 252 GPa for the bulk modulus of β-Si₃N₄.^[18] Ogata acquired the average bulk modulus of β-Si₃N₄, which was 225 GPa, by using the generalized gradient approximation (GGA) and the local density approximation (LDA).^[19] Until now, few experiments have been conducted to obtain the compressibility and bulk modulus of β-Si₃N₄ by means of in situ angle dispersive x-ray diffraction (ADXRD) in a diamond anvil cell (DAC). Li et al. experimentally determined the bulk modulus of β-Si₃N₄, K₀ = 270(5) GPa with by using ADXRD techniques.^[20] However, the data were too limited to permit reliable analysis. In addition, Cartz et al. obtained the bulk modulus of β-Si₃N₄, 256 GPa, by neutron diffraction methods, as shown in Table 2.^[21]

Table 1.

Table 1.

Table 1. The predicted lattice parameters, Wyckoff positions, and space group of δ-Si3N4. . Space group P3 C2/m cmcm pnma Ref. N1 1b (1/3,2/3,0.300) 1c (1/3,2/3,0) 1c (2/3,1/3,0.333) 1f (2/3,1/3,1/2) N2 1c (2/3,1/3,0.333) 3j/(0.269,0.013,0) [15] 3d (0.625,0.021,0.795) 3k(0.630,0.994,1/2) Si 3d (0.136,0.733,0.293) 3j/(0.148,0.741,0) 3d(0.860,0.294,0.773) 3k (0.853,0.257,1/2) a/Å 9.85 2.66 8.70 b/Å 2.80 8.91 2.75 [32] c/Å 2.80 9.18 9.57

Table 1. The predicted lattice parameters, Wyckoff positions, and space group of δ-Si3N4. .

Table 2.

Table 2.

Table 2. Comparison of compressibility and phase transition pressure: bulk modulus K0, its pressure derivative and phase transition pressure P of β-Si3N4. . K0/GPa Techniques P/GPa Ref. 252 4.0 LDA [18] 237.2 GGA [35] 225 LDA [19] 270(5) 4(1.8) ADXRD [20] 256 neutron diffraction [21] 241 3.4 LDA [17] 273(2) 4(fixed) ADXRD this work 278(2) 5 ADXRD this work 42.6 [15] 34 [17] 41 this work

Table 2. Comparison of compressibility and phase transition pressure: bulk modulus K0, its pressure derivative and phase transition pressure P of β-Si3N4. .

In this work, we investigated the compression behavior of β-Si₃N₄ at room temperature using ADXRD measurement and determined the equation of state (EOS) of β-Si₃N₄ under high pressure of up to 37 GPa. The pressure-induced reversible phase transformation process from β-Si₃N₄ to δ-Si₃N₄ was observed at ambient temperature.

The initial silicon nitride (β-Si₃N₄) powder (99.9% purity, average particle size) was purchased commercially from Alfa Aesar. The sample was baked at 800 °C for 60 min to remove any possible hydroxide and moisture before loading into the DAC. Characterizations of the starting material were carried out by using both XRD and scanning electron microscopy (SEM) techniques. The XRD pattern (Fig. 1(a)) confirmed that the initial powder had a pure hexagonal structure (P63/m space group, Z = 2 formula units per unit cell). The average particle size of the sample was estimated to be about from the SEM micrograph (Fig. 1(b)).

Fig. 1.

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	Fig. 1. (color online) (a) The XRD pattern of the initial β-Si3N4 powder under normal pressure and room temperature. Black solid line: measured pattern, red short vertical lines: all possible Bragg positions. (b) The SEM image of the initial β-Si3N4 powder.

