Isotopic Raman broadening due to Anderson localization of harmonic phonons in partially deuterated ice VII and VIII

Raman spectra from molecular systems are typically regarded as comprising a set of sharp peaks. These arise from both single-molecule modes and extended $\mathrm{\Gamma }$ point phonons being, in theory, harmonic oscillators. Broadening is typically assigned to thermal, linewidth, and anharmonic effects. Here we measure significant broadening in the Raman signal from partially deuterated water ices VII and VIII, which is absent in the pure systems. This isotopic broadening is much greater than any anharmonic effects and is reproduced by lattice dynamics calculations assuming only harmonic bonding. Instead, it arises from mass disorder induced phonon localization. This localization leads to many overlapping modes with a range of frequencies dependant on local isotopic environment and Raman activity due to lack of distinct molecular or crystalline symmetry.

Figure 1

Raman spectra of ice VII at 10 GPa. (a), (b), (c): the lattice modes, background subtracted O-D stretching region, and O-H stretching region experimentally observed. (d), (e), (f): DFT simulation of the same regions. Intensity scale varies between frames. The dotted lines under the simulated spectra of the isotopically mixed system give the projections of the modes onto each molecular species.

Figure 2

Experimental ice VII Raman mode frequencies vs. pressure for various isotopic compositions: (a) the O-H stretching region, (b) the O-D stretching region, (c) the lattice modes. Both the maximum intensity and FWHM of the stretching features for 50% deuterated ice are shown, revealing substantial broadening in the O-H stretch region with increased pressure.

Figure 3

(a) DFT zone-center phonon DOS's for the ice VIII structure at 10 GPa for ${\mathrm{H}}_2\mathrm{O}, {\mathrm{D}}_2\mathrm{O}$, and the 50:50 mixture (averaged over 16 isotope distributions). (b) Example 16-molecule supercell for mixture phonon calculations; O/H/D atoms are red/white/blue spheres. (c) Simulated Raman and IR intensities for the same structures. (d) Inverse participation ratio (IPR) distribution for the phonons of the three compounds.

Figure 4

Analysis of DFT phonon data of the ice VIII 50:50 isotope mixture at 10 GPa, colors refer to molecule type within the partially deuterated ice. (a), (c) Zone-centered phonon DOS and simulated Raman projected onto ${\mathrm{H}}_2\mathrm{O}/{\mathrm{D}}_2\mathrm{O}$/HOD molecules. (b) Inverse participation ratio (IPR) $L_{\nu }$ of O-D and O-H vibrons against frequency, shaded by Raman activity (using all data from 16 configurations). (d) Distribution of $L_{\nu }$, with modes assigned to dominant molecule type.