High-pressure isostructural transition in nitrogen. As shown in Fig. 1a, the main Bragg diffraction peaks of sample in the 10°-22° can be followed from 35.6 to 65.1 GPa, and all the peaks move towards a higher angle with the increasing pressure, indicating the decrease in lattice volume without significant structural phase transition. The diffraction peaks of gasket rhenium can be observed at higher pressures due to the shrinking of the sample cavity, and the intensity increase with the applied pressure. The pressure of the diffraction peaks calibrated by the gasket rhenium is close to the value measured with the high-frequency edge of the first-order Raman mode of the diamond. Because of the preferred orientation of the solid molecular phase under pressure, diffraction peak along the (h00) direction can not be clearly discerned. The HPLT phase λ-N2 was first discovered by Frost et al. [30], and a theoretical structure that previously predicted by Pickard and Needs [39] (space group P21/c; a= 2.922 Å, b= 2.891 Å, c= 5.588 Å and β = 132.54˚ for lattice parameters; x=0.5678, y=0.3764 and z=0.4534 for N atomic coordination at 40 GPa) was successfully used to fit the obtained experimental diffraction data. In this work, the structure given by Pickard and Needs [39] was also used for the initial model. Fig. 1b shows a excellent Rietveld refinement of data taken at 48.5 GPa (a= 2.908 Å, b= 2.869 Å, c= 5.367 Å and β = 131.87˚). However, our refinement results do exhibit abnormal discontinuous in the atomic volume (Fig. 2b) and β angle (Fig. 2c) at around 50 GPa, in conflict with our simulation parameter values with their structure which keeps decreasing in volume and increasing in β angle monotonically with the anisotropy increase under compression (Fig. 2a-c and Supplementary Fig. 1). We note that only 4 valid X-ray diffraction data, covering from 30 to 70 GPa, for λ-N2 were given in the literature [30]. The reason why the discovery of the abnormal discontinuous in the structural parameters for λ-N2 is more than 24 available diffraction data collected in the present work.
Thus, we reoptimized the crystal structure of λ-N2 using VASP software. The calculations suggested that the monoclinic structure (space group P21/c) with atomic coordination (4e, x=0.0711; y=0.3720; z=0.4526) has higher enthalpy with the crystal structure in Ref. [39] below 50 GPa. Once the simulated external pressure of λ-N2 exceeds 50 GPa (see Supplementary Fig. 5), both of the two structures have very similar enthalpy. The monoclinic structures with different coordination were plotted in Fig. 1c (Pickard et al.) and Fig. 1e (this work), respectively. Thus the obtained experimental XRD data are refined once again with the newly atomic positions calculated in this work and its reliability factor is better than the previous one. A representative Rietveld-refined diffraction picture at 55.4 GPa (a= 2.864 Å, b= 2.825 Å, c= 5.333 Å and β = 132.37˚) is displayed in Fig. 1d.
Figure 2b and Fig. 2c compared atomic volume and β angle of λ-N2 at various pressure experimentally and theoretically. The lattice parameter β angle is the degree between the (002) and (100) planes. Associated with the structural instability of molecular solid and orientation of the local molecular pairs, the β angle is a key parameter to evaluate the behavior of solid nitrogen at high pressure. Without any change in the symmetry, the β angle exhibits significantly discontinuous compressive behaviors both in the experiment and theoretical calculation with the new atom positions (x=0.0711; y=0.3720; z=0.4526), indicating the occurrence of a unique structural transition. On the other hand, the volume of each nitrogen atom in λ phase does not decrease smoothly with increasing pressure, and a kink can be clearly observed at around 50 GPa (Figure 2b). The slope change in the P-V curve also underlining a discontinuity transition (Figure 2b). However, no signal of the anomaly on the P-V or P-β curve is observed with the previous structure (Pickard et al.) in the calculation. Combined the careful structural refinements with theoretical calculations, we prefer to think that a monoclinic-to-monoclinic isostructural transition occurs in the solid nitrogen, and the previously reported λ-N2 should be indexed to as two different monoclinic structures, the low-pressure phase λ-N2 (the structure given by Pickard and Need [39]) and the high-pressure phase λ’-N2 (the structure presented in this work).
The P-V relation on major molecular nitrogen phases is drawn in Fig. 2a. Our experimental data on λ-N2, λ’-N2, δ-N2, δloc-N2 and ε-N2 are plotted and data from the literature (λ-N2[30, 31], δ-N2[23], δloc-N2[24], ε-N2[23, 26], ζ-N2[26], κ-N2[28]) are also shown for comparison. Further detailed work on δ-N2, δloc-N2 and ε-N2 could be seen in Supplementary materials Fig. 3 and Fig. 4.
In order to probe the influence of lattice dynamics in the HPIT, the phonon spectra and phonon density of states (PDOS) of λ’-N2 structure were calculated over the pressure range of 30 to70 GPa. As shown in Supplementary Fig. 6, the structure is dynamically stable up to 70 GPa, i.e. none of the phonon modes featured imaginary frequencies, the N≡N stretching modes were much higher in energy (from 2331 to 2497.5 cm−1). No obvious change in phonon spectra and PDOS is observed. We plotted the band gap of λ-N2 and λ’-N2 as a function of pressure [Supplementary Fig. 7]. The electronic structure calculation showed that these phases are insulators, the insulating state is the result of the complete localization of valence electrons. In contrast to the pressure-induced isostructural electronic transitions in Os, Ce and H2 et al., the HPIT in N2 seems to have nothing to do with the change of phonon dispersion and electronic state.
