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H4O and Other Hydrogen-Oxygen Compounds at Giant-Planet Core Pressures

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H4O and Other Hydrogen-Oxygen Compounds at Giant-Planet Core Pressures H4O and other hydrogen-oxygen compounds at giant-planet core pressures Shuai Zhang,1, ∗ Hugh F. Wilson,1 Kevin P. Driver,1 and Burkhard Militzer1, 2 1Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA 2Department of Astronomy, University of California, Berkeley, California 94720, USA Water and hydrogen at high pressure make up a substantial fraction of the interiors of giant planets. Using ab initio random structure search methods we investigate the ground-state crystal structures of water, hydrogen, and hydrogen-oxygen compounds. We find that, at pressures beyond 14 Mbar, excess hydrogen is incorporated into the ice phase to form a novel structure with H4O stoichiometry. We also predict two new ground state structures, P 21=m and I4=mmm, for post- C2=m water ice. PACS numbers: 64.70.K-, 61.50.Ah, 62.50.-p, 96.15.Nd using density functional theory. In the AIRSS process, randomly generated unit cells are filled with randomly positioned atoms, and the structures are geometrically As one of the most abundant substances in the solar relaxed to the targeted pressure. Structures with com- system, water ice at high pressure [1, 2] is of fundamen- petitive enthalpy are picked out and re-evaluated with tal importance in planetary science [3]. Over the last more accurate thermodynamic calculations, from which two years, a significant effort has been devoted to finding the most stable structure can be determined. Although the ground-state structures of ice at the multimegabar the AIRSS is not guaranteed to find the most stable pressures corresponding to the cores of gas giant planets phase, it has achieved remarkable success in discovering (15-20 Mbar for Saturn and 40-60 Mbar for Jupiter). Mil- structures across a wide range of materials [11{13]. itzer and Wilson [4] demonstrated that the P bcm phase In our calculations, structural optimization is per- [2] becomes unstable above 7.6 Mbar and predicted a formed using the Vienna ab initio simulation package new structure of P bca symmetry. Wang et al. [5] showed (VASP) [14]. Projector augmented wave (PAW) pseu- that, at 8.1 Mbar, water ice assumes another structure dopotentials [15] and the Perdew-Burke-Ernzerhof [16] ¯ of I42d symmetry instead of transforming into a Cmcm exchange-correlation functional are used. The pseudopo- structure as proposed in Ref. [4]. Refs. [6{8] instead pro- tential cutoff radii equal to 0.8 and 1.1 Bohr for H and posed a structure with P mc21 symmetry to appear in the O. For efficiency of the AIRSS, a cutoff energy of 900 eV same pressure regime, but it has a higher enthalpy than is chosen for initial relaxation, which is then increased ¯ the I42d structure. Around 12 Mbar, a transition to a to 1700 eV for precise calculations on favorable struc- structure with P 21 symmetry was consistently predicted tures. Likewise, a relatively sparse Monkhorst-Pack grid in Refs. [5{8]. Even higher pressure studies predict a [17, 18] (6×6×6) is used initially, which is later replaced P 21=c structure at 20 Mbar [7], and a metallic C2=m by a 20 × 20 × 20 grid. Tests at the largest energy cutoff structure at 60 Mbar [6, 8]. In nature, however, high- and grid size show that the total system energies are con- pressure water phases are rarely found in isolation, and, verged to the order of 1 meV, while the energy difference in gas giants, an icy core may be surrounded by a vast is converged to 0.1 meV. reservoir of hydrogen-rich fluid or exist in a mixture with As an initial step, we recomputed enthalpies of re- the other planetary ices, such as ammonia and methane. cently reported [4{7] H2O structures as a function of Recent works have emphasized the fact that counterin- pressure, assembling all proposed structures for com- tuitive stoichiometries can occur in post-perovskite ma- parison. Figure 1 shows the transition sequence up terials at extreme pressures [9]. This raises the question to the highest reported pressure (70 Mbar) as follows: of whether H2O is indeed the ground-state stoichiometry X ! P bcm ! P bca ! I42¯ d ! P 2 ! P 2 =c ! C2=m, for water at high pressure in hydrogen-rich environments, 1 1 consistent with previous reports. Note that the P mc21 or whether pressure effects are likely to result in the in- structure predicted in