Transparent polycrystalline cubic silicon nitride

Glasses and single crystals have traditionally been used as optical windows. Recently, there has been a high demand for harder and tougher optical windows that are able to endure severe conditions. Transparent polycrystalline ceramics can fulfill this demand because of their superior mechanical properties. It is known that polycrystalline ceramics with a spinel structure in compositions of MgAl2O4 and aluminum oxynitride (γ-AlON) show high optical transparency. Here we report the synthesis of the hardest transparent spinel ceramic, i.e. polycrystalline cubic silicon nitride (c-Si3N4). This material shows an intrinsic optical transparency over a wide range of wavelengths below its band-gap energy (258 nm) and is categorized as one of the third hardest materials next to diamond and cubic boron nitride (cBN). Since the high temperature metastability of c-Si3N4 in air is superior to those of diamond and cBN, the transparent c-Si3N4 ceramic can potentially be used as a window under extremely severe conditions.

2 wt%. The phases present in the recovered samples were examined by X-ray diffraction (XRD) measurements. The sample synthesized at 1600 °C consists mainly of c-Si 3 N 4 but the XRD peaks of α -and β -Si 3 N 4 were also observed. The presence of the hexagonal phases may be explained by a kinetic hindrance of the transformation to c-Si 3 N 4 at relatively lower temperature. This recovered sample was loosely sintered. The samples synthesized at 1700 and 1800 °C consist of a single phase of c-Si 3 N 4 and they are well-sintered. These samples look translucent and transparent, respectively.
We determined a unit cell parameter of c-Si 3 N 4 using an XRD pattern of a sample synthesized at 1800 °C: a = 7.7373 ± 0.0006 Å, which is consistent with that determined in a previous study (a = 7.7381 ± 0.0002 Å) 3 . The bulk density of this polycrystalline sample was measured to be 4.07 ± 0.08 g/cm 3 , which is also consistent with a theoretical density 3 of 4.022 g/cm 3 . This result supports the fact that the sample consists of a single phase of c-S i3 N 4 and indicates that the porosity of this sintered sample is negligibly small. In addition, we measured the bulk chemical composition of this sample. The values we obtained are as follows: Si, 60.1 ± 0.3 wt%; N, 37.1 ± 0.4 wt%; O, 2.5 ± 0.2 wt%; Total, 99.7 ± 0.5 wt%. These values are very close to the calculated values for the stoichiometric Si 3 N 4 (Si, 60.06 wt%; N, 39.94 wt%) and an oxygen-bearing α -phase 6 , Si 11.5 N 15 O 0.5 (Si, 59.69 wt%; N, 38.83 wt%; O, 1.48 wt%). Figure 1a shows a photograph of a recovered sample synthesized at 1800 °C, and it is transparent pale gray. A letter on a ruler behind the sample is clearly seen. Real in-line transmission 7 (RIT) was measured as a function of wavelength (Fig. 1b). In these measurements, all light that is scattered at an angle > 0.3° is not detected. Therefore, the RIT is a good measure for the visual transparency 7 . The RIT of this sample is 18-38% for visible light (wavelength of 400-800 nm). We can see the presence of a weak and broad absorption at a wavelength of 500-700 nm, which may cause the pale grey color of this sample. The very low RIT values up to 300 nm can be related to the bandgap energy of 258 nm ( = 4.8 ± 0.2 eV) 8 .
We observed the microstructure of the transparent polycrystalline c-Si 3 N 4 . Figure 2a shows an example of the bright-field TEM images. The presence of equigranular texture was observed and the average grain size is 143 ± 59 (one standard deviation) nm. No residual pore and no triple pocket was observed at multi-grain junctions (Fig. 2b), which is consistent with the results of the density measurements. Most of the c-Si 3 N 4 grains have straight grain boundaries and they are almost dislocation-free, which is consistent with the presence of sharp peaks in the XRD patterns ( Supplementary Fig. S1). Atomic-resolution STEM observations at grain boundaries between two grains show the presence of disordered/amorphous intergranular films 9 (IGFs) with a thickness of less than 1 nm (Fig. 2c). The results of electron energy-loss spectroscopy (EELS) measurements at the IGFs and grain interiors show that oxygen atoms preferentially segregate to the IGFs (Fig. 2d).
Atomic resolution STEM observations were also performed at multi-grain junctions (Fig. 3a). We observed that the thickness of IGFs near the multi-grain junctions (~1 nm) is similar to that between two grains, which causes the absence of triple pockets. Elemental mappings of silicon, nitrogen, and oxygen (STEM-EDS, energy dispersive X-ray spectroscopy) confirmed that oxygen atoms segregate to the IGFs and revealed that the IGFs consist of silicon oxynitride (Fig. 3b-d).
