J. W. GLEN: This final session of the Symposium is a general discussion. It is, therefore, an opportunity to discuss matters on the Physics and Chemistry of Ice. They may be matters which were cut off in the middle of a good discussion, or they may be things which people wished they had asked immediately after a paper, or which on more mature, scientific reflection they think they would like to ask, I hope there will also be a chance for a discussion which looks back over where we have got to in improving our understanding of the physics and chemistry of ice, which takes stock of the advances made in the last five years, and which then looks forward in an attempt to sec on what it might be worthwhile focusing our attention in the future.

N. W. RILEY: A large number of people (I have found, in conversation) feel that a lot of very interesting information was put over by Dr Rice but, as he said, the spread of our ability is such that we cannot appreciate just what he has done. Perhaps if he could explain further in written answer to this (as he is not here), or maybe Dr Whalley could explain to us what Dr Rice seems to be seeing. In other words, what are the salient differences between the amorphous solid and the ice Ih?

GLEN: Dr Whalley, could you give your views? I think Dr Rice said, correct me if I am wrong, that he did not have evidence for a large fraction of broken bonds.

E. WHALLEY: That’s right! He thought he had but he changed his mind subsequently; he published a statement which he has now withdrawn.

GLEN: By an appreciable number he means per cents, I think.

WHALLEY: 10 or 12%.

GLEN: That is to say, each water molecule is connected, by and large, to that sort of accuracy to four other water molecules by hydrogen bonds.

WHALLEY: AS far as one can tell. These hydrogen bonds are a little longer, but not very much longer, than in ice Ih. From the neutron diffraction and X-ray diffraction, the angles are appreciably different, almost certainly. There is a great deal of distortion in the bond angles not much distortion in the bond lengths. The bond angles are a little bit broader, but there is a slight spread in the bond lengths, apparently, in the infrared spectrum for example. But there is a big spread in the bond angles.

GLEN: DO we know anything about density?

WHALLEY: There are supposedly two kinds of amorphous ice according to Rice. There have been a number of others reported.

GLEN: For example, as Dr Johari has pointed out, this is all different from glassy ice.

WHALLEY: Rice claims to have made two kinds of ice. One is high density which as far as I know he has made only once and which he has not been able to reproduce. Then there is the ordinary amorphous ice with which we are all readily familiar. He has, of course, made this many times.

GLEN: The density of that?

WHALLEY: Not much different from ice Ih.

GLEN: Although, of course, if it were more like the liquid, one might expect it to be more dense.

WHALLEY: I could not speak with authority. Maybe some per cent, I do not know,

GLEN: Rice also suggested, did he not, that this high-density form, which he got when he happened to try a single copper crystal substrate, might bear some relation to the structure of a high-pressure phase of ice. It occurs to me that it might be a good idea to try depositing amorphous ice on substrates of the kind which L. F. Evans (1967) used when he found that you could nucleate the high-pressure phases of ice outside their range of stability using these things. I don’t know whether this is a suggestion of some interest. I mentioned this to Dr Rice last night and he seemed to think it might be worth thinking about.

RILEY: If you could clarify a point for mc here. The temperature at which I thought Dr Rice was looking at ice Ih seemed to me to be in that part of the phase diagram where we would be looking at ice Ic.

GLEN: Well, ice Ic is not at present thought to be stable anywhere; it is in that region where, if we had had a high-pressure phase and it had transformed, it might have got to ice Ic.

RILEY: So, despite the temperature, he was definitely looking at ice Ih.

WHALLEY: If he devitrified or crystallized his amorphous ice by just heating it, then almost certainly it would go to ice Ic, but the measurements on “amorphous ice” are all on the amorphous phase; whether they relate to the hexagonal or cubic phase is hard to tell. Essentially all the properties you use are identical for hexagonal and cubic, or very nearly identical, if not exactly the same.

GLEN: Not only high-pressure phases, but low-pressure phases if one counts the clathrates which have five-membered rings.

J. E. BERTIE: I would like to comment on the densities. The low-density form has a density of 0.93 g/cm³ and the high-density form has a value of 1.19 g/cm³. I am absolutely certain that Rice would agree that the speculation that the high-density form might be a distorted ice-II structure is simply based on the fact that its density is comparable with that of ice II.

