Dielectric Properties of Ices II, III, V, and VI

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  • Dielectric Properties of Ices II, III, V, and VIG. J. Wilson, R. K. Chan, D. W. Davidson, and E. Whalley Citation: The Journal of Chemical Physics 43, 2384 (1965); doi: 10.1063/1.1697137 View online: http://dx.doi.org/10.1063/1.1697137 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/43/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Designer interfaces in IIVI/IIIV polar heteroepitaxy J. Appl. Phys. 69, 7021 (1991); 10.1063/1.347641 Acoustic velocities and densities of polycrystalline ice Ih, II, III, V, and VI by Brillouin spectroscopy J. Chem. Phys. 92, 1909 (1990); 10.1063/1.458021 Dielectric properties of ice VI at low temperatures J. Chem. Phys. 64, 4484 (1976); 10.1063/1.432074 The Nature of Surface States on IIIV and IIVI Semiconductors J. Vac. Sci. Technol. 6, 549 (1969); 10.1116/1.1315679 Transformations of Ice II, Ice III, and Ice V at Atmospheric Pressure J. Chem. Phys. 38, 840 (1963); 10.1063/1.1733772

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  • THE JOURNAL OF CHEMICAL PHYSICS VOLUME 43, NUMBER 7 1 OCtOBER 1965

    Dielectric Properties of Ices II, III, V, and VI*

    G. J. WILSON,t R. K. CHAN,t D. W. DAVIDSON, AND E. WHALLEY Division of Applied Chemistry, National Research Council, Ottawa, Canada

    (Received 28 April 1965)

    The dielectric properties of Ices II, III, V, and VI have been measured up to 300 kc/sec over a range of temperatures and pressures. All except Ice II exhibited well-defined dielectric dispersion and so are orienta-tionally disordered under the experimental conditions. The dispersion loci were slightly broader than Debye curves, which may reflect the presence of nonequivalent crystal sites. As for Ice I, the static dielectric constants correspond to values of about 3 for the Kirkwood orientational correlation factor. This suggests that these forms of ice are four coordinated, in agreement with infrared and (for Ice III) x-ray evidence at low temperatures. The relaxation rates are considerably faster than for Ice I, and the activation energies and entropies somewhat lower. The volumes of activation are all about 4.6 cm' mole-i. The relaxation mechanism appears to be similar to that in Ice I, i.e., relaxation occurs by diffusion of orientational defects.

    X-ray and infrared studies have indicated that Ice II is rotationally ordered near liquid-nitrogen tem-perature. The absence of orientational polarization in Ice II at temperatures as high as -300 shows it to be ordered throughout its region of stability.

    I. INTRODUCTION

    SINCE the dielectric properties of ordinary ice (see preceding paper! and references quoted there) are largely determined by the arrangement of the water molecules and by the hydrogen bonds between them, it is of interest to compare them with the dielectric properties of other polymorphic forms of ice in which the arrangement of the water molecules is different. The dielectric properties have recently been reported2

    of some clathrate hydrates, which are essentially ex-panded ice structures stabilized by relatively inert molecules in some of the holes. Water forms several solid phases that are stable only under pressure, namely Ices II,a III, a V,4 VI,4 and VII,5 as well as a number of metastable phases.67 A partial phase diagram is shown in Fig. 1. In this paper, the dielectric properties of Ices II, III, V, and VI are reported.

    This work appears to be the first reported on the dielectric properties of a phase that is stable only under pressure.

    II. EXPERIMENTAL METHODS

    The high-pressure and electrical apparatuses were described in the preceding paper.

    1. Preparation of the Ices

    There are at least two metastable phases of ice, Ice IV which has been firmly identified only for D20 6

    * National Research Council No. 8654. t Present address: Polymer Corporation, Sarnia, Ontario. t Present address: University of Western Ontario, London,

    Ontario. 1 R. K. Chan, D. W. Davidson, and E. Whalley, J. Chem. Phys.

    43, 2376 (1965). 2 G. J. Wilson and D. W. Davidson, Can. J. Chern. 41, 264,

    1424 (1963) j D. W. Davidson, M. Davies, and K. Williams, J. Chern. Phys. 40, 3449 (1964).

