Bond Strengthening in Dense H2O and Implications to Planetary Composition

Home , Ice VII, Ice VIII, Superionic water

Bond strengthening in dense H2O and implications to planetary composition

Zachary M Grande,† Chenliang Huang,‡ Dean Smith,† Jesse S Smith,¶ John H Boisvert,‡ Oliver Tschauner,§ Jason H Steﬀen,‡ and Ashkan Salamat∗,†

†Department of Physics and Astronomy and HiPSEC, University of Nevada Las Vegas, Las Vegas, Nevada 89154, USA ‡Department of Physics and Astronomy, University of Nevada Las Vegas, Las Vegas, Nevada 89154, USA ¶HPCAT, X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA §Department of Geoscience, University of Nevada Las Vegas, Las Vegas, Nevada 89154, USA

E-mail: [email protected]

Abstract mantle a potential long-term reservoir of ancient water. H2O is an important constituent in plane- The pressure-temperature phase diagram of tary bodies, controlling habitability and, H2O exhibits remarkable polymorphism, with in geologically-active bodies, plate tec- as many as 18 phases currently reported.1,2 At tonics. At pressures within the interior low pressures, this complexity arises from steric of many planets, the H-bonds in H2O col- rearrangements of hydrogen-bonded molecules, lapse into stronger, ionic bonds. Here we while the H–O–H bond angle and length represent agreement between X-ray diffrac- main almost constant. H-bonds are established tion and Raman spectroscopy for the through correlated disorder of the protons be- transition from ice-VII to ice-X occurring tween adjacent oxygen atoms such that, at each at a pressure of approximately 30.9 GPa moment, two protons and one oxygen form an 3 by means of combining grain normaliz- H2O molecule. Ice structures generally exhibit ing heat treatment via direct laser heat- network-like topologies similar to those of sil- ing with static compression. This is ev- ica and silicates.4 The behavior of condensed idenced by the emergence of the charac- H2O phases (ices) is dominated by this H-bond teristic Raman mode of cuprite-like ice- network. Under the conditions found in the X and an abrupt 2.5-fold increase in bulk interior of Earth and many other planets, the arXiv:1906.11990v1 [cond-mat.mtrl-sci] 27 Jun 2019 modulus, implying a significant increase H-bonds in ice are gradually replaced by ionic in bond strength. This is preceded by a bonds in ice-X.5–7 transition from cubic ice-VII to a struc- At room temperature, ice-VII becomes the ture of tetragonal symmetry, ice-VIIt at stable solid phase of H2O at pressures above 5.1 GPa. Our results significantly shift 2.7 GPa.8 The subsequent transition into ice- the mass/radius relationship of water- X has been observed in spectroscopic measure- rich planets and define a high-pressure ments and inferred from structural data, but limit for release of chemically-bound wa- there has been no consensus between stud- ter within the Earth, making the deep ies. Estimates of the transition pressure range

