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Submitted on 1 Jan 1987
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INELASTIC PROPERTIES OF SEVERAL HIGH PRESSURE CRYSTALLINE PHASES OF H2O : ICES
II, III AND V
W. Durham, S. Kirby, H. Heard, L. Stern
To cite this version:
W. Durham, S. Kirby, H. Heard, L. Stern. INELASTIC PROPERTIES OF SEVERAL HIGH PRES- SURE CRYSTALLINE PHASES OF H2O : ICES II, III AND V. Journal de Physique Colloques, 1987, 48 (C1), pp.C1-221-C1-226. �10.1051/jphyscol:1987130�. �jpa-00226275�
INELASTIC PROPERTIES OF SEVERAL HIGH PRESSURE CRYSTALLINE PHASES OF H,O : ICES 11, I11 AND V
W.B. DURHAM, S.H. KIRBY*, H.C. HEARD and L.A. STERN*
Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S.A.
"u.s. Geological Survey, 345 Middleroad M.S.977, Menlo Park, CA 94025, U.S.A.
~esum6. Des cylindres polycristallins de H20 ont Qt6 d6formks 2
des temperatures entre 178 K et 257 K, et pressions atteignant 500 MPa, dans les domaines de stabilitk des glaces 11, 111, et V. La glace I1 est la plus dure des trois phases, ayant une r6sistance mgcanique dans les conditions exp6rimentales, gquivalente ?I celle de la glace Ih. La resistance mecanique de la glace V est un peu moindre. Celle de la glace I11 est extrsmement faible, et pendant des durges g6010giques ce materiau se comporte effectivement comme un liquide, limit6 au dessous par la glace V et au dessus par la glace I1 Les relations entres ces phases sont compliqu6es par la i&:s~abilit& de certaines dtentres elles, la plus importante &ant ltexistence de la glace, I11 dans le domaine de la glace 11, m$rne,apr&
des periodes prolongees. M6me pendant la dgformation a des temperatures aussi basses que 211 K (plus de 30 K au dessous de la temp6rature theorique dtapparition de la glace 111) la transformation de 111 A 11 ne peut pas etre provoquke en laboratoire.
Abstract. We have performed deformation experiments on cylinders of polycrystalline H20 at temperatures from 178 to 257 X at pressures to 500 MPa in the stability fields of ices 11, 111, and V. Ice I1 is the strongest of the phases, having a strength under laboratory condi- tions roughly comparable to that of ice Ih. Ice V is somewhat weaker than ice 11. Ice I11 is extremely weak and over geologic times must behave essentially as a liquid bounded below by ice V and above by ice 11 or I Phase relationships are complicated by a number of phase metastsilities, the most important of which is the existence of ice I11 in the ice I1 field for extended periods of time. Even under deformation at temperatures as low as 211 K (over 30 K below the ice I11 field), the transformations from I11 to I1 can not be made to happen in the laboratory.
Introduction
Jupiter's two largest moons Ganymede and Callisto have a composition that is by weight roughly half rocky material and half volatile material with the volatile phase probably being predominantly H20(1,2). It is very likely that H20 ice exists within those moons in several of its high-pressure forms, meaning that the understanding of the evolutionary history of those moons requires knowledge of the rheological properties of the appropriate high-pressure forms of ice.
To acquire such knowledge, we have performed a number of deformation experiments on samples of pure, polycrystalline water ice at pressures and temperatures simulating the conditions within the giant icy satellites. We summarize here results of
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987130
JOURNAL DE PHYSIQUE
experiments on ices 11, 11, and V.
For a more detailed description of these results we refer the reader to
270 other work by the authors (3).
The samples begin the experiments as cylinders of synthetic polycrystalline ice Ih measuring 63.5 mm in length and 25.4 mm in diameter, jacketed in 0.5-mm-thick indium tubes sealed at both ends.
Conversion to the higher pressure phase is accomplished shortly before the deformation experiments themselves, so there is no need (although it is sometimes possible) to handle samples of high-pressure ice.
Despite the volume reduction of approximately 20% in passing from ice I to I1 or 111, the indium jackets invariably remain intact. The phase changes are observed by looking at the pressure gauge, where a sample volume change is easily seen, and by constantly monitoring sample length, accomplished by moving the piston and observing the force gauge for the moment of contact.
260 - Pioneering work on the phase
relationships in water ice through the phase ice VI has been carried out
250 - by Tammann (4) and Bridgman (5)
.
Thephase diagram (Fig. 1) is complicated
2LO - by the existence of a number of important metastabilities, some of
-
which are described below.230-
-
Deformation experiments on thesephases are almost nonexistent.