GLEN: Of course, one of the troubles is that as soon as something is known not to be stable, there are inherently an infinity of possibilities for what it might be. There is one stable form; there is an infinity of non-stable forms. So that the fact is that Rice has two different amorphous ices and that Johari has pointed out that neither of them fit with what one might expect for ice cooled to a glass.

G. P. JOHARI: I expect that it would.

GLEN: Do you know if anyone has done work on glassy aqueous solutions?

JOHARI: Yes. Professor G. A. Angel at the University of Purdue at Lafayette has been studying the glass transformations of aqueous solutions of zinc chloride, potassium nitrate, and glycerol. We have ourselves studied mixtures of glucose and glycol in water. They all show a glass transition in their differential thermal analysis curves.

GLEN: Do we know if any work similar to that of Rice has been carried out on these materials?

JOHARI: The spectroscopy has not been done, but there are certain doubts whether the structure of water when acting as a solvent is the same as the structure which pure water would be expected to have if supercooled to the glass-transition temperature.

GLEN: Does that apply both to the salts and to those organic substances which appear to suppress freezing by condensing onto any potential freezing nuclei? One of the organics was reported as being in the bodies of Antarctic fish which survive at temperatures at which one would expect them to freeze—which is Nature having done the job already. Such materials are well known to the biological electron microscopists because they put them into their samples deliberately so that cells will not suffer dendritic damage when cooled, but instead the water goes glassy. (I was invited to give a paper to a low-temperature biological microscopy conference earlier this year and I discovered that this is what they think of as being the important part of ice physics.)

M. R. BLOCH: Has the viscosity of glassy ice been measured as the temperature changes?

JOHARI: As far as I know it has not. The viscosity of water has been measured down to —20^°C in the supercooled state, however.

GLEN: One suspects that the glassy ice, like the amorphous ice, might be very rigid, very hard to deform. Interestingly, the electron microscopists have to cut sections of this material with a microtome so they might know something about this.

BERTIE: I would like to make a semantic point about vitreous ice: What do we call what? Rice called his material “amorphous solid water”, I have always called it “vitreous ice”, and synonymous with that “glassy ice”. These are the terms, it seems to me, we generally use for the non-crystalline form obtained when one condenses from the vapour. What, then, do we call the hypothetical phase we get when we supercool water to the point where it reaches the glass transition?

GLEN: I hope you would not call something glassy which had not passed through a glass transition.

JOHARI: I agree with Dr Glen. Unless a material has undergone a glass transformation it should not be called a glass. There are at least five names which have frequently been used in the literature to describe the vitreous or non-crystalline forms of water and certain terms are in danger of being contradictory. Take “vitreous ice” as an example. One implies that “ice” is crystalline, so to use the term “vitreous ice” is equivalent to saying a “vitreous crystalline material”!

GLEN: I find it difficult to counter that argument, but I must say that it sounds a very strange ruling. It is important that we try to develop a consistent usage.

R. W. WHITWORTH: I would like to extend this discussion of the nomenclature of amorphous or non-crystalline ice. We have been talking up to now about things which are rigid. There is, of course, another transition from ordinary crystalline ice to things in which molecules can move more easily, ultimately, of course, to liquid water. But what about intermediate states? I think that one might draw attention to the boundary layer between crystalline ice and liquid water. How do the molecules behave in that layer, and, if one can gel a region of such material as, perhaps, at a dislocation core, what ought it to be called?

GLEN: I do not see an army of hands going up to answer this question. I suspect therefore that anyone who writes on this subject must be very careful to explain how they are using the terms—that is the best message we can give at the moment.

J. L. KASSNER: I would like to speculate upon the molecular processes that Dr Whitworth’s question is seeking to examine. I would suggest that the liquid state has a structure which is clathrate-like with five-membered rings. This structure could propagate almost indefinitely but not have any crystallographic order. It would be full of cracks and crevices where most of the bond breaking and making is probably taking place.

GLEN: Except, of course, that at those temperatures it goes, experimentally, to the Ic form instead of Ih.

N. K. SINHA: On behalf of glass physicists, I think I should make one comment. Twenty or thirty years back we used to define a “glass transition temperature” in the case of ordinary (silica) glasses. Now general experiments by different authors have shown that nothing alters at this “transition”—it depends on the experimentalist concerned. So now we tend not to refer to a “transformation” but rather a “so-called transformation”.