The very thin IGFs and the absence of triple pockets could be the reasons for the optical transparency of the bulk polycrystalline c-Si 3 N 4 . Scattering of incident light is caused by the following factors 10 : (1) optically inhomogeneous materials with secondary phases that have different refractive indices; (2) not isotropic crystals by birefringence. The absence of triple pockets (no second phase) and the cubic spinel structure (MgAl 2 O 4 spinel 11 Although α -and β -Si 3 N 4 phases are intrinsically transparent because of the wide bandgaps 13 (single crystals of α -Si 3 N 4 were reported to be transparent) 14 , the Si 3 N 4 sintered compacts that consist of α -and β -phases look opaque 1 . In the case of the sintering at lower pressures (e.g. hot-pressing), sintering aids such as MgO, SiO 2 , and Al 2 O 3 are required to obtain the toughened and highly densified compacts 1 . For example, MgO reacts with silicon and oxygen in the system and the magnesium silicate is molten under high temperature; after cooling, it remains mainly in triple pockets as an amorphous phase 1 . Even in the case of sintered β -Si 3 N 4 ceramics without additives, the presence of amorphous triple pockets was observed 15 and their dimensions are several tens to several hundreds of nanometers 16 . The chemical composition of the β -Si 3 N 4 grains is nearly pure Si 3 N 4 and that of the amorphous triple pockets is SiO 2 with a small amount of nitrogen 16 . Since the β -Si 3 N 4 cannot incorporate the impurities into its structure, the formation of the triple pockets may be inevitable as reservoirs of additives and impurities in the sintered bodies. The refractive index of the amorphous phase in the triple pockets can be different from those of the crystalline phases (α -and β -phase with hexagonal symmetry), which causes scattering of the incident light resulting in opaque sintered bodies. On the other hand, it has been reported that some polycrystalline α -SiAlONs exhibit optical transparency 17 . These materials are isostructural with α -Si 3 N 4 , in which silicon and nitrogen are partially substituted by aluminum and oxygen (Si 3 N 4 -based solid solutions) 17 . The incorporation of the additives into the structure produces little or no triple pocket, which causes small scattering losses of light resulting in optical transparency. This mechanism may be applied to the case of the transparent c-Si 3 N 4 . The absence of triple pockets in this material (Fig. 3a) indicates that at least a part of the oxygen impurities is incorporated into the c-Si 3 N 4 structure.
The composition of the hypothetical oxygen-bearing c-Si 3 N 4 may be inferred by analogy from that of α -Si 3 N 4 . It was reported that α -Si 3 N 4 contains oxygen in its crystal structure, which could be explained by nitrogen vacancies with electrical neutrality being obtained by an appropriate number of silicon vacancies or Si 3+ species 1 (Fig. 2d). The silicon and nitrogen vacancies might cause the pale grey color of this transparent c-Si 3 N 4 (Fig. 1a). Further studies are required to elucidate the mechanism of oxygen incorporation into c-Si 3 N 4 and the resultant optical transparency.
In order to show a potential of the transparent c-Si 3 N 4 ceramic as a hard and tough window, the mechanical properties of this material were measured. Since it is optically transparent, Brillouin scattering was performed to measure longitudinal and transverse wave velocities (V P and V S , respectively). We obtained V P = 12.55 km/s and V S = 7.84 km/s with estimated errors of 0.5%. Then, we can calculate all the elastic moduli at ambient  Table 1.
Vickers indentation tests were carried out at indentation loads between 0.196 and 19.6 N to measure the Vickers hardness (H V ) and evaluate the fracture toughness (K Ic ). Fig. 4a shows the indentation load dependence of H V . The H V decreases with indentation load to an asymptotic value beyond 5 N. We employed H V = 34.9 ± 0.7 GPa at 9.8 N as a representative value of this material. The comparison with previous results 4,5 is also shown in this plot. Figure 4b shows an indentation load dependence of K Ic . The average of all the measured values is 3.5 ± 0.2 MPa·m 1/2 . The transparent c-Si 3 N 4 is tougher than transparent MgAl 2 O 4 spinel (K Ic~1 .7 MPa·m 1/2 ) 23 and γ -AlON (K Ic~2 .4 MPa·m 1/2 ) 23 , and is as tough as polycrystalline alumina, which is a popular structural ceramic in industry. The obtained mechanical properties and comparison with previous results 4,5,[20][21][22]24,25 are also shown in Table 1.
In order to compare the hardness of c-Si 3 N 4 with those of other materials, we have updated a plot proposed by Teter 26 , H V vs. G (Fig. 4c, the details are shown in supplementary information). c-Si 3 N 4 is as hard as and elastically stiffer than B 4 C and B 6 O. These three materials are in the group of the third hardest materials (not superhard materials) next to diamond and cBN.

