Superionicity in Ammonium Polyhydrides at Extreme Pressures

TL;DR

This study investigates hydrogen-rich ammonium polyhydrides predicted to form metastable $NH_7$–$NH_{24}$ under 100–300 GPa, using density functional molecular dynamics to map solid, superionic, and liquid phases and to quantify diffusion mechanisms. The authors determine solid-to-superionic transition temperatures $T_{SI}$ and melting temperatures $T_m$ across 13 structures and show that both transitions decrease with increasing proton fraction $n_{ m H}/n_{ m total}$, with some systems exhibiting a negative Clapeyron slope. The phase behavior indicates that high hydrogen content lowers the stability of a superionic phase, and near $n_{ m H}/n_{ m total} ightarrow 0.97$ the materials are more likely to melt directly, resulting in liquids under ice-giant interior conditions. These findings imply that in Uranus/Neptune interiors ammonium polyhydrides would predominantly be liquids, not superionic solids, and highlight multiple diffusion pathways (including paddle-wheel-like proton exchange) that govern transport in hydrogen-rich planetary materials.

Abstract

Polyhydrides have been shown to form novel structures at high pressure, which may be found in the interiors of giant planets. With density functional molecular dynamics simulations we studied the behavior of ammonium polyhydride compounds with stoichiometries of NH$_7$, NH$_9$, NH$_{10}$, NH$_{11}$, NH$_{14}$, NH$_{20}$, and NH$_{24}$ which were predicted with crystal structure search methods to be metastable at 100-300~GPa. For every compound, we performed simulations at a range of temperatures (and for several compounds, pressures) covering the solid, superionic and liquid phases. We show that when heated, high pressure ammonium polyhydride compounds exhibit hydrogen superionic diffusion. We demonstrate a number of metrics by which the solid-to-superionic and superionic-to-liquid transitions can be detected from simulation data, including changes in the internal energy and pressure, formation of new chemical species, and atomic diffusion rates. We find that both the solid-to-superionic and the superionic-to-liquid transitions decrease in temperature as proton fraction increases. These trends indicate that above a proton fraction of $\sim$0.97, ammonium hydride structures are likely to directly melt instead of first exhibiting a superionic phase. Our observed melting trend further indicates that at the extreme conditions of ice giant interiors, hydrogen rich ammonium hydrides such as those studied in this work would exist predominantly as liquids rather than exhibiting a superionic phase.

Figures (10)

• Figure 1: Conventional unit cells of several of the structures considered in this study, with the chemical systems present denoted in brackets. (a) NH$_7$-$Ima2$ [NH$_4^+$, H$_2$, H$^-$], (b) NH$_9$-$P2_1/m$ [NH$_4^+$, 2 H$_2$, H$^-$], (c) NH$_{10}$-$Pnma$ [NH$_4^+$, 2 [H$_3^{0.5-}$]$_\infty$], (d) NH$_{10}$-$C2/m$ [NH$_4^+$, 2.5 H$_2$, H$^-$], (e) NH$_{11}$-$Cmc2_1$ [NH$_4^+$, H$_7^-$], and (f) NH$_{24}$-$C_2$ [NH$_4^+$, 7.5 H$_2$, [H$_5^-$]$_\infty$]. Nitrogen atoms are blue, hydrogen atoms in ammonium are white, H-containing molecular units are green, polymeric hydrogen chains are yellow, and H$^-$ ions are red. The molecular partitioning is highly sensitive to the chosen bond length criterion. In the present work, a cutoff of 1 Å was adopted, consistent with our previous study in which H–H bonds with $-$ICOHP values exceeding 2 eV per bond were regarded as significant wang2024superconductivity. The remaining structures studied (NH$_7$-$P4_12_12$, NH$_9$-$Cmcm$, NH$_9$-$P2_1$, NH$_9$-$Pmnm$, NH$_{14}$-$P$-1-I, NH$_{14}$-$P$-1-II, and NH$_{20}$-$P$-1) are shown in Supplemental Fig. 1.
• Figure 2: Visualization of superionic diffusion in the NH$_{10}$-$Pnma$ structure. The phase is labeled in the lower right corner of each panel: S for solid, SI for superionic, and L for liquid. (a-c) Mean squared displacement (MSD) plots for H and N ions in the solid phase (100 K), the superionic phase (1000 K), and the liquid phase (2500 K). The H MSD has been divided by 20 in all panels for ease of comparison with N. (d-e) Trajectory plots for the solid phase looking at two different faces. Blue spheres show N, and gray lines trace the motion of H ions. For the solid phase, we see H ions are well constrained in their potential wells. (f-g) Trajectory plots for the superionic phase. Gray lines now show the pathways of H ions as they rotate in NH$_4^+$ and diffuse through the cell. (h-i) Isosurfaces of the time averaged H positions match well with the trajectory plots in (f-g), showing that H ions spend much of their time bound in rotating NH$_4^+$ ions, and diffusing through interconnected pathways surrounding the N ions.
• Figure 3: A series of metrics by which the solid-to-superionic transition temperature may be determined using simulation results of the NH$_{10}$-$C2/m$ structure at 1.43 g/cm$^3$ as an example. Blue and red shaded bars indicate the temperature range of the solid-to-superionic transition and the superionic-to-liquid transition, respectively. (a-b) When performing DFT-MD simulations in 50 K increments, small jumps in energy and pressure are often observed at the superionic transition. (c-d) A jump in H ion diffusivity (abbreviated D) is the typical signature of superionicity, though this is best visualized on log or log$_{10}$ scale. (e-f) We find that upon the transition to the superionic state, the concentrations of existing H-bearing species change as H ions diffuse and form new bonds. Similarly, new species are formed, which facilitate H ion diffusion through proton exchange. (g) Superionic hydrogen diffusion typically follows an Arrhenius relationship, where the natural log of diffusivity (calculated from the MSD) follows linearly with 1/T. A high R$^2$ value in this least-squares fit indicates the temperature regime of superionicity has been successfully identified.
• Figure 4: The phase diagram of the NH$_9$-$P2_1/m$ structure from 100--400 GPa showing the solid, superionic, and liquid phases. Also plotted are the melting and solid-to-superionic transitions of waterWilson2013 and ammoniahernandez2023melting, and the solid-to-superionic transition of NH$_7$ ($R-3m$ from 20-60 GPa and $P4_12_12$ from 60-200 GPasong2019exotic). These phase transitions are compared to the isentropes of Uranus and Neptunemilitzer2025ab. Because of its higher proton fraction, the NH$_9$-$P2_1/m$ structure becomes superionic and melts at lower temperatures than NH$_3$ and NH$_7$ compounds.
• Figure 5: Pressure-temperature and energy-temperature trends for the NH$_{10}$-$C2/m$ and NH$_{14}$-$P$-1-I structures. Yellow, light blue, and dark blue markers correspond to the solid, superionic, and liquid phases, respectively. For the NH$_{10}$-$C2/m$ structure, we see increases in pressure and energy at the solid-to-superionic and superionic-to-liquid transitions. For the NH$_{14}$-$P$-1-I structure, we observe no such increases but the pressure decreases upon melting, which means the liquid is denser than the superionic phase, and the melting line has a negative Clapeyron slope, $dT_m/dP<0$.