Refs. [6{8] is less stable than the corporation of hydrogen into the ice lattice to form novel I42¯ d structure reported by Wang et al. [5] at all pres- ice-like phases with non-H2O stoichiometry. sures; as the I42¯ d structure has eight formula units (f.u.) In this Letter, we apply ab initio random structure per unit cell, it was less likely to be generated by random searching (AIRSS) methods [10] to determine the ground- search algorithms. state structure of hydrogen-oxygen compounds at ex- With quickly increasing number of known massive exo- treme pressure to explore whether the H2O stoichiom- planets, it is worthwhile to explore stable H2O structures etry of water is maintained at high pressure. The AIRSS at even higher pressure. We use AIRSS to generate be- method relies on the generation of a large number of tween 1000 and 3500 H2O unit cells with 1-4 f.u. at random geometries whose structures are then optimized pressures of 100, 150, 300, 400, and 500 Mbar. Addition- 2 0.00 Ice X[1] -0.05 Pbcm[2] 0.015 I-42d -0.10 Pbca[4] Pbcm I-42d[5] 0.000 -0.15 Pbca P21[5-8] -0.015 Pmc21[6-8] -0.20 7.6 8.0 8.4 2 3 4 5 8 10 12 14 16 18 20 0.15 0.00 C2/m -0.15 P21[5-8] P21/m Enthalpy (eV/f.u.) Enthalpy -0.30 P21/c[7] I4/mmm C2/m[6,8] -0.45 P21/m -0.60 I4/mmm 20 40 60 80 120 180 240 300 360 420 480 Pressure (MBar) FIG. 1. (color online) Enthalpy versus pressure of different water ice structures. The reference following the name of each phase is the corresponding earliest report. In the lower panel, structures are provided for C2=m, P 21=m and I4=mmm, where large red and small blue spheres represent O and H atoms, respectively. The dashed line at 70 Mbar indicates the highest pressure explored in previous work. ally, we generate between 750 and 1150 structures with Cmcm structure of Ref. [20], hereafter Cmcm-12, be- 5-8 f.u. at pressures of 100 and 200 Mbar. comes less stable than a new Cmcm-4 structure, in which Figure 1 shows two new, stable phases with P 21=m and three groups of bonds (different in length) exist without I4=mmm symmetry that appear at high pressure. More forming in-plane H3 clusters [20]. As pressure increases stable than C2=m above 135 Mbar, the P 21=m phase to 87 Mbar, the hcp structure (symmetry P 63=mmc) be- is also a monoclinic, layered structure that resembles comes stable. Different from the P 63=mmc structure pre- the C2=m phase except that O-H-O bonds are divided dicted in Ref. [21] (c=a ≈ 2), our hcp lattice exhibits a into two classes: one is shortened and straight, while the smaller c=a ratio of 1.58. The hcp structure remains sta- other is squeezed and distorted in different directions. At ble until being replaced by the fcc lattice at 180 Mbar. 330 Mbar, P 21=m is replaced by a tetragonal I4=mmm Having computed the ground state structures of H phase, which has the same structure as the L'2 phase of and H2O throughout a wide pressure range, we now ex- ThH2 [19]. I4=mmm remains the most stable structure plore novel hydrogen-oxygen stoichiometries, including up to 500 Mbar. Like the C2=m structure, an analysis of hydrogen-enriched structures H3O, H4O, H6O and H8O the electronic band structure shows that the P 21=m and and oxygen-rich structures HO, HO2 and HO4. Between I4=mmm phases are metallic. Structural parameters of 200 and 3000 random structures with up to 8 f.u. at these two phases are listed in Supplemental Table I. pressures of 20-500 Mbar were generated, depending on In addition to our initial studies on water ice, we per- the specific computational cost and searching efficiency. formed AIRSS on hydrogen (results see Fig. 2). Below 50 Figure 3 compares the stability of structures with dif- Mbar we find the same progression of ground state struc- ferent stoichiometries using a convex hull diagram [23]. tures, Cmca ! C2=c ! I41=amd (or F ddd) ! Cmcm, This diagram shows the per-atom enthalpy of the com- as has been reported previously [20{22]. When pressure pound HmOn, as a function of fractional concentration exceeds 54 Mbar, we find that the 12-atom per unit cell of oxygen, x = n=(m + n), relative to a combination of 3 2.7 5 (a) HO 4 1.8 0 P=100 Mbar 0.9 Cmca[21] Cmcm-12 0.0 C2/c[20] H O HO H O Cmcm-4 8 -5 2 Fddd[22] -0.9 HO I41/amd[21] H O H O 6 2 H O Cmcm-12[20] -1.8 H O 4 3 -10 P63/mmc[21] 0.00 0.15 0.30 0.45 0.60 0.75 0.90 Cmcm-4 H O 0.08 4 Enthalpy (meV/atom) Enthalpy hcp -15 (b) fcc 0.00 4 8 12 16 20 30 60 90 120 150 180 H H O 2 Pressure (Mbar) -0.08 FIG.
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