The structure and ordering of ices III and VColin Lobban, John L. Finney, and Werner F. Kuhs Citation: The Journal of Chemical Physics 112, 7169 (2000); doi: 10.1063/1.481282 View online: http://dx.doi.org/10.1063/1.481282 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/112/16?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Bismuth Substitution for Rare Earth and Charge/Orbital Ordering Related Structural Effects in Some Half HoleDoped Manganites AIP Conf. Proc. 899, 263 (2007); 10.1063/1.2733137 The effect of proton disorder on the structure of ice-Ih: A theoretical study J. Chem. Phys. 123, 134505 (2005); 10.1063/1.2036971 The crystal structure of methane phase III J. Chem. Phys. 119, 1586 (2003); 10.1063/1.1580809 Structure genesis and magnetic orderings in compounds of the ThCr 2 Si 2 type Low Temp. Phys. 26, 874 (2000); 10.1063/1.1334437 Orientational order and rotational dynamics of the amide ions in potassium amide. II. Quasielastic neutronscattering J. Chem. Phys. 109, 3559 (1998); 10.1063/1.476951

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The structure and ordering of ices III and VColin Lobban and John L. FinneyUniversity College London, Gower Street, London WC1E 6BT, United Kingdom

Werner F. Kuhsa)

MKI, Universitat Gottingen, Goldschmidtstrasse 1, 37077 Go¨ttingen, Germany

~Received 14 December 1999; accepted 28 January 2000!

The structures of ices III and V have been studied under their thermodynamic conditions of stabilityby neutron diffraction. The results clearly indicate partial ordering of the water moleculeorientations for both ice structures. For ice V the ordering is both pressure and temperaturedependent, while no significant changes in ordering were noted for ice III within the small regionof stability. No reduction in symmetry, necessary for complete orientational ordering, was observedfor ice V at low temperatures. The ordering behavior of ice V at low temperatures (,150 K!, whenconsidered in conjunction with dielectric measurements at high temperatures, suggests that whilerelaxation is achieved predominantly through the diffusion of rotational defects at hightemperatures, the mechanism at low temperatures appears to be the migration of ionic defects whichrequire only a small activation energy for mobilization. ©2000 American Institute of Physics.@S0021-9606~00!51715-2#

I. INTRODUCTION

In all crystalline ice structures, of which thirteen differ-ent forms are now known, each water molecule bonds tetra-hedrally to four others through hydrogen bonding. The ori-entation of the water molecule, i.e., the direction in which itbonds with its four neighbors, can vary from an irregulararrangement, such as found in ice Ih,1 to a completely regu-lar one, such as found in ice II.2 The ices provide ideal en-vironments in which to test theoretical models of the watermolecule. In particular, ices for which the water moleculeorientations are partially ordered, i.e., neither fully orderednor disordered, provide particularly critical tests; this is aconsequence of the expectation that such ordering is sensi-tive to hydrogen-bond strain and nonbonded interactions be-tween surrounding water molecules. In order to reproducethe partial ordering of such ices, the water-molecule potentialmust accurately model both the hydrogen bond and the non-bonded interactions.

Ice III is thermodynamically stable between 240 and 260K and 2.2 and 3.4 kbar and occupies the smallestp,T regionof all the stable ice phases. Until the neutron diffraction workof Londono, Kuhs, and Finney,3 it was thought that the watermolecule orientations in ice III were random,4,5 with its or-dered equivalent, labeled ice IX, stable at temperatures be-low 165 K.5 Unfortunately, the powdered ice III sampleformed by Londono, Kuhs, and Finney was textured andalthough they were able to identify the existence of partialordering, they were unable to establish accurate numbers forthe degree of order. The true orientational order within iceIII, therefore, remains unknown.

The currently defined stability region of ice V extendsroughly between 210 and 270 K and 3.4 and 6.3 kbar. Unlikethe majority of other ice structures, published work on ice V

is rather limited. Dielectric measurements4 and entropyconsiderations6 suggest that ice V is orientationally disor-dered within its stability region. However, at temperaturesbetween 105 and 130 K, achieved by cooling through thestability region of ice II, ice V appears to undergo an order-ing transition, evidenced by calorimetric measurements onsamples recovered to ambient pressure.7 A single neutrondiffraction experiment,8 again performed on ice V recovered

a!Electronic mail: kuhs@silly.uni-mki.gwdg.de

FIG. 1. The D2O ice phase diagram~Ref. 26! in the p–T region of ices IIIand V. Solid lines represent measured transitions, the dashed line representsan extrapolation of the ice II–V transition, while the dotted line representsthe measured extrapolated melting curve of ice Ih. Diffraction data werecollected at the points indicated by circles~for ice III! and squares~for iceV!. The conditions, and in particular the temperatures, were chosen in orderto minimize recrystallization, which would have led to poor powder statis-tics, and to minimize argon clathrate growth, which was particularly severein the case of ice III. To this end, data on ice III were also collected withinthe established stability region of ice II; this was made possible due to thehysteresis present in the ice II–III transition.

JOURNAL OF CHEMICAL PHYSICS VOLUME 112, NUMBER 16 22 APRIL 2000

71690021-9606/2000/112(16)/7169/12/$17.00 © 2000 American Institute of Physics

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to ambient pressure, has confirmed that strong partial order-ing exists at 110 K. Nevertheless, the crystallographic struc-ture of ice V within its stability region remains unknown.

This paper presents results from several neutron diffrac-tion experiments which establish for the first time the crys-tallographic structure of ice V within its thermodynamic sta-bility region, and resolves the issue of orientational orderingin ice III.

II. EXPERIMENT

A. Sample preparation and data collection

Powdered ice was prepared by grinding frozen D2O~99.9% deuterated! with a mortar and pestle. Liquid nitrogenwas first poured into the mortar before'1.5 ml of D2O wasslowly added whereupon it froze to form small droplets ofice. The droplets were then ground using the pestle untilfinely powdered. This procedure normally took a few min-utes during which time liquid nitrogen was added occasion-ally to prevent the ice melting. All this took place inside aglove box in which the air had been saturated with D2O tominimize any possible H–D exchange.

Once the powdered ice had been prepared it was loadedinto a gas-pressure cell. During filling, the cell sat in a smallreservoir of liquid nitrogen to maintain subzero tempera-tures. Filling was carried out in small steps, allowing the iceto be compacted between steps. Once loaded, the cell wasscrewed onto the pressure center stick and lowered into ahelium cryostat.

Argon gas was used throughout as the pressure medium.Although it is known that argon forms a gas hydrate in the

presence of ice, the rates of formation are slow. The use ofhelium is not possible since it is known to be occludedwithin the ice II structure,9 thereby preventing the formationof ices III and V. Similarly, there is evidence of neon inclu-sion within the open channels of ices Ih and II.10

Ice III was formed by first pressurizing ice Ih to 2.8 kbarat 200 K, resulting in the ice Ih–II transition. Ice II was thenwarmed at 2.8 kbar with the ice II–III transition occurringbetween 245 and 250 K. The formation of ice III was ini-tially attempted by pressurizing ice Ih at 248 K. However,from the diffraction pattern observed, the ice appeared tomelt at around 2.8 kbar, corresponding to the extrapolatedice Ih melting curve, Fig. 1. Neutron diffraction data werethen collected at various temperatures and pressures, and onvarious instruments, as listed in Table I.

