Evidence for a High-Pressure Isostructural Transition in Nitrogen

Chunmei Fan(范春梅)$^{1}$, Shan Liu(刘珊)$^{1}$, Jingyi Liu(刘静仪)$^{1}$, Binbin Wu(吴彬彬)$^{1}$, Qiqi Tang(唐琦琪)$^{1}$,\\ Yu Tao(陶雨)$^{1}$, Meifang Pu(蒲梅芳)$^{1}$, Feng Zhang(张峰)$^{1}$, Jianfu Li(李建福)$^{2}$, Xiaoli Wang(王晓丽)$^{2\hyperlink{s}{*}}$,\\ Duanwei He(贺端威)$^{1}$, Chunyin Zhou(周春银)$^{3}$, and Li Lei(雷力)$^{1\hyperlink{s}{*}}$

doi:10.1088/0256-307X/39/2/026401

⇦Chinese Physics Letters, 2022, Vol. 39, No. 2, Article code 026401Express Letter⇨ Evidence for a High-Pressure Isostructural Transition in Nitrogen Chunmei Fan (范春梅)1, Shan Liu (刘珊)1, Jingyi Liu (刘静仪)1, Binbin Wu (吴彬彬)1, Qiqi Tang (唐琦琪)1, Yu Tao (陶雨)1, Meifang Pu (蒲梅芳)1, Feng Zhang (张峰)1, Jianfu Li (李建福)2, Xiaoli Wang (王晓丽)2*, Duanwei He (贺端威)1, Chunyin Zhou (周春银)3, and Li Lei (雷力)1* Affiliations 1Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China 2School of Opto-Electronic Information Science and Technology, Yantai University, Yantai 264005, China 3Shanghai Synchrotron Radiation Facility, Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201204, China Received 5 January 2022; accepted 19 January 2022; published online 23 January 2022 ^*Corresponding author. Email: lei@scu.edu.cn; xlwang@ytu.edu.cn Citation Text: Fan C M, Liu S, Liu J Y et al. 2022 Chin. Phys. Lett. 39 026401 Abstract We observed an isostructural phase transition in the solid nitrogen $\lambda$-N$_{2}$ at approximately 50 GPa accompanied by anomalies in lattice parameters, atomic volume and Raman vibron modes. The anomalies are ascribed to a slight reorientation of the nitrogen molecules, which does not seem to affect the monoclinic symmetry (space group $P2_{1}/c$). Our ab initio calculations further confirm the phenomena, and suggest an optimized structure for the $\lambda$-N$_{2}$ phase. In addition, a new high-pressure amorphous phase of $\eta '$-N$_{2}$ was also discovered by a detailed investigation of the pressure-temperature phase diagram of nitrogen with the aim of probing the phase stability of $\lambda$-N$_{2}$. Our result may provide helpful information about the crystallographic nature of dissociation transitions in diatomic molecular crystals (H$_{2}$, O$_{2}$, N$_{2}$, etc).

