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 III–V and II–VI 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 orientationally 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 temperature. 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 expanded 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.6•7 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 153°K.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 -35°C. This method is sometimes more convenient than the usual method4 of compressing Ice I at about -78°C. The simplest procedure is to cool liquid water at about 5 kbar to - 35°C, and when Ice V is formed, to decompress it to about 3 kbar. It was verified that Ice II was formed by measuring the pressure and temperature on the II-V boundary and by noting the transformation 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 decompressing at about - 26°C. Most of the dielectric measurements were made on Ice III made from the liquid. The liquid sometimes undercooled to about -30°C, 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 -30°C; 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 -30°C; and by decompressing Ice VI. Bridgman4 reported that Ice V was difficult to make from the liquid and that the metastable Ice IV was formed in preference. 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 corresponded 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 measurements 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 farthest, 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 evidence of contamination. The numerical results reported are thought to be unaffected by contamination.
The relative cell constants were estimated as described in the preceding paper.! The relative cell constants assumed for each phase at a pressure po approximately 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 constants, 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 attributed to a leak of oil into the ice (see Sec. II). Because the ices appear unable to sustain nonhydrostatic 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 -40°C), 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-frequency 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. Representative 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 according to the Cole-Cole representation, with small values of the distribution parameter a. We have used the circular-arc approximation to evaluate the relaxation times ro listed in Tables II-IV. (Not all the measurements were made at exactly the temperatures and pressures listed; in these cases small adjustments, which never exceeded 2%, to the nominal conditions were made.) There is however evidence of systematic departures from circular arcs in, for example, the approach of the values of e' toward their static values at low frequencies (see Sec. IV.S). The variation with pressure of logro at a fixed temperature (- 23.4 0) is illustrated in Fig. S.
Values of a were between 0.03 and 0.05 for Ice III, between 0.02 and 0.03 for Ice V, and about 0.05 for Ice VI, some uncertainty arising from the choice of the arc which best fits the data. With the possible exception of Ice V, the departures of the loci from simple Debye semicircles considerably exceeded the
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DIELECTRIC PROPERTIES OF ICES II, III, V, AND VI 2387
e"
40
COO ~ 20 l • ..
I
1'00 • , 0
FIG. 3. Complex dielectric constant plots for Ice V; A, -24.2°,4200 bar; B,-45.6°, 4740 bar.
likely experimental errors and therefore appear to be real.
Static dielectric constants ~o were obtained by extrapolation of the low-frequency data, with ~" approximately corrected for dc conductance. Values of Eo at -30° and rounded pressures po are given in Table V. Because of the possibility of systematic errors in the cell constants, the uncertainties in these values may amount to about 10%, or, for Ice VI, 15%. Figure 6 illustrates schematically the variation with pressure and phase of the static dielectric constant at - 30°.
Values of the limiting high-frequency dielectric constants ~oo are also given in Table V. Within the accuracy of the measurements they showed no variation with temperature or pressure within a given phase.
They were determined from the intercept with the real axis of a semicircle drawn through the experimental points on the high-frequency side of the locus (see Sec. IV.s). The uncertainty introduced by this extrapolation must be added to the uncertainty of the cell constant. Most other extrapolation procedures lead to smaller values of ~OO' Since the tabulated values are already smaller than those calculated from the ClausiusMossotti equation with ~oo of Ice I taken to be 3.2 (4.6, 4.4, 5.1, and 5.9 for Ices II, III, V, and VI, respectively), it is unlikely that the true values exceed the calculated values. There is, therefore, no evidence in our data for any of these ices of such an anomalously large value of ~oo as appears to characterize the microwave dispersion in liquid water. For water at 20°
TABLE III. Dielectric relaxation times TO/p.sec of Ice V.
Temp. (OC)
-12.16 -12.92 -18.80 -20.53 -24.20 -26.40 -32.10 -33.43 -41.20 -45.58
p/bar
3478 3820 4200 4400 4580 4720 4843 4930 5170 5330 5490 5708 5820 6000 6382
1.03 1.56
1.57 1.86 2.02 2.45 1.69 2.03 2.55 2.77 2.34 2.56 3.21 3.87
2.70 3.44 3.94 4.54 5.76 7.28 8.45
6.91 8.17 9.10 16.49 18.74 23.86 26.4 33.2
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2388 WILSON, CHAN, DAVIDSON, AND WHALLEY
40 •
20 •
FIG. 4. Complex dielectric constant plots for Ice VI: A, -22.9°,6720 bar; B, -38.4°,6735 bar.
extrapolation of a semicircular locus gives a value of Eoo of about 6,13 the Clausius-Mossotti equation based on Ice I a value of 3.5.
A preliminary determination of the parameters of activation yielded some evidence that the energy and entropy of activation varied with pressure and the volume of activation varied with temperature. These two variations are of course related by the equation
(MS~japh= - (aLlV~jaT)p.
