$\mathrm{Xe}({\mathrm{N}}_2{)}_2$ compound to 150 GPa: Reluctance to the formation of a xenon nitride

The $\mathrm{Xe}\text{−}{\mathrm{N}}_2$ binary phase diagram was determined at 296 K from the pressure evolution of 14 different concentrations. The properties of $\mathrm{Xe}\text{−}{\mathrm{N}}_2$ mixtures were characterized using visual observation, Raman spectroscopy, and powder x-ray diffraction. Above 4.9 GPa, the $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ van der Waals compound is stable and adopts the $\mathrm{MgC}{\mathrm{u}}_2$-type Laves phase structure $\left(Fd\text{−}3m\right)$ with ${\mathrm{N}}_2$ molecules orientationally disordered. At 10 GPa, this cubic lattice undergoes a martensitic phase transition into a tetragonal $(I{4}_1/amd)$ unit cell. This transition is associated with a partial ordering of the ${\mathrm{N}}_2$ molecules, possibly due to the growing ${\mathrm{N}}_2\text{−}{\mathrm{N}}_2$ quadrupole-quadrupole interaction with density. No other phase transition was detected up to 154 GPa, even after heating the sample to 2000 K. Above 30 GPa, a softening of the ${\mathrm{N}}_2$ vibron mode with pressure reveals a weakening of the ${\mathrm{N}}_2$ intramolecular bond that suggests an electronic redistribution between ${\mathrm{N}}_2\text{−}{\mathrm{N}}_2$ and $\mathrm{Xe}\text{−}{\mathrm{N}}_2$ entities. These interactions could explain the great stability of the $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ compound. However, no xenon nitride was observed.

Figure 1

(a) Binary phase diagram of $\mathrm{Xe}\text{−}{\mathrm{N}}_2$. Red dots and squares represent experimental data of the liquidus and of the appearance of the $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ solid (error bars in concentration and pressure are smaller than the dots’ diameter). The phases of pure nitrogen are indicated on the left-hand side of the diagram. $F_1$ and $F_2$ are nitrogen-rich and xenon-rich fluids, respectively, while $S_{\mathrm{Xe}}$ is a xenon-rich solid. The $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ van der Waals compound is formed at the same pressure (4.9 GPa) as the $\beta \to \delta$ phase transition in pure nitrogen. (b) Microphotograph of a 67.4 mol % Xe mixture at 0.7 GPa. An $F_1$ bubble (top) is seen in the $F_2$ fluid. (c) Microphotograph of a 6.5 mol % Xe mixture at 3.1 GPa. The fine $\beta \text{−}{\mathrm{N}}_2$ and $S_{\mathrm{Xe}}$ powder result from the brutal phase separation occurring at 2.6 GPa. (d) Microphotograph of a 13.9 mol % Xe mixture at 2.1 GPa. The $S_{\mathrm{Xe}}$ solid is observed in the $F_1$ fluid. (e) Raman frequency shift of ${\mathrm{N}}_2$ vibron modes in different solids with respect to pressure. The black lines represent the vibrational modes of pure ${\mathrm{N}}_2$ taken from Scheerboom et al. [27]. The black triangles, blue dots, and red squares were obtained from pure ${\mathrm{N}}_2$, $\mathrm{Xe}({\mathrm{N}}_2{)}_2$, and $S_{\mathrm{Xe}}$, respectively. The filled symbols were all taken from $\mathrm{Xe}\text{−}{\mathrm{N}}_2$ mixtures of 30 mol % Xe. The empty red squares are from a 96 mol % Xe mixture. The Raman shift difference between the empty and filled red squares illustrates the increasing miscibility of ${\mathrm{N}}_2$ in the xenon-rich solid with pressure. The dashed blue line indicates the phase transition in $\mathrm{Xe}({\mathrm{N}}_2{)}_2$, which is noticeable by a weak discontinuity in its ${\mathrm{N}}_2$ vibron frequency.

Figure 2

Powder XRD pattern $(\lambda =0.4117\AA )$ obtained from a 6.6 mol % Xe mixture at 4.2 GPa (decompressed from 5.2 GPa) superimposed with its Le Bail refinement. Even at this concentration, three solid phases $(S_{\mathrm{Xe}},\beta \text{−}{\mathrm{N}}_2$ and $\mathrm{Xe}{\left({\mathrm{N}}_2\right)}_2)$ are observed. A cubic $\left(Fd\text{−}3m\right)$ unit cell with $a=9.31\AA$ fits well the diffraction lines of $\mathrm{Xe}({\mathrm{N}}_2{)}_2$. The distance between the center of mass of the first-neighbor ${\mathrm{N}}_2\text{−}{\mathrm{N}}_2$ molecules is 3.29 Å, whereas the shortest $\mathrm{Xe}\text{−}{\mathrm{N}}_2$ distance is 3.86 Å. (Inset) Drawing of the Laves phase $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ where the Xe atoms (orange spheres) and the spherically disordered ${\mathrm{N}}_2$ molecules (blue spheres) occupy the Mg ($8a$) and Cu ($16d$) sites, respectively.

Figure 3

Evolution of the $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ compound $d$-spacings with pressure. The dotted blue line at 10 GPa evidences the $d$-spacing discontinuities associated with a cubic-to-tetragonal martensitic phase transition.

