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J. Phys. Chem. B 1997, 101, 6142-6145
Single-Crystal Neutron Diffraction Studies of the Structure of Ice XI S. M. Jackson,† V. M. Nield,‡ and R. W. Whitworth* School of Physics and Space Research, The UniVersity of Birmingham, Birmingham B15 2TT, U.K.
M. Oguro Physics Laboratory, Hokkaido UniVersity of Education, Asahikawa Campus, Hokkaido, Japan 070
C. C. Wilson ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, U.K. ReceiVed: October 11, 1996; In Final Form: February 15, 1997
Single crystals of KOH-doped ice Ih, transformed into the low-temperature ordered phase known as ice XI, have been studied by neutron diffraction. High-resolution measurements show a splitting of the 00l diffraction peaks into an ice XI and a residual ice Ih component, with about 37% transformation to ice XI. New diffraction peaks from the ice XI have been measured. These are consistent with a ferroelectrically ordered structure with space group Cmc21.
Introduction Pauling1 proposed that “under normal conditions the interaction of nonadjacent molecules in ice is not such as to appreciably stabilize any one of the many configurations satisfying the conditions” that ice is made up of H2O molecules linked by hydrogen bonds with only one H per bond. It is now well established that this is true, so that the orientations of molecules in normal ice (ice Ih) are disordered. However, in accordance with the third law of thermodynamics one ordered configuration must have a slightly lower energy than any others, and this will be the equilibrium structure at low temperatures. The structure of this lowest energy state is one of the long-standing fundamental questions in ice physics. The ordered phase cannot be produced in pure ice, because the disorder is frozen in, but the transformation is catalyzed by doping with KOH or other hydroxides, and the ordering transition has been observed at 72 K both by calorimetry2,3 and in dielectric experiments.4,5 The ordered phase has been named “ice XI”.6 Theoretical calculations7 based on electrostatic interactions, with the molecules fixed to their mean sites in the ice Ih structure, favour a nonpolar (antiferroelectric) ordering. However, in the ordered state molecules will move off their Ih sites in whatever way will minimize the energy, and this could affect which form of ordering finally has the lowest energy. The energy gained in ordering must be kBTc ln(3/2) per molecule, where Tc is the transition temperature and kB ln(3/2) is the entropy of disorder. This energy is about 2.5 meV, which is at the limit of current computational modeling of such structures. In dielectric experiments the sign of ∆ in the Curie-Weiss expression for the permittivity, ∝ 1/(T - ∆), indicates a tendency toward ferroelectric ordering along the c axis,8-10 and we have recently shown by thermally stimulated depolarization experiments11 that the ordering in ice XI is indeed ferroelectric in character. The obvious technique for determining the ordered structure is neutron diffraction, but this has presented some difficulties. * To whom correspondence should be addressed. † Current address: The Institute of Physics, 76 Portland Place, London W1N 4AA, U.K. ‡ Current address: Physics Laboratory, University of Kent, Canterbury, Kent CT2 7NR, U.K. X Abstract published in AdVance ACS Abstracts, June 1, 1997.
S1089-5647(96)03255-5 CCC: $14.00
The first attempt by Leadbetter et al.12 achieved, as we now know, a very small degree of transformation, but a larger degree of transformation was observed in an experiment on powdered KOH-doped H2O ice by Howe and Whitworth.13 Their data were interpreted as being consistent with the polar structure of space group Cmc21 that had been proposed by Kamb14 and predicted theoretically on the basis of the observed dielectric behavior by Minagawa.15,16 However, the powder diffraction data are dominated by features already present in ice Ih, and it provides rather little evidence about the ice XI. Limited data from the first single-crystal diffraction experiment17 suggested that the earlier conclusion that ice XI had the Cmc21 structure was unjustified. We have subsequently carried out a number of single-crystal neutron diffraction experiments, and our principal observations and conclusions are described here. Taken together with a recent powder diffraction experiment18 on D2O ice XI, the results show that ice XI must have the Cmc21 structure. Experimental Section The crystals were grown from 0.055 M KOH solution, and their dielectric activity was monitored according to the procedures described previously.10,17 To retain sufficient KOH in solid solution for the crystals to transform, the crystals have to be grown relatively quickly and stored in liquid nitrogen. At this concentration they are slightly cloudy and contain inclusions of concentrated solution which will freeze to the eutectic at low temperatures. All neutron diffraction experiments were performed at the ISIS pulsed neutron source at the Rutherford Appleton Laboratory. The results described here were obtained on two differently oriented cylindrical crystals (14 mm high and 11 mm in diameter) studied on separate occasions. For crystal 1 the c axis was perpendicular to the axis of the cylinder, and rotation about the axis of the cylinder gave access to all types of lowindex Bragg reflections at at least one point in reciprocal space. This crystal was transformed by nucleation for 14 h at 63 K followed by annealing for 4.5 days at 70 K. Diffraction data were collected at 10 K to minimize thermal effects. Following these measurements the crystal was warmed above 100 K to transform it back to ice Ih. It was then cooled as quickly as © 1997 American Chemical Society
Single-Crystal Neutron Diffraction Studies of Ice XI
Figure 1. High-resolution diffraction peak for 004 reflection from crystal 1 in its transformed state, measured at 10 K.
