Article pubs.acs.org/JPCC
Ice XI: Not That Ferroelectric P. Parkkinen, S. Riikonen, and L. Halonen* Laboratory of Physical Chemistry, Department of Chemistry, University of Helsinki, Post Office Box 55, FI-00014 Helsinki, Finland ABSTRACT: Ice XI, the proton-ordered phase of ordinary ice, features aligned water dipoles. It can be synthesized under laboratory conditions at T ∼ 72 K. Recently, speculations on ice XI in the solar system and the role of its possibly large electric fields in planetary formation have appeared in the literature. We have studied the energetics of ice Ih proton configurations using finite ice slabs and periodic supercell density functional theory (DFT) calculations, while properly taking into account the depolarization field associated with increasing proton order. The depolarization field, not taken into account in previous DFT calculations, dominates the energetics, making the existence of ferroelectric ice unlikely. A single order parameter is shown to describe both the surface danglingbond configuration and the overall polarization state of the slab. According to our calculations, doping ice with alkali hydroxides or placing it in contact with a metal surface stabilizes a net alignment of water molecule dipoles. However, this occurs only at the nonpolarized limit, and the composite systems have no net polarization. Thus, ice XI is antiferroelectric in nature, although it could contain small oppositely polarized domains.
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INTRODUCTION The most prevailing form of ice under atmospheric conditions is hexagonal ice (ice Ih). Although its oxygen atoms are placed in a strictly crystalline and periodic manner, considerable freedom remains in placing the hydrogen atoms while obeying the “ice rules”.1 The number of such proton configurations in an N-molecule ice Ih crystal is approximately (3/2)N.2,3 The large number of configurations and the high energy barriers between configurations lead to a significant residual entropy.2,4 An interesting special case arises when a few energetically favorable proton configurations dominate the available proton configurational ensemble. Here, the protons may arrange themselves in periodic, repeatable units (unit cells), and the system becomes proton-ordered. Ice Ih that exhibits proton ordering is referred to as “ice XI” (ice 11).5 There exists a longstanding and fundamental question whether ice XI can maintain its polarization from the alignment of water dipoles. Other ice phases feature disorder to order transitions, for example, the transitions from ice VII to ice VIII and from ice III to ice IX.6−8 However, the proton-ordered forms are believed to be antiferroelectric. Preparing ice XI requires cooling to temperatures where only the most stable proton configuration survives. However, the low temperatures inhibit the kinetics of finding the lowestenergy configuration, and therefore the system is trapped into ice Ih. Either extremely long time scales or special techniques (typically, doping with alkali hydroxides) are needed to overcome the sluggish kinetics and to synthesize ice XI. Calorimetric measurements for ice Ih doped with alkali metal hydroxides9−11 show a phase transition at T ≈ 72 K, where up to ∼65% of the residual entropy vanishes.12 Neutron diffraction measurements for the same system12−18 provide more evidence on the existence of ice XI, as additional Bragg peaks are observed.12 This observation implies proton ordering. Splitting of certain diffraction peaks suggests two coexisting phases, © 2014 American Chemical Society
namely, proton-ordered regions embedded in ordinary ice Ih.13,14,19 Leadbetter et al.12 were the first to discuss how the most simple, maximally ordered and orthorhombic eightmolecule ice unit cell has CmC21 symmetry, proposing it as a candidate for ice XI. Shortly after, more proton configurations for the eight-molecule orthorhombic unit cell were introduced.20 However, the consecutive neutron-diffraction studies have been interpreted in terms of the CmC21 symmetric structure,14−19 where the dipoles are maximally aligned. Stimulated depolarization experiments on alkali hydroxidedoped ices21,24 suggest ferroelectricity. However, the measured depolarization currents can also be attributed to hysteresis:23,24 that is, the applied electric field drives the sample into a highenergy state, and while being heated, it slowly returns to the nonpolarized ground state. Such behavior can be misinterpreted as a phase transition.23,24 Additionally, the measured polarization,22 as approximated from the depolarization currents, indicates only small ( 0.25. However, the antiferroelectric case f = 0 still remains the most stable system. As suggested by Figure 4, the system