GLEN: Is this merely a question of time scale? I remember Marcus Reiner referring to the “Deborah number” in this context. Old Testament scholars will see the connection.*

SINHA: Yes, it was just a question of time.

J. HALLETT: I think we have to be a little bit careful here and think about the so-called glass transition in terms of a real experiment. One way of doing this is to measure a crystallization velocity over the whole range of supercooling. In the case of water one can measure this crystallization velocity down to about —20^°C or a little further if one is more careful. The velocity increases dramatically as the temperature falls, reaching c. 1 m/s at the largest supercooling reached. But with the glass solutions, such as sodium thiosulphate or sodium acetate, the changing velocity can be measured very well as a function of temperature. At first, as the temperature falls, the crystallization velocity increases roughly as the square of the supercooling, then there is a broad range of temperature through which the velocity is constant (about 20 or 30 deg). The velocity then drops dramatically to a low value. This happens, typically, at about —60^°C.

GLEN: I think we have had quite a good discussion on this particular topic and perhaps we might move on to something rather different. I have asked two people to think around topics that they might suggest to us and I will ask the first of these, Dr Bilgram, if he has anything he could suggest to us as of interest in the areas in which he operates.

J. H. BILGRAM: One area is that of the dielectric properties of ice, in particular the mobility of point defects. From the experiments it turns out that Bjerrum defects and ion states (whatever we think about the nature of ion states) have the same mobility at 0^°C. Traditionally it is assumed that a water molecule has to rotate for the movement of a Bjerrum defect, whereas a quantum-mechanical tunnelling process is involved in the ion movement. In the light of the experimental data now available I find it very hard to believe that picture. Perhaps we should begin discussing this topic.

M. HUBMANN: Formerly, the number of ions in ice was estimated to be very low and so a very efficient process had to be invented for their movement. In so far as we are sure that the number of ions is large, we no longer need such an explanation; we can introduce a hopping process for the ions too. There is, however, another point of view; it may be that a great many of the ions are captured by some traps (whatever the nature of these traps may be)— we may not have as many mobile ions as we derive from the dopant concentration. If we have fewer mobile protons than we imagine then we appear to see a higher mobility. I do not think that, at the moment, any conclusions can be drawn definitely.

GLEN: Yes, we have heard on one or two occasions during this past week about the possibility that tome defects may couple rather strongly with Bjerrum L-defects. Dr Bilgram suggested that himself; it came out as one of the models which we could not distinguish as either better or worse in the paper which Camplin, Paren and I presented, it was suggested, though nothing more, by the orientation which water molecules adopted when approaching an ion in Plummer’s paper. I think we must ask the question: if this is happening on a large scale how does it affect the picture? If, of course, it happened at one temperature range and not at another, then we ought to see one transition that I suspect we have not seen (though perhaps we have seen it and failed to identify it). If, on the other hand, the association is pretty general through the temperature region, then there are probably two or three possibilities: the ions might be the mobile element, those few remaining ones as Dr Hubmann suggests or the ion-Bjerrum defect pairs may be the mobile element which is what Dr Bilgram suggests or the ions may be moving without the L-defects and the attraction between them may not be as big as we thought.

HUBMANN: There are other defects which can act in the same way. I am reminded of the vested vacancies proposed by Kopp in earlier times, I think we should keep them in mind especially when we think of the large number of vacancies which are present, as has been Shown by Eldrup (1976) and reported by Mogensen and Eldrup in this Symposium.

GLEN: Of course, the thing which we naturally think of as going to vested vacancies is the D-defect rather than the ions or the L-defect. Perhaps they all do; perhaps Mogensen and Eldrup have enough vacancies for everybody.

J. G. PAREN: This question about the relative mobilities of defects is a tricky one and I can only offer one piece of help. Camplin, Glen, and I (Camplin and others, 1978) have tried hard to analyse the data which we have on HF-doped ice. We are happy to give anyone access to this data because we are not sure what the way ahead should be. The experiments have been done, but no one is now suggesting vital, new dielectric experiments. If we cannot suggest new experiments all we can do is produce new data on different dopants such as HCl (of which we have heard quite a lot at this conference) and try to get one uniform analysis based on present ideas. Such an analysis should presumably be done by one laboratory or group who could take all the data on all dopants.

GLEN: Do we need to put these data together with those on vacancies?

PAREN: Yes, without any doubt at all.

GLEN: Is that a feasible thing to try?