Figure 4

Rietveld refinement of tetragonal $(I{4}_1/amd)$ $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ at 10.3 GPa. The image plate corresponding to the refined diffraction pattern is in the background. The diffraction pattern was obtained from a 6.6 mol % Xe mixture with a wavelength of $\lambda =0.4117\AA$. The $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ powder is of great quality, whereas the diffraction rings of solid ${\mathrm{N}}_2$ and $S_{\mathrm{Xe}}$ show a nonhomogeneous crystallite distribution. The reliability factors for the refinement are $R_{wp}=17.2\%$ and $R_{\exp }=18.1\%$, which yields a satisfactory goodness of fit of 0.95.

Figure 5

Tetragonal $(I{4}_1/amd)$ structure of $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ at 10.3 GPa. Xenon and nitrogen atoms are drawn as orange and blue spheres, respectively. (a) The nitrogen molecules are found only partially disordered after the phase transition. The disorder of the nitrogen molecules is modeled by an overlap of each of the nitrogen molecules with three others: one ${\mathrm{N}}_2$ center of mass is occupied by a total of four molecules. When taking into account the occupancy of a nitrogen atom (0.25), each ${\mathrm{N}}_2$ center of mass is effectively occupied by a single molecule, with a slightly varying orientation, representing the ${\mathrm{N}}_2$ molecule partial disorder. Each Xe atom has four Xe nearest neighbors at distances larger (3.51 Å) than in pure Xe at the same pressure (3.38 Å) [43]. The shortest $\mathrm{Xe}\text{−}{\mathrm{N}}_2$ and ${\mathrm{N}}_2\text{−}{\mathrm{N}}_2$ distances (position of the center of mass was used for the ${\mathrm{N}}_2$ molecules) are of 3.55 Å and 2.99 Å, respectively. (b) Distorted kagome nets in the tetragonal $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ structure. (Top) Top view of a distorted kagome plane. ${\mathrm{N}}_2$ hexagons and ${\mathrm{N}}_2$ triangles forming the distorted kagome lattice have two and one slightly shorter ${\mathrm{N}}_2\text{−}{\mathrm{N}}_2$ distances (7%), respectively. (Bottom) Side view of the kagome planes, which emphasizes the layered arrangement of kagome layer's nets of ${\mathrm{N}}_2$ molecules and puckered sheets of Xe. ${\mathrm{N}}_2$ molecules are interpreted to align due to the QQ interaction, known to minimize the energy with the slipped-parallel configuration. The orientation of the molecules was validated with a Rietveld refinement at both 10.3 and 30.0 GPa. Drawings were done using the vesta software [44].

Figure 6

(Top) Volume of $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ with respect to pressure. Measurements were made in a 30 mol % Xe mixture. The black line is a Vinet equation of state fit of the data points (blue dots) corresponding to the tetragonal $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ solid. The red line is the ideal volume of mixing, $V_{\mathrm{Xe}}+2V_{{\mathrm{N}}_2}$, obtained from the equations of states of the pure systems [51, 52, 53]. The discontinuity around 125 GPa corresponds to the $\zeta \to \kappa$ phase transition in pure nitrogen. Literature data were updated with the latest ruby pressure scale [24]. (Inset) Diffraction pattern obtained on a 30 mol % Xe mixture at 154 GPa with a wavelength of $\lambda =0.3738\AA$. The black lozenge and circle represent diffraction lines from the xenon-rich solid and LiF, respectively. LiF was used as a thermal insulator. (Bottom) Volume difference between the $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ structure and the ideal volume of mixing, $V_{\mathrm{Xe}}+2V_{{\mathrm{N}}_2}$. The phases of pure nitrogen are indicated and its phase transitions marked by vertical dashed lines.

Figure 7

Raman shift of ${\mathrm{N}}_2$ vibron modes in different solids with respect to pressure. Data were obtained from mixtures with concentrations between 11 and 30 mol % Xe. The red squares and blue circles were obtained from $S_{\mathrm{Xe}}$ and $\mathrm{Xe}({\mathrm{N}}_2{)}_2$, respectively. The filled symbols represent data points taken during compression, while the empty ones were acquired during sample decompression. The black dashed and dotted lines are the pure ${\mathrm{N}}_2$ vibrational modes taken from Schneider et al. [55] and Goncharov et al. [54], respectively. Around 110 GPa, the Raman mode of the $S_{\mathrm{Xe}}$ solid is overlapped by the more intense vibrational mode of $\mathrm{Xe}({\mathrm{N}}_2{)}_2$. Mixtures of 11 mol % Xe, which showed none of the $S_{\mathrm{Xe}}$ Raman modes allowed to confirm that the vibron observed above 110 GPa belongs to $\mathrm{Xe}({\mathrm{N}}_2{)}_2$.

Figure 8

Raman spectrum of a 30 mol % Xe mixture at selected pressures. An offset on the vertical axis was applied to improve clarity. Lozenges indicate the $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ vibrational modes. The modes at higher frequency belong to pure solid ${\mathrm{N}}_2$, while the ones at lower frequency belong to $S_{\mathrm{Xe}}$. The oscillations found in the spectra at 60.0 GPa are caused by the strong fluorescence emanating from the sample. From 100 GPa, the main Raman mode of $S_{\mathrm{Xe}}$ is overlapped by the $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ vibrational mode. At 141 GPa, the $\mathrm{Xe}({\mathrm{N}}_2{)}_2$ main vibron becomes of lower intensity than the pure ${\mathrm{N}}_2$ vibrational mode, which is a consequence of the ${\mathrm{N}}_2$ intramolecular bond weakening. (Inset) Microphotographs of a 30 mol % Xe mixture, illuminated in both transmission and reflection. At 125.5 GPa, the sample becomes completely dark. Light only goes through the ruby ball.