is stabilized by increasing the number of bilayers. However, fully polarized ferroelectric ice becomes unstable, as the depolarization field starts to break up water molecules in the system, spontaneously depolarizing the slab. Dangers of using model systems with large f values are evident, as exotic behavior and reactions, similar to the spontaneous splitting of water molecules observed here, can be expected on top of a highly polarized ice slab due to anomalously strong electric fields. In general, spontaneous and thermodynamically stable ferroelectricity in water ice seems unlikely according to our slab calculations and analysis. The instability of ferroelectric slabs, based on the completely ferroelectric CmC21 structure, has earlier been discussed in refs 35, 40, 48, and 49. NaOH-Doped Ice Films. Crystalline ice systems may switch between proton configurations in two ways: (a) by explicitly flipping water molecules with the aid of Bjerrum defects50,78 or (b) by Grothuss proton migration through the ice lattice.78 While mechanism a suffers from high energetic barriers,78 mechanism b has a vanishing barrier75,79 and can be evoked by doping ice with protonic defects (hydronium or hydroxide).78 The first observation of proton-ordered ice5 and consecutive laboratory studies of ice XI have been performed with alkali hydroxide-doped ice, while the synthesis of ice XI is then facilitated by mechanism b, making it easier for the system to find the lowest-energy proton configuration (ice XI). Apart from being a mere catalyst, NaOH doping could be an integral part of the ice XI structure itself, lowering the final free energy of proton-ordered ice. We ran geometry optimizations, where NaOH is placed in contact with our model ice films, having various dangling-bond configurations and f values. In all 10 preliminary test cases considered, NaOH ionized spontaneously on the ice surface, followed by a Grothuss migration of OH− away from Na+. In
The last case is characterized by small, but nonzero, values of the order parameter f. Structural stabilization mechanisms and energetics in these cases due to sodium hydroxide doping and deposition on Pt surface are studied in detail. Effective dipole fields arising in the systems are discussed. Ice films with 4 × 2 × 2 and 4 × 2 × 3 unit cells, having various polarization states and corresponding to different values of f, were considered. Each f value is associated with a certain proton configuration fullfilling the ice rules. The configurations were generated with the Ice Package program suite.68,69 For each system, full geometry optimization was performed. Ice Films in Vacuum. The studied ice film systems, having 4 × 2 unit cells and featuring various f values, are depicted in Figure 3. Energies of the systems are plotted in Figure 4. It is clear that slabs with increasing ferroelectricity are unstable, while the ∝ f 2 behavior suggested by eq 7 is observed in Figure 4. Setting f = 0 gives still a large degree of configurational freedom for the system, as suggested by Figure 1a,b. Additional energetic stabilization can be achieved by maintaining f = 0 and distributing the surface dangling bonds in rows, in the so-called “Fletcher striped phase”.35,45,49,70 It is also possible, within the ice rules, to distribute Fletcher striped phases on both surfaces, form domains inside the bulk, and simultaneously maintain f = 0. Large depolarization fields at large f values (eq 1) result in aggressive structural changes during the geometry optimizations. For example, in the f = 0.5 structure (Figure 3), two toplayer surface molecules dissociate spontaneously to form OH−/ H3O+ pairs. Such spontaneous bond-breaking and ionization due to a large depolarization field has earlier been reported for small water clusters.71,72 After the dissociation in the film, the charged OH− and H3O+ species migrate, via the Grothuss migration mechanism,73 to opposite sides of the slab. This is an expected behavior for free charges in an electric field: the charges migrate to opposite sides of the slabs in order to compensate for the depolarization field. The OH− and H3O+ species also have a natural preference for 3-fold-coordinated ice surface sites, OH− being a 3-fold hydrogen-bond acceptor (AAA)74 and H3O+ a 3-fold donor (DDD).75−77 In particular, OH− stays at the top face while H3O+ migrates to the bottom face, corresponding to Figures 3 and 1. The Grothuss migration 26269
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Figure 5. Top (upper row) and bottom (lower row) view of ice slab systems and their order parameter f values (eq 1). Red, white, and purple circles denote oxygen, hydrogen, and sodium atoms, respectively. In addition, oxygen atoms of OH− species are highlighted in green.