    3 G. Tammann, Ann. Physik 2,1 (1900). 4 P. W. Bridgman, Proc. Am. Acad. Arts Sci. 47, 441 (1912). 6 P. W. Bridgman, J. Chern. Phys. 3, 597 (1935). 6 P. W. Bridgman, J. Chern. Phys. 5, 964 (1937). 7 H. Konig, Z. Krist. 105, 279 (1944).

    but which probably exists in H20,4 and Ice Ic (Cubic Ice 1)7 which is unstable relative to Ice Ih (ordinary hexagonal ice), at least at temperatures above 153K.8.9 It is important to establish therefore which form of ice is being examined.

    20r-~--------~------------__ --~ __ ~

    10

    o

    -10

    c

    LIQUID

    o

    . . . e. e.

    o 0 o 111

    o

    000 o 0 0 0

    5, 6 7 8 9 P(kilobars')

    o

    10

    FIG. 1. Partial phase diagram of ice, showing the distribution of the dielectric measurements for: 0, Ice IIj +, Ice IIIj ., Ice Vj and 0, Ice VI.

    Ice II was made by decompressing Ice V at -35C. This method is sometimes more convenient than the usual method4 of compressing Ice I at about -78C. The simplest procedure is to cool liquid water at about 5 kbar to - 35C, and when Ice V is formed, to decom-press it to about 3 kbar. It was verified that Ice II was formed by measuring the pressure and tempera-ture on the II-V boundary and by noting the trans-formation of Ice II to Ice III at the proper4 pressure and temperature when the dielectric measurements of Ice II were completed.

    BL. G. Dowell and A. P. Rinfret, Nature 188,1144 (1960). 9 J. E. Bertie, L. D. Calvert, and E. Whalley, J. Chem. Phys.

    38, 840 (1963). 2384

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  • DIELECTRIC PROPERTIES OF ICES II, III, V, AND VI 2385

    Ice III was made in three ways: from the liquid by cooling at about 3 kbar; from Ice II (see above) by warming at about 3 kbar; and from Ice V by decom-pressing at about - 26C. Most of the dielectric meas-urements were made on Ice III made from the liquid. The liquid sometimes undercooled to about -30C, which is in the region of stability of Ice II (see Fig. 1). It was verified that Ice III was formed when the liquid froze by measuring the transition pressure to Ice V at about -30C; there is a difference of about 0.5 kbar between the III-V and II-V boundaries at this temperature. It is well verified4,9 that Ice III in the stability region of Ice II does not readily transform to Ice II.

    Ice V was made in three ways: by cooling the liquid at about 4.5 kbar; by compressing Ice III at about -30C; and by decompressing Ice VI. Bridgman4 re-ported that Ice V was difficult to make from the liquid and that the metastable Ice IV was formed in prefer-ence. In the present study, and in other work in this laboratory,1O there was no evidence that Ice IV was formed. In particular, the liquid-solid boundary cor-responded to the liquid-V boundary closer than to the liquid-IV boundary, the II-V and V-VI boundaries were in the correct place, and all samples of Ice V made by crossing the boundary lines had the same dielectric properties within the experimental error.

    Ice VI was made by cooling the liquid at about 9 kbar and by transforming Ice V. Samples made by the two methods had the same dielectric properties.

    2. Experimental Procedure

    Measurements were made within each phase on two to four different samples at several pressures at each of several temperatures.

    Phase changes were induced by slow pressure changes in the appropriate region of the p-T phase diagram. They were usually followed by capacitance measure-ments at 1 kc/sec, which reflected the change in both the dielectric constant at that frequency and in the volume. For some of the transformations the volume change was directly measured by means of the screw injector and compared with the values reported by Bridgman.4

    When the unguarded electrode moves in response to a change of pressure or temperature, there is a danger of leaking of oil past the 0 ring to contaminate the sample. A sliver of ice may remain between the 0 ring and the Teflon wall of the cell and provide a hole for leakage of oil. This is most likely to happen during a phase change, because then the electrode moves far-thest, and particularly during a phase change in which the volume increases. A film of oil may also be left behind as the piston moves outward. As long as the phase did not change, the dielectric properties were reversible to changes of pressure and temperature.

    10 J. P. Marckrnann and E. Whalley, J. Chern. Phys. 41, 1450 (1964).

    TABLE I. Estimated relative cell constants for the various phases of ice. a

    Phase T(C) po/kbar Vwo/V .. VT/VTo Co/Coo

    Liquid 25 0 1 1 1 Ih -30 0 0.923 0.986 0.92 II -35 3 1.187 0.933 1.16 III -30 3 1.158 0.934 1.13 V -30 5 1.261 0.897 1.22 VI -30 8 1.353 0.875 1.29

    a The symbols are defined in Ref. 1, Sec. II.S.

