Research ArticleWATER CHEMISTRY

A new phase diagram of water under negative pressure: The rise of the lowest-density clathrate s-III

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Science Advances  12 Feb 2016:
Vol. 2, no. 2, e1501010
DOI: 10.1126/sciadv.1501010
  • Fig. 1 Relative enthalpy per water molecule (DFT computation) versus negative pressure for clathrate phases of s-I, s-II, s-H, s-III, SGT, s-K, s-T, and ice i, with ice XI as a reference.

    The crossover pressures between ice XI and s-II, s-II and s-III, s-II and s-H, and s-H and SGT are −4009, −5500, −7614, and −8804 bar, respectively.

  • Fig. 2 P-T phase diagram of TIP4P/2005 water model in the region of negative pressures.

    The phase boundaries between liquid water and Ih or s-II ice phases are taken from the study of Conde et al. (21) using the same TIP4P/2005 potential.

  • Fig. 3 Configuration of filled s-III clathrate.

    (A) Structure of an individual 8668412 water cage with a C20H20 molecule encapsulated. (B) Structure of the s-III clathrate with one C20H20 molecule encapsulated in each large cavity (2 × 2 unit cell is shown for a clearer view).

  • Fig. 4 Structure of s-III ice clathrate.

    (A) Two types of building water cages (bottom: 8668412, 48-molecule with O symmetry; top: 8248, 16-molecule with D2 symmetry; only oxygen frameworks are shown). (B and C) Repeated unit cells (1 × 2) (B) and 2 × 2 unit cells (C) (the hydrogen bond network is shown with blue dash line, red for oxygen, and white for hydrogen).

  • Table 1 Number of water molecules per unit cell (Zcell), equilibrium volume of unit cell (Vcell), average distance between oxygen atoms in adjacent water molecules (dO-O), mass density (ρ), and lattice cohesive energy per water molecule (Elatt) for various ice and guest-free clathrate phases.

    The values in parentheses are experimental data.

    PhaseZcellVcell3)dO-O (Å)ρ (g/cm3)Elatt (kJ/mol)
    Ice XI8266 (257*)2.785 (2.735*)0.900 (0.930*)62.84 (58.86)
    Ice i82802.7850.85561.31
    s-I4616922.7650.81361.38
    s-K8029622.7650.80860.76
    s-II1365059 (5022)2.765 (2.751)0.804 (0.81)61.37
    s-T124532.7950.79260.23
    s-H3413252.7850.76860.79
    SGT6426502.7650.72259.27
    s-III4824232.7650.59355.77

    *Results of the study by Leadbetter et al. (12) obtained from neutron diffraction at 5 K.

    †Results of the study by Whalley (34) with zero-point energy contributions removed.

    ‡Results of the study by Falenty et al. (11) obtained from neutron diffraction at 5 K.

    Supplementary Materials

    • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/2/e1501010/DC1

      Table S1. Fractional coordinates of the structure III (s-III) clathrate with cubic lattice (space group: PFormula3n, lattice constant: 13.431 Å) from vdW-DF2 DFT calculation.

      Table S2. Average lengths of O–H covalent bond (dO–H) and hydrogen bond (dO…H) for different phases (ice XI, ice i, s-I, s-II, s-H, SGT, s-K, s-T, and s-III clathrates) based on vdW-DF2 DFT computation.

      Table S3. Mass density (ρ) and lattice cohesive energy per water molecule (Elatt) for different phases (ice XI, ice i, s-I, s-II, s-H, SGT, s-K, s-T, and s-III clathrates) based on vdW-DF2 (DFT) optimization, and another independent optimization using the TIP4P/2005 water model (at zero temperature and zero pressure).

      Fig. S1. Phonon dispersion for guest-free s-III ice clathrate based on vdW-DF2 DFT computation.

      Fig. S2. Crystal structures (2 × 2 unit cells) of ice i, ice XI, and clathrates of s-T, s-I, s-II, s-K, SGT, and s-H phases (blue dash lines for hydrogen bonds, red for oxygen, and white for hydrogen).

      Fig. S3. Lattice cohesive energies (Elatt) for structures ice XI, ice i, s-K, s-I, s-II, s-H, s-III, SGT, and s-T clathrates as a function of volume per water molecule.

      Fig. S4. Computed Helmholtz energy (Asol) of the s-III clathrate based on the TIP4P/2005 potential, using the Einstein method, as a function of real-space cutoff distance rcutoff.

    • Supplementary Materials

      This PDF file includes:

      • Table S1. Fractional coordinates of the structure III (s-III) clathrate with cubic lattice (space group: P 4 3n, lattice constant: 13.431 Å) from vdW-DF2 DFT calculation.
      • Table S2. Average lengths of O–H covalent bond (dO–H) and hydrogen bond (dO…H) for different phases (ice XI, ice i, s-I, s-II, s-H, SGT, s-K, s-T, and s-III clathrates) based on vdW-DF2 DFT computation.
      • Table S3. Mass density (ρ) and lattice cohesive energy per water molecule (Elatt) for different phases (ice XI, ice i, s-I, s-II, s-H, SGT, s-K, s-T, and s-III clathrates) based on vdW-DF2 (DFT) optimization, and another independent optimization using the TIP4P/2005 water model (at zero temperature and zero pressure).
      • Fig. S1. Phonon dispersion for guest-free s-III ice clathrate based on vdW-DF2 DFT computation.
      • Fig. S2. Crystal structures (2 × 2 unit cells) of ice i, ice XI, and clathrates of s-T, s-I, s-II, s-K, SGT, and s-H phases (blue dash lines for hydrogen bonds, red for oxygen, and white for hydrogen).
      • Fig. S3. Lattice cohesive energies (Elatt) for structures ice XI, ice i, s-K, s-I, s-II, s- H, s-III, SGT, and s-T clathrates as a function of volume per water molecule.
      • Fig. S4. Computed Helmholtz energy (Asol) of the s-III clathrate based on the TIP4P/2005 potential, using the Einstein method, as a function of real-space cutoff distance rcutoff.

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