Direct evidence of the proton-dynamics crossover in ice VII from high-pressure dielectric measurements beyond 10 GPa

We have conducted dielectric measurements of ice VII at pressures up to 12.2 GPa, and verified a dominant-dynamics change from a molecular rotation to a proton translation at approximately 10 GPa, using a newly developed high-pressure cell. Based on relaxation times of the two motions, which have a crossover point between 9 and 10 GPa, we show that the change in the disordered states in ice VII can be characterized by the time scale of the motions. Our results provide a suitable explanation of the long-standing problem of the anomalous behavior of ice VII at around 10 GPa.

Figure 1

(a) Schematic drawings of the proton dynamics crossover from the molecular rotation to the proton translation on the phase diagram of ice. The anomalous behavior of ice VII has been reported at around 10–15 GPa (shaded area) in many previous studies. The black and gray arrows refer to the two experimental paths in the dielectric experiments under high pressure. (b) Schematic drawings of the high-pressure cell overall (top) and around the sample space (bottom) of the cell assembly for the dielectric measurements based on the Bridgman type opposed anvils. Load is vertically applied using a Paris-Edinburgh press (type-V4).

Figure 2

(a) Complex-plane plots of the dielectric constant and loss of ice VII under high pressure obtained in Run No. 1. Numbers on the plots denote the frequenecies in kHz. (b) Frequency dispersion of the dielectric properties of ice VII obtained at 4.7 and 11.6 GPa. Red and blue dots represent raw data and solid curves are fitted ones based on Debye multidispersion model.

Figure 3

(a) Pressure dependence of frequency change of the dielectric constant of ice VII up to 12.2 GPa obtained in Run No. 2. In each dataset, black dots represent raw data, and light blue and blue colored curves are fitted curves for the lower and higher-frequency relaxations to reproduce the measured dielectric constant data by a sum of the light blue and blue curves (red dotted line). The multidispersion type Debye relaxation model was used to analyze the dielectric properties. (b) Pressure dependence of relaxation times corresponding to the molecular rotation and proton translation. Since the measured frequency is within 20 Hz–2 MHz in Run No. 1, the relaxation time of the space charge polarization (lower-frequency relaxation) cannot be obtained in the lower pressure. (c) Pressure dependence of dispersion parameters corresponding to the molecular rotation and proton translation. The black and red color correspond to Runs No. 1 and No. 2, respectively.

Figure 4

(a) Pressure dependence of the real and imaginary parts of the impedance of ice VII up to 12.2 GPa, represented by a Nyquist plot. The thick colored arrows represent the DC impedance of ice VII, and as drawn in the plot at 7.1 GPa, the real part of the impedance $\left(Z^{\prime }\right)$ decreases with increasing frequency. (b) Pressure change of the dielectric relaxation of ice VII (left), static dielectric constant (${\varepsilon }_{s,\mathrm{ori}}$, upper right) and correlation parameter ($g$, lower right) derived from the Bjerrum defect diffusion. In the figure for correlation parameter, its pressure change is described as density change of ice VII. In the left figure, the vertical position of the colored ticks shows frequencies corresponding to the relaxation times of the orientational polarization at respective pressures. (c) Schematic drawings of the molecular rotation and proton translation focusing on the change of the electric dipole moments of the water molecules toward the applied electric field ($E$). Positively charged point defects, D and + defect, are also shown for the schematic explanation of the relation between the rotational/translational motions and the $\mathrm{DL}/\pm$ defects.