The Journal of Physical Chemistry, Vol. 87, No. 21, 1983 4329
-
component (single relaxation time). At lower temperature (lowlo-‘ Hz) rotational defects out frequency measurements: 1 of equilibrium are in concentrations high enough so that the relaxation time depends only on the migration energy (0.24 eV). If these rotational defects (extrinsic?) would be homogeneously distributed, only one component of the relaxation peak would be observed; in fact, it does not seem to be the case: some regions might have more defects than others, implying several components in the peak. This is particularly clear in the case of aging experiments during the time of aging, the zone with higher content of rotational defects increases as the zone with less defects increases; consequently, the low-temperature component of the relaxation peak increases as the high temperature component decreases ( J . Phys. Appl. 1981).
Internal Friction in Ice Crystals (Y. Hiki) V. F. Petrenko: Your results do not appear to show any influence of doping on the internal friction. Why do you think that Na+ ions cause pinning? Hiki: Our results clearly show a large shift of the overdamped resonance frequency f, by the Na+ ion doping as small as 0.05 ppm. If the amount of the doping is too large, the peak position shifts to higher frequencies and we cannot observe the peak.
P. Duval: You have concluded that Na+ ions could pin dislocations. What is the evidence for the incorporation of Na+ ions in your ice single crystals? Hiki: The position of the overdamped resonance peak f, is proportional to the square of the pinning length L. The value of f, is shifted by doping crystals by NaCl and by NaOH, but not by KC1. Therefore, Na+ ions are effective pinning agents. Chemical analysis shows that undoped ice crystals also contain 0.4 ppm of Na+ ions (maybe due to some contamination in the course of growing crystals). Pinning agents in undoped crystals are thus considered also to be Na+ ions. R. W. Whitworth: What is the amplitude of dislocation movement? Hiki: The maximum displacement of a dislocation loop with l where v and b length L is shown to be n, = [ ~ -( u)/16b]L2S, are the Poisson’s ratio and the Burgers vector, and S is the strain in the crystal. In our ice specimens, L lo4 cm, and in our ultrasonic experiments, S Therefore, x , is less than a lattice spacing.
-
-
J . Perez: It is well-known that absolute ultrasonic measurements are difficult to interpret; so people generally do relative measurements. Did you compare the attenuation and the velocity of nondeformed and of plastically deformed ice? That should be a good way to be sure that the attenuation and the velocity you measured is really due to dislocations. Hiki: Our ice crystal is in a rigid specimen cell and cannot be deformed. We did consider all aspects of the ultrasonic losses caused from acoustic origins such as the diffraction loss and the nonparallelism loss, and also losses from physical origins such as the molecular reorientation and the thermoelastic damping. After that, we consider that the measured attenuation represents true energy loss in the crystal and all of our experimental results are showing the characteristics of the dislocation damping.
Effect of the Hydrostatic Pressure on the Rate of Grain Growth in Antarctic Polycrystalline Ice (A. Higashi) S. H. Kirby: You seem to suggest that the pressure effect on static grain growth stems from the pressure effect on grain boundary mobility. Have you considered the possibility that pressure changes the driving force for grain growth by inducing internal stresses due to the anisotropy in linear compressibility between grains? These stresses could be relaxed by dislocation production and motion and thus increase the driving force for grain boundary motion. Higashi: The driving force you mentioned was not considered in this work, because it could not be estimated properly in such a macroscopic analyses as ours. I do not know how to evaluate the driving force for polycrystalline ice of random orientation fabric, although we have calculated the driving force for a re-
crystallized grain in a bent specimen of the single crystal of ice according to the difference of dislocation density in the growing crystal and in the matrix (Fukuda, Kitakizaki, and Higashi, 1978).
J. Perez: Your measurements demonstrate the increase of the velocity of the grain boundary when a hydrostatic pressure is applied. If the so-called “heterophase” concept is admitted (quasi-liquidstate inside the grain boundary) as these experiments are made not too far from the melting point, one may look for a pressure-induced increase of the thickness of the grain boundary and consequently an increase of its velocity. Did you consider such a possibility? Higashi: Yes, this possibility is our conclusion derived from our results of the large negative values of the activation volume. K. Kamigaki: Could you observe any differences in the growth rates of the grain size in different phases under high pressure? Higashi: Since our pressure range was only up to 50 MPa (0.5 kbar) which corresponded to the possible pressure at the maximum depth of ice sheets, we could not reach any other highpressure phase than Ih.