1 from 40 GPa to above 120 GPa.6,7,9–17 However, treated pattern. the existence of a molecular-to-ionic transition above 40 GPa has been observed at temperatures beyond the melting curve.18,19 Results Bond states in soft molecular compounds are A single-phase sample of powdered ice-VII strongly affected by non-hydrostatic stress at is achieved by heating at the first appear- high pressure conditions. H O is especially sus- 2 ance of its coexistence with ice-VI, as con- ceptible to this since the use of a pressure trans- firmed with XRD measurements (See Meth- mitting medium is inhibited due to the forma- ods and Supplementary Information). Begin- tion of hydrates and clathrates. The result- ning at 2.7 ± 0.4 GPa, we unambiguously index ing distortions caused by non-hydrostatic com- and refine the phase as cubic ice-VII. Above pression are further exacerbated by the het- 5.1 ± 0.5 GPa, we observe deviations in the peak erogeneous nucleation of ice-VII within ice- positions and profiles both before and – more VI, which yields large crystalline domains and clearly – after heat treating. Specifically, we ob- causes significant anisotropic effects at grain serve splitting between the (2 0 0)/(0 0 2) which boundaries.20 are not accommodated by the cubic ice-VII To minimize these effects, we heat ice sam- (P n3m) structure. Figure1b shows the Bragg ples at high pressure using a CO laser and al- 2 feature at ∼ 14.5◦, where these deviations are low them to cool to ambient temperature. The most pronounced. Here, we find significant im- cooling rate is slower than rapidly quenching, provements in the Rietveld refinement when which can potentially trap internal stresses, and modelling with a tetragonal sub-group of cubic is faster than annealing, which typically results ice-VII (P 4 /nnm), and name this tetragonal in enlarged domains (see Methods and Supple- 2 phase ice-VII . mentary Information), and an analogy can be t Structural anomalies have been reported in made with metallurgical normalization.21 the 10–14 GPa regime,9,12,14,22 and are at- There are several benefits of this heat treat- tributed to a proton-disordered ice-VII0, but ment: anisotropic strain within both the sam- these claims have lacked spectroscopic evidence. ple and the Au pressure marker are relieved, One such anomaly has been suggested to result minimizing deviatoric stress for more accurate from a tetragonal distortion.12 We show that volume-pressure measurements; the recrystal- this transition from ice-VII to ice-VII is ac- lization of the ice produces a powdered sam- t companied by a 2.18 ± 0.01% volume collapse ple with nanoscopic domains in random orien- of the unit cell at this pressure (Supplementary tation (Supplementary Video); and provides a Information). We only confirm a transition in direct, localized method of heating. The re- the oxygen sublattice to a tetragonal symmetry duced domain size and their random orienta- and cannot comment on its relation to proton- tions yield well-resolved Debye-Sherrer rings for disordered ice-VII0, as the few observations of an extensive q-range (Figure1a), making our the (1 1 1) diffraction peak were dominated by data suitable for Rietveld powder X-ray diffrac- the background in our XRD patterns. tion analysis (Figure1b). The powdered na- We further examine the symmetry of the unit ture of the sample also reduces its susceptibility cell above ∼ 5 GPa, by combining structural to further strain as compression continues, de- refinements with a Bayesian model comparison spite the uniaxial nature of the DAC, allowing algorithm (see Methods).23 Figure1c shows the full structural refinement. Data that are not log Bayes factors comparing cubic and tetrag- heat treated display significantly fewer diffrac- onal models for a selection of points over the tion features and typically exhibit multi-grain pressure range of our data. A cubic model is spots or highly textured rings with significant favoured for pressures below 5 GPa, indicated peak broadening from deviatoric strain, shown by Bayes factors below unity. Meanwhile, the in Figure1a where the FWHM of the (1 1 0) tetragonal model is clearly preferred between peak improves from 0.24 to 0.088◦ 2θ in the heat