M. ELDRUP: I think that you can get some information about the vacancy formation energies from the migrating vacancies of our experiments, but if you have to include all the interactions between vacancies and the well-known defects, then it becomes a tall order to expect all these parameters from one set of experiments.

JOHARI: How sure is one that, by doping or contaminating ice with HF or some other material, one is obtaining a homogeneous mixture and that one is substituting oxygen by HF? Is there any evidence that this is so?

KASSNER: There is an experimental problem in all ice physics of which we need to be aware. De-ionized water may not be best for specimen preparation because it contains impurities which are organic in nature. These organic impurities may scavenge ionic impurities as time goes on. A more elaborate purifying technique may be needed. Although these organics might not have a direct influence on the conductivity immediately after preparation, they may make their way to the surface as some surface-active organics do, and they may scavenge the ionic dopant which has been added to the specimen before or after freezing.

C. JACCARD: We have discussed the isolated ion and the ion bound to a D-defect. But there is a third possibility, especially in a crystal in which the Bjerrum defects are in the majority. This third case is an ion with a diffuse cloud of D-defects in the shape of a Debye layer, it might have different properties from the other two models. It might look like a polaron (an electron coupled with a deformation of the lattice). It is quite different, of course, but it would bring some difference as regards the mobility for example.

P. CAMP: Let us back off from the details of the defects and ask a question. Are we all in agreement (and I assume that we are) when one does not ask about the details of the conductivity process in ice? Are we not in fundamental agreement on the basic idea of the Jaccard theory of two processes in series which give rise to the conductivity and two processes in parallel which give rise to the dielectric constant? These two processes are related to the microscopic model over which we may haggle.

GLEN: Are we in agreement? Or do some people want either to say that the series–parallel process is in question or that the two processes are in question? For example, might it be tour processes?

BLOCH: I would like to ask whether the dielectric changes are such that one can see this by comparatively coarse optical methods. Comets are made almost entirely of ice according to Whipple (1951) and I think this theory is accepted. It is possible that the optical changes in tee are large enough to establish the nature of the ice in comets. This ice might be crystalline or glassy, it might contain doped ices as, according to the Whipple theory the ice of a comet contains methane, ethane, ammonia, mixed hydrides (both water and ammonia are hydrides) silicon hydrides, and probably also the hydrides of alkali metals. All these are stable at 10 K providing that they do not warm up. If they do then they begin to react with each other. In other words it seems that a comet made of mixed hydrides is a store of chemical energy and hydrogen which can be liberated by a slight warming-up. Perhaps the methods of Raman spectra techniques, optical spectra investigations, even of X-ray spectra techniques (we have sufficient X-ray sources in space!) might give us the opportunity to look at the ice in a comet. Is this possible?

GLEN: I do not see a taker. It seems that you have made a daunting challenge. I suspect we have enough difficult? working out what ice docs when we know what we have put into it and that we are a little chary of looking at ice that has the sort of composition you have described. Clearly it is a field we should bear in mind.

BILGRAM: I have a question about the out-diffusion of impurities. In HF- and NH₃-doped samples out-diffusion of the impurity under investigation can be observed. It is possible to prevent out-diffusion by applying a high vapour pressure of the impurity in question to the ice sample. Hubmann has done such experiments. Dr Gross has reported new results on HCl-doped samples and he did not observe any out-diffusion. Are there additional differences between HCl and other impurities? Does there exist an interpretation? How is HCl incorporated in the ice?

G. W. GROSS: Dr Bilgram’s question brings me back to a statement made a while ago that all impurities appear to behave more or less the same in ice, at least from the dielectric standpoint hat ,s not exactly true. There are differences but you have to look for them? they are subtle. I am not in a position to answer the question directly, but I can point out a few differences between HCl and HF. The spectra of the two in ice are remarkably similar; mentioned that in my presentation. However, if you consider distribution coefficient, as an expression of the way in which an impurity is incorporated into the solid, then indeed you have some drastic differences between HCl and HF. The distribution coefficient of hydrogen chloride is practically independent of concentration while, as Jaccard and Levi (1961) showed the distribution coefficient of HF is very strongly concentration dependent. Moreover, the distribution coefficient of hydrogen chloride in ice is typically an order of magnitude lower than that of HF Gross and others, 1975 [a], [b], 1977). This suggests that the structural relations of the chloride to the ice lattice are indeed different from those of the fluoride, and his is as far as I wish to go at this point. We do not know what this difference is, and perhaps the method Professor Jaccard pointed out using X-ray absorption fine structure, or even scanning electron microscopy, might be useful for investigating where these impurities actually go. I think we have arrived at the limit of what we can do with dielectric measurements. These, as is well known, are rather non-specific—this is true with regards to other dielectrics as well, not just ice. We use dielectric measurements because we have no better methods, and Dr Johan’s point is well taken: we do not know where the impurities are in the ice lattice.

