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Condensed-matter science

Ferroelectric ice

Water molecules are dipolar, and while tumbling in the liquid state can be partly aligned by an electric field (Fig. 1). In ice, however, although the molecules are essentially static, there is no overall alignment (Fig. 2). A question that has long fascinated researchers is whether there is a form of normal ice in which the molecular dipoles have a net orientation towards one direction. Recent papers1,3 have revived an old debate about whether such ‘ferroelectric’ ice exists, and if so, what implications its existence would have for our understanding of condensed matter. The groups concerned report definite experimental evidence that at least partial ferroelectric alignment can be induced in normal ice, either by interaction with a substrate1,2, or by doping with impurities3.

Figure 1: Polarized water.
figure1

In a simple experiment, a stream of tap water is deviated by the static electricity of a plastic pen (which has previously been charged by rubbing on wool) because the water molecules are partially aligned in the electric field.

Figure 2: The structure of normal hexagonal ice Ih,showing the arrangement of oxygen atoms and one of the many possible random arrangements of hydrogen atoms (from ref. 9).
figure2

The cubic modification of ice, Ic, has the same tetrahedral coordination of oxygen atoms, but the six-membered oxygen rings shown in the figure are repeated in a three-layer, rather than a two-layer, stacking sequence. Other high pressure phases of ice have different oxygen lattices and are called II⃛X.Three groups1,2,3 have demonstrated the existence of ferroelectric ice in which some of the dipolar water molecules are thought to be aligned.

The debate dates back to the 1920s and the development of X-ray diffraction. Using this technique, it was established that the oxygen atoms of normal hexagonal ice (ice Ih)form a regular crystal structure in which each oxygen atom is coordinated with respect to four others in a tetrahedral arrangement (Fig. 2). X-rays are insensitive to hydrogen, but in 1933 Bernal and Fowler4 argued that each hydrogen must lie along the oxygen-oxygenline of contact, but displaced from the mid-point so as to form one shorter covalent bond and one longer hydrogen bond. To ensure that the structure consists entirely of water molecules, two hydrogens must be positioned closer to, and two others further away from, each oxygen. These ‘ice rules’ allow for many structures, differing in their relative orientations of the water molecules. In most ice structures the orientation of water molecules follows no regular pattern (Fig. 2), but Bernal and Fowler proposed that ice Ihhas the simplest ordered arrangement — a form of ferroelectric ice in which the molecules are, on average, aligned.

They were undoubtedly guided in their choice of structure by the third law of thermodynamics, which states that the entropy of a perfect crystal is zero at a temperature of absolute zero (0 K). Entropy is proportional to the logarithm of the number of arrangements or motions available to the system of molecules, and so zero entropy means one arrangement (log1 = 0). It was suspected at the time (and still is) that the third law arose from a much deeper truth: that for any substance one definite crystal structure is the most stable, and is adopted at 0 K provided that equilibrium is attained. So to postulate a unique structure for ice seemed very reasonable.

It did not, however, prove to be correct. In the same year that Bernal and Fowler's paper appeared, Giauque and Ashley5 definitively demonstrated that ice still had entropy at 0 K. They did this by carefully comparing the ‘spectroscopic’ entropy for gaseous water (calculated from spectroscopic data using a theoretical expression), with the ‘third law’ entropy (estimated from calorimetric measurements by summing the entropy from 0 K upwards, and assuming the third law). The two estimates should be identical, but the third law entropy was 0.82 ± 0.05 cal K−1 mol−1 (about 2% of the total) too small. Giauque and Ashley suggested that rotation of the water molecules might account for the discrepancy, but Pauling “consistently objected to” this explanation6. In a landmark paper in 1935 (ref. 7) he argued that ice could adopt any one of the huge number of molecular arrangements compatible with the Bernal-Fowler ice rules. He calculated this number and found it to be (1.5)N, where N is the number of molecules — which, for a 1 g crystal of ice, is a number with 6 × 1021 digits! This translates to a residual entropy of 0.81 cal K−1 mol−1, exactly the value found experimentally (within error). Pauling's explanation was immediately accepted6; but it was not until the advent of neutron diffraction, which can easily locate hydrogen in the form of its isotope deuterium, that the structure was directly confirmed8,9.