Ice V was formed by pressurizing ice, be it ice Ih or II,in excess of 4.5 kbar at 235 K. Again, data were collected onvarious instruments at the pressures and temperatures listedin Table II. The D2B data were collected during two differ-ent experiments; the second of these experiments being indi-cated by an asterisk in Tables II and III. In the first experi-ment the following path was employed: Having prepared iceV as described previously, data were collected at 5.0 kbarand 233.5 K. The sample was then removed from the cry-ostat and quenched in a bath of liquid nitrogen, before beingreplaced in the cryostat at 100 K. Data were then collectedon this quenched sample at 5.0 kbar and 102 K. Afterwards,the sample was warmed to 220 K and subsequently cooled ata rate well within the water-molecule relaxation times pub-lished by Wilsonet al.;4 in particular, 6 h were spent oncooling from 160 to 130 K, and on cooling from 130 to 100

TABLE I. Ice III lattice constants and densities for the various data sets collected under different conditions oftemperature and pressure.

P~kbar! T~K! a~Å! c~Å! c/a V(Å 3) r(g cm23) Inst.

2.50 240 6.671 11~22! 6.964 88~40! 1.044 04~7! 309.96~2! 1.285 76~8! D1A2.50 240 6.675 96~21! 6.955 00~33! 1.041 80~6! 309.97~2! 1.285 71~8! D2B1

2.50 250 6.677 95~29! 6.966 47~46! 1.043 20~8! 310.67~3! 1.282 83~12! D2B2

3.30 250 6.666 57~36! 6.924 82~53! 1.038 73~10! 307.76~3! 1.294 95~14! D2B3

3.00 250 6.670 92~28! 6.933 19~31! 1.039 31~6! 308.52~2! 1.291 75~10! HRPD

TABLE II. Ice V lattice constants and densities. All data sets were collected over a period of 12 h with the exception of those indicated by an asterisk inwhichonly 3 h werespent. The two data sets at ambient pressure were collected during a second D2B experiment and are denoted with a dagger. Samples quenchedfrom 235 K to liquid nitrogen temperatures are labeled with a~q!.

P~kbar! T~K! a~Å! b~Å! c~Å! b(°) V(Å 3) r(g cm23) Inst.

4.0 254.0 9.0980~3! 7.5620~4! 10.2652~4! 109.077~4! 667.45~5! 1.393 22~11! HRPD5.0 254.0 9.0744~2! 7.5435~3! 10.2373~3! 109.068~3! 662.32~4! 1.404 02~8! HRPD5.0 237.0 9.0704~2! 7.5271~2! 10.2273~2! 109.113~2! 659.77~3! 1.409 47~4! HRPD5.0 233.5 9.0926~4! 7.5409~4! 10.2547~5! 109.144~4! 664.24~6! 1.400 0~1! D2B5.0 218.7 9.0788~8! 7.5112~9! 10.2387~11! 109.123~8! 659.67~13! 1.409 7~3! D2B*5.0 198.9 9.0847~4! 7.5099~4! 10.2328~5! 109.190~4! 659.34~6! 1.410 4~1! D2B5.0 160.7 9.0883~4! 7.4974~4! 10.2251~5! 109.245~4! 657.79~6! 1.413 7~1! D2B5.0 130.8 9.1228~4! 7.5061~5! 10.2508~5! 109.287~4! 662.54~6! 1.403 5~1! D2B5.0 119.0 9.1347~8! 7.5078~9! 10.2577~10! 109.283~8! 664.02~12! 1.400 4~3! D2B*5.0 101.8~q! 9.1390~5! 7.5028~6! 10.2549~7! 109.363~5! 663.38~8! 1.401 8~2! D2B5.0 100.0 9.1461~8! 7.5038~9! 10.2598~10! 109.354~9! 664.35~12! 1.399 7~3! D2B*amb 127.0~q! 9.1617~4! 7.5407~5! 10.2968~6! 109.258~5! 671.55~7! 1.384 7~1! D2B†

amb 98.0~q! 9.1409~4! 7.5380~5! 10.2878~6! 109.307~5! 669.01~7! 1.390 0~1! D2B†*

7170 J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 Lobban, Finney, and Kuhs

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K. Data were then collected at various temperatures between220 and 100 K. In the second experiment, ice V was pre-pared at 5.0 kbar and 235 K, removed from the cryostat, andquenched in a bath of liquid nitrogen. Once at 77 K, thepressure on the sample was completely released and thesample replaced in the cryostat at 100 K.

Approximately 12 h were spent collecting data at each(p,T) point for both ices III and V with the exception ofthose indicated by an asterisk, where only 3 h were spent.The instruments used in this work were the HRPD diffracto-meter at the ISIS11 pulsed spallation source~Didcot, UK! andthe D1A and D2B diffractometers at the Institut LaueLangevin12 reactor source~Grenoble, France!.

B. Refinement

All data were refined by the Rietveld refinement tech-nique using the programGSAS.13 Reflections arising from thepressure cell, which were visible in the D1A and D2B data,were excluded from the diffraction profiles owing to theirstrongly textured nature.

The argon clathrate which formed during data collectionwas modeled according to previous neutron diffraction datacollected on the argon clathrate system only,14 at 2.5 kbarand 273 K for ice III and at 5.0 kbar and 273 K for ice V.

1. Ice III

The structure of ice III is based on a tetragonal unit cell,space groupP41212, lattice constants:a56.80 Å, c56.86Å, and comprises twelve water molecules, Fig. 4. The asym-metric unit required to describe the complete structure con-sists of two distinct oxygen and six distinct deuterium atoms.By application of the Bernal–Fowler rules,15 only two occu-pational parameters are required to describe the orientationalordering of the water molecules, labeled here asa and b.The atomic positions of ice III determined by Londono,Kuhs, and Finney3 were used as the initial model in refiningthe data. Although Londono, Kuhs, and Finney found evi-dence of partial orientational ordering, the deuterium sites at

the start of the refinement were populated in a fully disor-dered manner. In this way, no initial bias was placed onwater molecule orientations.

Free refinement of the HRPD data set led to unphysicalthermal factors for the deuterium atoms, with a negative iso-thermal factor for one of the atoms. This is thought to be dueto the smalld-spacing range sampled by the HRPD configu-ration employed, 1.2–3.1 Å, in comparison to D2B, 0.8–20Å. Free refinement of the D1A data, with a d-spacing rangeof 1.0–13 Å, fared better, although the thermal factors foratoms D~3! and D~4! were suspiciously high, 0.10 Å2, incomparison with the four other deuterium atoms in this dataset and those found for the D2B data sets,;0.06 Å2. TheHRPD and D1A data sets were therefore restrained such thatall deuterium atoms were refined with the same thermal fac-tor.