Figure 6. Relative total energies of NaOH-containing ice films with four and six bilayers of water molecules. For more details, see the caption of Figure 4. In panel b, electrostatic potential drop is indicated in green for a few systems (see also Figure 2). For f values indicated with an asterisk (*), a single water molecule ionizes spontaneously to form an OH−/H3O+ pair. For values marked with (+), two ion pairs are formed.
at the order parameter value f = 0.2. This increase in dipole ordering is explained in Figure 7 by a schematic representation: panel a depicts a slightly polarized slab in the (0001) direction. When NaOH is put in contact with the surface, dissociation occurs and OH− is released to migrate via the Grothuss mechanism against the direction of the electric field, as shown in panel b. After the migration, the direction of hydrogen bonds along the migration path have been reversed, resulting in
order to determine the most optimal sites for both ions in the polarized slab geometries, we performed geometry optimizations for five different systems (with f = 0.067), where Na+ was placed on different surface sites in these systems, while the OH− ion was simultaneously placed either at another surface site or at a 4-fold coordinated site. Energetics were seen to favor surface sites where OH− can become a triple hydrogen-bond acceptor, zero-donor (AAA) species, while the Na+ ion was seen to prefer locations where it was surrounded by three oxygen atoms. Slabs of six bilayers exhibited the lowest total energies, when Na+ and OH− were placed on opposite sides of the slab. The described behavior of Na+ and OH− in our slab system is consistent with earlier theoretical and experimental results,74,80,81 as in ice, hydroxyl prefers to be an AAA species. When placed inside the bulk, the hydroxyl goes to an off-thelattice site (see Figure 2 of ref 74). However, it has a propensity for the surface,81 where it can become an AAA species in in-thelattice sites. In liquid water, the sodium ion can be surrounded by up to ∼6 oxygen atoms. (see ref 82), while inside bulk ice, high solvation with oxygens can be obtained by evoking Bjerrum defects.80 In our case, the surface provides natural sites having high densities of hydrogen-bond acceptors and donors. All cases considered and their corresponding order parameter f values are shown in Figure 5, and the relative total energies are plotted in Figure 6. When comparing Figures 4 and 6, we observe that for NaOH-doped slabs a minimum energy occurs
Figure 7. (a) Schematic of polarized ice slab in contact with NaOH. (b) Ice slab with an OH−/Na+ pair. Solid and open ellipses represent dangling OH and dangling O bonds, respectively. For spontaneous ionization, the migration path is indicated with a green dashed line. P, E, and Eion symbols show the direction of the polarization field, depolarization electric field, and electric field, respectively, due to the OH−/Na+ ion pair. The order parameter f is defined by eq 1. See also Figure 1. 26270
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Figure 8. (a) Structure of the energetically most stable ice/Pt(111) system at f = −0.125 and (b) relative energies of calculated ice/Pt(111) systems as a function of f (eq 1). Potential drop ΔV values along the slab normal (see Figure 2) are indicated for a few systems near the energy minimum. For f values indicated with an asterisk (*), a single water molecule ionizes spontaneously to form an OH−/H3O+ pair. For values marked with (+), two ion pairs are formed.