A. HIGASHI: We are now working with many dopants for ice, not just HF or NH₃ which introduce electrical defects, but other materials like HCl, NaCl and so on. I am never sure that all of these dopants are always in solid solution except at very low concentrations. Are there any phase diagrams for ice with other materials?

P. CAMP: I believe that Brill (1957, p. 28) has published the phase diagram with NH₄F.

G. NOLL: I would be glad if we clarify what Dr Gross has mentioned about the distribution of impurities in a crystal. Without casting any aspersions on the early measurements of Jaccard and Levi, I think that the art of growing crystals has advanced a good deal in the meantime. Bilgram has done work on the growth and segregation of impurities and I think we now know a little more about the distribution during growth and I think perhaps we can clarify any important differences regarding concentrations.

BILGRAM: It is possible to produce pure water by distillation but this is very difficult and also expensive. We prepare pure water by zone-refining. The total concentration of organic impurities in our samples is comparable to that obtained after distillation with K MnO₄. This has been measured by means of gas chromatography in the Electrochemisches Institut of the ETH.

BERTIE: A comment on this which might be relevant if the preparation of pure water is a problem: Brian Conway, who is an electrochemist, said some years ago that the Ottawa water could not be purified by any method except electrolysis followed by combustion of hydrogen and oxygen. They had a lot of organics in the water and all other attempts at purification failed. If water purity is a problem then you might think about electrolysing the water and then burning the hydrogen and oxygen to form water. Conway published this a few years ago (Conway and others, 1973).

GLEN: It sounds as though we are in for a period of drastically difficult specimen preparation.

RILEY: Taking Dr Bilgram’s point before last, where he was asking what we know about different impurities, as someone on the mechanical rather than the electrical side, I do not think we have mechanical data in depth as do the dielectricians, but we certainly have data in width; that is, we have a wide range of dopants which have been tested. I am interested in whether doped single crystals of ice will creep faster or slower than pure material. Are they going to have accelerating or decelerating creep curves? Most dopants tested to date have shown an accelerating curve, but if the work which we reported here (Riley and others, 1978) is correct then NaCl as a dopant will produce a decelerating curve.

GLEN: Unless your detailed internal structure is different.

RILEY: Is this telling us where dopants are going into the crystal?

GLEN: Is it worth asking Dr Jones how he made his doped crystals, was it the same method as we used?

S J. JONES: I think essentially the same method, in glass tubes. I would add one comment· although you observe decelerating creep you are still getting very high strain-rates and so the ice may not in fact be that much harder.

GLEN: Did you test NaOH as a dopant?

JONES: Yes.

GLEN: We seem to be moving on to mechanical properties. I did ask Dr Goodman to think around where we have got to in this area.

D. J. GOODMAN: I would like to ask Dr Whitworth what he thinks about basal and non-basal glide in the light of his core theory; is his model able to predict the large difference between non-basal and basal glide? I wonder, from Johari’s points about the homogeneity of HF-doping in ice, whether the core model is more helpful because with re-orientation at the core the dopant need only go into the core; therefore we need not worry about inhomogeneities in the lattice.

WHITWORTH: The basic answer to your first question is that we do not have a model. The point that really comes out is that none of the models that have been worked on can explain the speed at which dislocations are observed to move and we are left with the only other possibility—which has not been formulated yet! There is little prospect of explaining why we get slip on one plane rather than another if we cannot explain slip on the simplest plane. If a suitable model were worked out in detail then it might be possible to explain why one plane differs from another.

GLEN: I suspect the question is; if you have a liquid core and it is reasonably big, why does the Burgers vector matter much?

GOODMAN: Why is there a difference between the two systems? We know that the non-basal system is harder than the basal.