DOI:10.1088/0256-307X/39/2/026401 © 2022 Chinese Physics Society Article Text High-pressure isostructural transitions (HPIT) are generally identified with symmetrical invariance in crystal structures, always signatured with the anomalies in cell volume, axial ratio and phonon behavior, possibly induced by the changes of the electronic states or by the slight displacements of atoms.[1–14] HPITs have been reported in metals such as Cd,[1] Zn[2,3] and Os,[4–6] metallic compounds like CaB$_{4}$[7] and MgB$_{2}$,[8] and molecular crystals such as H$_{2}$O,[9] NH$_{3}$,[10] ND$_{3}$,[11] H$_{2}$[12] and O$_{2}$.[13,14] As a simple type of homonuclear diatomic molecule, nitrogen exhibits similar high-pressure behavior with hydrogen and oxygen.[13–20] Owing to the strong N$\equiv$N covalent triple bonds, nitrogen becomes the most stable diatomic molecule and displays behavior of complex high-pressure phase transitions under high pressure.[21–42] Since the first report of nitrogen solids in the early last century, at least 20 solid nitrogen phases have been experimentally reported in a wide area of pressure-temperature ($P$–$T$) space.[22–38] Despite the important progress, additional work is needed to explain HPIT transitions. On the basis of previous works, the stability of lattice structure and electronic band dispersion components on compression are those key factors for occurrence of HPITs.[1–14] As a high-pressure and low-temperature phase, monoclinic $\lambda$-N$_{2}$ ($P2_{1}$/c) may be the most stable solid molecular nitrogen.[41–44] The $\lambda$-N$_{2}$ can be formed by cold compression from liquid phase, once synthesized, it can stabilize between 5 to 105 GPa at 77 K, and from 30 to 150 GPa at 300 K, covering nine other ordinary phases in $P$–$T$ space.[41–43] The formation of $\lambda$-N$_{2}$ was driven by a progressive reduction of the free rotation of the nitrogen molecules and therefore by the consequent lowering of the local symmetry. Low formation enthalpy and unique lattice structure make the distinct phase unique and very stable. However, the extraordinary phase stability of monoclinic $\lambda$-N$_{2}$ require an important attention and additional investigations are needed to study the structural arrangement of this phase. It is often controversial to identify newly discovered high-pressure isostructural transitions. In situ x-ray diffraction, high-pressure Raman scattering and ab initio calculations are the main three methods used to search for convincing evidence to support the HPIT theory. In this work, we investigate the phase stability of $\lambda$-N$_{2}$ and revisit the phase diagram of nitrogen along six independent $P$–$T$ experimental paths. The investigation of the structural vibrational information of solid nitrogen phases ($\lambda$-N$_{2}$, $\delta$-N$_{2}$, $\delta_{\rm loc}$-N$_{2}$ and $\varepsilon$-N$_{2}$) is carried out by employing high-pressure angle dispersive x-ray diffraction (ADXRD) (three runs) and high-pressure Raman scattering (ten runs). Ab initio calculations are performed to analyze the structural properties and transition mechanism. Frost et al.[41] first discovered the $\lambda$-N$_{2}$ using a theoretical structure predicted by Pickard and Needs[44] (space group $P2_{1}/c$; $a= 2.922$ Å, $b= 2.891$ Å, $c= 5.588$ Å and $\beta = 132.54^\circ\!$ for lattice parameters; $x=0.5678$, $y=0.3764$ and $z=0.4534$ for N fractional atomic coordinates at 40 GPa) for fitting the obtained experimental diffraction data. Nevertheless, we used the CALYPSO structure search algorithm and first principles calculations. Employing the software VASP, we demonstrated an optimized monoclinic structure ($\lambda$-N$_{2}$ with space group $P2_{1}/c$; $a= 2.9183$ Å, $b= 2.8934$ Å, $c= 5.5503$ Å and $\beta = 132.5177^\circ\!$ for lattice parameters; $x =0.0695$, $y =0.3751$ and $z =0.4540$ for N fractional atomic coordinates at 40 GPa) and structure is posted in Fig. 1(b). The complete methods in experiments and calculations are given in the Supplemental Material (SM). These two structures are very similar, the major difference seems to be the N fractional atomic coordinates. After the standardization of crystal data by using the Vesta software, the N fractional atomic coordinates are slightly different, and the major difference between these two structures is the $\beta$ angle (see Table S1 in the SM). Our calculations show that the pressure dependences of unit cell volume (Fig. 2), enthalpy, band gap and N$\equiv$N bonding length (Figs. S4–S6 in the SM) of the two structures follow different trends. They are not exactly the same structure. As shown in Fig. 2, while Pickard's crystal parameters are expected to exhibit very good linear relationship with pressure, our crystal data demonstrates the existence of an obvious discontinuity at around 50 GPa.