    Practically always when a phase was formed from a phase of higher volume, and often when it was formed from one of lower volume, there was no detectable contamination by oil. Specifically, Ice III had the same dielectric properties whether made from Ice I, Ice II, or the liquid; Ice V had the same dielectric properties whether made from Ice III, Ice VI, or the liquid; and Ice VI had the same dielectric properties whether made from Ice V or the liquid. When a phase was formed from a phase of lower volume, there was sometimes evidence of contamination during the phase change. The greatest effects were observed in the transition of Ice III to Ice I, at which an increase of volume of about 25% occurs. There was a considerable increase in the apparent relaxation rate of Ice I, a broadening of the dispersion curve, and a decrease in the static dielectric constant. Sometimes a boundary could be traversed back and forth several times without evi-dence of contamination. The numerical results reported are thought to be unaffected by contamination.

    The relative cell constants were estimated as de-scribed in the preceding paper.! The relative cell con-stants assumed for each phase at a pressure po approxi-mately in the middle of the experimental range of the phase, together with the relative volumes of the water4 and the Teflon,ll ,12 assumed in calculating the cell con-stants, are summarized in Table I. It is doubtful if the compressibilities of the ices and of Teflon are known well enough for the pressure coefficient of the cell constant to be calculated with useful accuracy.

    m. RESULTS

    1. Hydrostaticity of the Stresses

    It was emphasized in the preceding paper,! that the pressure in the ice was changed by first applying a mainly uniaxial stress, which then decays towards a hydrostatic stress by plastic flow. It seemed likely that the plastic flow had no significant effect on the dielectric properties of Ice Ih, at least for the small amounts of plastic flow required when no phase change occurred. Evidence for an effect of shear on the dielec-

    11 C. E. Weir, J. Res. Natl. Bur. Std. 53,245 (1954). 12 R. 1. Beecroft and C. A. Swenson, J. Appl. Phys. 30, 1793

    (1959).

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  • 2386 WILSON, CHAN, DAVIDSON, AND WHALLEY

    ._.!.?~.-.-.-"-.---.~50 150 . r~ A 01"' .. .

    2,....- 30

    / " 40

    c-" 300. '020

    60

    tric properties, particularly the relaxation time, of the high-pressure ices was looked for, but none was found. For example, the properties of a particular phase were independent of whether the phase had been made from a higher-density or a lower-density phase, except for differences that sometimes occurred that could be at-tributed to a leak of oil into the ice (see Sec. II). Because the ices appear unable to sustain nonhydro-static stresses, an apparatus with fixed electrodes should yield more accurate dielectric constants (see Ref. 1, Sec. ILl).

    2. Ice II

    Within the experimental range of frequency (45 cps-300 kc/sec) and temperature (-30 to -40C), this phase alone showed no dispersion characteristic of the rotational relaxation of the water molecules. Over the frequency range of the measurements, the dielectric constant E' was about 4.2, which is similar to the limit-

    TABLE II. Dielectric relaxation times 'To! p'sec of Ice III.

    p/bar

    Temp. Cc) 2400 2700 2920 3100 3355

    -24.13 1.56 -26.39 1.72 1.96 2.06 -30.03 2.56 2.70 -32.31 3.10 3.50 3.62 -34.31 4.10

    4.07 -39.35 6.33 7.30 8.17 -39.76 6.35 6.95 7.47 -44.00 10.56 11.57

    ~\

    \0 \ .0.4

    20

    FIG. 2. Complex dielectric constant plots of Ice III; A, -26.4,3100 bar; B, -43.8, 2895 bar. Frequencies are given in kilocycles per second.

    ing high-frequency values of Ices I, III, V, and VI (see Table V). At low frequencies, there was a small increase in the apparent dielectric constant E' and a larger increase in the dielectric loss E" with decreasing frequency, which varied considerably from sample to sample. A similar behavior occurred on the low-fre-quency side of the dispersion region in the other ices, and it is attributed to electrode polarization, i.e., to the presence of an ionic space charge.

    3. Ices III, V, and VI

    Well-defined dielectric dispersion and absorption curves were shown by Ices III, V, and VI. Repre-sentative examples of plots of the complex dielectric constant E=e'-iE" are given in Figs. 2-4. The loci could all be fitted approximately by circular arcs ac-cording to the Cole-Cole representation, with small values of the distribution paramete...

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