Bulk modulus of ${\mathrm{H}}_2\mathrm{O}$ across the ice VII–ice X transition measured by time-resolved x-ray diffraction in dynamic diamond anvil cell experiments

We have studied the ${\mathrm{H}}_2\mathrm{O}$ ice VII–ice X phase transition at room temperature by performing three quasicontinuous synchrotron time-resolved x-ray-diffraction experiments in a dynamic diamond anvil cell, reaching pressures of 180 GPa. The dense pressure coverage of our volume data allows us to directly derive the bulk modulus for ${\mathrm{H}}_2\mathrm{O}$ over the entire pressure range. Our data document three major changes in compression behavior in the ranges of 35–40, 50–55, and 90–110 GPa, likely corresponding to the formation of pretransition dynamically disordered ice VII and ice X, and static ice X, respectively. Our results confirm that ice X has a very high bulk modulus.

Figure 1

Contour plot showing the time evolution of diffraction patterns (peaks) collected for dDAC-1 in time-2θ space. In our experiments, the (110) diffraction line of ice VII is the most intense and can be traced over the full $P$ range of the individual experiments.

Figure 2

Exemplary integrated diffraction pattern for the dDAC-2 experiment at 26 GPa. Blue shows the original pattern after integration of the detector image with dioptas; orange the pattern after application of an IIR filter with zero phase shift.

Figure 3

Diffraction patterns collected from dDAC-3 after application of the IRR filter (blue) at (a) 24 GPa and (b) 45 GPa with assigned indices and the calculated/theoretical peak positions (CPPs) shown as vertical lines. The solid curves represent the Gaussian model peaks.

Figure 4

(a) Volume-pressure points for ${\mathrm{H}}_2\mathrm{O}$ ice as derived from the reduced datasets of the dDAC-1 (blue solid circles), dDAC-2 (black solid circles), and dDAC-3 experiments (gray open circles). Error bands using the resolution limit ($0.{05}^{\circ }$ in 2θ) of the fitting routine are shown for dDAC-1 and dDAC-2 (shaded regions). (b) Difference between the data points and the spline with smoothing factors of 9.0 (dDAC-1), 1.0 (dDAC-2), and 18.0 (dDAC-3) is <1% over the complete compression range for all experiments. (c) Previous XRD measurements in static DAC experiments by Wolanin et al. [19] (powder, squares), Sugimura et al. [18] (powder, diamonds), and Loubeyre et al. [27] (three single-crystal datasets, three differently pointing triangles) are plotted in comparison to our data. The dashed (maroon) and dotted (blue) curves represent the equations of state by French and Redmer [44] and Klotz et al. [45], respectively, the latter extrapolated significantly beyond the $P$ range of the experiments (14 GPa).

Figure 5

Bulk modulus of ${\mathrm{H}}_2\mathrm{O}$ ice as a function of pressure calculated from the smoothed spline interpolation of the $V$($P$) data from dDAC-2 in comparison to previous studies (for results from dDAC-1 and dDAC-3, see Fig. S2 in the Supplemental Material [41]). Right-pointing triangles, solid squares, left-pointing triangles, and solid circles represent Brillouin inelastic scattering (BS) data [46, 47, 48, 49]. The solid and dotted thin gray lines show equations of state for ice VII and ice X, respectively [50]. Diamonds represent computational predictions of the bulk modulus of ice X [51]. The dashed maroon line refers to computational results [44]. Background colors guide the eyes to the approximate $P$ ranges for the stability of ice VII, ice VII′, ice X′, and ice X based on the $P$ ranges where a quasilinear $P$ dependence of $K_T$ is observed in our work.