2 220- Extrusion experiments by Echelmeyer
3 and Kamb(6) show that ice I11 is
-I- 2 210-
a a E zoo
cl~
I- 190 180 170- 160-
200 300 500 pressure vessel with a 600-MPa Pressure ( M Pa) working capacity and a piston that
slides along the vessel axis through high-pressure seals in order to Fig. 1. H20 phase diagram. impart a component of nonhydrostatic stress to the sample within. The vessel resides in a cryostatic tank capable of cooling to arbitrary temperatures as low as 77 K. These experiments are exclusively constant strain rate (or, properly, constant displacement rate) tests wherein pressure (P) ,
temperature (T), and piston velocity are prescribed and the dependent variable--force on the sample--is measured by an internal force gauge.
Ordinarily we speak in terms of the intensive variables strain rate
(!) , piston velocity divided by sample length, and stress (a) , force
dlvided by sample cross-sectional area.
-
- -
I Its principal features are a gas
-
-
- - I x -
I I I I
_
considerably weaker than ice 11, a result that we confirm here, and Sotin et a1. ( 7 ) have reported results of sapphlre anvil experiments on ice VI. A few preliminary results of the experiments reported here were included in Kirby et a1. (8)
.
The Experiments
The experimental apparatus is a standard triaxial deformation rig.
often takes place metastably in the ice !?I stability field.
(Bridgman(5) observated that many of the nonequilibrium peculiarities among the ice phases are strongly apparatus-dependent, hence the phrase "in our apparatusw should be understood hereafter when we refer to observations of phase-change behavior.) Ice I1 forms from ice Ih by pressurization at T < 233 K without transforming to 11, as is evident from the well-known I11
-
IX transformation at T = 173 K (9).We have generally made ice V by further pressurizing ice I11 (sometimes as it exists metastably in the I1 field) and from ice 11.
On one occasion we formed a solid ice phase from the liquid in the V field. This phase may have been ice VI. Bridgman (5) found ice V to be the most difficult of the phases to create; in particular, he was never able to produce V directly from the liquid.
conditions for the deformation experiments covered a temperature range from 178 to 257 K, a pressure range from 220 to 500 MPa, and a strain rate range from 3.7 x to 5.2 x sel. A total of 36 samples were converted to a high-pressure phase, of which 29 were deformed plastically. Nine samples were successfully recovered to room pressure in a metastable high-pressure form by cooling to low temperature before depressurizing the vessel.
Results and Discussion
stress levels during the tests typically reached a constant value after a few percent of axial strain in the samples. We gathered 77 data points from this constant stress level, and those data are presumed to apply to the condition of the steady-state plastic flow.
Figure 2 shows curve fits to the data and Table 1 gives the values of the flow parameters cast in terms of the standard creep equation
where R is the gas constant and A, n, Q, and V* are the four flow parameters or material constants in question.
The data for ice 11 are the best resolved and define, with little co.ntroversy, two different flow laws, one applicable above 220 K and the other applicable below that temperature. The data for ices V and I11 are more scattered than those for ice 11. In the case of ice V, the cause is primarily related to difficulties in working at very high gas pressures, such as the occurrence of small pressure leaks. The scatter in the ice I11 data is not yet fully understood and is discussed below. Despite the scatter, it is quite certain that two different sets of parameters are required to describe the flow of ice 111, with the break between flow laws occurring near 230 K. Note that the lower temperature flow law for ice I11 applies to (PIT) conditions entirely outside the ice I11 equilibrium field.
The strength of ice I1 is comparable to that of ice Ih, so that an ice I I1 boundary might not disrupt large-scale flow In an icy body. greatest contrast between ices Ih and 11 comes in the pressure dependence, which for I1 is positive and for Ih is negative
(v* = -20 cm3/mole for ice Ih).
Ice I11 is extremely weak in contrast to the other phases. If the relative strengths found in the laboratory stand up to the several order of magnitude strain rate extrapolation to planetary interiors, then an ice I11 layer over extended times must model effectively as a
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Table 1: Flow Parameters
Phase log A (o in MPa) n Q (kJ/mole) V* (cm3/mole)
11, T<220 K 1.84 5.3 5 5 7
11, T>220 K 11.7 5.2 98 4
111, T<230 K 13.3 6.3 103 not determined 111, T>230 K 26.4 4.3 151 not determined
V 31.3 6.9 173 4 1
Fig.2. Flow laws for ices 11, 111, and V.
liquid, unable to communicate meaningful shear stresses between layers that bound it above and below. A fixed shear stress at an ice 111-V boundary would result in strain in strain rates lo1 to lo2 times higher (depending on temperature) in the ice I11 layer. Similarly, at an ice Ih-I11 or 11-111 layer, strain rates in the I11 layer would be a factor of 10' to l o 4 higher.
The scatter in the ice I11 data is unusually large. It is only partially explained by the fact that certain fixed measurement errors, in particular, pressure fluctuations influencing the zero point of the force gauge, become proportionally larger as sample strength decreases. Additionally, ice I11 seems to occasionally exhibit rather poor reproducibility, even in a sample where measurement conditions were changed once and then returned to original values. Physical examination of anomalous samples has not yet revealed the cause of the
Ice V under laboratory conditions has a strength intermediate to that of ices I1 and 111. Over the 30-K temperature range studied, ice V shows adherence to a single set flow parameters with a fairly strong temperature dependence and the strongest pressure dependence thus far encountered in ice. Extrapolated to a common pressure of, say, 350 MPa, the strengths of ices I11 and V do not differ by as much as appears in Fig. 2, but direct experimentation with ices I11 and V on the same sample has confirmed that ice V is distinctly stronger than 111.