WHITWORTH: I must insist that I have not put forward a model, and I said that I was forced to a conclusion which is a very dangerous one. It was put up to encourage thought about a problem in the ice system which we really do not know how to think about yet. When we have thought about it we may decide it is not really a workable scheme either and then we have to find some other way of allowing dislocations to move more quickly.

GOODMAN: I think the experiments of Joncich and others (1978) were in the direction we need to take if we are to separate dislocation density effects from velocity effects; if we are going to use mechanical properties at all to examine the relationship of dislocation velocity against stress.

WHITWORTH: Those measurements are extremely good at sorting out the way in which velocity depends on stress, but by their very nature, they do not give you the constant of proportionality. If you change from a pure specimen to a doped specimen you lose the constant which you need to know.

GOODMAN: The dopant may also change the dislocation density.

GLEN: We are pretty sure that most of the ways of introducing dopants do change the dislocation density; is this not true from the Ottawa work, even if you introduce the dopant by diffusion ?

WHITWORTH: Yes, but it is more serious than that. You can change the dislocation density by-adding a dopant and you can observe this by X-ray topography. However, even if you put in a dopant that only affects the dislocation velocity, then, in a mechanical test the dislocation density will adjust itself to a different value from that in a similar test on the undoped crystal.

GOODMAN: Could we move on to “crystallization and its effect on the mechanical properties? Recrystallization has hardly been mentioned in this Symposium.

GLEN: I think the one moral which we can draw from this is that these deformation maps which sometimes have grain sizes on them may have regions where that grain size just is not stable. I imagine that is so.

R. C. LILE: I have made the fundamental assumption that for compatibility between the orientation fabric and the specimen configuration, strain-rate is governed by the resolved shear stress on basal planes. My experiments at low stress and temperature tend to bear out the validity of this assumption. Additional work is under way to investigate the results which could be expected when one moves away from this region of the deformation map.

GLEN: Do we think that if we go to the top right-hand region of Figure D3 (p. 499) that the assumption is no longer true? Is fabric still controlled by where the basal planes are? Dr Goodman is probably as good a person to ask as any.

GOODMAN: There is not a reasonable equation for the recrystallization mechanism.

GLEN: So that is a thing which is still to be worked out. We have identified another thing which looks like a big query mark on the map.

GOODMAN: What I am trying to say is that we are very concerned about a dislocation glide mechanism and that we are putting a lot of effort into understanding such a mechanism. But for the understanding of ice sheets in general, we need also an equation which will tell us how a fabric develops or, having attained a particular fabric, what the strain-rates are.

GLEN: One might have thought this was also important knowledge for the study of temperate glaciers.

GOODMAN: As we saw in Budd’s film, at much higher stress the effect of recrystallization must dominate over dislocation effects.

BUDD: That film showed what happens if you have a stress that is too high for a given situation. Other long-term tests that Matsuda and I have done at Compatible stress levels and higher temperatures began with randomly-oriented ice with tiny grains instead of crystals with aligned grains. The aligned grains break up into smaller grains but the randomly-oriented grains gradually grow into well interlocked glacier-type grains with a fabric compatible with the appropriate stress situation. In the experiments we carried out we ended with the two-maximum fabric exactly the same as one finds in the field under the same stress situations.

P. DUVAL: question for Dr Goodman: why is there no region on your map where creep is recovery controlled?

GOODMAN: We assume from what Glen said in 1968 that the dislocation glide controlled by proton re-arrangement is a slower process than climb control. The crucial experimental evidence is that HF-doping affects the dislocation glide mechanism but does not affect diffusion rates—if it did affect diffusion rates we would not be able to rule out diffusion control of climb.

GLEN: But is recovery not, in fact, involved in that top right-hand corner we have been talking about?

GOODMAN: We think that in a recrystallization mechanism the change of shape of the grain is by dislocation glide (i.e. by proton-reorientation-controlled glide). That is why there is a dotted line on the deformation map; it is still controlling the rate.

GLEN: It might not be, we have already put a big query mark against it.

DUVAL: I have a comment on tertiary creep and specially on the processes which produce the increase in creep rate during tertiary creep. The first is the modification of fabric, principally in simple shear. The second is dynamic recrystallization. In this latter case, the variation in creep occurs without modification of the fabric.

GOODMAN: We are only trying to construct, with the deformation map, a framework within which to discuss the mechanisms which govern ice. So we only plot secondary creep rates.