Fig. 1. X-ray diffraction data and structural information of $\lambda$-N$_{2}$. (a) X-ray diffraction patterns with the wavelength of 0.6199 Å on room-temperature compression. The arrows mark the diffraction peaks of gasket rhenium. (b) The re-optimized crystal structure of $\lambda$-N$_{2}$ with fractional atomic coordinates ($x=0.0695$, $y=0.3751$ and $z=0.4540$). (c) Representative Rietveld-refined diffraction patterns with the corresponding unintegrated patterns (inset) for the $\lambda$-N$_{2}$ at 48.5 GPa.

As shown in Fig. 1(a), the five main Bragg diffraction peaks of $\lambda$-N$_{2}$ in experimental range from 10$^{\circ}$ to 22$^{\circ}$ can be followed from 35 to 65 GPa. All the observed peaks are found to shift towards higher angles without exhibiting peak broadening, as the pressure increases. This observation appears to indicate the presence of a decrease in the lattice-volume parameter without significant structural phase transitions. The diffraction peaks of gasket rhenium can be observed at higher pressures and their intensities increase with the applied pressure due to the shrinking of the sample cavity on compression. Due to the preferred orientation of the solid molecular phase under pressure, the diffraction peak along the ($h$00) direction cannot be clearly discerned. We used both Pickard's crystal structure and our calculated structure for the $\lambda$-N$_{2}$ structural refinements.[44] High-quality refinements are shown in Fig. 1(c). Interestingly, the results display the presence of unusual features at approximately 50 GPa in the pressure dependence trend of atomic volume parameter. Noticeably, this effect is evident when considering the ratio of lattice parameters and the $\beta$ angle (Figs. 2 and 3). We note that our calculated structure is more consistent with our experiment data than the initial model given by Pickard and Needs,[44] it is a more optimized structure for the $\lambda$-N$_{2}$. The $P$–$V$ relation on major molecular nitrogen phases is presented in Fig. 3(a). Our experimental data on $\lambda$-N$_{2}$, $\delta$-N$_{2}$, $\delta_{\rm loc}$-N$_{2}$ and $\varepsilon$-N$_{2}$ are plotted together with data extracted from other literature reports ($\lambda$-N$_{2}$,[41,43] $\delta$-N$_{2}$,[26] $\delta_{\rm loc}$-N$_{2}$,[29] $\varepsilon$-N$_{2}$,[26,30] $\zeta$-N$_{2}$,[30] $\kappa$-N$_{2}$[32]) are also shown for comparison. Detailed analyses on $\delta$-N$_{2}$, $\delta_{\rm loc}$-N$_{2}$ and $\varepsilon$-N$_{2}$ can be found in Figs. S1 and S2 in the SM. Figure 3(c) shows the compared $\beta$ angle of $\lambda$-N$_{2}$ at various pressure as resulting from both experiment and theoretical calculations. The error bars of the experimental data are found to be smaller than the data points shown in the figures. The lattice parameter $\beta$ 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 $\beta$ angle is a key parameter to evaluate the behavior of solid nitrogen at high pressure. Noticeably, without any change in the symmetry, the $\beta$ angle does exhibit significantly discontinuous compressive behavior in both the experiment and theoretical calculation. The anomalies in the parameters of $\lambda$-N$_{2}$ seem to have no direct connection with the change of phonon dispersion and electronic states (Fig. S7). On the other hand, the volume of each nitrogen atom in $\lambda$-N$_{2}$ does not decrease smoothly with the increase of the pressure parameters. A kink can be clearly observed at around 50 GPa [Fig. 3(b)]. In the regular room-temperature compression path, the phase transition from $\varepsilon$-N$_{2}$ to $\zeta$-N$_{2}$ is expected to occur at about 56 GPa.[40] The slope change in the $P$–$V$ curve at around 50 GPa underlines a discontinuity transition, possibly indicative of a transition in the $\lambda$-N$_{2}$. We note that only four valid XRD diffraction data for $\lambda$-N$_{2}$ were reported from 30 to 70 GPa in the literature.[41] The the discovery of the abnormal discontinuous trend evidenced by the structural parameters for $\lambda$-N$_{2}$ presented in this work is revealed in a large dataset, consisting into more than twenty-four available sets of acquired diffraction signals.