For the D2B3 data set, low thermal factors, 0.03 Å2,were found for atoms D~3! and D~8! after a free refinement.A similar behavior, if somewhat less severe, was also ob-served for the D2B1 data set. The deuterium atoms D~3! andD~8! are in fact the weakly occupied positions within the iceIII structure. In the fully ordered structure the occupancies ofthese two sites are zero. Since we can find no apparent struc-tural reasons why these two atoms should have a small ther-mal motion in comparison with the other deuterium atoms, itwould appear that the refinement had problems in decorre-lating the thermal factor and occupancy for these weaklyoccupied atoms. For the D2B3 data set, the thermal factorsfor the two atoms were therefore restrained to the same valueas their strongly occupied counterparts, i.e., D~3! U iso5D~7!U iso and D~8! U iso5D~6! U iso.

The profile fits resulting from the refinement of theHRPD data collected at 3.0 kbar and 250 K, and the D2Bdata collected at 2.5 kbar and 240 K, are shown in Fig. 2.

2. Ice V

The structure of ice V is based on a monoclinic unit cell,space groupA2/a, lattice constants:a59.22, b57.54, c510.35 Å, b5109.2°, and comprises twenty-eight water

TABLE III. The RietveldR factors and fractional occupancy parameters for the deuterium atoms of ice V. Alldata sets were collected over a period of 12 h with the exception of those indicated by an asterisk in which only3 h were spent. The two data sets at ambient pressure were collected during a second D2B experiment and aredenoted with a dagger. Samples quenched from 235 K to liquid nitrogen temperatures are labeled with a~q!.

P~kbar! T~K! Rwp Rp a~%! b~%! g~%! d~%! Inst.

4.0 254.0 0.0790 0.0724 48.1~1.8! 30.6~2.0! 48.7~1.7! 72.6~2.3! HRPD5.0 254.0 0.0665 0.0625 47.0~1.6! 29.9~1.6! 48.5~1.2! 74.6~1.8! HRPD5.0 237.0 0.0791 0.0641 43.5~1.5! 29.9~1.6! 50.2~1.2! 76.4~1.9! HRPD5.0 233.5 0.0155 0.0118 44.1~1.3! 29.2~1.4! 50.8~0.9! 76.0~1.8! D2B5.0 218.7 0.0304 0.0239 53.1~1.9! 23.0~2.0! 44.8~1.1! 79.1~2.4! D2B*5.0 198.9 0.0170 0.0133 45.4~1.5! 27.6~1.6! 48.5~1.0! 78.6~1.8! D2B5.0 160.7 0.0176 0.0137 42.5~1.1! 26.1~1.3! 52.7~0.8! 78.8~1.4! D2B5.0 130.8 0.0174 0.0135 41.2~1.2! 21.1~1.3! 53.3~0.9! 84.4~1.4! D2B5.0 119.0 0.0362 0.0293 39.6~1.7! 17.4~1.8! 54.0~1.0! 89.0~2.0! D2B*5.0 101.8~q! 0.0195 0.0147 41.1~1.4! 14.0~1.7! 56.2~1.2! 88.7~1.8! D2B5.0 100.0 0.0359 0.0289 37.3~1.5! 13.4~1.7! 55.6~1.0! 93.7~1.9! D2B*amb 127.0~q! 0.0164 0.0128 39.8~1.0! 18.9~1.2! 56.4~0.8! 85.0~1.2! D2B†

amb 98.0~q! 0.0188 0.0148 41.9~0.9! 22.7~1.0! 53.6~0.6! 81.9~1.0! D2B†*

7171J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 The structure and ordering of ices III and V

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molecules, Fig. 5. The asymmetric unit consists of four dis-tinct oxygen and fourteen distinct deuterium atoms. The deu-terium occupancies, again by virtue of the Bernal–Fowlerrules, can be described by just four variables,16 a, b, g, andd, ~Table V!. Oxygen atoms of the type O~4! are bound toone another across twofold axes and symmetry centers. Forthis reason the two deuterium atoms D~16! and D~18! areconstrained to fully disordered occupancies of 50%.

The initial model used in the refinement of all ice V datawas based on the single crystal results of Hamiltonet al.8

Their data, collected on a sample recovered to ambient pres-sure at 110 K, indicated strong partial order of the deuteriumatoms. However, as with ice III, no initial bias was placed onthe occupancies of the deuterium atoms. The initial modeltherefore comprised the atomic positions described byHamiltonet al.with the deuterium atoms populated in a fullydisordered way.

The data collected on D2B at 5.0 kbar and 219, 119, and100 K, and at ambient pressure and 100 K, data that werecollected for only 3 h, were refined with the deuterium posi-tions constrained to the values obtained after refinement ofthe data collected at 5.0 kbar and 199, 131, and 98 K, and atambient pressure and 127 K, respectively.

Additional peaks were found within the ice V data pro-

files and could not be identified as any known phase of ice orargon hydrate. Since this work represents the first diffractiondata collected on ice V at high temperature and pressure, i.e.,within the established stability region of ice V, the additionalpeaks may have been an indication of a different structure tothat reported. Fortunately, the additional peaks were laterfound in diffraction data collected on ice IV.14 The peaks aretherefore the result of a different, as yet unidentified, phasewhich, due to its slow growth with time, is thought to besome form of argon hydrate.

The profile fits resulting from the refinement of theHRPD and D2B data collected at 5.0 kbar and;235 K areshown in Fig. 3.

III. RESULTS

Due to the large number of data sets collected in thiswork at various pressures and temperatures, the atomic pa-rameters for ices III and V are given for a single (p,T) pointonly, Tables IV and V, respectively. The atomic parametersarising from the refinement of all other data sets can be ob-tained from the Electronic Physics Auxiliary Publishing Ser-vice ~EPAPS!.17

FIG. 2. The profile fits for the ice III data collected on HRPD at 3.0 kbarand 250 K~top! and on D2B at 2.50 kbar and 240 K~bottom!. The two setsof ticks present in each profile fit represent reflections arising from the argonclathrate~upper! and ice III ~lower!. Aluminum peaks arising from the pres-sure cell, present within the D2B data, were excluded.

FIG. 3. The profile fits for the ice V data collected on HRPD~top! and D2B~bottom! at 5.0 kbar and;235 K. The two sets of ticks present in eachprofile fit represent reflections arising from the argon clathrate~upper! andice V ~lower!. Peaks arising from the pressure cell~D2B data! and an, as yetunidentified, phase were excluded.

7172 J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 Lobban, Finney, and Kuhs

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Since argon at 5.0 kbar solidifies at 180 K,18 it is un-known what pressure is experienced by the ice V samplebelow this temperature. A comparison of the lattice con-stants, Table II, for data sets below this temperature cannottherefore be made.