Creep of Ice as a Function of Hydrostatic Pressure (S.J. Jones) S. H. Kirby: You suggested that the pressure softening observed at pressures greater than 30 MPa might be due to the lowering of the melting temperature of ice such that partial melting occurs at your test temperature, leading to enhanced creep rates like those observed at T > -8 “C in uniaxial tests. Erland Schulson just proposed that this hypothesis could be tested by doing experiments at much lower temperatures, thereby suppressing partial melting. My colleagues at Lawrence Livermore Laboratory, Hugh Heard and Bill Durham, and I have done such experiments at temperatures as low as 158 K and still observe a pressure softening in the ductile regime, indicating that it is a phenomenon intrinsic to the rheology of ice as a solid crystalline phase. Jones: This sounds like a very interesting experiment and I look forward to seeing the results. S. H . Kirby: I note that in your experiments, the silicone oil pressure medium is in contact with the ice samples. In similar experiments on rocks, considerably different pressure effects on strength and creep are observed in samples that are jacketed to deny access of the continuing fluid to the sample compared to experiments which are not so jacketed. Unjacketed samples are weaker and more brittle due to the confining fluid penetrating into pores, grain boundaries, and microcracks, thereby reducing the effect of pressure in increasing the hydrostatic component of the stress tensor and in suppressing deformation processes which result in volume increases, such as microfracturing or grain boundary sliding with cavity formation. Can you be sure that your confining fluid is not penetrating into your samples and leading to some pressure softening? Jones: I do not believe that the confining fluid is penetrating the sample. There are no cracks in the samples and strains are only about 3%. Some years ago I did some strength tests with and without jackets and saw no effect, but they were not long term creep tests. A. Higashi: Have you observed any change of substructures in the ice after the experiments? Jones: There are changes but we have not yet made a detailed study of them.
E. M. Schulson: If the pressure at which the minimum in creep rate begins to increase with further hydrostatic pressure is related to the pressure-induced lowering of the meeting point of ice, then I would expect that the “critical pressure” would increase with lowering temperature. Would you please comment on this point? Jones: I agree, the pressure a t which the minimum occurs should be a function of temperature and I hope to repeat the experiment at another temperature. Also, single crystals should give a rather different result if it is water at grain boundaries which is important. R. W. Whitworth: Your results suggest that there is no decrease in creep rate when the pressure is applied to a specimen that is already undergoing creep. If this is a genuine feature, then perhaps
4330
The Journal of Physical Chemistry, Vol. 87, No. 21, 1983
one should consider the buildup of the dislocation substructure as the source of the decrease observed when specimens are deformed throughout a t a particular pressure. Jones: A t the moment I think that there is a slight decrease in creep rate in the "one sample" experiment, but I have not done enough of these tests to be certain. If there is a significant difference between the two types of test than I agree that dislocation substructure may be the source of the decrease in strain rate.
Rate-ControllingProcesses in the Creep of Polycrystalline Ice (P.Duval) E. M . Schulson: In view of the behavior of metals, it is rather surprising that in ice recrystallization begins after a plastic strain of only 0.01 a t temperatures around -5 "C. What is the evidence for this recrystallization? Do you think that hydrostatic pressure retards the rate of recrystallization? Duual: The evidence of recrystallization after a strain of 0.01 has been shown by observing the modification of the ice texture. An indirect evidence of recrystallization is that tertinary creep is observed at low stresses (CO.1 Pa). The formation of cracks cannot be involved. The small strain necessary for driving recrystallization is probably due to the importance of internal stresses, as discussed in the paper. The effect of hydrostatic pressure on creep rate has been verified (see the paper of S. Jones and A. Chew). But, it cannot be concluded that hydrostatic pressure has an effect on the critical strain for recrystallization. S. H . Kirby: You mentioned the reduction of total grain boundary energy as a driving force for dynamic grain growth. How does this driving force compare to that resulting from reduction in dislocation line energy in ice? Duual: Grain growth is driven by the grain boundary energy (=3/27GB/d).With d = m, the driving force is about 90J/m3. The driving force associated with dislocations is pGb2/2, where p is the dislocation density and G is the shear modules. With the relation ug= Gbp1I2/3and for a typical stress of 0.5 MPa3, this driving force is too small to drive dynamic recrystallization. But, if certain badly oriented grains deform at a stress comparable to that for nonbasal glide, the driving force associated with dislocation is about lo5 J/m3 compared to lo2 J/m3 associated with the grain boundary energy.
The Velocity of Dislocations in Ice on [OOOl] and [lOiO] (R. W.Whitworth) T. Hondoh: To observe extended dislocations by HVEM, the separation width of the two particles has to be much larger than its resolution limit. What width, or stacking fault energy, are you expecting? Whitworth: I do not know what value to assume for the stacking fault energy and am looking forward to hearing your paper about this. My attitude to the electron microscopy experiment is that dissociation has been observed in many materials with related structures, and it is therefore worth having a look at ice. Whatever is seen still provide evidence about the stacking fault energy even if only a lower limit.
