Plastic and Superionic Helium Ammonia Compounds under High Pressure and High Temperature

Both helium and ammonia are main components of icy giant planets. While ammonia is very reactive, helium is the most inert element in the universe. It is of great interest whether ammonia and helium can react with each other under planetary conditions, and if so, what kinds of structures and states of matter can form. Here, using crystal structure prediction methods and first-principles calculations, we report three new stable stoichiometries and eight new stable phases of $\mathrm{He}\text{−}{\mathrm{NH}}_3$ compounds under pressures up to 500 GPa. These structures may exhibit perovskitelike structures for ${\mathrm{HeNH}}_3$ and ${\mathrm{He}}_2{\mathrm{NH}}_3$, and a host-guest crystal structure for $\mathrm{He}{({\mathrm{NH}}_3)}_2$. Superionic states are found in all these $\mathrm{He}\text{−}{\mathrm{NH}}_3$ compounds under high pressures and temperatures in which the hydrogen atoms are diffusive while the nitrogen and helium atoms remain fixed. Such dynamical behavior in helium ammonia compounds is quite different from that in helium water compounds, where weakly interacting helium is more diffusive than stronger bound hydrogen. The low-density host-guest phase of space group $I4cm$ is found to be stable at very low pressures (about 3 GPa) and it enters into a plastic state, characterized by freely rotating ammonia molecules. The present results suggest that plastic or superionic helium ammonia compounds may exist under planetary conditions, and helium contributes crucially to the exotic physics and chemistry observed under extreme conditions.

Popular Summary

Helium—the most inert element on the periodic table—and ammonia are major components of icy giant planets. While helium is generally considered to be unreactive, it is not clear whether these two components can react with each other under planetary conditions, or what kinds of states might emerge. Using crystal structure search techniques and ab initio molecular dynamics simulations, we find that three types of helium ammonia compounds can form in eight stable phases over a wide pressure range.

Our investigation identifies that the eight phases belong to three helium ammonia compositions: $\mathrm{He}{({\mathrm{NH}}_3)}_2$, ${\mathrm{HeNH}}_3$, and ${\mathrm{He}}_2{\mathrm{NH}}_3$. Some of the phases resemble host-guest structures, where two or more molecules are held together by forces other than covalent bonds, and perovskitelike systems, in which the compound has a crystalline structure similar to the mineral perovskite. We find that these helium ammonia compounds can even form plastic and superionic states at different pressure and temperature conditions.

Our study provides new and surprising insights into the properties of compounds that may exist in icy giant planets and into new chemistry and physics of helium compounds under extreme conditions.

Figure 1

Energetics of the $\mathrm{He}\text{−}{\mathrm{NH}}_3$ system and crystal structures of the most interesting stable compounds. (a) Convex hulls for formation enthalpies ($\mathrm{\Delta }{H}_f$, with respect to pure He and ${\mathrm{NH}}_3$) at different pressures, calculated with the $\mathrm{PBE}+\mathrm{DFT}\text{−}\mathrm{D}3$ functional [49]. (b) Pressure-composition phase diagram of the $\mathrm{He}\text{−}{\mathrm{NH}}_3$ phases discovered in this work (red bars), together with the previously known phases (green bars) up to 500 GPa. (c) Typical perovskite ${\mathrm{HeNH}}_3$ crystal structure of the $Pnma$ phase at 100 GPa. (d)–(f) Typical crystal structures of host-guest phases in $\mathrm{He}{({\mathrm{NH}}_3)}_2$. (d) the $I4cm$ phase at 3 GPa and (e) the $Ama2$ phase at 500 GPa. (f) Representation of the host-guest structure of the $\mathrm{He}{({\mathrm{NH}}_3)}_2$ structures. Nitrogen atoms are arranged in two layers highlighted by yellow and magenta. Blue, gray, and cyan balls represent N, H, and He atoms, respectively.

Figure 2

Dynamical behavior of H (green) and He atoms (cyan) compared to N atoms (blue) in the helium ammonia compounds under high pressure and temperature. AIMD simulations were performed at 105 GPa and 500 K, 120 GPa and 2000 K for the $Pnma$ ${\mathrm{HeNH}}_3$ phase, and at 31 GPa and 200 K, 36 GPa and 1000 K for $I4cm$ $\mathrm{He}{({\mathrm{NH}}_3)}_2$. (a)–(d) The averaged mean-squared displacements (MSD) at different temperatures. (e)–(h) Atomic trajectories from the simulations representing three different states of matter: the solid $Pnma$ ${\mathrm{HeNH}}_3$ phase (500 K), the superionic phase (2000 K), the solid $I4cm$ $\mathrm{He}{({\mathrm{NH}}_3)}_2$ phase (200 K), and the plastic phase (1000 K); the liquid phase is not shown. The N, H, and He atoms are respectively plotted with blue, green, and cyan.

Figure 3

Proposed phase diagram of ${\mathrm{HeNH}}_3$ (a) and $\mathrm{He}{({\mathrm{NH}}_3)}_2$ (b) at high pressures obtained from structure searches and AIMD simulations. The simulations are marked with four different symbols: blue square, dark green diamond, cyan triangle, and orange circle represent the solid, plastic, superionic, and fluid states, respectively. Black dashed lines are fitted to the phase transition boundaries. The calculated isentrope for Uranus (Neptune) is shown as a thick dark green (dark blue) line. The white dash-dotted line covers the superionic phase in pure ammonia, taken from Redmer et al. [20]. Red solid circles mark some trajectories in which the superionic hydrogen or plastic phases coexist with diffusive helium, which has much smaller diffusion coefficients than superionic hydrogen near the phase boundaries.

Figure 4

Vibrational density of states (VDOS) for the $Pnma$ phase ${\mathrm{HeNH}}_3$ (left) and ${\mathrm{HeND}}_3$ phase (right). Colored areas under black curves give the phonon DOS of N (blue), $\mathrm{H}/\mathrm{D}$, (orange) and He (cyan) from static phonon calculations at 0 K. The red lines represent the vibrational DOS of each atomic species in the superionic phase at $100\mathrm{GPa}+2000\mathrm{K}$, calculated from the Fourier transform of the velocity autocorrelation function. Note that the zero (nonzero) vibrational DOS at zero frequency is due to the fixed (diffusive) behavior of O, $\mathrm{H}/\mathrm{D}$, and He in the superionic phase [22].

Figure 5

RDG analysis and corresponding structural environment of helium atoms in the ${\mathrm{HeNH}}_3$ compound, compared with that in the helium water system. (a)–(c) Plots of RDG versus the electron density multiplied by the sign of the second Hessian eigenvalue for $Pnma$ ${\mathrm{HeNH}}_3$ at 100 GPa, $I{4}_{1}md$ ${\mathrm{He}}_2{\mathrm{H}}_2\mathrm{O}$ at 10 GPa, and $Fd\overline{3}m$ ${\mathrm{He}}_2{\mathrm{H}}_2\mathrm{O}$ at 100 GPa. The solid magenta (dashed green) line region represents the hydrogen bond (vdW interactions) in the crystalline. (d)–(f) Crystal structure of the abovementioned three structures. The covalent bond length and hydrogen bond length are marked nearby. In the ${\mathrm{HeNH}}_3$, blue highlighted helium atoms are enclosed in a light yellow highlighted distorted cubic sublattice, consisting of $\mathrm{N}─\mathrm{H}$ covalent bonds and $\mathrm{H}─\mathrm{N}$ hydrogen bonds.