IV. DISCUSSION

A. Positional and orientational disorder

The geometry of the water molecule in ice is not thoughtto differ significantly from that found in the vapor, O–D50.97 Å and D–O–D5104.6°.19 However, the bondlengths and angles determined by crystallography are oftenvery different for ices in which the water molecules are ori-entationally disordered. There are six possible orientationsthat a water molecule can adopt. The positions of atoms de-termined by crystallography are the space–time average ofall six orientations. However, the position of the water mol-ecule for each of the six orientations may differ. These localdisplacements from the crystallographic mean lead to artifi-cial bond lengths and angles.1

There are two main mechanisms thought to be respon-sible for displacing the water molecules from their crystallo-graphic mean.8,20–22First, the water molecules move to bet-ter accommodate theO–O–O bond angles and therebydecrease the strain on the O–D•••O hydrogen bonds. Sec-ond, the water molecules experience intermolecular interac-tions, both attractive and repulsive, from the surroundingnonbonded water molecules.23–25

Since the bond angles and nonbonded interactions maydiffer for each of the six different orientations, the potentialenergy of a water molecule occupying each of the six differ-ent orientations may also differ. This is therefore likely tolead to partial ordering of the water molecules, with someorientations more energetically favorable, and therefore moreoccupied, than others.

B. Ice III

During the experiment carried out on HRPD, ice IIItransformed over a period of 6 h to ice II at 3.3kbar and 250K. The slow rate of transition suggests that the pressure andtemperature conditions were very close to the ice II–III tran-sition line, but just inside the ice II stability region; this is inagreement with the ice II–III transition line determined byBridgman,26 Fig. 1. However, the ice II that resulted washighly textured. The formation of texture from a good pow-der would suggest that either nucleation of ice II from ice IIIcrystals is rare and/or that ice III is first melting and thenrefreezing to form ice II. The suggestion that ice III may beinitially melting, 8 K below the established ice–liquidtransition,26 is feasible with a subcooling of 11 K reportedfor the formation of ice III from the liquid.3 However, theformation of a liquid through a solid–solid transition is cer-tainly unexpected and is, to the best of our knowledge, thefirst report of such behavior.

Although Arnold et al.27 formed textured ice II in at-tempting to form ice III by pressurizing ice Ih, the pressuresand temperatures involved suggest that their ‘‘unstable liq-uid’’ formed as a result of extending the extrapolated Ihmelting curve. Similar behavior was also found in this workwhen the formation of ice III was attempted from ice Ih; theextrapolated ice Ih melting curve cannot, however, explainthe texture arising from the ice II–III transition at 3.3 kbarand 250 K, Fig. 1.

The deviation in O–D bond lengths, Table VI, from thatfound in fully ordered ices reflects the positional disorderpresent within ice III. To try and ascertain the sources of thepositional disorder is difficult by crystallographic meansonly, particularly in the case of ice III in which it is unknown

TABLE IV. The ice III fractional coordinates, isotropic thermal factors, andfractional occupancies for the data set collected on D2B at 2.5 kbar and 240K. The occupancies of the individual deuterium atoms are labeled accordingto the corresponding ordering parameters.

x y z U iso (Å 2) Occ.

O~1! 0.113~3! 0.311~3! 0.287~3! 0.062~3! 1O~2! 0.397~2! 0.397~2! 0 0.044~4! 1D~3! 0.239~6! 0.321~5! 0.195~6! 0.048~10! aD~4! 0.132~3! 0.437~4! 0.404~4! 0.052~11! bD~5! 20.004~5! 0.338~5! 0.243~7! 0.072~14! 12bD~6! 0.109~3! 0.182~4! 0.318~3! 0.068~7! 12aD~7! 0.290~3! 0.358~2! 0.102~3! 0.047~6! 12aD~8! 0.383~5! 0.576~5! 20.037~2! 0.038~9! a

TABLE V. The ice V fractional coordinates, isotropic thermal factors, andfractional occupancies for the data set collected on D2B at 5.0 kbar and 234K. The occupancies of the individual deuterium atoms are labeled accordingto the corresponding ordering parameters.

x y z U iso(Å2) Occ.

O~1! 0.25 20.176~2! 0 0.0349~12! 1O~2! 0.466~2! 0.065~1! 0.157~1! 0.0349~12! 1O~3! 0.276~2! 20.349~2! 0.245~1! 0.0349~12! 1O~4! 0.391~1! 0.363~2! 20.019~1! 0.0349~12! 1D~5! 0.332~2! 20.108~3! 0.042~2! 0.0489~15! 12aD~6! 0.246~3! 20.245~3! 0.076~3! 0.0489~15! aD~7! 0.401~3! 20.021~3! 0.095~2! 0.0489~15! aD~8! 0.422~5! 0.059~5! 0.218~4! 0.0489~15! bD~9! 0.471~2! 0.161~3! 0.099~2! 0.0489~15! gD~10! 0.566~2! 0.002~2! 0.205~2! 0.0489~15! dD~11! 0.248~2! 20.304~2! 0.156~2! 0.0489~15! 12aD~12! 0.355~6! 20.444~6! 0.272~5! 0.0489~15! 12dD~13! 0.331~2! 20.265~3! 0.317~3! 0.0489~15! 12gD~14! 0.182~2! 20.388~2! 0.257~1! 0.0489~15! 12bD~15! 0.437~3! 0.269~3! 0.054~3! 0.0489~15! 12gD~16! 0.299~2! 0.389~2! 20.005~2! 0.0489~15! 0.5D~17! 0.369~3! 0.312~3! 20.099~3! 0.0489~15! gD~18! 0.467~3! 0.447~3! 20.021~3! 0.0489~15! 0.5

TABLE VI. Ice III O–D bond lengths~angstroms!.

D2B1 D2B2 D2B3 HRPD D1A

O~1!–D~3! 1.05~4! 1.08~6! 1.02~6! 1.06~6! 0.96~4!O~1!–D~4! 1.18~4! 1.17~4! 1.20~5! 1.11~2! 0.97~4!O~1!–D~5! 0.86~5! 0.84~4! 0.90~5! 0.83~5! 0.94~4!O~1!–D~6! 0.89~3! 0.94~3! 0.91~4! 0.96~6! 0.94~2!O~2!–D~7! 1.04~2! 1.08~3! 1.01~3! 1.06~4! 1.00~2!O~2!–D~8! 1.23~3! 1.20~5! 1.20~6! 1.00~9! 1.08~3!

7173J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 The structure and ordering of ices III and V

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how frequently each of the six orientations per water mol-ecule are occupied. This, it should be noted, cannot be de-termined directly from the values ofa andb. For example,an a of 33.3% implies that of the six orientations presentedto water molecules of type O~2!, Fig. 4, three are occupiedtwice as often as the other three. No information, however,can be obtained on the frequency of occupation of the sixindividual orientations.

The results of the refinements clearly indicate partial or-dering of the water molecule orientations within ice III,Table VII. The ordering found is consistent for all data setswith occupancies of about 35% and 50% fora and b, re-spectively. The variation in theO–O–Obond angles fromthe D–O–Dbond angle of 104.5°, Fig. 4 and Table VIII,implies significant hydrogen-bond bending is occurringwithin the structure. Partial ordering of the water moleculesmight therefore be expected, particularly with the occurrenceof an O–O–Obond angle of as high as 144°. However, theobserved ordering cannot be easily explained by theO–O–Obond angles alone. Of the six orientations occupied by watermolecules of type O~1!, only one, O~18) –O~1!–O~28) with abond angle of 144°, seems particular unfavorable. Were thisorientation occupied less frequently than the other five, thenan increase ina, and an equivalent decrease inb, from thenominal value of 50% would result, Fig. 4; yet we observethe direct opposite. A full discussion on the individualO–O–Obond angles and their expected roles in the orderingprocess is too detailed, and perhaps speculative, for this re-port; a more detailed account can be found elsewhere.14

Since theO–O–Obond angles alone are unable to accountfor the observed ordering, nonbonded interactions must alsoplay an important role in the partial ordering of ice III.