Consequently, the relaxation times were fitted by least squares to the equation
T lnTo= AT+B+[C+D(T- To) J(p-po),
where To and po are a temperature and pressure approximately in the middle of the experimental range for each phase, and the parameters A, B, C, and Dare as follows
A = In (hjekT) -LlStj R,
C=LlVtjR,
D= (Ll vt)-1(aLl V~jaT)p= - (Ll vt)-1(aLlstjaph,
where LlSt is the entropy of activation, EA is the
TABLE IV. Dielectric relaxation times To/p.sec for Ice VI.
p/bar Temp.
(0C) 6550 6737 6981 7111 7504 7723 7916 8007 8324 8784 8876 9392 9726
-12.90 1.09 1.57 -15.36 1.44 -22.94 2.01 2.84 2.80 3.95 -31.54 5.37 6.24 7.40 8.28 -32.11 4.52 6.76 8.16 9.31 -38.40 8.94 10.5 13.1 -40.84 12.8 14.9 17.2 19.5
13 R. W. RampoIla, R. C. Miller, and C. P. Smyth, ]. Chern. Phys. 30, 566 (1959).
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DIELECTRIC PROPERTIES OF ICES II, III, V, AND VI 2389
Arrhenius energy, and .1 V t is the volume of activation. In this analysis the mixed derivative a2.1GtjapaT of the free energy of activation is included, but the two pure derivatives a2.1Gtjap2 and a2.1Gtjap are neglected. The results are not accurate enough to detect a heat capacity or a compressibility of activation. The activation parameters and their statistical standard errors are summarized in Table VI. The standard errors of the least-squares treatment do not include possible systematic errors in the measurements.
Except at the lowest temperatures of measurement, ionic conductivity led to some rise in E" with decreasing frequency at the lowest frequencies. Although the dc conductivities were similar in magnitude to those noted in Ice II the overlap with the dipolar absorption was much less, since the dipolar absorption in Ices III, V, and VI occurs at frequencies some 100 times as great
o 6 p, kilobars) 8 10
FIG. 5. Variation of the relaxation time at - 23.4° with pressure_
as in Ice I. The accompanying polarization effects were minor (d. Figs. 2-4).
The ionic conductivities, estimated by subtracting the dipolar contributions from the low-frequency values of E", varied considerably with the sample and to some extent with sample history. Samples prepared directly from liquid water usually had lower conductivities than those prepared from other ices. For samples made directly from the liquid, approximate conductivities were: Ice III at -32 0 and 3 kbar, 1.1X1Q-9; Ice V at -330 and 5 kbar, 5X1Q-ll; Ice VI at -320
and 8 kbar, 3X1Q-IO n-1ocm-1. The conductivities showed a small, but inconsistent, decrease with increasing pressure in Ice III, generally a pronounced decrease with increasing pressure in Ice V, and a definite increase with increasing pressure in Ice VI (as in Ice I). It is likely that ionic impurities obscured the contribution from ionized water molecules, except perhaps for Ice VI.
TABLE V. Limiting dielectric constants of the ices.
To Ice po/kbar (OC) p/gocm-a• EO E", nD2 g
I 0 -30 0.917 99 3.2 1.72 3.3 II 3 -35 4.2 III 3 -30 1.155 117 3.5 1.96 2.7 V 5 -30 1.258 144 4.6 2.08 2.9 VI 8 -30 1.350 193 5.1 2.19 3.4
• From Bridgman.-
IV. DISCUSSION
1. Order and Disorder in the Ices
Among the polymorphs of ice (including Ice VII at 22 014) and the clathrate hydrates2 so far examined, Ice II is the only form to show no dielectric dispersion at relatively high temperatures which may be attributed to rotational relaxation of the water molecules. The water molecules of Ice II are therefore frozen in either ordered or disordered orientations. Recent singlecrystal x-ray studies15 ,16 have confirmed the conclusion from the infrared spectrum17 that Ice II in the metastable state near liquid-nitrogen temperature at atmospheric pressure is four coordinated and ordered with respect to positions of the hydrogen atoms, i.e., orientationally ordered. Provided that there is no change of phase, cooling to liquid-nitrogen temperature, followed by a release of pressure, of a form in which orientational
,------ .----.-----.--~--.-----l
20J ~ I I I
Tl I
.....J 150
r-' I I
ill I I ,, _____ J
I I 100~-- I
I I I I I I I
50 I I I I I I I
I ]I I I ~ I I
o 2 4 6 8 10
P(kilobors)
FIG. 6. Variation of the static dielectric constant at -30° with pressure. Ice III may exist for long periods in the region of stab ilisy of Ice II.