Fig. 2. The pressure dependence of $a/a_{0}$, $b/b_{0}$ and $c/c_{0}$ for the $\lambda$-N$_{2}$. The red circle represents the experimental data. The green and black circles represent calculation data with Pickar's and our structure, respectively. Solid and dashed lines are the guides for the eyes.

Fig. 3. Structural parameters of solid nitrogen under high pressure. (a) The $P$–$V$ compression curves for the major molecular nitrogen phases. Solid shapes represent the present experimental data for $\lambda$-N$_{2}$, $\delta$-N$_{2}$, $\delta_{\rm loc}$-N$_{2}$ and $\varepsilon$-N$_{2}$, respectively. The black dashed lines represent our calculation data for $\lambda$-N$_{2}$. Data from the literature are also shown for comparison, $\lambda$-N$_{2}$,[41,43] $\delta$-N$_{2}$,[26] $\delta_{\rm loc}$-N$_{2}$,[29] $\varepsilon$-N$_{2}$,[26,30] $\zeta$-N$_{2}$,[30] $\kappa$-N$_{2}$.[32] (b) The detailed area of the red frame is in Fig. 2(a). (c) The pressure dependence of $\beta$ angle for the $\lambda$-N$_{2}$. The white and light red sections correspond to the change of anomalies region of $\lambda$-N$_{2}$. The data error bars are smaller than the data points shown in the figures.

Fig. 4. (a) Representative Raman spectra of $\lambda$-N$_{2}$ on room-temperature compression. (b) High-frequency Raman peaks of the $\lambda$-N$_{2}$ as a function of the pressure at ambient temperature in experiments. The red circles are the present work. The hollow squares and vertical crosses represent previously reported experimental data.[41,42] (c) The atomic displacement diagram of $\lambda$-N$_{2}$ includes the A$_{\rm g}^{(1)}$, A$_{\rm g}^{(2)}$, B$_{\rm g}^{(1)}$, B$_{\rm g}^{(2)}$, B$_{\rm g}^{(3)}$ and B$_{\rm g}^{(3)}$ modes.

Fig. 5. Transformation and phase diagram of nitrogen. The deep orange section and lighter section are the forming region of $\lambda$-N$_{2}$. The red section is the region of $\eta '$-N$_{2}$. The six colorful lines represent different $P$–$T$ paths to explore $\lambda$-N$_{2}$ formation and transition. The red dashed lines represent the revised transition boundaries of $\lambda$-N$_{2}$. The black dashed lines show the boundaries of $\lambda$-N$_{2}$ in Refs. [41,42]. The gray lines show the phase boundaries of nitrogen previously reported under compression at room temperature.