In ice II, the water molecules are all orientationally or-dered, but the water molecules do not occupy preferentially

those orientations with the least amount of bond bending.2,28

Rather than occupying sites withO–O–O bond angles of99° and 115°, the water molecules prefer sites with bondangles 88° and 99°. The ordering process in ice II is there-fore not solely controlled by the desire for linear hydrogenbonds. Although the water molecules in ice IX~the orderedequivalent of ice III! occupy sites of least bond strain, thewater molecules are not symmetrically oriented with respectto the donor angles which they occupy,21 a feature also foundin ice II. The amount of hydrogen-bond bending is thereforeincreased unnecessarily. This points to strong influencesother than that of bond strain on the orientation of the watermolecules. The mechanism responsible is most likely non-bonded interatomic interactions.

The ordering determined here,a535(3)%, b550(4)%, differs from that found by Londono, Kuhs, andFinney,3 a533(7)%, b541(1)%. There are several rea-sons why this may be the case, the most likely being texture.Londono, Kuhs, and Finney found that their ice III samplewas textured and, in refining the data, chose a single axis ofpreferred orientation which led to the biggest improvementin fit. However, the texture most probably arose from poorpowder statistics, in particular the formation of several largecrystallites within an otherwise good powder, and cannot beeasily modeled, particularly not by a single axis of orienta-tion. In addition, Londono, Kuhs, and Finney refined theatomic positions with an O–D bond-length restraint of0.97~5! Å, based on the bond lengths determined by La Placaet al. for ice IX. However, the water molecule orientations inice IX are almost completely ordered and the positional dis-order will therefore be small. The restraint is likely to be tooconstrictive for the more disordered ice III structure; it hasalready been noted that positional disorder within ice III re-sults in large variations in the O–D bond lengths from the

FIG. 4. The ice III structure viewed along thec axis.Only deuterium atoms of the asymmetric unit areshown for clarity.

TABLE VII. The RietveldR factors and fractional occupancy parameters for the deuterium atoms of ice III.aandb represent the orientational ordering permitted by the Bernal–Fowler ice rules. 0 and 100% represent fullorder, 50% full disorder.

P~kbar! T~K! Rwp Rp a~%! b~%! Inst.

2.5 240 0.0516 0.0450 35~1! 49~2! D1A2.5 240 0.0156 0.0115 35~2! 52~4! D2B1

2.5 250 0.0156 0.0117 35~3! 50~4! D2B2

3.3 250 0.0159 0.0118 36~3! 50~4! D2B3

3.0 250 0.0750 0.0656 36~4! 53~2! HRPD

7174 J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 Lobban, Finney, and Kuhs

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value of 0.97 Å. When the same bond-length restraint wasused to refine the data collected in this work, botha andbwere found to decrease.14

There were no measurable changes in the ordering of iceIII upon changes in pressure and temperature within thesmall region of stability. This is not totally surprising sinceany significant changes would have previously been ob-served dielectrically4,5 and/or spectroscopically.29

Nishibata and Whalley30 recorded a change in entropy of1.3460.29 J K21 mol21 for the transition ice III–IX. How-ever, the figure is only 40% of that expected, 3.37J K21 mol21, if the water molecule orientations in ice IIIwere fully disordered and fully ordered in ice IX. At thattime dielectric measurements gave no indication of partialorder within ice III,4,5 leaving Nishibata and Whalley to con-clude that ice IX must be partially disordered. However, nowthat the extent of orientational order within ice III is known,the entropy change can be used to determine the residualdisorder present in ice IX. Using the configurational statisticsdescribed by Howe and Whitworth,31 the measured entropychange corresponds to a massive 36% of the water moleculesin ice IX occupying disordered sites, i.e.,a5b518%. Thisis much larger than the disorder found by Londono, Kuhs,and Finney,a52.9(3)% andb55.6(4)%, and by LaPlacaet al., a53.4(7)% andb55.1(9)%, for their recoveredsample, both through neutron diffraction. Conversely, if it isassumed that the residual disorder within ice IX is 8.5% (a1b), then the entropy change would correspond to 64% ofthe water molecules in ice III occupying ordered orienta-tions. The entropy difference measured by Nishibata andWhalley cannot therefore be explained purely in terms ofconfigurational entropy based on the ordering found here forice III and by others for ice IX.

The compressibility and expansivity of ice III were cal-culated using only the refined D2B lattice constants, Table I.In this way, any systematic errors associated with measuringthe temperature, pressure, and wavelength were removed.The compressibility of ice III is found to be 11.4~2! Mbar21

at 250 K, which corresponds to an isothermal bulk modulusof 88~2! kbar. This figure is in general agreement with theadiabatic bulk moduli determined from acoustic velocitymeasurements by Shaw,32 85 kbar, and by Tulket al.,33 92.7kbar, for H2O ice III at 248 and 253 K, respectively. The

expansivity of ice III is 239~12! MK21 at 2.5 kbar. Thisrepresents the first information on the expansivity of this icestructure. A comparison with other ice structures, Table IX,reveals that the expansivity of ice III is similar to that of theother high pressure forms of ice. Only ice Ih, with its linearhydrogen bonds, shows less lattice anharmonicity.

The change in thec/a ratio with pressure and tempera-ture, Table I, immediately indicates anisotropic compress-ibility and expansivity. The linear compressibilities and ex-pansivities in theab and c axis directions are 2.12~12! and7.34~17! Mbar21, and 30~8! and 172~12! MK21, respec-tively. Since no change in orientational ordering was ob-served with temperature or pressure, these figures imply thatthe flexibility of the hydrogen bonds in thec-axis direction isgreater than those in theab-axis direction. An examinationof the structure indicates a possible reason why changes withtemperature and pressure are greater in thec-axis direction.Water molecules of type O~1! form spirals which run parallelto thec-axis, while water molecules of type O~2! act to bindfour neighboring spirals together. In this way, the spirals canbe thought of as springs, with compression and thermal ex-pansion of the structure easiest along the axis of the springs,i.e., along thec axis.

C. Ice V

The structure of ice V recovered to ambient pressure,determined by Kamb, Prakash, and Knobler34 and later con-firmed by Hamiltonet al.,8 is established by this presentwork as the structure formed at high pressure.

The water molecule orientations within ice V are clearlynot random as previously thought,4,6 but exhibit partial or-dering which is particularly strong across some bonds, Fig. 5

TABLE VIII. Ice III O–O–O bond angles~degrees!.

