American Mineralogist, Volume 92, pages 1550–1560, 2007
SolidiÞcation and microstructures of binary ice-I/hydrate eutectic aggregates
CHRISTINE MCCARTHY,1,2,* REID F. COOPER,2 STEPHEN H. KIRBY,1 KAREN D. RIECK,3
AND LAURA A. STERN1
U.S. Geological Survey, 345 MiddleÞeld Road, Menlo Park, California 94025, U.S.A.
Brown University, Department of Geological Sciences, Providence, Rhode Island 02912, U.S.A.
3
State University of New York at Albany, Department of Earth and Atmospheric Sciences, Albany, New York 12222, U.S.A.
1
2
ABSTRACT
The microstructures of two-phase binary aggregates of ice-I + salt-hydrate, prepared by eutectic
solidiÞcation, have been characterized by cryogenic scanning electron microscopy (CSEM). The
speciÞc binary systems studied were H2O-Na2SO4, H2O-MgSO4, H2O-NaCl, and H2O-H2SO4; these
were selected based on their potential application to the study of tectonics on the Jovian moon Europa.
Homogeneous liquid solutions of eutectic compositions were undercooled modestly (∆T ~ 1–5 °C);
similarly cooled crystalline seeds of the same composition were added to circumvent the thermodynamic barrier to nucleation and to control eutectic growth under (approximately) isothermal conditions. CSEM revealed classic eutectic solidiÞcation microstructures with the hydrate phase forming
continuous lamellae, discontinuous lamellae, or forming the matrix around rods of ice-I, depending
on the volume fractions of the phases and their entropy of dissolving and forming a homogeneous
aqueous solution. We quantify aspects of the solidiÞcation behavior and microstructures for each
system and, with these data, articulate anticipated effects of the microstructure on the mechanical
responses of the materials.
Keywords: Crystal growth, ice, salt-hydrate, phase equilibria, eutectic reaction, thermodynamics,
aqueous solutions, lunar and planetary studies, icy satellites
INTRODUCTION
Arresting images of Europa reveal a complex network of dark
lineations crisscrossing an otherwise smooth, bright surface,
which is considered an “icy shell” (Pappalardo et al. 1999).
When trained on the areas of darker (lower visible albedo), reddish terrains, Galileo’s Near-Infrared Mapping Spectrometer
(NIMS) observed distorted and asymmetric water absorption
bands at wavelengths ~1.5 and ~2.0 μm. Such features suggest
H2O in a physical state other than crystalline ice-I. Although
some spectroscopists proposed that such features could be due
to scattering effects from bubbles (Dalton and Clark 1998),
most researchers surmise that such spectra are indicative of
a non-ice material being present (in addition to ice-I) on the
surface. Consideration of laboratory spectroscopy studies and
thermochemical models based on solar abundances suggests that
the absorption bands seen in the NIMS data likely arise from a
type of highly hydrated sulfate, sodium carbonate (Carlson et
al. 2002; McCord et al. 1998, 1999), or more likely a mixture of
these (Kargel 1998; Dalton et al. 2005). The presence of these
hydrated phases in the shell is consistent with models of evolution
of Europa’s interior. Such models posit a dehydration of initial
chondritic materials followed by formation and differentiation
of an impure hydrous crust (Kargel 1991; Kargel et al. 2000).
* E-mail: [email protected]
0003-004X/07/0010–1550$05.00/DOI: 10.2138/am.2007.2435
This crust would contain hydrated sulfates—particularly magnesium and sodium sulfate hydrates having the highest degree
of hydration, though sulfuric acid hydrate and hydrohalite are
plausible as well—that are thermodynamically stable on the
surface (Zolotov and Shock 2001).
The paucity of impact craters on the surface of Europa suggests a young, resurfacing crust. Features such as cracks, ridges,
and bands are indicative of surface deformation and tectonics
conjectured to be caused by tidal forces (Greenberg et al. 1998).
The tidal forces—which create deviatoric stresses on the order
of 105 to 107 Pa—result from the strong eccentricity of Europa’s
orbit due to resonance with Io and Ganymede (e.g., Sotin and
Tobie 2004). Most of the mechanical energy dissipation from
the tidal forcing occurs within Europa’s icy crust. The magnitude of this dissipation is controlled by the effective viscosity
of the icy material. Using the steady state viscosity of pure ice
(1013–1015 Pa s), Tobie et al. (2003) calculated that the dissipation
in Europa’s crust was large enough to give rise to and sustain an
underlying liquid ocean. It can be inferred, then, that a material
with higher viscosity—as we propose might comprise the surface
of Europa—would mean greater dissipation, a thinner crust, and
the possibility of a larger liquid layer. The interface between the
crust and this liquid layer would be a site of crystallization of new
crust. With a composition suggested by the spectra, it is expected,
then, that within the crust there will be regions where at least
two phases form via a eutectic solidiÞcation reaction. Although
1550
MCCARTHY ET AL.: EUTECTIC SOLIDIFICATION IN ICE-I/HYDRATE SYSTEMS
there could be coarsening of eutectic material over geologic time,
dark features on the surface in the complex networks and chaos
regions likely correspond to recent crystallization of brine (McCord et al. 1999). It is in these regions—at least—that eutectic
microstructure could be present today.