High pressure was generated using a symmetric-type DAC with the culet size of . The stainless steel (T301) gasket with an initial thickness of was pre-indented to about and a sample chamber with a diameter of about was drilled in the center. The initial powder (β-Si₃N₄) was pre-compressed to a thickness of less than with a pair of tungsten carbide (WC) cubes and loaded into the sample chamber.^[22] A tiny ruby sphere was placed near the sample in the chamber as the pressure standard,^[23] which can decrease the error of the measured pressure. The pressures were determined by the ruby fluorescence method.^[23] The methanol–ethanol (4:1) mixture was used as the pressure-transmitting medium for quasihydrostatic conditions.^[24]

In situ high pressure ADXRD experiments were performed at room temperature at the 4W2 beamline of the Beijing Synchrotron Radiation Facility (BSRF, China), Chinese Academy of Sciences. In all experiments, the synchrotron source with a wavelength of 0.6199 Å was tuned by a Si (111) monochromator. The incident x-ray beam was focused to approximately (vertical) (horizontal) full width at half-maximum (FWHM) by a pair of Kirkpatrick–Baez mirrors. The two-dimensional diffraction patterns at various pressures were collected using a Mar345 image plate detector. The collected two-dimensional diffraction patterns were integrated into one-dimensional diffraction profiles with the software FIT2D.^[25] High-purity CeO₂ powder was used to calibrate the distance and orientation of the detector.^[26] Rietveld analysis was performed using the general structure analysis system (GSAS) program as implemented in the EXPGUI package.^[27–29]

Figure 2 shows the XRD spectra of β-Si₃N₄ during compression and decompression to atmosphere. The hexagonal structure β-Si₃N₄ remains stable up to 37.0 GPa. New diffraction peaks marked with asterisks emerge at the pressure of 41.0 GPa, clearly indicating that the phase transition begins. The phase transition pressure (PTP) is in excellent agreement with that in the previous study.^[15] However, this PTP is about 7 GPa higher than that confirmed by Xu et al. and the phase transition confirmed by Xu et al. was not obvious.^[17] The deviation of the PTP could be ascribed to the different grain sizes or impurities of the starting sample being used, the different pressure calibration methods and different assemblies. In addition, the PTP is also influenced by the experimental conditions, such as non-hydrostaticity of pressure.^[16,30] Zerr and Xu et al. did not elaborate upon the grain size, purity of the initial powder and experimental assembly. Upon further compression, the (100), (200) and (101) planes in the initial β-Si₃N₄ phase disappear gradually with the rapidly enhancement of the three new diffraction peaks. Finally, three original peaks are replaced by three new diffraction peaks, suggesting the accomplishment of the phase transition at the pressure of 43.2 GPa. The phase transition can also be confirmed by the collected Debye rings from β-Si₃N₄ at pressures of 33.8 GPa (Fig. 3(a)), 37.0 GPa (Fig. 3(b)) and 41.0 GPa (Fig. 3(c)). At 41.0 GPa, the Debye ring changes obviously. In addition, the typical XRD pattern at 5.6 GPa by Rietveld refinements is presented in Fig. 4, which confirms that the crystal structure of β-Si₃N₄ is stable under high pressure up to 37.0 GPa. Upon releasing pressure to ambient pressure, all the diffraction peaks of β-Si₃N₄ are retained, suggesting that the pressure-induced phase transition is reversible.

Fig. 2.

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	Fig. 2. (color online) Representative high-pressure synchrotron radiation XRD patterns of β-Si3N4 at various pressures.

Fig. 3.

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	Fig. 3. Typical two-dimensional ADXRD patterns obtained from β-Si3N4 under different pressures: (a) P = 33.8 GPa, (b) P = 37.0 GPa, (c) P = 41.0 GPa.

Fig. 4.

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	Fig. 4. (color online) Powder XRD structure refinement pattern of β-Si3N4 at 5.6 GPa. Red dotted line: measured pattern, black solid line: calculated curve, green short vertical lines: all possible Bragg positions, bottom line: difference curve.