diminished and eventually lost as ice starts forming regular crystals at higher temperatures (∼120 K).24 We mimicked an experimental system24 by placing a 4 × 2 × 2 ice slab in contact with a Pt(111) model surface that consists of three atomic layers of Pt (see Figure 8a). The lattice constant of the ice system was scaled to match the computationally determined Pt lattice constant, which in our case was a = 2.67 Å. The f values considered range from −0.5 to 1, where negative f values imply higher dangling-OH bond density facing the metal slab. While the experiments deal mostly with ASW, our computational setup of Figure 8a can be thought as a first approximation for studying proton ordering in ASW and in crystalline ice on a metal surface. Similar to the model systems considered in previous sections, the relative total energies as a function of the order parameter f are plotted in Figure 8b. The minimum energy basin near f = 0 now becomes wide, when compared to Figure 4. The almost antiferroelectric but slightly effectively polarized cases surrounding f = 0 become energetically favorable, with energy differences from f = 0 being less than 0.1 eV. Unfortunately, studying computationally cases f → 0− and f → 0+ requires ever-increasing unit cells. However, comparing Figures 4 and 8, there is a stabilization of proton ordering at limits f → 0− and f → 0+, and the ice film can become effectively (but only slightly) proton ordered. The slight stabilization of negative f values with respect to positive values near f = 0 in Figure 8 implies that the system prefers a configuration where more free hydrogen atoms point toward the metal than toward the vacuum, in accordance with experiment.24,26,29 Moreover, the cited value24 of 0.2% corresponds to f = 0.002, that is, to f → 0−, as reflected by our results. The depolarization field arising in ice due to positive (negative) f values should create positive (negative) potential drops along the slab normal (see Figures 1 and 2); however, for f ≥ 0 in Figure 9, the drop in the electrostatic potential is negative. This implies that the metal substrate develops a field which dominates over the ice depolarization field: films with nonzero f values are stabilized, as the metal electric field compensates for the depolarization field from proton ordering;
increased ordering of the slab. The same result is obtained if one considers geometries where OH− and Na+ are a priori placed on opposing sides of the slab, while maintaining the ice rules for the whole system and requiring that the OH− ion is an AAA species and that the Na+ ion is at the predefined optimal site, surrounded by oxygen atoms. The fact that Na+ and OH− ions reside on opposite sides of the slab creates a potential drop and an electric field Eion along the slab normal, the magnitude depending on the NaOH concentration. The field Eion compensates for the depolarization field E, stabilizing the proton ordering. In an optimal situation, Eion and E would cancel each other, according to eq 11. This situation is difficult to achieve with periodic supercell simulations, as the lateral dimensions of the unit cell fix the values for both NaOH concentration and possible values of the order parameter f. Thus, situations can arise where the parameters do not match and fulfill the condition of eq 11. This is the case in our model systems, where we observe a potential drop along the slab normal in Figure 6b, at the optimal order parameter value f = 0.2. At dilute NaOH concentrations with small ρ values, the order parameter behaves as f → 0, according to eq 11. As a consequence, a small nonvanishing proton ordering can be achieved, while the overall system lacks net polarization. Ice Films on Pt. Several experiments have reported proton ordering83 and ferroelectricity24,26,27,29 in ice films that have been deposited on surfaces, namely, on Pt(111)24,29,29 and on copper.26 Steadily increasing electric potential over the film, as a function of the film thickness, has been measured,24,26,27 indicating ferroelectricity and, consequently, proton ordering. The ferroelectric effect mentioned above is typically observed at deposition temperatures below ∼100 K; that is, at temperatures where vapor-deposited water molecules form amorphous films.24 The synthesized films might then be described better as ASW/FE than ice XI/FE and are not necessarrily related to (alkali hydroxide-doped) crystalline ice XI samples. Furthermore, the observed ferroelectricity is small in the vapor-deposition experiments, on the order of 1% or less,24,26,27 not resembling the completely ferroelectric CmC21symmetric ice unit cell. The ferroelectric effect is also 26271