possible back to 10 K, and data were collected on this disordered phase. Crystal 2 was oriented with the c axis parallel to the cylinder, giving more examples of some types of Bragg reflection but excluding other types altogether; otherwise it was similar to crystal 1. Two different instruments were used at ISIS: the high-resolution diffractometer HRPD and the single-crystal diffractometer SXD. In HRPD, which is primarily intended for powder samples, the neutrons are detected in almost back scattering and analyzed by time of flight, which is equivalent to d spacing. With an appropriately oriented single crystal, this instrument gave very high-resolution measurements of the 00l Bragg reflections. In the transformed ice these are split as shown in Figure 1. This splitting is similar to that observed previously in powder samples.13,18 The peak with the smaller lattice parameter is that for the ice XI and is absent after conversion back to ice Ih. The fraction of transformation could be estimated from the integrated area of the component peaks, making allowance for relatively small changes in the predicted structure factors. For crystal 1 the results for the 004, 006, and 008 peaks were 37, 42, and 31%, respectively, giving a mean value of 37 ( 5%; this is similar to that observed in several other single crystals treated and examined in the same way. (Such data are not available for crystal 2 because of its different orientation.) The component peaks have similar widths, which are typically 50% larger than for the untransformed ice. In the more detailed study of the lattice parameters in powder samples by Line and Whitworth18 this broadening is attributed to strain associated with the transformation. In SXD scattered neutrons are detected over a range of angles using a time-resolved area detector which records diffracted intensities simultaneously over large regions of reciprocal space. Neutron counts as a function of time of flight for a particular diffraction direction are shown in Figure 2, in which time of flight has been converted to d spacing and the count rate has been normalized to the background of incoherent scattering from the hydrogen. The examples in Figure 2 show the 131, 261, and 331 diffraction peaks which are produced by ice XI but are absent in ice Ih; the second-order peaks (262 etc.) are present in both phases. All indices quoted relate to the eight-molecule orthorhombic cell required for ice XI and shown in Figure 3. The integrated intensities can be extracted from the data according to standard procedures, but in this case there were difficulties in obtaining precise structure factors. These were in part due to using rather large samples in order to gain intensity in weak peaks, which leads to problems with absorption. In addition there were some technical difficulties leading to uncertainties in the data normalization. Consequently, even for ice Ih, while the Bragg peaks had about the expected intensities,
J. Phys. Chem. B, Vol. 101, No. 32, 1997 6143 it was found to be impossible to use the usual structure refinement procedure. In analyzing the results for ice XI there is a further complication that if the ordered state loses the hexagonal symmetry of ice Ih the new phase can be formed in three orientations about the original hexagonal axis. We have no evidence about the size and geometry of these domains of the ordered phase, other than that they did not give greatly enhanced particle size broadening in the high-resolution powder experiment.18 A consequence of there being three orientations of the ice XI unit cell is that at a given diffraction angle up to three different types of ice XI peak will be superimposed (e.g., 131 and 201, or 311, 241, and 151). The observed intensities will be appropriately weighted combinations of these, with the Ih peak present as well if its intensity is not zero. The following section is concerned with drawing conclusions from the more well-established features of the data. Experiments on KOD-doped D2O crystals using both HRPD and SXD showed that these crystals also transformed to about the same extent, but even for ice Ih extra peaks were observed such as 00l with l odd. The strengths of these forbidden peaks depended on the instrumental settings, and the ice XI reflections could not be satisfactorily separated from them. Such peaks were never observed for H2O crystals, and they were tentatively attributed to multiple scattering involving the 110, 111, and 002 reflections which are extremely strong for D2O but almost absent in H2O ice. Interpretation