Frequency Dependence of the Surface Conductivity of Ice (A. J. Illingworth) J . Ocampo: Have you seen any aging effect on cleared surfaces? Zllingworth: No-we have only done aging studies on rime.
J. Glen: Does the great increase in roughening the rimed crystal not have any serious effect? Zllingworth: Both the riming and rubbing should be isotropic with no preferred direction along the surface. The most convincing evidence, however, is when the surface is melted and rapidly frozen with a blast of cold air; the surface is reasonably smooth yet the dc surface conductivity falls. T. Takahashi: Can the surface conductivity of rimed ice be modified by the increase of surface potentials? Zllingworth: I think its more likely that the change in potential and the change in surface conductivity both result from the rapid freezing.
Time-Induced Changes in the Dielectric Properties of Ice Ih (P. R. Camp) G. P. Johari: I wonder if the effect of aging you observed is not due to a continuous shear of ice during the course of aging. Camp: I doubt it for the following reasons. First, the magnitude of the stresses are very small. The weight of the top electrode is only a few times that of the sample itself. Indeed, weightproduced stresses on the ice in storage may well exceed those during measurement. Long ago (Nature (London) 1957, 169, 623-4) I did find a pressure effect but it was small at pressures 500 times as large as those exerted here. Second, if continuous shear were responsible, I would have expected all observers t o have found an increase in low-frequency dispersion with time regardless of the electrode material used. Third, it would not seem possible in this way to explain the change in direction of the process Gbserved when the temperature was lowered from -2.5 to -14 "C.
J. Perez: In the case of your work you have concluded in terms of extrinsic defects. But we have done experiments of aging by putting ice single crystals in organic liquid for more than 1000 h a t -2 "C (J.Phys. Appl. 1981). We have observed (i) an increase of the dislocations density (X-ray topography) and (ii) an increase of the point defect concentration (mechanicalspectroscopy). Thus it seems difficult to discard in all cases the possibility of the apparition of intrinsic defects during the aging of ice. Camp: This work addresses directly only the cause of the low-frequency dielectric dispersions. Whether or not the appearance of point defects can be influenced by the nature of the ice surroundinginterface, I do not know. It might be an interesting subject of study. If the kind of increase in dislocations and defects which you have found is interface independent, then apparently these do not affect the low-frequency dispersion. Otherwise our experiments should have been substantially the same as those of others who used different electrodes. Moreover the reversal of the direction of change upon cooling the sample would imply that cooling reduced the concentration of such defects. V. F. Petrenko: I did not quite catch whether there is some influence of aging on high-frequency conductivity? If there is some diffusion of carriers from the electrodes into the volume of ice one can expect an increase of the high-frequency conductivity as well as the low-frequency one. Camp: The increase in conductivity is almost frequency dependent (rising slightly with frequency) so the high-frequency conductivity increases as well. However this is dwarfed by the effect of the Debye dispersion.
Relevance of Ice Studies to Bioenergetics (J. F. Nagle) F. H. Stillinger: I presume that Halobacterium in which the bacteriorhodopsin resides can be acclimated to pure D20. It would be valuable to know if the resulting deuteron pumping and ATP synthesis rates track the corresponding shift in ice mobility for D+ vs. H+.If so, your mechanistic suggestions would seem to be supported. Any major discrepancy would constitute an invitation to further thought. Nagle: The photocycle of bacteriorhodopsin has been studied in D20 (Lozier, R. H.; Niederberger, W. Fed. Proc. Fed. Am. SOC. Exp. €301. 1977,36,,1805). Although this complicated photocycle has not been fully deciphered, it is encouraging that two of the decay rates are strongly isotope dependent, being slower by ratios of 2 and 5, respectively. This compares to an isotope effect of 2 for Bjerrum defects and 2.7 for ions (Kunst and Warman, this conference). Unfortunately, even though this is moderately encouraging, one must remember that the rate-limiting steps for the photocycle may be due to the active site and not the proton channels. The experimental finding (Keszthelyi, L.; Ormos, P. FEBS Lett. 1980, 109, 189) that the electrical response of bacteriorhodopsin closely follows the photocycle is consistent with this and with our prediction that the transport along the channels is very fast. Therefore, at the present time the D/H isotope effect offers neither support nor refutation of the proton channel mechanism.
P. Deulin: (1)Along that line (of possibly too fast predicted