D2B1 D2B2 D2B3 HRPD D1A

O~18) –O~1!–O~19) 114.3~0.3! 114.0~0.4! 112.6~0.4! 113.0~0.5! 114.0~0.2!O~18) –O~1!–O~2! 90.5~0.3! 90.9~0.4! 90.5~0.4! 88.4~0.5! 90.2~0.4!O~18) –O~1!–O~28) 96.2~1.1! 93.4~1.4! 98.5~2.0! 92.3~1.0! 96.0~1.0!O~19) –O~1!–O~2! 100.1~0.8! 101.7~1.2! 99.0~1.4! 103.4~1.1! 100.5~0.9!O~19) –O~1!–O~28) 143.6~0.6! 144.3~0.7! 143.4~1.1! 148.2~0.5! 144.0~0.6!O~2!–O~1!–O~28) 99.0~0.6! 100.2~0.9! 98.5~0.9! 95.9~1.0! 98.8~0.8!O~1!–O~2!–O~1-) 104.6~0.4! 103.1~0.6! 105.5~0.8! 105.8~0.4! 104.7~0.4!O~1!–O~2!–O(18v ) 103.1~0.8! 104.1~1.3! 103.5~1.3! 109.8~1.5! 104.0~1.3!O~1!–O~2!–O(1v ) 126.9~0.7! 126.4~1.0! 127.1~1.2! 120.2~0.8! 126.2~0.9!O~1-) –O~2!–O(18v ) 126.9~0.7! 126.4~1.0! 127.1~1.2! 120.2~0.8! 126.2~0.9!O~1-) –O~2!–O(1v ) 93.4~1.1! 96.3~0.6! 90.7~2.0! 95.1~1.2! 93.4~1.1!

O(18v) –O~2!–O(1v ) 104.6~0.4! 103.1~0.6! 105.5~0.8! 105.8~0.4! 104.7~0.4!

TABLE IX. The density and thermal expansivity of various ice phases~Ref.14!.

Ice phase P~kbar! T~K! r~g cm23) b~MK21)

Ih 0 242.5 1.0203~2! 173~11!III 2.5 245.0 1.2843~1! 239~12!II 4.2 225.0 1.3346~1! 261~2!V 5.0 245.5 1.4068~1! 240~5!XII 5.0 257.5 1.4355~3! 274~5!

7175J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 The structure and ordering of ices III and V

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and Table III. Unfortunately, the factors responsible for thepartial order cannot be easily identified for such a compli-cated structure.

Ice V possesses a large number ofO–O–Obond angleswhich differ greatly from theD–O–Dbond angle of 104.5°,Table X. Competition between orientations makes the task ofunderstanding the ordering within ice V difficult. For ex-ample, water molecules of type O~2! have twoO–O–O do-nor angles which are much more favorable in terms ofhydrogen-bond strain than the rest, namely O~1!–O~2!–O(38v ) and O~1!–O~2!–O~4!, Table X and Fig. 5. The occu-pation of only these orientations would lead to order param-eters:a5100%, b50%, andg5d550%. However, themost favorable donor angle available to water molecules oftype O~1!, O~2!–O~1!–O~28!, would suggesta50%. Thereis therefore competition between different factors in deter-mining what the ordering should be. With four crystallo-graphically different water molecules, each of which mayoccupy one of six different orientations, the large number ofcombinations makes any justification of the observed order-ing in terms of theO–O–Obond angles extremely difficult.

Moreover, it is highly unlikely that the observed partialorder is purely related toO–O–Obond angle distortion. Forices II and III there are other factors, most probably non-bonded interactions, which are thought to influence the ob-served order. Since ice V is denser than both ices II and III,it seems reasonable to assume that nonbonded interactionswill also have an important influence on the ordering of thewater molecules’ orientations.

As already noted, each of the six orientations for a par-ticular water molecule will have a different occupation en-ergy arising from differences in hydrogen-bond bending andnonbonded interactions. A water molecule will therefore re-quire more energy to occupy an orientation for which theO–O–Obond angle is 140° than one for which the angle is110°. As the temperature is decreased, the total energy of thesystem and hence the average energy of the individual watermolecules decreases. The occupation of orientations withhigh hydrogen-bond strain will therefore decrease with tem-perature resulting in a gradual increase in the orientationalordering.

Changes in orientational order with pressure are of adifferent nature to that of temperature and can be attributedto two effects. First, the increase in pressure further distortsthe ice structure. As the water framework of any ice structureis compressed, the hydrogen bonds linking water moleculesbend under strain and eventually break, leading to the forma-tion of a new ice phase. As the hydrogen-bond strain in-creases, the energy required for occupation of the differentorientations increases. The situation is similar to that of de-creasing temperature in that the energy of the water mol-ecules relative to that required for occupation of given sitesdecreases. Second, as the pressure is increased the density ofthe ice naturally increases. The fraction of free space occu-pied by each water molecule therefore decreases and thenonbonded interactions become increasingly important.While the changes in the individual ordering parameters ofice V were small with respect to the estimated errors, TableIII, the total amount of ordering increased from 13.8~2!% at4 kbar to 15.3~1!% at 5 kbar. The increase in hydrogen-bondstrain over this pressure range was negligible with a rmsbond-angle deviation from the ideal tetrahedral angle of18.2~1.2!° and 18.3~0.8!° at 4.0 and 5.0 kbar, respectively.This would suggest that the observed increase in orderingwith increase in pressure resulted most likely from changesin the nonbonded interactions.

The space-group symmetry of ice V within the thermo-dynamic stability region isA2/a, constraining two of thedeuterium atoms, D~16! and D~18!, to fully disordered occu-pancies of 50%. For ice V to achieve full orientational orderat low temperatures (,150 K!, such as found for ice III/IX,the space-group symmetry must be degraded. Kamb and LaPlaca35 reported such a degradation for ice V recovered toambient pressure. They found, through single-crystal neutrondiffraction, a reversible change in the space-group symmetryfrom A2/a to P21 /a, in the temperature range 105–130 K,which they attributed to a disorder–order transition. Unfor-tunately, their findings have only been reported in anabstract35 and have never been published fully. Nevertheless,Handa, Klug, and Whalley7 appear to have found the same

FIG. 5. The structure of ice V viewed along theb axis. The oxygen atoms ofthe unit cell are shown as large circles with some of the deuterium atomsshown as small circles; the fractional occupancies of the deuterium atomsare also shown. The atoms are labeled according to Table V.

TABLE X. Ice V O–O–Obond angles~degrees! for the data set collectedon D2B at 5.0 kbar and 234 K.

O~2!–O~1!–O(28) 98.1~7! O~1!–O~2!–O~3! 82.6~4!O~2!–O~1!–O(38) 131.9~4! O~1!–O~2!–O(38v ) 100.4~5!O~2!–O~1!–O(39) 86.9~4! O~1!–O~2!–O~4! 100.0~6!O(28) –O~1!–O(38) 86.9~4! O~3!–O~2!–O(38v ) 133.6~6!O(28) –O~1!–O(39) 131.9~4! O~3!–O~2!–O~4! 89.4~5!O(38) –O~1!–O(39) 124.1~8! O(38v ) –O~2!–O~4! 134.3~6!O(18) –O~3!–O~2! 126.6~6! O~2!–O~4!– O(3-) 92.4~5!O(18) –O~3!–O(29) 114.3~4! O~2!–O~4!– O(48) 87.1~5!O(18) –O~3!–O(48) 114.3~5! O~2!–O~4!– O(49) 119.1~7!O~2!–O~3!–O(29) 114.3~5! O(3-) – O~4!–O(48) 91.1~5!O~2!–O~3!–O(48) 86.6~5! O~3!–O~4!–O(49) 126.1~7!O(29) –O~3!–O(48) 89.5~6! O(48) –O~4!– O(49) 129.6~5!

