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Phase stability and lattice dynamics of ammonium azide under hydrostatic compression

We have investigated the effect of hydrostatic pressure and temperature on phase stability of hydro-nitrogen solids using dispersion corrected Density Functional Theory calculations. From our total energy calculations, Ammonium Azide (AA) is found to be the thermodynamic ground state of N$_4$H$_4$ compounds in preference to Trans-Tetrazene (TTZ), Hydro-Nitrogen Solid-1 (HNS-1) and HNS-2 phases. We have carried out a detailed study on structure and lattice dynamics of the equilibrium phase (AA). AA undergoes a phase transition to TTZ at around $\sim$ 39-43 GPa followed by TTZ to HNS-1 at around 80-90 GPa under the studied temperature range of 0-650 K. The accelerated and decelerated compression of $a$ and $c$ lattice constants suggest that the ambient phase of AA transforms to a tetragonal phase and then to a low symmetry structure with less anisotropy up on further compression. We have noticed that the angle made by Type-II azides with $c$-axis shows a rapid decrease and reaches a minimum value at 12 GPa, and thereafter increases up to 50 GPa. Softening of the shear elastic moduli is suggestive of a mechanical instability of AA under high pressure. In addition, we have also performed density functional perturbation theory calculations to obtain the vibrational spectrum of AA at ambient as well as at high pressures. Further, we have made a complete assignment of all the vibrational modes which is in good agreement with the experimental observations at ambient pressure. Also the calculated pressure dependent IR spectra show that the N-H stretching frequencies undergo a red and blue-shift corresponding to strengthening and weakening of hydrogen bonding, respectively below and above 4 GPa.