2 5 and 30 GPa, shown by values much larger nated by a feature at 280 cm−1 which is fit to than unity. Above 30 GPa, the cubic model a single mode and a weaker mode at 211 cm−1 becomes increasingly viable – consistent with (Figure3a and b inset). Due to the close sim- our Reitveld refinements, as well as previous ilarities between the Raman spectra of proton- diffraction-based studies.11,13 We find no static disordered ice-VII and its proton-ordered ana- displacement of the O-sublattice in tetragonal logue, ice-VIII, these modes have previously ice-VIIt, suggesting that the gradual softening been assigned to the analogous translational- of the O–H vibrational mode over its stability vibration modes of ice-VIII, B1g and A1g, re- range5–7 is solely related to the weakening of spectively.15,25 We also observe a very weak the H-bond. mode which is not reported previously near We perform a similar Bayesian analysis com- 160 cm−1 (Supplementary Information). Fea- paring a single-phase equation of state (EOS) tures were also observed in the 500 cm−1 to −1 to a three-phase EOS and find that a three- 800 cm range corresponding to the known Eg 15 phase model is required to reproduce our data. and B2g rotational modes. In doing so, we fit a three-phase P -V Vinet Beginning at approximately 5.0 GPa, the EOS to the data using Markov Chain Monte dominant feature near 280 cm−1 displays an in- Carlo (MCMC). This model includes two tran- creasingly asymmetric profile requiring multiple sition pressures as fitting parameters as well as modes to reproduce the peak profile (Figure3a two parameters, β and γ, to model pressure- and b inset). This asymmetry arises due to the dependent systematic uncertainties (Supple- appearance of new lattice modes (Figure3b in- mentary Information). The uncertainties for set) which is consistent with a lowering of sym- data that were not heat treated are adjusted metry from the cubic P n3m space group to the by the function, σ = σ0(β + γP ) (orange er- tetragonal P 42/nnm space group. This asym- ror bars in Figure2a), while heat treated data metric profile continues with further compres- (where distortions in our Au pressure marker sion and at approximately 21.1 GPa, the peak are relieved) use their nominal error, σ0. The profile becomes increasingly symmetric (Fig- results of our three-phase fit of the P -V EOS ure3b), mirroring the results obtained from the and the transition pressures between the phases Bayesian model comparison of our XRD data is shown in Figure2a. The Bayes factor com- shown in Figure1c. paring the three-phase fit to the single-phase By 38.7 GPa, we observe a new feature at fit is 3.21× 1086 – strongly favoring the three- 618 cm−1 (Figure3b), the intensity of which in- phase model (See Supplementary Information creases with pressure, and is observed to disap- for likelihoods and priors). pear upon decompression with little hysteresis This three-phase model is best highlighted (Figure3c). We interpret this new mode as 10,26 with the linearized form of the Vinet EOS the T2g mode, signifying the onset of ice-X. relating the normalized pressure to Eulerian Furthermore, there is a noticeable stiffening of strain,24 which is sensitive to the starting phase the the frequency of the lattice modes, shown in volume, V0. Using V0 from a single-phase fit Figure3a, following the emergence of this new to ice-VII fails to describe the compressibility peak which agrees with our observation of bond across the entire pressure range as seen by the strengthening at the onset of ice-X in this re- abnormal curvature in Figure2b. Conversely, gion. The emergence of a new mode correlates linear trends appear when modelling with three with our calculated transition pressure to ice-X distinct phases (Figure2c). based on the Bayesian analysis of our equation Additionally, we confirm both the tetrago- of state data (Figure2a), as well as the obser- nal structure near 5 GPa and onset of ice-X vations of Hirsch and Holzapfel 26, in which the near 30 GPa through Raman spectroscopy. We transition from ice-VIII to ice-X is accompa- first observe the lattice modes of ice-VII near nied by the emergence of the T2g mode – the 3.3 GPa after heat treatment of the solidified only Raman active mode of cuprite-like ice-X. sample (Figure3a). This spectrum is domi- Due to the aforementioned similarities between

3 a b Pn3m P4 /nnm c 6×103 D 2 D 5×103 D 4×102 D 3×102

14 14.5 14 14.5 D 2

(BF) 10 D 2 (degrees) θ 10 D 6×101 1 Data log 4×10 1 Fit 3×10 101 D units) Intensity (arb. Residual 0 D 10 Tetragonal 10-1 -10-1 -100 Cubic 19 GPa D -101 23 GPa melt-quenched 10 12 14 16 18 20 22 24 26 28 101 102 D 2θ (degrees) Pressure (GPa) Figure 1: Tetragonal distortion of ice-VII. a Comparison of raw XRD images of ice: (left) highly strained and textured diffraction pattern at 23.2 ± 0.6 GPa without heat treating and (right) full Debye-Sherrer rings from heat treating an annealed powder of ice at 19.1 ± 0.4 GPa. Each red letter D indicates a reflection from the single-crystal diamond anvil. b Rietveld refinement of ice-VIIt (P 42/nnm) at 6.5 ± 0.5 GPa (a = 3.2279 ± 0.0002 Å and c = 3.2372 ± 0.0003 Å, 3 V = 33.719 ± 0.002 Å , wRP = 1.81% and RP = 1.41%). Inset: (left) Rietveld refinement of the (2 0 0) Bragg peak using a cubic cell (P n3m)(a = 3.2275 ± 0.0002 Å, V = 33.621 ± 0.005 Å3, wRP = 2.36% and RP = 2.43% ) and (right) improved fit using a tetragonal cell (P 42/nnm) (2 0 0) and (0 0 2) Bragg peaks. c Log Bayes Factors (BFs) for a tetragonal model vs cubic model for our data on a logarithmic scale. Positive values indicate that the data favor the tetragonal model where negative values indicate preference for the cubic model. Red points indicate pressures that the sample was laser heated. We used a random sampling of points across the pressure range of our experiment to conduct this analysis.