Actually, λ-N2 possesses the monoclinic structure and has a flexible β angle. And its space group, P21/c, is based on an fcc lattice, but with molecular displacements and a significant cell distortion. There are two diatomic polarized molecular pairs with different orientations in the unit cell. The blue molecular pairs in the edges of the unit cell are parallel to each other, whereas the red ones are in the center of the structure. It is to be expected that along the isotherm the orientation effect is weaker than the configuration effect at high densities. Hence, the unite cell parameters a, b and c are decreasing and the β angle is increasing under compression. However, the orientation stability of the polarized molecular pairs is prone to be distorted and the β angle is easier to be damaged at higher pressure (> 50 GPa). In addition, the vibration-rotation coupling (VRC) [40] also exists in solid nitrogen. Besides, medium pressure is a node of the van der Waals bond and the N≡N covalent bond in the nitrogen molecules. At low to moderate pressure (approximately 5 to 50 GPa), the electronic quadrupole-quadrupole interaction between nitrogen molecules increases sharply as intermolecular distances decrease under compressing. Whereas the electrons’ energy surpasses the electrostatic potential energy above 50 GPa, part of molecules’ triple bond electronic density is shifted to intermolecular regions, leading to the weakening of N≡N intramolecular triple bond [37]. In the case of the ordinary phase via regular room-temperature compression path, it is occurred that the structural phase transition from ε-N2 to ζ-N2 at about 56 GPa because of the change of interaction in nitrogen molecules [41]. Based on a combination of the above reasons, the nitrogen atoms rearrange and orientation change under extreme stain environment with the increasing anisotropy, indicating an isostructural phase transition from λ-N2 to λ’-N2, associating with the molecular-symmetry breaking.
The phase of λ’-N2 was originally observed on the basis of anomaly in Raman spectra. Fig. 3a displays the typical Raman spectra of λ-N2 (λ’-N2) at room temperature and the subtle variation of high-frequency Raman shift verse pressure is depicted in Fig. 3b. The complete Raman peaks of the λ-N2 (λ’-N2) at various pressure could be seen in supplementary materials Fig. 2. λ-N2 has seven Raman active optical modes. As shown in Fig. 3c, the low-frequency lattice phonon modes (Ag(1), Bg(1), Ag(2), Bg(2)) are related to the motion between nitrogen molecules (van der Waals force) and high-frequency vibron modes (Ag(3) and Bg(3)) are connected with the linear symmetrical tensile vibrations of atoms within a molecule (force of the covalent bond). The emergence of Ag’, a disorder-activated Raman mode, is due to the broken space translation symmetry by limited size, elemental doping, local strain and fluctuations induced by thermodynamic factors [32]. From our experiments, three high-frequency modes show discontinuous changes in adjacent pressures. Slight kinks are emerged in Ag(3) and Bg(3) around 49 GPa and 46 GPa, respectively. What is more, the strongest vibration mode, Ag(3), gets the maximum frequency (2393.5 cm−1) and then performs a sudden anomalous softening behavior at about 55 GPa. It is likely that different lattice vibration modes have distinct responses to the compression.
The phase stability and revisited diagram of λ-N2. In this work, we also probed the phase stability of λ-N2 (λ’-N2). The transformation and phase diagram of nitrogen is shown in Fig. 4, six independent P-T paths via compression at 77 K up to at least 35, 36, 55, 61, 115 and 117 GPa are exhibited, which further refined the thermodynamic region of λ-N2 and λ’-N2. The former P-T space of λ-N2 in Ref 32. should be divided into two parts, a lower-pressure region for the λ-N2 and a higher-pressure region for the λ’-N2. Contrasted with the previous work, our finding shows that the λ’-N2 can stabilize up to at least 176 GPa at room temperature accompanied with the broaden and weaken of Raman peaks (Fig. 5b). When external load exceeds 178 GPa, all Raman peaks of λ’-N2 disappeared and the sample was completely became opaque. It is also the highest pressure that molecular nitrogen phases could exist up to now. Once gained the target nitrogen phase, cooled it to 77 K and 64 GPa, we found out that λ’-N2 and ζ-N2 can coexist at the same P-T condition (seen in Fig. 5d). Therefore, the low-temperature (77 K) boundary between λ’-N2 and ζ-N2 should be down to 64 GPa, which is much lower than the previously reported 107 GPa in Ref.32. It is noteworthy that the coexistence phase (λ’-N2 and ζ-N2) was also observed in the 115 GPa and 300 K (Fig. 5f). Thus, it means that the sample goes into a metastable region above 64 GPa and could continually keep up to 115 GPa at low temperature. What is more, loading purity liquid nitrogen more than 117 GPa at 77 K and a new high-pressure nitrogen phase, referred to as η’-N2, with significant inactivation in Raman bands was formed (Fig. 5f). It has not been verified whether η’-N2 belongs to an amorphous phase like η-N2. The reported amorphous η-N2 can be obtained around 140 GPa at 300 K and has a large hysteresis, accompanied with the disappearance of the Raman signal and the emergence of a measurable resistance [27, 28]. And the transition condition from molecular to nonmolecular phase could shift to a higher pressure when decreasing temperature. Differ from the synthetic condition of the η-N2, the η’-N2 is easier to access at a lower pressure and room temperature via λ’-N2 transforming probably owing to minimizing the energetic barriers with the unique structure.
After the hydrogen and oxygen, the HPIT has also been observed in nitrogen, which allow us to think that the transition associated with molecular-symmetry breaking is a common phenomenon in diatomic molecules under high pressure, even difference in the transition mechanisms, it is an indispensable step toward the dissociation and metallization.