It is now accepted that below about 160 K the water molecules of hexagonal ice settle into a random arrangement (Fig. 2), which is always preferred to an aligned one because there are so many more random structures to choose from. But in reality would an aligned structure be more stable? It may be that once ice has adopted a random form at high temperature, relaxation into the preferred state at low temperature is immeasurably slow. An early report10 found a maximum in the electrical response of slightly impure ice at 100 K, suggestive of a transition to a ferroelectric state, but this was later ascribed to slow relaxational effects11.

The latest work1,2 provides experimental evidence of some net ferroelectric alignment in films of ice grown on ultra-clean platinum surfaces. Ice films deposited at temperatures below about 120 K are amorphous, whereas those deposited at higher temperatures are crystalline, with either the hexagonal structure of the bulk, or a closely related cubic modification to which the Bernal-Fowler ice rules and Pauling's arguments also apply (see caption to Fig. 2). Iedema et al.1 use potential difference measurements to demonstrate a net polarization in amorphous or cubic ice films of 103−105 monolayers, deposited between 40 and 150 K. They argue that interaction with the substrate during growth aligns a surface layer of molecules, which then influence the orientation of water molecules in the rest of the sample. Only a small proportion (0.2%) of the molecules are actually aligned, but this is sufficient to give the sample a sizeable polarization, and may in fact be relevant to the agglomeration of ice particles in interstellar space1.

Su et al.2 show that surface interactions can indeed make ice ferroelectric: ultra-thin hexagonal ice films (1-10 monolayers thick) have a net polarization that decays with distance from the substrate. They use ‘sum frequency generation’ to measure polarization in the sample — an ingenious method of overlapping a tunable-frequency infrared laser beam with a fixed-frequency visible laser beam. A vibrational spectrum at the summed frequency results only if the sample medium lacks inversion symmetry, a characteristic of aligned (ferroelectric) but not of random ice. The third approach to ferroelectric ice3 is to dope normal hexagonal ice with a catalytic quantity of hydroxide ions, a process that enhances the alignment (perhaps by enabling relaxation), without significantly disrupting the oxygen structure. Below 72 K this substance, known as ice XI, is suspected to be ferroelectric. Jackson et al.3 show that the neutron diffraction of ice XI is consistent with a ferroelectric arrangement, although the exact structure and degree of alignment are not unambiguously determined.

The experimental realization of ferroelectric ice would allow thermodynamic measurements to establish whether nature really does prefer order at low temperature. However, as Iedema et al.1 write “Over the years there have been many UFI citings (underidentified ferroelectric ices) in the literature”, and it is not yet clear whether one of these elusive objects — a fully hydrogen-ordered ice — has finally fallen to earth.

References

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    Iedema, M. J. et al. J. Phys. Chem. B 102, 9203–9214 (1998).

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    Su, X., Lianos, L., Ron Shen, Y. & Somorjai, G. A. Phys. Rev. Lett. 80, 1533–1536 (1998).

  3. 3

    Jackson, S. M., Nield, V. M., Whitworth, R. W., Oguro, M. & Wilson, C. C. J. Phys. Chem. B 101, 6142–6145 (1997).

  4. 4

    Bernal, J. D. & Fowler, R. H. J. Chem. Phys. 1, 515–548 (1933).

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    Giauque, W. F. & Ashley, J. W. Phys. Rev. 43, 81–82 (1933).

  6. 6

    Giauque, W. F. & Stout, J. W. J. Am. Chem. Soc. 58, 1144–1150 (1936).

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    Pauling, L. J. Am. Chem. Soc. 57, 2680–2684 (1935).

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    Wollan, E. O., Davidson, W. L. & Shull, C. G. Phys. Rev. 75, 1348–1352 (1949).

  9. 9

    Li, J. C. et al. Phil. Mag. B 69, 1173–1181 (1994).

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    Dengel, O., Eckener, V., Plitz, H. & Riehl, N. Phys. Lett. 9, 291–292 (1964).

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    Johari, G. P. & Jones, S. J. J. Chem. Phys. 62, 4213–4223 (1975).

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