There are two types of diatomic molecular pairs with different orientations in the unit cell of $\lambda$-N$_{2}$ [Fig. 1(b)]. 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. The orientation stability of the polarized molecular pairs is prone to be distorted and the $\beta$ angle is easier to be damaged at higher pressure ($> 30$ GPa). The lattice modes do not exhibit such a strong broadening, this observation seems to imply that the reported phenomenon is related to the distortion of the molecule and not to nonhydrostatic conditions. By combining the careful structural refinements with our theoretical calculations, we propose that a monoclinic-to-monoclinic isostructural transition occurs in the $\lambda$-N$_{2}$. There are some potential structures for the $\lambda$-N$_{2}$,[43,44] and their enthalpies are quite close. It is possible that the abnormality of $\lambda$-N$_{2}$ at 50 GPa is due to the structural phase transition from Pickard's structure to the present structure. Considering our structure agrees better with the experimental results throughout the entire pressure region (Figs. 2 and 3), it is reasonable to conclude that our solution is the optimized structure for the $\lambda$-N$_{2}$. The HPIT of $\lambda$-N$_{2}$ was also observed in high-pressure Raman scattering, and the subtle variation of high-frequency Raman shift with pressure is depicted in Fig. 4 (also see Fig. S3). As shown in Fig. 4(c), the low-frequency lattice phonon modes A$_{\rm g}^{(1)}$, B$_{\rm g}^{(1)}$, A$_{\rm g}^{(2)}$ and B$_{\rm g}^{(2)}$ are associated with the relative movement of nitrogen molecular pairs, and high-frequency vibron modes A$_{\rm g}^{(3)}$ and B$_{\rm g}^{(3)}$ are connected with the N$\equiv$N stretching vibrations for different nitrogen molecules, and the A$_{\rm g}'$ is a disorder-activated Raman mode.[42] The three high-frequency vibrons show discontinuous changes in the vicinity of 50 GPa, but the kinks are found to emerge at different pressures, due to different vibration modes having distinct responses to the applied pressure.

Fig. 6. (a) The Raman spectra correspond to the $P$–$T$ points (A, B, C and D) in the $P$–$T$ phase diagram. The selected Raman spectra along the path 3 (b), path 1 (c), path 2 (d), path 4 (e), paths 5 (upper) and 6 (lower) (f).

The transformation and phase diagram of nitrogen is shown in Fig. 6, six independent $P$–$T$ paths via compression at 77 K up to at least 35, 36, 55, 61, 115 and 117 GPa are presented, which further refine the thermodynamic region of $\lambda$-N$_{2}$. The former $P$–$T$ space of $\lambda$-N$_{2}$ in Refs. [41,42]. should be divided into two parts, a lower-pressure region for $\lambda$-N$_{2}$, a higher-pressure region for $\lambda$-N$_{2}$. In contrast with the previous work, our finding shows that $\lambda$-N$_{2}$ can be stabilized up to at least 176 GPa at room temperature, with a broadening and weakening Raman peaks [Fig. 6(b)]. When the external load pressure exceeds 178 GPa, all Raman peaks of $\lambda$-N$_{2}$ disappear and the sample becomes opaque. Once gained upon cooling to 77 K and at the pressure of 64 GPa, $\lambda$-N$_{2}$ and $\zeta$-N$_{2}$ are found to coexist under the same $P$–$T$ condition [see Fig. 6(d)]. Therefore, the low-temperature (77 K) boundary between $\lambda$-N$_{2}$ and $\zeta$-N$_{2}$ should be down to 64 GPa, which is much lower than the previously reported pressure of 107 GPa in Ref. [42]. Noticeably, the $\lambda$-N$_{2}$ and $\zeta$-N$_{2}$ were also found to coexist at pressure of 115 GPa and at $T \sim 300$ K [Fig. 6(f)]. This observation implies that the sample goes into a metastable region above 64 GPa and could continually keep up to 115 GPa at low temperature (77 K). Together with the phase-transformations discussed above, it is also important to highlight presence of an extra component at 117 GPa and for $T \sim 77$ K. This new high-pressure nitrogen phase, referred to as $\eta '$-N$_{2}$, is found with significant inactivation in Raman bands [Fig. 6(f)]. It has not been verified whether $\eta '$-N$_{2}$ belongs to an amorphous phase like $\eta$-N$_{2}$. The reported amorphous $\eta$-N$_{2}$ 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.[31,32] Interestingly, the $\eta '$-N$_{2}$ is easier to access at a lower pressure and room temperature through transformation of $\lambda$-N$_{2}$ probably owing to a minimization of the energetic barriers, with its unique structure. In summary, the phase stability and structural information of the $\lambda$-N$_{2}$ have been investigated by high-pressure Raman scattering synchrotron x-ray diffraction, and ab initio calculations. A high-pressure monoclinic-to-monoclinic isostructural transition in the $\lambda$-N$_{2}$ has been observed at $\sim $50 GPa supported by the discontinuous changes in lattice parameters and Raman vibrons, which is of the utmost importance for our physical understanding of such “simple” molecular systems and for benchmarking theoretical calculations. Acknowledgments. We thank Professor Filippo Boi for helpful discussion. This work was supported by the Sichuan University Innovation Research Program of China (Grant No. 2020SCUNL107), the National Natural Science Foundation of China (Grant No. U2030107, 11774247, and 11974154), Chinese Academy of Sciences (Grant Nos. 2019-BEPC-PT-003237 and 2020-SSRF-PT-012109), and the Natural Science Foundation of Shandong Province (Grant Nos. 2019GGX103023 and Z2018S008). References Anomalies in the structure of solid Cd under pressure: an x-ray diffraction studyPhonon Anomaly in High-Pressure ZnElectronic topological transitions in Zn under compressionExperimental Evidence for a High-Pressure Isostructural Phase Transition in OsmiumElectronic and crystal structures of osmium under high pressureThe most incompressible metal osmium at static pressures above 750 gigapascalsPressure-induced isostructural phase transition in CaB ₄Isostructural Transition of MgB ₂ Under High PressureMelting Curve and Isostructural Solid Transition in Superionic IceSolid ammonia at high pressure: A single-crystal x-ray diffraction study to

