Reassigning Hydrogen-Bond Centering in Dense Ice

Hydrogen bonds in ${\mathrm{H}}_2\mathrm{O}$ ice change dramatically upon compression. Thereby a hydrogen-bonded molecular crystal, ice VII, is transformed to an atomic crystal, ice X. Car-Parrinello simulations reproduce the features of the x-ray diffraction spectra up to about 170 GPa but allow for analysis in real space. Starting from molecular ice VII with static orientational disorder, dynamical translational disordering occurs first via creation of ionic defects, which results in a systematic violation of the ice rules. As a second step, the transformation to an atomic solid and thus hydrogen-bond centering occurs around 110 GPa at 300 K and no novel phase is found up to at least 170 GPa.

Figure 1

Properties of ice at 300 K as a function of pressure. (a) Intensity ratio $R=I_{111}/I_{222}$ (filled circles) and representative proton densities $P(\xi )$ (insets) averaged over all ${\mathrm{O}}_{\mathrm{a}}\mathrm{H}{\mathrm{O}}_{\mathrm{b}}$ atom triples where $\xi =(d_{{\mathrm{O}}_{\mathrm{a}}\mathrm{H}}-d_{{\mathrm{O}}_{\mathrm{b}}\mathrm{H}})/d_{{\mathrm{O}}_{\mathrm{a}}{\mathrm{O}}_{\mathrm{b}}}$ and $\int d\xi P(\xi )=1$ for all insets. For each ${\mathrm{O}}_{\mathrm{a}}\mathrm{H}{\mathrm{O}}_{\mathrm{b}}$ triple the corresponding sign of $\xi$ is defined based on both the fictitious antiferroelectric sublattices that would correspond to ice VIII at low temperatures (dotted lines) and on the actual random static orientational disorder configuration of paraelectric ice VII that was used to initialize the particular simulation (solid lines). (b) Scaled Edwards-Anderson order parameter ${\tilde{q}}_{\mathrm{E}\mathrm{A}}=q_{\mathrm{E}\mathrm{A}}/10$ (filled squares) and relative number of defects $C=⟨n_{\mathrm{b}\mathrm{r}\mathrm{o}\mathrm{k}\mathrm{e}\mathrm{n}}⟩/n_{\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{s}}$ (open squares) obtained as the number of broken water molecules (based on a geometric criterion) normalized by the number of available lattice sites; note that $C$ ultimately becomes ill-defined in centered ice (small open squares). (c) Oxygen-hydrogen $d_{\mathrm{O}\mathrm{H}}$ (filled up-triangles) and half the oxygen-oxygen $d_{\mathrm{O}\mathrm{O}}/2$ (open down-triangles) distances as obtained from the first moment of the corresponding distribution functions. Experimental values [4] of $d_{\mathrm{O}\mathrm{H}}$ (open circles) and $d_{\mathrm{O}\mathrm{O}}/2$ (filled circles) within the $⟨111⟩$ site-disordered model of ${\mathrm{D}}_2\mathrm{O}$ at 288 K are also shown. (d) Mean-square displacements ${\sigma }_{\alpha }^2=(1/N_{\alpha })\sum _{I_{\alpha }=1}^{N_{\alpha }}⟨({\mathbf{R}}_{I_{\alpha }}-⟨{\mathbf{R}}_{I_{\alpha }}⟩{)}^2⟩$ for $\alpha =\mathrm{H}$ (filled diamonds) and $\alpha =\mathrm{O}$ (open diamonds) atoms with respect to their respective average positions $⟨{\mathbf{R}}_{I_{\alpha }}⟩$. (e) Reanalyzed experimental intensity ratio [6] obtained as the average $R=(I_{111}/I_{222}+I_{11\overline{1}}/I_{22\overline{2}})/2$ (circles) of the indicated $hkl$ and $hk\overline{l}$ reflections for fixed $2\theta =11.67°$; $I_{111}/I_{222}$ and $I_{11\overline{1}}/I_{22\overline{2}}$ are shown by the error bar symbol. In (a)–(d) the vertical dashed lines are at $p\approx 55\mathrm{G}\mathrm{P}\mathrm{a}$, where $C$ [panel (b)] increases strongly and the vertical dotted lines are at $p\approx 100\mathrm{G}\mathrm{P}\mathrm{a}$, where $d_{\mathrm{O}\mathrm{H}}$ and $d_{\mathrm{O}\mathrm{O}}/2$ [panel (c)] become identical. At about 5 and 20 GPa two statistically independent data points are depicted in (a)–(d) which correspond to two static disorder configurations of molecular ice VII.