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= 0 and distributing a Fletcher striped phase on the surface.45,49,70 Earlier ab initio studies have employed computational techniques that assume zero depolarization fields. This can be justified by postulating a mechanism that compensates for the polarization, for example, surface charges, or equivalently that the simulated bulk material is placed in a closed electrical circuit. We propose another justification for PBC ab initio studies, namely, oppositely polarized domains, in the spirit of Figure 1c, giving f = 0 and an overall nonpolarized medium. In this case, ab initio studies are modeling only one of the domains in Figure 1c. Neutron diffraction studies have established the existence of ice XI domains.12,13,16,18,19,28,86 However, in these studies, the results have been interpreted in terms of the fully ferroelectric CmC21 structure embedded in ice Ih. It would be interesting to see if the salient features of the neutron diffaction studies12,13,15,19,28,86 could be produced by explicit diffraction simulations, using larger unit cells with f = 0, while such systems could feature small domains along the lines of Figure 1c. For alkali hydroxide-doped ice and for ice in contact with a metal surface [Pt(111) in our case], we observe a preference for proton ordering. However, this does not imply ferroelectric systems. For alkali metal hydroxide-doped slab, a net alignment of dipoles is stabilized by surface charges of the ions and by the “ice rules” for OH− and Na+ ions. At vanishing dopant concentration, the net alignment becomes vanishingly small and the system is effectively antiferroelectric. The doping facilitates Grothuss migration (i.e., it acts as a catalyst as proposed in the literature) so that the system can find the essentially antiferroelectric ground-state proton configuration. Slabs in contact with Pt(111), on the other hand, are stabilized by metallic screening of the depolarization field. This creates a small preference for polarized ordering in the slab models, but at the f → 0 limit. A system with a small amount of proton ordering (i.e., with f → 0) needs, according to eq 11, only a small surface charge to cancel out depolarization fields and potential drops across the ice film, irrespective of the thickness of the f ilm. In other words, for a film where only a small relative amount of protons are aligned, as in ref 24, only a small concentration of surface ions is needed to cancel out any dipole field and huge potential drop over the material, even if the ice block would be large.24 In this light, macroscopic extraterrestial ice particles, consisting of slightly proton-ordered ice XI and developing large dipole fields,24 seem unrealistic, as tiny concentrations of ions would cancel out such fields. Effective ferroelectricity has been measured in ice films, vapor-grown on substrates at low temperatures (T < 100 K),24,26,27,83 while the measured potential drops indicate 1% or less aligned water molecules. This picture is definitely far away from the completely ferroelectric CmC21 unit cell, while the surface grown films are not even crystalline but mostly amorphous (ASW);24 that is, they are not necessarily related to ice XI. On the basis of our results, we suggest that in the vapordeposition experiments,24,26,27,83 metallic screening stabilizes initial proton ordering, while the consecutive (amorphous) layers grow out of equilibrium and are trapped in a high-energy polarized state by the ice rules. In other words, the first “oxygen up” layers force the consecutive layers into the same direction. Similar trapping could also result from directional hydrogen bonds in a hydroxylated silica surface,87−89 leaving room for
Figure 9. Coupling of ice order parameter f (eq 1) to polarization of the metal substrate. In panels a and b, arrows indicate the directions of the electric fields. Solid and open ellipses are dangling OH and dangling O bonds, respectively. Inside ice, there is a depolarization electric field, while between the ice sample and the substrate a field with opposite direction is formed (see also Figure 1). Panel c shows charge transfer Δρ = ρPt+ice − ρPt − ρice for a part of the system of Figure 8a, where ρPt+ice, ρPt, and ρice are the self-consistent electron densities of composite system, isolated Pt(111) surface, and isolated ice surface, respectively. Red (blue) isosurfaces correspond to electron accumulation (depletion).