Phase Identification and Relations
~ i n e samples have been successfully recovered to room pressure in their high-pressure form and two have been directly studied by xrays to determine their structure. That the other samples exist in their high pressure form is obvious from their greatly reduced volume. The two samples that were observed with xrays were confirmed to be ice 11, the phase we had expected in both cases to see. Even without xrays, and in spite of the very confusing effects of phase metastability (discussed below), phase identification by indirect means was usually straightforward. For instance, ice I1 and I11 exist for extended periods in overlapping portions of (P,T) space, but their strengths are so disparate that they cannot possibly be confused. Ice V was usually identifiable from the 111-V phase transformation near 350 MPa and/or from its intermediate strength to those of ices I1 and 111.
Phase identification is uncertain in only two samples, the two warmest entries into the rce V phase field. Both samples achieved identifiable transformations (one out of the ice 111, the other out of liquid), but based on the experience of Bridgman(5), both transformations would be consistent with the formation of metastable ice VI in the V phase field. Identifying the three values of flow data from these two samples as belonging to ice VI, however, does not meaningfully improve the scatter of the ice V data, so the "VIn and V have been grouped together in the synthesis in Table 1. Either ices V and VI have similar strengths or we did not achieve ice VI in these two samples.
The metastability of ice I11 in the I1 field initially caused us considerable experimental confusion. he' differing strengths of ices I1 and I11 plus the sharply different character of the Ih-111 and Ih-11 phase transformations finally lead us to an explanation that was self-consistent and in agreement with the observations of Bridgman(5). We are not alone in our difficulty with phase metastability in ice. In Tammannis(4) experiments the metastability of ice I11 was so pronounced that he concluded that both ices were actually stable in overlapping portions of the phase diagram and that the 11-111 phase boundary did not exist.
Transformation out of the Ih phase shows an unusual dependence of transformation kinetics upon temperature: at warmer temperatures the transformation required a larger overpressurization than at lower temperatures. The warmer temperature transformation, which turned out to be Ih-111, had other distinguishing features. It was relatively rapid, causing volume to change so fast that the needle on the pressure gauge shook dramatically, and except in cases where we passed beyond the extension of the ice Ih melting curve (Fig. l), the samples became shorter and wider than would be predicted from an isotropic volume collapse. The cooler temperature transformation was a controlled one, proceeding only to the extent required to keep pressure constant as gas was being pumped in, and the samples
(21-226 JOURNAL DE PHYSIQUE
exhibited isotropic volume collapse. That these results are apparatus-dependent is illustrated by contrasting effects in Tammannts apparatus. He observed the Ih-I1 transformation to run only at 193 K and below (in contrast to our 233 K and below) and found the I h r I I transformation to proceed with explosive rapidity and the IhtIII transformation to be relatively gentle. Bridgman(5) found as we did that Ih-I11 was the explosive transformation.
We routinely perforined deformation experiments on ice I11 in the ice I1 stability field to temperatures as low as 211 K without inducing the transformation to 11. Only once did we produce the I I I ~ I I transformation, this at 204+7 K in a sample that had been deformed but was not currently undergoing deformation. For this reason, we are able to identify a "steady-statew flow law for ice 111 to temperatures far outside its stability field (Table 1). The applicability of metasable ice 111 flow to the 4.5-By-old icy moons is at best questionable, but because the strength of ice I11 is so unusually low, the question should probably be researched.
References
(1) Poirier, J.-P., Nature 299 (1982) 683-688.
(2) Consolmagno, G.J., J. Chem. P h ~ s . 87 (1983) 4204-4208.
(3) Durham, W.B., Kirby, S.H., Heard, H.C., J. Geo~hys. Res., submitted.
(4) Tammann, G., Kristallisieren und Schmelzen (Barth, Leipzig) 1903, pp. 315-344.
(5) Bridgman, P.W., Proc. Am. Acad. Arts Sci. 47 (1912) 347-438.
(6) Echelmeyer, K., Kamb, B., Geophys. Res. Lett. 13 (1986) 693- 696.
(7) Sotin, C., Gillet, P., Poirier, J.-P, Ices in the Solar System, Ed. Klinger, J. et al. (Reidel, Dordrecht, Holland) 1985, p.
109-118.
(8) Kirby, S.H., Durham, W.B., Heard, H.C., Ices in the Solar Svstem, Ed. Klinger, J. et al. (Reidel, Dordrecht, Holland) 1985, p. 89-107.
(9) Whalley, E., Heath, J.B.R., Davidson, D.W., J. Chem. Phys. 48 (1968) 2362-2370.