4 a b 37.5 VII 5.0

VIIt X 35.0 Hemley et al. 1987 4.5 Loubeyre et al. 1999 Frank et al. 2004 32.5 Bezacier et al. 2014 )

3 4.0

30.0 Normalised pressure

3.5 27.5 0.00 0.04 0.08 0.12 0.16 0.20

Unit cell volume (Å Unit cell volume Eulerian strain 25.0 c VII 22.5 VII 5 t X

20.0

1 4 ) -5 0 5 3 0.5 P residual (GPa) 0 Normalised pressure 3 -0.5 (Å V residual -1 0 20 40 60 80 0.04 0.08 0.12 0.16 Pressure (GPa) Eulerian strain Figure 2: Equation of state fitting. a Pressure-volume plot of our data and Vinet EOS fit from MCMC for the three phases. The calculated uncertainty in transition pressures are indicated by the blue regions at 5.1 ± 0.5 GPa and 30.9 ± 2.9 GPa, respectively, and the grey lines are results from previous experiments. Curves are colour coded by phase 0 3 (blue: cubic ice-VII (K0 = 18.47 ± 4.00 GPa, K0 = 2.51 ± 1.51, V0 = 42.50 ± 0.88 Å ), black: non- 0 3 cubic ice-VIIt (K0 = 20.76 ± 2.46 GPa, K0 = 4.49 ± 0.35, V0 = 41.11 ± 0.53 Å ), and red: ice-X 0 3 (K0 = 50.52 ± 4.16 GPa, K0 = 4.50 ± 0.15, V0 = 33.82 ± 0.43 Å )). In comparison, fitting all of the 0 3 data to a single phase yields K0 = 12.57 ± 0.50 GPa, K0 = 6.06 ± 0.07, and V0 = 43.05 ± 0.20 Å . Or- ange error bars indicate our systematic uncertainty from deviatoric stresses in non heat treated data. b Linearized Vinet EOS when applying a single phase. c Three-phase linearized Vinet EOS.

5 the Raman spectra of ice-VII and ice-VIII,15,25 temperature-dependent, and that the change in this agreement supports our claim of a transi- bonding in high-pressure H2O ices is primarily tion to ionic-bonded ice-X in this region. The pressure-driven, consistent with the observation frequency of this mode is tracked with pres- of ionic fluids at similar pressures and high tem- sure up to 51.5 GPa, and is in good agreement peratures.19 with measurements made by Goncharov et al. 10 These results have fundamental consequences above 80 GPa as shown in Figure3d. for the global water cycle. Most chemically- bound water on Earth is released from sub- ducted slab at shallow depths in the upper Discussion mantle, transition zone, and the shallow lower mantle.31,32 However, our data show that H O The results of our multi-phase fit show that 2 in the ionic-bonded pressure regime will be room temperature H O takes the form of cu- 2 significantly less compressible than in the H- bic ice-VII from 2.7 ± 0.4 to 5.1 ± 0.5 GPa, fol- bonded regime. This has the effect of stabilising lowed by tetragonal ice-VII to 30.9 ± 2.9 GPa, t chemically-bound water in lower mantle miner- then cubic ice-X thereafter (Figure4). These als,33 inhibiting fluid release at greater depths. transitions are similarly observed in our Raman Thus, residual water that is chemically bound study and marks the first agreement between in the deep lower mantle will remain trapped, XRD and spectroscopy for the transition from making this region of the Earth a reservoir of ice-VII to ionic-bonded ice-X. The low transi- ancient water that is possibly only released by tion pressure into non-cubic ice-VII based on t mantle plumes.34 an observed lowering of symmetry, implies that The observed bond strengthening of ionic cubic ice-VII is stable for only a small win- H O also affects the assessment of the inferred dow of phase space – contrary to existing as- 2 composition and structure of water-rich plan- sumptions,27 making ice-VII the most abun- t ets.37 Planetary constituents in the crust and dant phase of ice in the crust and upper mantle upper mantle contribute most significantly to a of water-rich planets. At 30.9 ± 2.9 GPa, a 2.5- planets mass/radius profile due to their lower fold increase in bulk modulus marks a signifi- density and higher susceptibility to changes in cant strengthening of the O–H–O bond.28 We pressure and temperature. The greater incom- interpret this bond strengthening as the tran- pressibility of ice-X produces larger planets for sition from H-bonded ice-VII to ionic-bonded t a given mass, thereby either reducing the at- ice-X as is supported by the emergence of the mospheric contribution to the volume of many T mode. 2g exoplanets or limiting their water content. For There is an abrupt steepening of the melt example, the amount of water in planets such curve of H O near 44 GPa,18,19 which must re- 2 as Kepler-19b and GJ-3651b must be less than sult from a change in physical properties either previous results allow. While planets such as within the fluid phase above, or the solid phases EPIC-246471491b and K2-18b cannot be mod- below (Figure4). Our observed abrupt tran- elled with condensed material alone and must sition to ice-X near 30 GPa is consistent with have substantial atmospheres. The mass-radius this increase in the slope of the melting tem- relationship in Figure5 shows that the system- perature around 44 GPa, and the occurrence of atic differences between previous EOS measure- superionic ice as an intermediate phase between ments and our own are comparable to uncer- ice-X and melt at around 50 GPa.29,30 Assign- tainties in planet sizes. Thus, ongoing improve- ment of the inflection in the melting line to the ments in exoplanet mass and radius measure- onset of ice-X above 30 GPa results in a steep, ments require similar improvements in the EOS positive Clapeyron slope at the phase bound- of planetary materials – such as those presented ary as shown in Figure4. Our results suggest here – to understand their bulk composition, that the transition from H-bonded to ionic H O 2 structure, and internal dynamics. (solid black lines in Figure4) is not strongly