Figure 5 shows the pressure-dependent volume measurements. The third-order Birch–Murnaghan EOS is given as^[31,32] where V₀, K₀ and are the volume at zero pressure, the zero pressure bulk modulus and the bulk modulus pressure derivative, respectively. By the least-squares fit to our data obtained at BSRF using the Birch–Murnaghan EOS, we obtain bulk modulus K₀ = 273(2) GPa with its pressure derivative (fixed) and K₀ = 278(2) GPa with . Our results are well consistent with the experimental bulk modulus, K₀ = 270(5) GPa.^[20] Nevertheless, the bulk modulus of our experiment is much higher than the results of theoretical calculations, 225 GPa and 237.2 GPa (Table 2).^[19,35] This can be attributed to the larger non-hydrostatic compression caused by solidification of the pressure media methanol–ethanol (4:1) mixture.^[33] To better understand the compression behavior of the unit cell axes, we plot the pressure dependence of the normalized lattice parameters and (Fig. 6), where a₀ and c₀ are the equilibrium structural parameters under ambient conditions. Obviously, the compression behaviors of β-Si₃N₄ are anisotropic between the a-axis and c-axis under high pressure up to 37.0 GPa. The compression of the a-axis is more obvious than that of the c-axis. Among the elastic constants, C₁₁ and C₃₃ represent the incompressibility of the a and c directions, respectively. Previous studies reported the calculated elastic constants C_ij (GPa) of β-Si₃N₄ under pressures up to 35.0 GPa (Table 3).^[34] In our work, the anisotropic compressibility of the a-axis and c-axis is not obvious in the low pressure section. With increasing pressure, the anisotropic property of β-Si₃N₄ becomes more and more distinct (Fig. 6). Our experimental results are in agreement with the theoretical calculations (Table 3). In order to understand the anisotropic behavior, it is necessary to investigate the crystal structure of β-Si₃N₄. Figure 7 displays the crystal structure of hexagonal β-Si₃N₄, which consists of SiN₄ tetrahedrons connected by three coordinated N atoms within the plane. Six SiN₄ tetrahedrons round a ring stacking structure along the c-axis. However, the ring-type structure does not lie in the a–b plane, but has an angle relative to the a–b plane. Thus, the specially puckered ring structure layers and SiN4 tetrahedrons may enhance the incompressibility along the c-axis.

Fig. 5.

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	Fig. 5. (color online) Pressure dependence of the normalized unit-cell volumes in β-Si3N4 measured from 0 to 37.0 GPa at room temperature. The black solid squares represent the experimental data. The red solid and blue dashed lines correspond to the fitting results generated via second- and third-order Birch–Murnaghan EOSs, respectively.

Fig. 6.

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	Fig. 6. (color online) Compressibility of the normalized lattice parameters of β-Si3N4. As the pressure increases the anisotropy of β-Si3N4 becomes more and more distinct.

Fig. 7.

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	Fig. 7. (color online) Crystal structure of β-Si3N4. Large blue spheres represent Si atoms and small green spheres are N atoms.

Table 3.

Table 3.

Table 3. Calculated elastic constants Cij (GPa) of β-Si3N4 under pressures up to 35 GPa from Ref. [30]. . Pressure/GPa C11 C12 C13 C33 C44 0 444.96 186.35 119.65 583.27 109.84 5 459.77 204.83 135.70 606.49 108.18 10 473.88 227.17 151.49 628.41 102.84 15 490.82 246.87 168.50 651.76 100.10 20 508.44 264.53 182.49 680.26 96.67 25 517.41 283.41 198.90 704.70 92.17 30 537.12 292.64 216.10 724.21 93.95 35 541.81 318.40 232.16 743.49 85.25

Table 3. Calculated elastic constants Cij (GPa) of β-Si3N4 under pressures up to 35 GPa from Ref. [30]. .

In summary, the phase transition and compressibility of β-Si₃N₄ were investigated at pressure up to 45.6 GPa by synchrotron ADXRD at room temperature. A pressure-induced reversible phase transition was observed at 41 GPa. The compression curve of β-Si₃N₄ yielded a bulk modulus GPa with (fixed) and GPa with its pressure derivative . We also plotted the pressure dependence of the normalized lattice parameters and , indicating that the compression behavior of the a-axis and c-axis of β-Si₃N₄ under high pressure up to 37.0 GPa is anisotropic.