We deal first with the identification of the unit cell and space group from among the possibilities surveyed by Howe.19 A careful search of reciprocal space revealed no Bragg peaks other than those corresponding to the eight-molecule orthorhombic cell shown in Figure 3 with the condition h + k even, which implies that the cell is C-centered. This immediately eliminates all possible forms of antiferroelectric ordering parallel to the c axis (of which the simplest has the space group Pna21), because these have to have two oppositely oriented c-axis bonds at each level in the cell, and in the eight-molecule cell the C-centering does not allow this. It also eliminates the simplest ordered hexagonal structure with the 12-molecule cell suggested by Bernal and Fowler20 and other structures with yet larger cells. In all we have observed 380 peaks for ice Ih and an additional 84 for ice XI. Changes to the peaks that are already strong in ice Ih are not sufficiently significant to analyze, and our interpretation must be based on the 13 types of new peak observed for ice XI. These are tabulated in Table 1, where they are classified as either forbidden in ice Ih or not forbidden but too small to detect. The presence of the forbidden peaks and the evidence of orthorhombic splitting in the a-b plane from the powder diffraction experiment18 eliminate the partially ordered structure with the c-axis bonds ferroelectrically ordered but the remaining bonds disordered. This leaves two possibilities, of which the simplest is the Cmc21 structure shown in Figure 3. It is ferroelectrically ordered along the c axis, and the layers perpendicular to c are polar in the b direction with alternate layers oppositely polarized. The other possibility is similar but with alternate layers oriented at 60° instead of 180° to one another. It is monoclinic with space group Cc and is polar along [100] as well as [001]. We cannot convincingly distinguish these structures from the diffracted intensities, but we note that the thermally stimulated depolarization experiments11,21 indicate no ferroelectric character perpendicular to the c axis, and that the powder diffraction experiment18 showed that if the structure is monoclinic, then
6144 J. Phys. Chem. B, Vol. 101, No. 32, 1997
Jackson et al.
Figure 2. Single-crystal neutron diffraction profiles for angles corresponding to the 131, 261, and 331 Bragg reflections from both the transformed crystal 1 (XI plus residual Ih) and the same crystal transformed back to the Ih phase, both measurements at 10 K. Plots show neutron counts normalized to the incoherent background scattering versus time of flight, which is here represented as equivalent d spacing.
TABLE 1: Observed and Predicted Diffraction Intensities in Transformed Icea F2obs indexes
Figure 3. Orthorhombic Cmc21 structure of ice XI. Open circles represent oxygen and solid circles hydrogen. The shifts Rb and γc discussed in the text are as indicated.
the β angle does not differ from 90° by more than 0.2°. We therefore conclude that ice XI has the Cmc21 structure. Table 1 shows the mean intensities of the “new” peaks scaled to those of ice Ih so as to represent squared structure factors F2obs. Data are given separately for the two crystals studied. The table also shows the predicted values F2pred based on the usually accepted parameters for ice Ih,22 a 37% conversion to ice XI taken from the HRPD data for crystal 1, and weighted averaging of the intensities of equivalent peaks. There is no direct evidence of the percentage transformation in crystal 2, but based on the values of F2obs it could be somewhat higher than in crystal 1. The fit can be improved by refinement of the free parameters permitted by this symmetry. The most significant of these parameters is a displacement of alternate layers of puckered hexagonal rings in opposite directions by amounts Rb as indicated in Figure 3. A shift with positive R as in the figure reduces the 131 peak and increases 261, which is what is required to fit the data. It has the opposite effect on these peaks for D2O, and this is consistent with the powder diffraction data.18 The other structural parameters involve the distortion of the
crystal 1
crystal 2
F2pred 37% ice XI F2ref
Forbidden in Ice Ih 131 133 135 261 263
0.49 ( 0.08 (2) 0.64 ( 0.10 (6) 0.55 ( 0.17 (2) 1.27 ( 0.15 (1) 2.78( 0.42 (2) 3.28 ( 0.48 (6) 1.49 ( 0.23 (1)
1.02 0.82 0.53 1.09 0.88
0.51 0.60 1.35 2.62 1.40
Zero in Ice Ih 221 151 134 331 154 333 171 117
0.56 ( 0.09 (2) 1.73 ( 0.26 (4) 1.23 ( 0.15 (2) 1.52 ( 0.23 (2) 2.26 ( 0.41 (4) 1.70 ( 0.33 (2) 3.47 ( 0.38 (4) 0.97 ( 0.15 (3)