7176 J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 Lobban, Finney, and Kuhs

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order–disorder transition. Heat capacities, measured assamples recovered to ambient pressure were warmed from77 K, highlighted an endothermic transition over the tem-perature range 106–132 K, thought to be the reorientation ofwater molecules from an ordered to disordered state. In-creases in the transition entropy were found with increasingannealing times and for samples doped with KOH, addingweight to the suggestion that the transition was one involvingorientational ordering of the water molecules. Their work,however, was unable to establish figures for the orientationalorder before or after the transition.

In contrast, no such transition has been observed in thiswork. Instead, the orientational ordering of the water mol-ecules is found to increase gradually with decreasing tem-perature at 5.0 kbar; certainly no dramatic change in orderingwas observed between 131 and 102 K which may have beeninterpreted by others as a ordering transition. The behaviorobserved by both Kamb and La Placa, and Handa, Klug, andWhalley does not appear to be an artifact of recovering ice Vto ambient pressure, since again, no changes in the orderingwere noted at ambient pressure, 98 K and 127 to suggest atransition, Table III. Handa, Klug, and Whalley found thetransition entropy to increase with annealing time at 100 K.The data at 5.0 kbar and 102 K were collected over a 12 hperiod. If the ordering increases linearly with time at thistemperature, as suggest by the annealing–enthalpy plots ofHanda, Klug, and Whalley,7 then the diffraction data repre-sent the structure annealed at 102 K for 6 h. According toHanda, Klug, and Whalley, the transition entropy for asample annealed for 6 h at 100 K isapproximately 0.29J mol21 K21. The change in ordering found in this work canonly account for a third of this value. While changes in ori-entational ordering cannot account for all of the transitionentropy measured by Handa, Klug, and Whalley, it mustnevertheless account for some~in this case around a third!.Longer annealing times, and better-still doping, must there-fore lead to further increases in the ordering of ice V at 100K, which may eventually result in a change in space group.

Bridgman36 examined the ice III–V and V–VI transi-tions over a range of pressures and temperatures and foundthat the equilibrium lines defining the transitions werestraight. The Clausius–Clapeyron relation, (]p/]T)eq

5DS/DV, states that the gradient of the equilibrium curve isproportional to the entropic difference between the twophases. Since the amount of orientational order within ice Vis sensitive to temperature, the gradient of the equilibriumcurves, III–V and V–VI, should also change with tempera-ture. However, the difference in the orientational order forthe two temperatures 254 and 237 K, corresponds to achange in entropy of only 0.03 J mol21, i.e., 0.0018J mol21 K21. The average change in volume for the transi-tion ice III–V was 0.98 cm3 mol21. From this, the change ingradient of the equilibrium curve is 0.02 bar K21. This is ofcourse too small to be measured experimentally and hence astraight equilibrium curve is recorded. For the ice V–VItransition, the change in volume is slightly smaller,0.69 cm3 mol21, but a similarly small change in gradient,0.03 bar K21, is expected.

D. Point defects

It is well known that reorientation of the water mol-ecules, and therefore ordering, cannot occur without pointdefects, and that the rate of reorientation is determined by thenumber density and mobility of such defects. There are twomain types of defect thought to occur in ice: rotational~L andD! and ionic (H3O

1 and OH2). The number density andmobility of these defects in the high pressure ices remainunknown, and only a little is known for ice Ih. The numberdensities of the two different forms of defects are37

nr52NH2O expS 2Ear

2kBTD , ni'2

3NH2O expS 2

Eai

2kBTD , ~1!

where Ear and Eai are the activation energies required tocreate a rotational and ionic defect, respectively. There issome disagreement in the literature concerning the precisevalues for the activation energies of defects in ice Ih. How-ever, it is agreed that the energy required to create a rota-tional defect (;0.7 eV! is less than that for an ionic defect(;1.3 eV!, while the energy required for mobilization of arotational defect (;0.2 eV! is higher than that for an ionicdefect (;0 eV!.37 The actual mobilities, i.e., the rate atwhich the defects migrate through the structure, is not clear,though it is thought that rotational defects move quicker thanionic defects, and that OH2 ions move quicker than H3O1.37

Wilson et al.4 performed a dielectric study of H2O ice Vin the pressure–temperature region: 3.5–6.4 kbar and 232.3–261.3 K, from which they obtained water molecule relax-ation times, i.e., the time elapsed between two successivedefects arriving at a particular water molecule. From Eq.~1!,the known activation energies, and the nuclear magneticresonance work of Fujara, Wefing, and Kuhs,38 the defectschiefly responsible in ice Ih for relaxation at these tempera-tures seem to be rotational defects. Wilsonet al. found therelaxation times for ice Ih to be two orders of magnitudelonger than those for ice V. This would suggest that eitherthe activation energy of creation and/or mobilization of de-fects is lower in ice V. Wilsonet al. went on to suggest thatthe observed relaxation in ice V was dominated by rotationaldefects based on measured volumes of activation. However,at that time it was thought that the activation volume wasnegative for ionic defects and positive for rotational defects.It has since been shown39 that both types of defects require apositive activation volume, at least in ice Ih. The positivevolume of activation measured by Wilsonet al.cannot there-fore be a direct measure of the type of defects present.

The increasing relaxation time with decreasing tempera-ture, as recorded by Wilsonet al., implies a positive energyof mobilization for the defects within ice V. If it is assumedthat the mobilization energy of ionic defects in ice V is zero,as it is in ice Ih, then the relaxation at high temperaturesmust be dominated by rotational defects.

It is thought that ionic defects migrate through the struc-ture of ice Ih via incoherent tunneling, hence the zero energyof mobilization. By the very nature of the ice Ih structure,each water molecule sits in a potential well of almost equalenergy, and with energetic fluctuations the difference in po-tential energy between neighboring water molecules can be

7177J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 The structure and ordering of ices III and V

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zero allowing the ionic defect to tunnel. This is not the casefor ice V in which the water molecules experience differentdegrees of hydrogen-bond strain and nonbonded interactions.The same features responsible for orientational ordering willalso mean that the potential energy of each water moleculewill differ from that of its neighbor. Nevertheless, tunnelingmay also be possible in ice V with energetic fluctuations.Unlike the case of ice Ih however, the difference in potentialenergy between neighboring water molecules may be large,and hence the tunneling of defects in a particular directionmay be extremely rare.

The relaxation times recorded by Wilsonet al., whenextrapolated to low temperatures, suggest relaxation times

for ice V of 1 s at 160 K, 1 min at 145 K, and 112 h at 130 K,

Fig. 6. While the following discussion will make use of therelaxation times for H2O ice V, it should be noted that relax-ation times for D2O are thought to be much longer, perhapsby as much perhaps as two orders of magnitude.40 The aver-age rate of cooling on quenching ice V in liquid nitrogen was1.5 K s21 between 160 and 100 K. This would suggest thatthe water molecules were frozen into their orientations ataround 155 K. Data were then collected over a period of12 h at 102 K. However, with a relaxation time of 37 years atthis temperature, no further ordering would have occurred.The degree of ordering for the quenched sample shouldtherefore be similar to that observed at 155 K, i.e., not toodissimilar to that measured in this work at 160 K. Yet theordering is not only greater than that observed at 160 K, but

also greater than that at 130 K. Clearly the relaxation timesat lower temperatures are much shorter than those predictedby Wilson et al.

