Intermediate-range order in water ices: Nonresonant inelastic x-ray scattering measurements and real-space full multiple scattering calculations

We report measurements of the nonresonant inelastic x-ray scattering (NRIXS) from the $\text{O}1s$ orbitals in ice Ih, and also report calculations of the corresponding spectra for ice Ih and several other phases of water ice. We find that the intermediate-energy fine structure may be calculated well using an ab initio real-space full multiple scattering approach and that it provides a strong fingerprint of the intermediate-range order for some ice phases. Both experiment and theory find that the intermediate-range fine structure, unlike the near-edge structure, is independent of momentum transfer $\left(q\right)$ to very high $q$. These results have important consequences for future NRIXS measurements of high-pressure phases of ice.

Figure 1

Top: the XRS near-edge structure of ice Ih (present study); middle: present data, after partial removal of instrumental broadening (see text for details); bottom: XAS results from Zubavichus et al. (Ref. 17).

Figure 2

Calculated XRS spectra for ice Ih at $q=8{\text{Å}}^{-1}$ as a function of the muffin-tin radius at the hydrogen sites. For subsequent calculations, we chose a muffin-tin radius of $0.47\text{Å}$ due to its agreement in the placement of features D and E and the overall shape of the spectrum in the first 10 eV.

Figure 3

The upper sequence of displaced curves show the dependence on the cluster size for RSFMS calculations of the $\text{O}K$-edge XRS spectrum for ice Ih at $q=8{\text{Å}}^{-1}$. The curves are labeled by the cluster radius and the number of molecules that were used in the calculation. By means of reference, the bottommost two curves are the measured XRS spectrum and the same data after partial removal of instrumental broadening.

Figure 4

The sequence of curves shows the converged, large-cluster RSFMS calculations for several phases of water ice. See the text for discussion.