1.33 1.44 0.68 0.46 0.95 1.01 1.22 0.35
0.68 1.96 1.23 1.77 2.38 1.59 2.82 1.28
0.96 ( 0.15 (6) 2.54 ( 0.38 (12) 2.14 ( 0.32 (6) 3.52 ( 0.44 (4) 3.98 ( 0.58 (6)
a Numbers in parentheses in columns 2 and 3 represent numbers of diffraction peaks included in average value given. F2ref are predicted values for 48% ice XI, R ) 0.02 and γ ) 0.005
hexagonal rings making up the layers perpendicular to the c axis and displacements of hydrogens off their sites on the OsO lines. The only one of these which has a significant effect in improving the fit to our data is an increase in the puckering of the layers by z displacements of the oxygen atoms by amounts γc. In attempts to adjust the parameters to fit the observations for crystal 1 with 37% transformation, the overall level is consistently too small. A better fit is achieved by assuming a higher percentage of transformation even though this is inconsistent with the evidence from the splitting of the 00l line. It is of course probable that the degree of order within the ice XI phase is less than 100%, but this lowers the predicted intensities, which is the opposite of what is required. The best fit to the data of crystal 1 is shown as F2ref in the last column of Table 1. This “refinement” requires a 48% transformation, R ) 0.02 and γ ) 0.005. An R-shift was
Single-Crystal Neutron Diffraction Studies of Ice XI recognized as present in the early experiment of Howe and Whitworth,13 where the value of R was estimated as 0.008. Indications of a γ-shift are new and represent an increase in the puckering of the layer by 8%, but this feature is less well established. Conclusion The weight of experimental evidence is now overwhelmingly in favor of ice XI having the Cmc21 ferroelectrically ordered structure, and a well-established feature is the relative shift of alternate layers of hexagonal rings in the [010] direction. This shift may be crucial in favoring this ferroelectrically ordered structure over the theoretical prediction of antiferroelectric ordering if no shifts are allowed. There is need for a further neutron diffraction experiments, to obtain data of sufficient quality for a full crystallographic structure refinement to be carried out. Significant problems are that the relevant information on ordering is contained in a number of comparatively weak lines and that the observed intensities are averages over the three possible orientations of domains. Acknowledgment. We acknowledge the support of a research grant and studentship (for S.M.J.) from the Engineering and Physical Sciences Research Council, and the use of the ISIS facility at the Rutherford Appleton Laboratory. We are grateful
J. Phys. Chem. B, Vol. 101, No. 32, 1997 6145 for assistance from Dr. R. M. Ibberson and Dr. D. A. Keen and for discussions with Dr. J. W. Glen and Dr. C. M. B. Line. References and Notes (1) Pauling, L. J. Am. Chem. Soc. 1935, 57, 2680. (2) Tajima, Y.; Matsuo, T.; Suga, H. Nature 1982, 299, 810. (3) Tajima, Y.; Matsuo, T.; Suga, H. J. Phys. Chem. Solids 1984, 45, 1135. (4) Kawada, S. J. Phys. Soc. Jpn. 1972, 32, 1442. (5) Kawada, S. J. Phys. Chem. Solids 1989, 50, 1177. (6) Matsuo, T.; Tajima, Y.; Suga, H. J. Phys. Chem. Solids 1986, 47, 165. (7) Barkema, G. T.; deBoer, J. J. Chem. Phys. 1993, 99, 2059. (8) Kawada, S. J. Phys. Soc. Jpn. 1978, 44, 1881. (9) Takei, I.; Maeno, N. J. Phys. (Paris) 1987, 48 Colloque C1, 121. (10) Oguro, M.; Whitworth, R. W. J. Phys. Chem. Solids 1991, 52, 401. (11) Jackson, S. M.; Whitworth, R. W. J. Chem. Phys. 1995, 103, 7647. (12) Leadbetter, A. J.; Ward, R. C.; Clark, J. W.; Tucker, P. A.; Matsuo, T.; Suga, H. J. Chem. Phys. 1985, 82, 424. (13) Howe, R.; Whitworth, R. W. J. Chem. Phys. 1989, 90, 4450. (14) Kamb, B. In Physics and Chemistry of Ice; Whalley, E., Jones, S. J., Gold, L. W., Eds.; Royal Society of Canada: Ottawa, 1973; pp 28-41. (15) Minagawa, I. J. Phys. Soc. Jpn. 1990, 59, 1676. (16) Minagawa, I. In Physics and Chemistry of Ice; Maeno, N.; Hondoh, T., Eds.; Hokkaido University Press: Sapporo, 1992; pp 14-19. (17) Oguro, M.; Whitworth, R. W.; Wilson, C. C. In Physics and Chemistry of Ice; Maeno, N.; Hondoh, T., Eds.; Hokkaido University Press: Sapporo, Japan, 1992; pp 9-13. (18) Line, C. M. B.; Whitworth, R. W. J. Chem. Phys. 1996, 104, 10008. (19) Howe, R. J. Phys. (Paris) 1987, 48 Colloque C1, 599. (20) Bernal, J. D.; Fowler, R. H. J. Chem. Phys. 1933, 1, 515. (21) Jackson, S. M.; Whitworth, R. W. J. Phys. Chem. 1997, 101, 6177. (22) Kuhs, W. F.; Lehmann, M. S. Water Sci. ReV. 1986, 2, 1.