Zaretskii and co-workers41,42 have found that the relax-ation times for ice Ih increase in a similar manner to that ofice V between 270 and 200 K. However, below this tempera-ture the increase in relaxation time begins to slow down andeventually levels out at around 140 K. At this point onlyionic defects, with a mobilization energy of zero, are respon-sible for the observed relaxation. Shorter relaxation times atlow temperatures can only occur within ice V if a similarbehavior exists. For a change in gradient in the relaxationtime versus temperature, there must be a change in the typeof defect predominant at low temperatures. The questionthen is: which defect is operative at high temperatures andwhich at low temperatures?

Handa, Klug, and Whalley7 found increases in the tran-sition entropy of ice V at ambient pressure with increasingannealing time at 110 K. Furthermore, samples doped withKOH, thought to increase the number of OH2 defects, dra-matically increased the transition entropy. This thereforesuggests that the ionic defects are responsible for relaxationat low temperatures and consequently rotational defects athigh temperatures. For this to occur, the activation energyrequired for the creation of rotational defects must be lowerthan that for ionic defects, as found in ice Ih. In addition, theactivation energy required for mobilization of ionic defectsmust be lower than that of rotational defects. Although thecase for a zero mobilization energy of ionic defects withinice V is feasible, according to the above-mentioned argu-ments on tunneling, it cannot be established purely from theresults obtained in this work. However, if the migration ofionic defects in ice V is an activated process, then the acti-vation energy itself must be very small to account for theshort relaxation times at such low temperatures.

The sensitivity of orientational ordering within ice Vwith temperature may in fact be of use in determining therelaxation times at low temperatures and hence the activationenergy of mobilization for ionic defects. For example, therate of cooling in this work was 1.5 K s21 between 160 and100 K. Unfortunately, the exact numbers on the orderingbetween 130 and 100 K are not known and it is thereforeimpossible to say exactly at what temperature the water mol-ecules were frozen into their orientations upon quenching.Nevertheless, since the ordering present within the quenchedsample is greater than that at 130 K, either the relaxationtime at 130 K is shorter than 1.5 s or the relaxation time at

TABLE XI. The densities, hydrogen-bond bending, and shortest nonbonded contacts for the various ‘‘nonor-dered’’ ices (D2O). ^(du)2&1/2 is the rms of O–O–Obond angle deviations from the ideal tetrahedral angle of109.5°.

Ice phase P~kbar! T~K! r(g cm23) ^(du)2&1/2 O•••O ~Å! Ref.

Ih 0 223 1.03 0.1 4.51 37III 2.5 250 1.28 15.5 3.51V 5.0 254 1.40 18.5 3.27VI 11.0 225 1.53 23.2 3.34 44VII 24.0 263 1.79 0 2.74 44

FIG. 6. Arrhenius plot of the relaxation times of ice V as determined byWilson et al. ~Ref. 4! at high temperatures and extrapolated to low tempera-tures, and possible relaxation behavior which can account for the observedorientational ordering found in this work at low temperatures.

7178 J. Chem. Phys., Vol. 112, No. 16, 22 April 2000 Lobban, Finney, and Kuhs

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100 K is of the order of 1 h; this argument follows sinceordering cannot occur at a rate quicker than water moleculerelaxation. If rotational defects are negligible at low tempera-tures, as in the case of ice Ih, then the gradient of the Arrhen-ius plot must remain constant at low temperatures, say below140 K as is found for ice Ih.41,42 A possible scenario for iceV is shown in Fig. 6.

The situation for ice V appears to be very different thanthat for ice VI. Johari and Whalley43 measured the relaxationtimes of ice VI down to 128 K without noting any deviationin relaxation times from Arrhenius behavior. Since the relax-ation times of the two ices are almost identical at high tem-peratures, the results at low temperature suggests that theactivation energy required for mobilization of ionic defectsmust be higher in ice VI than in ice V.

A comparison of ices Ih, III, V, VI, and VII reveals thatwhile the relaxation times of all the high pressure ices aresimilar, typically 2ms at 240 K, relaxation in ice Ih is twoorders of magnitude greater, 200ms.4 It has been suggestedthat hydrogen-bond strain and nonbonded interactions de-crease the relaxation times in the high pressures ices by de-creasing the activation energy of either creation and/or mo-bilization of rotational defects. However, the varying degreeof hydrogen-bond bending and nonbonded contacts in thehigh pressure ices, Table XI, suggests that changes shouldalso be recorded within the high pressure ices. The fact thatthe relaxation times in all the high pressure ices are similarsuggests that, while hydrogen-bond strain and nonbonded in-teraction must to some degree influence relaxation, their in-fluence is small and that the difference in relaxation times,between the high pressures ices and ice Ih, simply arisesfrom an anomalous feature of ice Ih.

V. CONCLUSIONS

The structure of ice V under its thermodynamic condi-tions of stability has been established for the first time. Thewater molecule orientations in both ices III and V are par-tially ordered. While no significant changes in the orderingwere observed for ice III, the ordering in ice V increases withboth increasing pressure and decreasing temperature. Nochange in symmetry, required for full orientational ordering,was noted for ice V at low (,160 K! temperatures. Theordering found here in conjunction with the enthalpy mea-surements conducted by Handa, Klug, and Whalley7 suggeststhat a change in symmetry may occur with lengthy annealingat 100 K, and/or doping with KOH. The dielectric measure-ments recorded by Wilsonet al.4 at high temperatures sug-gest long relaxation times for ice V at temperatures below130 K. However, this does not correlate with the orderingfound in this work since ordering cannot occur at a rate fasterthan orientational relaxation. The relaxation times at lowtemperatures must therefore be shorter than those obtainedthrough extrapolation. Such a change in relaxation requires achange in the type of point defect predominant at high andlow temperatures. Current knowledge on point defects in iceIh,37 along with the behavior noted by Handa, Klug, andWhalley7 of annealing and doping ice V, suggests that therotational defects are responsible for relaxation in ice V athigh temperatures and ionic defects at low temperatures.

ACKNOWLEDGMENTS

We thank the CCLRC and the Institut Laue-Langevin foraccess to the ISIS and ILL neutron facilities, respectively.We also thank the instrument scientists: Richard Ibberson~HRPD!, Alan Hewat~D1A!, Paolo Radaelli~D2B! and Em-manuelle Suard~D2B!, along with the high pressure techni-cians: John Dreyer and Trevor Cooper~ISIS! and Louis Me-lesi ~ILL ! for their invaluable help. Particular thanks toFrank Gotthardt for help in performing one of the experi-ments and determining the cooling rates on quenching. Fi-nally, one of the authors~C.L.! would like to acknowledgeUniversity College London for financial support.

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