6 a b c 30.1 d This work 1000 46.0 * Goncharov, 1999 * 43.0 38.7 37.2 800 * 120 33.5 43.4

) X *

-1 29.5 100 46.0 600 21.1 VII t 80 16.1 11. 3

VII 43.0 (GPa) Pressure 400 11. 3

Intensity (arb. units) Intensity (arb.

Raman shift (cm shift Raman Intensity (arb. units) Intensity (arb. 60 7. 4 3.3 38.7 5.0 200 40 3.3 300 400 33.5

0 20 40 200 400 600 800 600 700 600 800 1000 Pressure (GPa) Raman shift (cm-1) Raman shift (cm-1) Raman shift (cm-1)

Figure 3: Raman spectrum of heat treated H2O ices under compression. a Frequency shift of measured Raman modes of H2O ice with pressure. Splitting of the dominant lattice mode near 280 cm−1 due to tetragonal distortion above 5 GPa is highlighted in blue and green. Red diamonds show the emergence of the ice-X T2g mode above 33 GPa. Dashed lines represent transition pressures based on analysis of XRD data. b Progression of Raman features on increasing pressure. The dominant mode near 280 cm−1 exhibits asymmetry above 5 GPa, and tends towards a single mode above 21 GPa. Red asterisks (*) denote the emergence of ice-X T2g Raman mode. (Inset) Dominant Raman feature in ice-VII at 3.3 GPa is ﬁt to a single peak, whereas the same feature in ice-VIIt at 11.3 GPa is a triplet. c (bottom-to-top) Development of ice-X T2g mode on compression above 33 GPa, and its reversible disappearance on decompression. d Frequency shift of ice-X T2g Raman mode with pressure, showing correlation with those reported by Goncharov et al. 10 at higher pressures.