in other words, the ice depolarization is screened by the metal. The situation is illustrated schematically in Figure 9a, where an ice slab having positive f values creates a depolarization field. However, at the same time, there are more negatively charged oxygen atoms facing the metal, resulting in positive image charges and a field that opposes the depolarization field. The proton ordering then intimately couples to the polarization of the metal substrate. The analysis performed here for various values of the order parameter f also sets an example for theoretical studies of (sub)monolayers of water on various metal surfaces (see, for example, refs 84 and 85 and references therein) that lack systematic study of the f order parameter and the polarization, as typically only two values, f = 1 and f = −1, are studied.84 Examples of periodic, 2D ice-like systems with a wide range of f values are available at the Ice Package web page.69
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DISCUSSION The simplest fully proton-ordered and orthorhombic ice structure is the completely ferroelectric, eight-molecule unit cell having CmC21 symmetry. This simple structure was proposed as a candidate for ice XI in the context of neutron diffraction studies of alkali hydroxide-doped ice XI.12 The CmC21 structure is maximally ferroelectric, having a maximal P and, equivalently, f = 1 (eq 1). This has led to great excitement and speculation whether polarized ice exists in the solar system.15,16,18,28,29 However, as seen in the present work, the resulting depolarization fields for f = 1 are huge, up to the point where they start to break up the constituent water molecules. After the first discovery, more proton configurations for the eight-molecule orthorhombic cell, other than the fully ferroelectric CmC21 structure, were introduced,20 the exact number of symmetry-independent configurations being 16.31 All of these structures are either antiferroelectric structures, with P = 0 and f = 0, or ferroelectric, with f = 1. Creating larger unit cells or slabs, as in the present work, makes it possible to sample more f values. The value f = 0 (and P = 0) is, according to our study, energetically the most favorable option, with the energy cost growing as f 2. Keeping f = 0 does not retain the system in the simplest antiferroelectric structure, depicted schematically in Figure 1d, but a rich variety of domains is possible, as in Figure 1c. Additional stabilization is provided by maintaining f 26272
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(4) Giauque, W. F.; Stout, J. W. The Entropy of Water and the Third Law of Thermodynamics: The Heat Capacity of Ice from 15 to 273 K. J. Am. Chem. Soc. 1936, 58, 1144−1150. (5) Kawada, S. Dielectric Dispersion and Phase Transition of KOH Doped Ice. J. Phys. Soc. Jpn. 1972, 32, 1442−1442. (6) Whalley, E.; Davidson, D. W.; Heath, J. B. R. Dielectric Properties of Ice VII. Ice VIII: A New Phase of Ice. J. Chem. Phys. 1966, 45, 3976−3982. (7) Whalley, E.; Heath, J. B. R.; Davidson, D. W. Ice IX: An Antiferroelectric Phase Related to Ice III. J. Chem. Phys. 1968, 48, 2362−2370. (8) La Placa, S. J.; Hamilton, W. C.; Kamb, B.; Prakash, A. On a Nearly Proton-Ordered Structure for Ice IX. J. Chem. Phys. 1973, 58, 567−580. (9) Tajima, Y.; Matsuo, T.; Suga, H. Phase Transition in KOHDoped Hexagonal Ice. Nature 1982, 299, 810−812. (10) Tajima, Y.; Matsuo, T.; Suga, H. Calorimetric Study of Phase Transition in Hexagonal Ice Doped with Alkali Hydroxides. J. Phys. Chem. Solids 1984, 45, 1135−1144. (11) Matsuo, T.; Tajima, Y.; Suga, H. Calorimetric Study of a Phase Transition in D2O Ice Ih Doped with KOD: Ice XI. J. Phys. Chem. Solids 1986, 47, 165−173. (12) Leadbetter, A. J.; Ward, R. C.; Clark, J. W.; Tucker, P. A.; Matsuo, T.; Suga, H. The Equilibrium Low-Temperature Structure of Ice XI. J. Chem. Phys. 1985, 82, 424−428. (13) Howe, R.; Whitworth, R. W. A Determination of the Crystal Structure of Ice XI. J. Chem. Phys. 1989, 90, 4450−4453. (14) Fukazawa, H.; Hoshikawa, A.; Yamauchi, H.; Yamaguchi, Y.; Ishii, Y. Formation and Growth of Ice XI: A Powder Neutron Diffraction Study. J. Cryst. Growth 2005, 282, 251−259. (15) Fukazawa, H.; Hoshikawa, A.; Ishii, Y.; Chakoumakos, B. C.; Fernandez-Baca, J. A. Existence of Ferroelectric Ice in the Universe. Astrophys. J. Lett. 2006, 652, L57−L60. (16) Arakawa, M.; Kagi, H.; Fukazawa, H. Laboratory Measurements of Infrared Absorption Spectra of Hydrogen-Ordered Ice: A Step to the Exploration of Ice XI in Space. Astrophys. J., Suppl. S. 2009, 184, 361−365. (17) Arakawa, M.; Kagi, H.; Fukazawa, H. Annealing Effects on Hydrogen Ordering in KOD-doped Ice Observed Using Neutron Diffraction. J. Mol. Struct. 