Discussion
The polycrystalline c-Si 3 N 4 shows intrinsic transparency (Fig. 1b): no strong light absorption at wavelengths below its bandgap energy. Diamond is the hardest material and the synthesis of transparent nano-polycrystalline diamond (NPD) was reported 27 . NPD shows its characteristic brownish color, which is given by a continuous absorption at wavelengths between 500 and 700 nm. This absorption could be attributed to lattice defects induced by plastic deformation during the synthesis process 28 . This material also shows strong continuous absorption at wavelengths between 225 nm (band gap energy) and 450 nm, which is attributed to electron transitions from nitrogen (impurity) to the conduction band 28 . Thus, NPD is transparent, but does not show its intrinsic transparency. Polycrystalline cBN materials have been reported to be translucent 29 ; B 4 C and B 6 O materials are opaque. Thus, the polycrystalline c-Si 3 N 4 is nearly color-less and the second hardest ceramic window (Fig. 4c).
The transparent polycrystalline c-Si 3 N 4 can potentially be employed in industry to protect optical sensors and detectors under severe conditions. One of the advantages of this material is an excellent thermal metastability in air 24 , at least up to 1400 °C, which is superior to that of diamond, cBN, and other hard materials 30 . On the other hand, one of the limitations of this material for industrial applications is the small size of the bulk material because of synthesis under high pressure above 13 GPa (ref. 3). In this article, we reported the synthesis of the transparent disks with diameter of ~2 mm (Fig. 1a). If one of the world's largest high-pressure instruments is employed for the synthesis, transparent c-Si 3 N 4 disks with diameter larger than 10 mm can be synthesized 31 . The centimeter-sized transparent disks can be used in industry as windows for small devices.

Methods
Starting material and the container for synthesis under high pressure and temperature. The starting power was commercially available α -Si 3 N 4 powder (SN-E10, Ube Industries, Ltd., Ube, Japan). According to the product catalog, the proportion of the α -phase is > 95 wt%; the oxygen content is < 2 wt%.; the specific surface area is 9-13 m 2 /g. The as-received powder was dried in an oil-free vacuum oven (~8 hPa) at 200 °C for ~12 hours. The dried powder was enclosed in a sample capsule made of a platinum sleeve and disks, which were embedded into an outer MgO sleeve with MgO lids. Before loading the sample, the platinum and MgO parts were heated at 1000 °C for ~10 min. After loading the sample, the assembled sample container was dried again in the vacuum oven at 150 °C for more than 2 hours before the synthesis runs.  XRD measurements. XRD patterns of the recovered samples were obtained using an X-ray diffractometer with Cu-Kα radiation (MiniFlex-600; Rigaku, Japan). The measurements were also carried out at the P02.1 in PETRA III, Germany. X-rays monochromatized by a (111) diamond and a (111) silicon crystal in Laue geometry with an energy of ~60 keV were used. The incident beam-size was 300 × 300 μ m 2 . The transmission geometry and a two-dimensional detector (XRD 1621, PerkinElmer) were employed. The sample-to-detector distance (~900 mm) and the detector orthogonality were calibrated using the diffraction pattern for cerium dioxide powder.

Bulk density and chemical composition measurements. Density of a recovered sample was measured
with an AccuPyc II 1340 pycnometer, using He gas displacement and mass measurements. Chemical composition of the recovered sample was measured using a scanning electron microscope equipped with an energy-dispersive detector. The accelerating voltage, current, and working distance was 20 kV, 1 nA, and 10 mm, respectively. During the data collection, the electron beam was scanned over the surface of the sample in the area of ~1 μ m × ~1 μ m. . For atomic-resolution imaging and spectroscopy, we used an aberration-corrected STEM of ARM 300CF (JEOL Ltd.), installed at University of Tokyo, equipped with a JEOL ETA corrector, a cold field-emission gun, Gatan Quantum ER EELS spectrometer, and a JEOL silicon drift detector for EDX spectrometer. The used illumination semi-angle is 24 mrad and the ABF-and ADF-detector is spanning 12-24 and 80-200 mrad, respectively. We used dual-EELS mode to simultaneously acquire core-loss and zero-loss spectra (the energy dispersion is 0.25 eV per channel) and the energy drift was corrected via post processing. We operated the STEM at 300 kV with typically 20 pA beam current, where no significant beam damage was observed. The grain size of the sample was determined by direct measurement of 100 grains that appear black (satisfying the Bragg condition) in a conventional BF-TEM image 32 .
Brillouin scattering measurements. Elastic wave velocities were measured using the Brillouin system, installed at University of Bayreuth, employing 532 nm laser light, a multi-pass tandem Fabry-Perot interferometer and an avalanche photodiode for signal detection. Measurements were performed in symmetric forward scattering geometry using a scattering angle of 80°. Spectrum collection times were about 5 minutes at a laser power of 70 mW.