Pressure-induced loss of electronic interlayer state and metallization in the ionic solid ${\text{Li}}_3\text{N}$: Experiment and theory

Results of x-ray diffraction and nitrogen $K$-edge x-ray Raman scattering (XRS) investigations of the crystal and electronic structure of ionic compound ${\text{Li}}_3\text{N}$ across two high-pressure phase transitions [A. Lazicki et al., Phys. Rev. Lett. 95, 165503 (2005)] are interpreted using density-functional theory. A low-energy peak in the XRS spectrum which is observed in both low-pressure hexagonal phases of ${\text{Li}}_3\text{N}$ and absent in the high-pressure cubic phase is found to originate from an interlayer band similar to the important free-electron-like state present in the graphite and graphite intercalated systems, but not observed previously in ionic insulators. XRS detection of the interlayer state is made possible because of its strong hybridization with the nitrogen $p$ bands. A pressure-induced increase in the band gap of the high-pressure cubic phase of ${\text{Li}}_3\text{N}$ is explained by the differing pressure dependencies of different quantum-number bands and is shown to be a feature of several low-$Z$ closed-shell ionic materials.

Figure 1

(Color online) Crystal structures of each phase with larger spheres representing the nitrogen ions, smaller representing lithium.

Figure 2

(Color online) Experimental and calculated equation of state of $\beta$- and $\gamma {\text{-Li}}_3\text{N}$. In the inset, the high-pressure bulk modulus of $\gamma {\text{-Li}}_3\text{N}$ is compared to other common highly compressible materials (Refs. 19, 20). (NaCl, MgO, and Ne curves are interpolated up to 200 GPa).

Figure 3

(Color online) Measured nitrogen $k$-edge XRS spectra from the three phases of ${\text{Li}}_3\text{N}$ compared with calculated nitrogen $p$ and lithium $s$ projected density of states and with the calculated x-ray absorption spectrum. The calculated curves were offset by 394.2 eV (arbitrary) in every case, for the sake of qualitative comparison with the experimental results. The vertical dashed line indicates the calculated energy of highest-occupied valence states.

Figure 4

(Color online) Calculated electronic band structure for the three phases of ${\text{Li}}_3\text{N}$, with the interlayer band highlighted in orange in the two hexagonal phases.

Figure 5

(a) $\alpha {\text{-Li}}_3\text{N}$ valence density and (b) (unoccupied) interlayer band density contours perpendicular to the basal plane (left panels) and within the basal plane (right panels). Large regions of white space in (a) signify very low density whereas the contours in the same areas in (b) denote a maximum in the IL density. Contours are labeled in units of $0.01\text{e}/{\text{Å}}^3$ and separated by (a) 0.05 and (b) $0.01\text{e}/{\text{Å}}^3$.

Figure 6

(a) $\beta {\text{-Li}}_3\text{N}$ valence density and (b) (unoccupied) interlayer band density contours perpendicular to the basal plane (left panels) and within the basal plane (right panels). Large regions of white space in (a) signify very low density whereas the contours in the same areas in (b) denote a maximum in the IL density. Contour lines are labeled in units of $0.1\text{e}/{\text{Å}}^3$ and separated by $0.05\text{e}/{\text{Å}}^3$.

Figure 7

(Color online) Total density of states of valence and low-lying conduction bands of $\beta {\text{-Li}}_3\text{N}$ between 0 and 35 GPa.

Figure 8

(Color online) Sample image at (a) ambient pressure and at (b) the $\beta \to \gamma$ phase transition near 40 GPa. The bright spot at 40 GPa is the ruby grain used for pressure calibration.

Figure 9

(Color online) Change in valence-band energies relative to bottom of the conduction band in the $\gamma$ phase from the phase transition to metallization. Energy gaps explained in the density of states plot (inset): open circles give the fundamental band gap, and the energy separation between the bottom of the conduction band and the center of mass of the valence band (open triangles) and the bottom of the valence band (closed triangles) are also shown. $V_0$ is the volume of $\alpha {\text{-Li}}_3\text{N}$ at ambient pressure.

Figure 10

(Color online) Band gap increases as a function of volume reduction for related close-shelled cubic Li compounds. LiF and ${\text{Li}}_2\text{O}$ are cubic at ambient pressure and $V_0$ refers to the ambient pressure volume. ${\text{Li}}_3\text{N}$ $V_0$ (in this instance alone) is taken as the volume at the $\beta \to \gamma$ phase transition.