14 D. W. Davidson and E. Whalley (unpublished work). 16 B. Kamb, Acta Cryst. 17, 1437 (1964). 16 M. Crute and L. D. Calvert, Am. Cryst. Assoc. Meeting,
Bozeman, Montana, July, 1964, Paper H3. 17 J. E. Bertie and E. Whalley, J. Chern. Phys. 40, 1646 (1964).
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2390 WILSON, CHAN, DAVIDSON, AND WHALLEY
TABLE VI. Enthalpies, entropies, and volumes of activation for dielectric relaxation in Ices III, V, and VI as -30°C.
Standard No. of deviation EA AS t Avt (aAVt/aT)p
Ice points of InT po/kbar (kcal mole-i) A (cal deg-1·rnole-1) (crn3 mole-i) (crn3 rnole-1.deg-1)
III 19 0.025 3.0 11.63±0.14 -36.9±0.3 13.1±0.6 4.5±0.5 -0.06±0.07
V 29 0.026 5.0 11.51±0.07 -35.94±0.14 11.3±0.3 4.8±0.2 +0.03±0.02
VI 22 0.062 8.0 11.00±0.19 -34.9±0.4 9.2±0.8 4.4±0.3 +0.06±0.05
disorder is already frozen in at - 30° is unlikely to be accompanied by the onset of orientational ordering. It may therefore be inferred from the dielectric results that Ice II is orientationally ordered throughout its region of stability. There is evidence of this in the phase diagram, as was pointed out by Kamb.15 Ice II, relative to its neighboring phases, is in an entropy well of depth very roughly R In!, as would be expected if the neighboring phases had entropies of disorder of this amount, as has Ice I, but Ice II had not.18
The dielectric properties of Ices III, V, and VI strongly suggest that these forms are four coordinated (Sec. IV.2) and orientationally disordered (Sec. IV.4).
X-rayI9 and infraredl7 studies show Ice III to be four coordinated at liquid-nitrogen temperature and atmospheric pressure. The x-ray diffraction study provided no information about the positions of the hydrogen atoms. The infrared results, however, indicated that the hydrogen atoms are ordered at low temperatures. There is probably an order-disorder transition in Ice III between the liquid-nitrogen temperature of the infrared study and the higher temperatures of the dielectric measurements. This inference is supported by an analysis of the phase diagram.18
X-ray studies of Ices V and VI have been confined to powder photographs.9,20 The infrared and Raman spectralO ,17,21 at one atmsophere and liquid-nitrogen temperature indicate that these forms are still four coordinated. The infrared results for Ice V 17 and Ice VI 22 show that the hydrogen atoms are again disordered. The similar conclusions from the present dielectric study within the regions of stability of these forms at much higher temperatures and pressures make it evident that Ices V and VI, like Ice I, are in all probability disordered under all conditions examined. This is consistent with the known (i.e., high-temperature) part of the phase diagram.I8
2. Static Dielectric Constants
The static dielectric constants of Ices III, V, and VI have been used to evaluate the Kirkwood correla-
18 E. Whalley and D. W. Davidson, J. Chern. Phys. 43, 2148 (1965).
19 W. B. Kamb and S. K. Datta, Nature 187, 140 (1960). 20 J. E. Bertie, L. D. Calvert, and E. Whalley, Can. J. Chern.
42, 1373 (1964). 21 M. J. Taylor and E. Whalley, J. Chern. Phys. 40, 1660 (1964). 22 J. E. Bertie, E. D. Hallman, and E. Whalley (unpublished
work).
tion factors g (cf. Eq. (IV.1) of the preceding paperl). For this purpose values of n2 were calculated from nD2= 1.72 of Ice I with the assumption of a constant value of the Lorentz-Lorenz function for the different phases of ice. These values of n2 and g are listed in Table V.
For the four ices listed, g lies between 2.7 and 3.4. This suggests not only a strong directional correlation of neighboring water molecules in these ices, but also that, like Ice I, Ices III, V, and VI are four coordinated, in agreement with the other evidence reviewed in Sec. IV. 1.
3. Relaxation Times
The similarity of the relaxation times of Ices III, V, and VI is striking (see Fig. 5). At -30° they are all within a factor of 2 of 2.2 ILsec, whereas that of Ice I is about 200 ILsec. The relaxation of Ice VII has not yet been studied at -30°, but at room temperature its relaxation timel4 appears to be much faster than that of Ice VI extrapolated from the data in this paper. The similarity between Ices III, V, and VI also appears in the activation parameters (see Table VI). The volumes of activation are the same within experimental error. Both the energy and the entropy of activation decrease :n the series III, V, VI, although the energies of activation of Ices III and V differ by less than the combined statistical standard error.
The similarity between these three ices is reflected at least partly in other properties. When the highpressure ices are heated9,20 from the metastable state of liquid-nitrogen temperature at atmospheric pressure, they transform first to Ice Ic. For heating rates of 1° to 2°/min, Ice VII transforms at about 1300K, Ices III, V, and VI at about 1500K, and Ice II at about 1700K.