123 GPa

Hydrogen bonding in

{ND}_{3}

probed by neutron diffraction to 24 GPaUltrahigh-pressure isostructural electronic transitions in hydrogenNew High-Pressure Structural Transition of Oxygen at 96 GPa Associated with Metallization in a Molecular SolidSolid oxygen revisitedMetallization and molecular dissociation of dense fluid nitrogenSynchrotron infrared spectroscopic evidence of the probable transition to metal hydrogenRoute to high-energy density polymeric nitrogen t-N via He−N compoundsPressure-Stabilized New Phase of CaN ₄Pressure-induced disordering of site occupation in iron–nickel nitridesNew Members of High-Energy-Density Compounds: YN ₅ and YN ₈Cagelike Diamondoid Nitrogen at High PressuresCrystal Structures of the Three Modifications of Nitrogen 14 and Nitrogen 15 at High PressureSingle‐Crystal X‐Ray Diffraction Study of β NitrogenRaman spectroscopy and melting of nitrogen between 290 and 900 K and 2.3 and 18 GPaCrystal Structure of Gamma NitrogenHigh pressure x‐ray diffraction studies on solid N ₂ up to 43.9 GPaAnomalous behavior of the vibrational spectrum of the high-pressure δ phase of nitrogen: A second-order transitionStructures of Molecular Nitrogen at High Pressures.The crystal structures of δ and δ[sup ∗] nitrogenStructural transformation of molecular nitrogen to a single-bonded atomic state at high pressuresHigh-pressure amorphous nitrogenHigh P-T transformations of nitrogen to 170GPaRaman, infrared, and x-ray evidence for new phases of nitrogen at high pressures and temperaturesNovel High Pressure Structures of Polymeric NitrogenHexagonal Layered Polymeric Nitrogen Phase Synthesized near 250 GPaEvidence for a New Extended Solid of NitrogenNitrogen in black phosphorus structureHigh-Pressure Polymeric Nitrogen Allotrope with the Black Phosphorus StructureSemiconducting non-molecular nitrogen up to 240 GPa and its low-pressure stabilityRaman study of pressure-induced dissociative transitions in nitrogenNovel high-pressure nitrogen phase formed by compression at low temperatureRaman spectroscopy and phase stability of λ-N2Theoretical assessment of the structure and stability of the

λ

phase of nitrogenHigh-Pressure Phases of Nitrogen

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