7 Methods

Equation of state data collection. We perform equation of state measurements using a diamond anvil cell (DAC) of custom de- sign, driven by a gas membrane. Diamond 2000 Melt curves VII--X culet sizes typically range from 100–300 µm. Frank, 2004 Loubeyre, 1999 H2O (electrophoresis and spectroscopic grade; Lin, 2004 Schwager, 2008 Schwager, 2008 Meier, 2018 Sigma-Aldrich) is loaded into sample chambers Goncharov, 2009 This work formed by laser micromachining39 in the liquid 1500 Fluid phase, cooled slightly to avoid risk of evapora- tion from the diamond surface, with a ∼ 10 µm piece of polycrystalline Au to serve as a pressure marker. The risk of unwanted chemistry on 1000 40 Temperature (K) Temperature laser heating or the formation of clathrates guides our choice to not include a pressure Superionic transmitting medium in our experiments. In- stead, laser heating was employed to directly 41,42 500 anneal residual stresses in the sample. VIIt X We perform powder X-ray diffraction at the VII 20 40 60 80 HPCAT diffraction beamline (Sector 16-ID-B, Pressure (GPa) Advanced Photon Source, Argonne National Figure 4: High-pressure high-temperature Laboratory, IL, USA) using a monochromatic phase diagram of H2O. Dark blue, green and beam with wavelength λ = 0.406626 Å. Two- red shaded regions denote ice-VII, VIIt and X, dimensional diffraction patterns are integrated respectively, and projected phase boundaries into conventional one-dimensional spectra with separating high-pressure ice phases from our the Dioptas software package,43 and Rietveld work are shown as solid black lines. Ice-X phase refinements performed using GSAS. boundaries connect our measured transition at Heat treating by CO2 laser. To pre- 30.91 ± 2.90 GPa and 300 K to the inflection pare powdered water ice under high pressure, point in the melt curve observed by Schwager we utilize its high absorbance in the mid- and Boehler 18 and Goncharov et al. 19, which infrared. 10.6 µm radiation from a Synrad Evo- have been associated with the transition from lution125 CO2 laser is focused to a minimum molecular to ionic fluid. The same procedure spot size ∼ 30 µm through the diamond anvil has been used to project phase boundaries from and directly onto the compressed sample, us- Loubeyre et al. 11 and Meier et al. 16 In doing an instrument built in-place at the HPCAT ing so, we deduce a steep, positive Clapey- diffraction beamline (Sector 16, Advanced Pho- ron slope defining the transition from hydrogen ton Source, Argonne National Laboratory, IL, 44 bonding to ionic bonding in dense H2O, consis- USA), or on a system housed at UNLV. Vis- tent with a pressure-driven change in bonding ible imaging confirms the formation of a melt nature. Dashed lines show measured melting "bubble" within the single- or few-crystal sam- curves.18,19,35,36 Superionic boundary from Sug- ples, surrounded by dynamically recrystallizing imura et al. 29 is highlighted. powdered ice (Supplementary Video). The focused beam is translated throughout the sample chamber – in this way, both the powder and the Au pressure marker are thoroughly annealed. At higher pressures (> 50 GPa), a melt is not always achieved. In these cases, CO2 laser annealing is employed to anneal a pow-

8 3.00 Kepler-307 b Pure water (Zeng) GJ 1214 b Pure water (this work) 2.75 K2-18 b Pure water (Frank@300K)

50 wt% rock/water (Zeng) EPIC 246471491 b K2-2 b 2.50 50 wt% rock/water (this work) 50 wt% rock/water (Frank@300K) Kepler-10 c Kepler-19 b Pure rock (Zeng) 2.25 GJ 3651 b Pure iron (Zeng) Men c ) (TESS)

R 2.00 (

55 Cnc e s 300 500 1200 2300 u

i WASP-47 e Teq(K) d Kepler-30 b

a 1.75 R GJ 892 b CoRoT-7 b K2-141 b 1.50 Kepler-10 b Kepler-36 b GJ 892 c

Mass (M ) 1.25 1 2 10 TRAPPIST-1 g 10 TRAPPIST-1 b ) 50 wt% rock/water %

TRAPPIST-1 c ( TRAPPIST-1 f 5 Pure water R

1.00 /

TRAPPIST-1 e R 0 TRAPPIST-1TRAPPIST-1 d h 1 2 5 10 Mass (M )

Figure 5: Mass-radius curve of planet models compared to observational data. Results from the three-phase EOS in this work are shown by the solid mass-radius curves. Dotted curves show the result from Zeng et al. 37, which considered the eﬀects of planet interior temperature variations. The dashed curves show a more direct comparison to our results by removing the temperature dependence by substituting the high-pressure phases of ice in their model with a layer of ice-VII at 300 K using the EOS from Frank et al. 35 (Methods). Planets whose radii and masses are measured to better than ∼ 10% and ∼ 20% respectively are plotted and colour-coded by their surface temperatures. Source: NASA Exoplanet Archive, TEPCat38 and thereafter (see Supplementary information). The increased planet radius suggested by the new EOS is larger than the radius uncertainty of many planets. Thus, the contribution of the atmosphere or of water content to the planet structure for planets such as π Mensae-c, Kepler-10c, and EPIC-246471491b may be less than previously inferred. (Inset) The percent diﬀerence in radius between our three- phase EOS and Frank et al. 35.