The frequencieslo ,21 of the main Raman band at low temperature and pressure may be grouped as follows: Ice I, 3085; Ices II, III, V, and VI, 3159 to 3206; Ice VII, 3348 cm-I . This grouping of the frequencies is probably connected with a grouping of hydrogenbond strengths, the strength decreasing as the frequency increases. Clearly, a decrease in hydrogen-bond strength in the order I; III""V""VI; VII correlates well with a decreasing relaxation time. The lack of relaxation of Ice II, although its Raman band occurs at about the same frequency as that of Ices III, V, and VI, must be due to the details of the crystal structure
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DIELECTRIC PROPERTIES OF ICES II, III, V, AND VI 2391
which favor an ordered arrangement of the hydrogen atoms even at high temperatures. The infrared bands!7 can be correlated in much the same way as the Raman bands.
4. Mechanism of Dielectric Relaxation
It seems almost certain that Ices III, V, and VI are still four coordinated and fully hydrogen bonded (see Secs. IV.1 and IV.2). The general problem of determining the mechanism of the relaxation in the highpressure ices is therefore similar to the problem of determining it in Ice I. The distortion of the hydrogen bonds and the closer approach of the non-nearest neighbors in the high-pressures ices will affect the problem quantitatively but not qualitatively. Therefore, the conclusion23 that rotation in Ice I can occur at the rate observed only at defects in the structure is also valid for Ices III, V, and VI.
The defects likely to playa part in dielectric relaxation are the rotational D and L defects (see preceding paper for a description) and ionized states HsO+ and OH-.24 Relaxation due to ionized states would probably require a negative volume of activation because of the negative volume of ionzation of water, whereas relaxation due to rotational defects, as appears to occur in Ice I, would have a positive volume of activation.! The volumes of activation for dielectric relaxation in Ices III, V, and VI are all about 4.6 cms mole-! (see Table VI), and they clearly strongly favor relaxation by means of rotational defects rather than by ionized states. It is safe to conclude that dielectric relaxation occurs by similar mechanisms in Ices I, III, V, and VI. The entropies of activation, which are also given in Table VI, are all positive, and this supports the similarity of mechanism (see preceding paper!).
In Ice I the volume of activation for dielectric relaxation is 2.9 cm3 mole-i. The larger values in the highpressure ices are probably a consequence of the closer packing of non-nearest neighbors; these are pushed further away from their undisturbed positions when the transition state for rotation at a defect is formed.
The energies of activation for Ices III, V, and VI are appreciably smaller than that for Ice I. This means that either the energy of formation of an orientational
23 N. Bjerrum, Kg!. Danske Videnskab. Selskab, Mat. Fys. Skrifter 27,3 (1951).
24 H. Griinicher, Z. Krist. 110, 432 (1958).
defect or the activation energy for the diffusion of defect, or both, are smaller in Ices III, V, and VI than in Ice I. Also, the energy of activation for Ice VI is slightly smaller than for Ices III and V. These facts could be naively understood if the hydrogen bonds in Ices III and V were bent to about the same extent, and more than in Ice I, and those in Ice VI were slightly more bent than in Ices III and V. Such an increasing distortion of the regular tetrahedral hydrogen bonding found in Ice I is a likely requirement for the formation of phases of increasing density.
5. Resolution of the Dispersion Curves
The shapes of the dispersion-absorption curves of Ices III and V depart systematically from circular arcs in the perpendicular approach to the E' axis at low frequencies and in the low values of E" at frequencies somewhat above the frequency of maximum E". These are in the direction to suggest that a better representation would be by two Debye semicircles, with discrete relaxation times so close to each other that the overlap makes resolution difficult. Thus, the experimental loci of Ice III may be satisfactorily described by the superposition of two semicircular dispersion regions of relative relaxation times about 2.8: 1 and relative diameters about 4.3: 1. The same is true for Ice VI, for which the corresponding ratios are about 3.6: 1 and 5.3: 1, respectively. In either case, the relaxation time of the dominant dispersion region is about 1.17 times as great as the most probable relaxation time TO of the circular-arc approximation. The calculated loci are not very sensitive to changes in these parameters, which are therefore not well defined. The possibility of resolution into discrete relaxation times, as has also been indicated for the relaxation of the water molecules in the clathrate hydrates,2 does, however, provide additional support for the Bjerrum model if, as is known to be the case for Ice III, and can be inferred for Ices V and VI from the probable distorted tetrahedral coordination, water molecules occupy two or more nonequivalent crystal sites. A cooperative relaxation process in which more than a very few molecules was involved would be inconsistent with discreteness of the relaxation spectrum.
ACKNOWLEDGMENT
We are greatly indebted to A. Lavergne for help with the high-pressure apparatus.
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