Combining crystal structure prediction and simulated spectroscopy in pursuit of the unknown nitrogen phase $\zeta$ crystal structure

The structure of nitrogen phase $\zeta$ remains unknown decades after it was first observed spectroscopically, despite numerous experimental and theoretical investigations. The present computational study performs crystal structure prediction using ab initio random structure searching and density functional theory to identify candidate structures. These candidates are then analyzed for consistency with experiment in terms of their simulated x-ray diffraction patterns and Raman spectra. While none of the structures generated here is a clear match for the phase-$\zeta$ experimental data, several of the candidates do exhibit features in common with the experiments and could provide an interesting starting point for future studies. The techniques here also rule out several candidate $\zeta$ nitrogen structures that have been identified previously. Finally, one of the structures might be considered a candidate for phase $\kappa$, whose structure is also unknown.

Figure 1

Predicted crystal energy landscape for orthorhombic molecular ${\mathrm{N}}_2$ phases at 80 GPa. Structures that have been reported in earlier structure prediction studies are shown in orange, while candidates in blue are new structures discussed in detail below. The enthalpy and volume for the optimized $\epsilon$ phase is shown for comparison, along with the reported molar volume of phase $\zeta$.

Figure 2

Selected candidate crystal structures discussed in the text as optimized with DFT at 80 GPa.

Figure 3

Comparison of predicted equations of state for all predicted structures against experimental data for nitrogen phase $\zeta$. Dashed lines correspond to the B86bPBE-XDM predicted equations of state for all candidate structures from Fig. 1, with the lines for structures B8, 12, and 19 highlighted in green, blue, and red, respectively. Solid lines show the new equation of state for the selected structures after fragment-based MP2/CBS $+$ pHF refinement.

Figure 4

Comparison between predicted and experimental lattice constants for several known phases of nitrogen and two $\zeta$-phase candidates. The calculations were performed using B86bPBE-XDM with a $6\times 6\times 6 k$-point grid at the experimental pressure. Where experimental data was available at multiple pressures, errors are shown as computed for each pressure. See the Supplemental Material, Table S1, for details [47].

Figure 5

(a) Simulated powder x-ray diffraction patterns at 80 GPa ($\lambda =0.3683\AA$) and (b) predicted Raman spectra at 30 GPa for selected candidate structures compared against the experimental data for $\zeta {\mathrm{N}}_2$ [8, 13]. See Supplemental Material, Sec. 3, for the complete set of simulated spectra [47].

Figure 6

(a) Reducing the pressure used to compute the predicted spectrum to 20 GPa improves the agreement between theory and experiment considerably for the known $\epsilon$ phase. (b) Comparison of the 20-GPa spectra predicted for structures B8 and 19 against the unknown $\zeta$-phase spectrum at 30 GPa. Experimental spectra at 293 K for $\epsilon$ and 32 K for $\zeta$ taken from Ref. [8].

Figure 7

Comparison of the simulated powder x-ray diffraction patterns of structures 12 and 19 before and after constraining the lattice constants to match the experimentally reported values. All spectra employ a wavelength of $\lambda =0.3683\AA$.

Figure 8

DFT enthalpies vs pressure for the predicted candidate structures and several experimentally known phases. Colored lines correspond to the key structures; dashed gray lines correspond to other structures from the crystal structure prediction landscape which are not discussed in detail.