9 der prepared at lower pressures – observable in they yield a set of at least ten thousand inde- the reduction of Bragg peak widths. XRD mea- pendent samples per model. The chains are ini- surements were taken once the sample cooled to tialized using the parameter values from a max- 300 K. imum likelihood estimate, with each parameter Heterogeneous nucleation of ice-VII in ice-VI scattered by a sufficiently small amount to allow has a tendency of growing large domains with the ensemble sampler to fill the posterior mode. a preferred orientation, creating anisotropic The resulting posterior distributions yield accu- stress and shearing at grain boundaries, and re- rate, correlated errors on the model parameters. sulting in a great degree of texturing and broad- Finally, our procedure quantitatively com- ening of Bragg peaks in XRD.45 The onset of pares models by calculating the Bayes factor, ice-VII is thus determined by heat treating im- the ratio of the probabilities of the data given mediately upon its coexistence with ice-VI – two competing models. The Bayes factor is es- fine control of pressure from the membrane- timated from the ratio of their fully marginal- driven DAC allows incremental compression un- ized likelihoods (FML, i.e. Bayesian evidence) til the onset of phase coexistence is evident from and accounts for different numbers of model pa- XRD. The heat treated sample comprises ice- rameters. The FML is approximated using an VII only, and we begin measurements on the importance sampling algorithm where the sam- phase at the very beginning of its field of ther- pling distribution is informed by a set of pos- modynamic stability. This gives us accurate de- terior samples taken from the aforementioned 23,47 termination of the starting volume, VP, of ice- MCMC. VII at the transition pressure. Planet mass-radius model. Following the 37 To avoid reactions between the heated H2O treatment in Zeng et al. , we consider a fully and the Re gasket which can cause catastrophic differentiated spherical symmetric planet com- gasket failure, we line the inside of our sample posed of a rocky core and an ice shell. For chamber with Pt. Polycrystalline Pt is loaded the rocky core, we continue to use their Pre- inside a prepared Re gasket, compressed flat, liminary Reference Earth Model extrapolated and a new sample chamber drilled to leave only EOS37 in solving the hydrostatic equation. For a thin ring of Pt isolating the heated sample the ice shell, the third-order Vinet three-phase from the Re (Supplementary Information). ice EOS is adopted above the phase transition Raman spectroscopy We perform Raman pressure from ice-VI to ice-VII at 2.1 GPa.1 spectroscopy on a home-built system using the ice-X EOS is extrapolated to the pressure above 514.5 nm line of an Ar-ion laser and a f/9 88 GPa. The Vinet EOS is chosen because it Princeton spectrometer employing OptiGrate extrapolates better to high pressures than the filters for near-Rayleigh measurements. Load- third-order Birch-Murnaghan EOS.48 In planet ings were performed as in equation of state ex- models we considered here, the pressure of the periments. ice can reach up to ∼ 700 GPa at the center Unit cell and EOS model compari- of a 10 Earth mass pure water planet. Shown son using MCMC. Starting values for our in the dotted line in Figure5, Zeng et al. 37 MCMCs are determined by maximizing the used the derived EOS along the melting line for likelihood function. See the Supplementary In- 2.2 ≤ P ≤ 37.4 GPa,35 and an interpolated EOS formation for the likelihood functions. The from quantum molecular dynamics simulations posterior distributions of the model parameters at a series of discrete pressure and temperature using an ensemble sampler MCMC.46 See the points for 37.4 GPa ≤ P ≤ 8.89 TPa.49 To bet- Supplementary Information for the priors used. ter show the affect of the ice measurement on Each run has a number of Markov chains equal planet structure and avoid the impact of un- to five times the number of model parameters certain planet inner temperature profile, we re- (plus one if the result is odd), thins the chains produce the model of Zeng et al. 37, replacing every hundred steps, and ignores the first 20% their EOS of ice above 2.2 GPa with the EOS of the chain as burn-in. The chains evolve until of ice-VII at 300 K that is also given by Frank

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