2010, 972, 111−114. (18) Arakawa, M.; Kagi, H.; Fernandez-Baca, J. A.; Chakoumakos, B. C.; Fukazawa, H. The Existence of Memory Effect on Hydrogen Ordering in Ice: The Effect Makes Ice Attractive. Geophys. Res. Lett. 2011, 38, 16101. (19) Line, C. M. B.; Whitworth, R. W. A High Resolution Neutron Powder Diffraction Study of D2O Ice XI. J. Chem. Phys. 1996, 104, 10008−10013. (20) Howe, R. The Possible Ordered Structures of Ice Ih. J. Phys., Colloq. 1987, 48 (C1), 599−604. (21) Dengel, O.; Eckener, U.; Plitz, H.; Riehl, N. Ferroelectric Behaviour of Ice. Phys. Lett. 1964, 9, 291−292. (22) Jackson, S. M.; Whitworth, R. W. Thermally-Stimulated Depolarization Studies of the Ice XI-Ice Ih Phase Transition. J. Phys. Chem. B 1997, 101, 6177−6179. (23) Johari, G. P.; Jones, S. J. Study of the Low-Temperature ”Transition” in Ice Ih by Thermally Stimulated Depolarization Measurements. J. Chem. Phys. 1975, 62, 4213−4223. (24) Iedema, M. J.; Dresser, M. J.; Doering, D. L.; Rowland, J. B.; Hess, W. P.; Tsekouras, A. A.; Cowin, J. P. Ferroelectricity in Water Ice. J. Phys. Chem. B 1998, 102, 9203−9214. (25) Rabe, K. M.; Ahn, C. H.; Triscone, J.-M. Physics of Ferroelectrics: A Modern Perspective; Springer Science & Business Media: Berlin and Heidelberg, Germany, 2007. (26) Kutzner, K. Spontaneous Polarization of Condensing Carbon Monoxide and Other Gases with an Electrical Dipole Moment. Thin Solid Films 1972, 14, 49−61. (27) Onsager, L.; Staebler, D. L.; Mascarenhas, S. Electrical Effects during Condensation and Phase Transitions of Ice. J. Chem. Phys. 1978, 68, 3823−3828.
speculation about the existence of ASW/FE in the solar system.15,16,18,28,29 The resulting dipole fields could be important in the initial growth of ASW on silica particles, with the dipole field enhancing the sticking coefficient of incident water molecules. Such ASW/FE is out of thermodynamic equilibrium and loses its polarization at higher temperatures, as seen in the experiments. If depolarization fields grow high enough during vapor growth, the polarization should diminish due to spontaneous ionization of water molecules.
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CONCLUSIONS Depolarization fields make proton-ordered, ferroelectric ice thermodynamically unstable. The proton-ordered ice XI structure is then antiferroelectric in nature and the existence of ice having even the slightest degree of spontaneous polarization, and surrounding dipole fields in outer space,15,16,18,28,29 seems unrealistic. The depolarization experiments showing phase transition to ice XI are controversial,23,24 while results from a typical dielectric polarization experiments are not related to the possibility of having a thermodynamically stable and “free-standing” material with a permanent dipole field. In fact, a crystal of proton-ordered ice with a permanent dipole field (a unit cell with a nonzero dipole moment) should have an infinite surface energy.53 However, small spontaneous dipole fields have been observed by explicit electrostatic potential measurements for vapor-grown ASW24,26,27 (not ice XI), while such fields could play a role in the aggregation of icy grains in extraterrestial environments. We propose that the long-sought structure of ice XI consists of a unit cell that has a vanishing polarization. This cell could feature an internal structure of compensating domains. This means that the actual unit cell is much larger than the orthorhombic minimal unit cell considered up to date. Thermodynamically stable and polarized ice systems can, however, exist at the nanoscale: when ice is confined into small dimensions, the ice rules may give rise to spontaneous ferroelectricity.68,90,91
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AUTHOR INFORMATION
Corresponding Author
*E-mail lauri.halonen@helsinki.fi. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the Center for Scientific Computing (CSC) for the use of its facilities. This work was supported by the Academy of Finland through the FiDiPro, CoE (2006-2011), and Lastu programs, and by University of Helsinki through a graduate program. S.R. acknowledges useful discussions with Julen Larrucea and Garold Murdachaew.
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REFERENCES
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