GLEN: Yes, but of course if you are talking about creep which goes on for a long time then it is the point at which tertiary creep settles down that you are interested in.

GOODMAN: I could suggest a possible low-stress-creep experiment here. Paterson (1977) has recently published a paper on bore-hole closure rates. I think that it is perfectly feasible to make a device which can measure bore-hole closure continuously and which could be put into the bore hole. Stress in the ice is a function of depth and it would be possible to fill the bore hole with a liquid of say half the density of ice so that there would be a stress distribution down the bore hole. The closure rate would be a function of that stress and so one could do creep experiments at very low stresses.

GLEN: I think one would have to be very careful what the liquid was and whether it came into contact with the ice or not because of the things which we discussed earlier this afternoon. I believe that the “Byrd” bore hole had ethylene glycol in it, and goodness knows what that did. One of the things that has been reported is, of course, a measurement of dielectric properties around the bore hole (Rogers and Peden, 1973) and they proved to be quite different from any other dielectric measurements on polar ice. Our group, at least, is worried that this might be due to the ethylene glycol.

C. J. L. WILSON: A comment to Dr Goodman about his deformation maps. The ice of the Gape Folger Antarctic core, and a number of other cores that I have observed, often contains small misorientations and these could be called sub-grains within the large grains. On these sub-grain boundaries there are a great many very small bubbles. Is there any way that your deformation map can take into account these small bubbles and the presence of inclusions on the sub-grain boundaries?

GOODMAN: No, such effects have not been included in the constitutive equations used to construct the maps. If the constitutive equation which is used to describe diffusional creep at high homologous temperature (Nabarro–Herring creep) is applied to ice with a grain size of o. i mm (a typical sub-grain size, say) the diffusional creep rate would be faster than dislocation creep at 0.1 MN m^-2 and —10^°C. We know linear creep, which characterizes diffusional creep, is not observed for this temperature and stress, and therefore we could conclude that diffusional creep does not occur between sub-grains. The sub-grain boundary cannot be a good source or sink of vacancies or interstitials.

GLEN: Are there any other topics? Time is getting on.

O. E. MOGENSEN: I would like to ask what really is the resolution of the Lang camera technique? If I understand it correctly the resolution is something like one micrometre and that means that any three-dimensional cluster of vacancies, or any bubble containing less than one billion molecules has not been studied. A two-dimensional dislocation loop if it contains less than 10⁶ molecules has not been studied either. It could be that clusters play a role also in all the electrical measurements.

HIGASHI: The resolution of X-ray diffraction topography is about 10 μm so what you say is correct. As far as dislocations are concerned, they can be quite well detected due to the elastic distortion around them, but I do not think we can identify vacancies.

GLEN: Let us be clear on this—the resolution is of that magnitude but this does not mean that an object has to be that large for us to see it as a spot. You could see something smaller, but you could not resolve two things.

MOGENSEN: No, but as far as I know, the bubbles and the vacancy clusters do not give rise to any kind of spot because they have little or no lattice strain associated with them.

GLEN: But a dislocation loop which introduced a stress field might be. It is a useful technique but it will not solve all our problems.

WHITWORTH: If one is just looking for small objects then I would have thought we could do better than X-ray topography by looking at things with light, say with an ultramicroscope I wonder to what extent people have looked very carefully at ice with optical scattering techniques.

SINHA: I am examining this problem very carefully, and obviously the problem is the resolution of the microscope, particularly at high magnification, and the interference produced by internal reflection within the ice crystal—that is the biggest problem—even with the resolution of a good microscope the scattered light destroys the image. I have tried some scattered laser light but the scattered light coming out of separate angles from the beam was again reflected between the multiple surfaces.

HALLETT: I think perhaps it might be worth reminding ourselves here that just by using ordinary thin-film interference we can go down to resolutions, in some forms of epitaxial ice growth, of a few hundreds of ångströms. This gives us some feeling for the surface structure; steps of height down to about 200 Å have been observed.

KASSNER: As far as individual inclusions are concerned perhaps 0.1 μm is about the best that we can do just by observing the optical scattering, and even that will be difficult.

GLEN: I think the time has come when I should draw this discussion to a close. We have ranged quite widely; I think we have identified some interesting problems and I hope to see the solutions to some of these problems in the literature in the not too distant future. Finally, I would like to thank the participants to this discussion for their contributions to it.