Figures 1–4 illustrate phase equilibria in four potential binary
systems for the Europa shell: H2O-Na2SO4, H2O-MgSO4, H2ONaCl, and H2O-H2SO4. Note that the magnesium sulfate and the
sulfuric-acid hydrates have multiple levels of hydration, that is,
the q value in the formula, e.g., MgSO4⋅qH2O, varies, creating a
variety of compounds each with a unique crystal structure. For
this study then, we are interested in the most water-rich hydrates,
Na2SO4⋅10H2O (mirabilite), MgSO4⋅11H2O (undecahydrate),
NaCl⋅2H2O (hydrohalite) and H2SO4⋅6.5H2O, and their stable
eutectic reactions with ice-I.1 The various metastable eutectic
reactions of other hydrate forms are possible, however. For
1551
example, in Figure 2, note the stable eutectic reaction for magnesium sulfate undecahydrate (“MS11”) and ice-I, in which a
homogeneous liquid solution of 17.28 wt% MgSO4 transforms
through the reaction Liquid → ice-I + MS11 as the temperature
(T) is lowered below 269.55 K (Marion and Farren 1999). Thermodynamically possible, though, is a metastable eutectic reaction
where a homogeneous liquid of 19.55 wt% MgSO4, by avoiding
nucleation of primary MS11, solidiÞes to ice-I + MgSO4⋅7H2O
Previously, the most hydrated phase in the system H2O-MgSO4
was listed at q = 12 (dodecahydrate); a recent study, however,
has identiÞed the hydration level for the stable phase as q = 11
(Peterson and Wang 2006), which we follow here.
1
FIGURE 1. Equilibrium phase diagram for the system H2O-Na2SO4 at
P = 1atm. The eutectic isotherm for the equilibrium L = ice-I + mirabilite
occurs at 272 K; the liquid composition corresponding to this equilibrium
is ~4 wt% Na2SO4 (point E). [Diagram adapted from Kargel (1991)].
FIGURE 3. Equilibrium phase diagram for H2O-NaCl at P = 1
atm. The eutectic isotherm for the equilibrium L = ice-I + hydrohalite
(NaCl⋅2H2O) occurs at 252.35 K; the liquid composition corresponding
to this equilibrium is ~23.3 wt% NaCl (point E). The metastable eutectic
isotherm for the equilibrium L = ice-I + NaCl occurs at ~244 K and
corresponds to liquid composition ~26.3 wt% NaCl. [Diagram adapted
from Roedder (1984).]
FIGURE 2. Equilibrium phase diagram for H2O-MgSO4 at P = 1 atm.
The eutectic isotherm for the stable equilibrium L = ice-I + MS11 occurs at
269.55 K; the liquid composition corresponding to this equilibrium is ~17.3
wt% MgSO4 (point E). The metastable eutectic isotherm for the equilibrium
L = ice-I + MS7 occurs at ~268 K and corresponds to liquid composition
~19.55 wt% MgSO4 (point E'). There is a peritectic reaction at 274.8 K that
is resorptive of primary epsomite (MS7); the liquid composition associated
with the reaction is ~21.1 wt% MgSO4 (point P). [Diagram adapted from
Hogenboom et al. (1995) and Peterson and Wang (2006).]
FIGURE 4. Equilibrium phase diagram for H2O-H2SO4 at P = 1 atm.
Several eutectic equilibria are represented. The isotherm for the most
water-rich stable eutectic (L = ice-I + H2SO4⋅6.5H2O) occurs at ~211 K.
The liquid composition corresponding to this equilibrium is 35.6 wt%
H2SO4. A metastable eutectic for the equilibrium L = ice-I + H2SO4⋅4H2O
occurs at ~198 K and corresponds to a liquid composition ~37 wt% H2SO4.
A peritectoid reaction (ice-I + H2SO4⋅6.5H2O → H2SO4⋅8H2O) occurs at
T < 200.4 K. [Diagram adapted from Hornung et al. (1956), Mootz and
Merschenz-Quack (1987), Kargel et al. (2001), and Beyer et al. (2003).]
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MCCARTHY ET AL.: EUTECTIC SOLIDIFICATION IN ICE-I/HYDRATE SYSTEMS
(“MS7;” epsomite) at T < 268.2 K (Marion and Farren 1999).
The H2O-H2SO4 system (Fig. 4) has several metastable eutectic
reactions, including one where a homogeneous liquid of ~37.5
wt% H2SO4 solidiÞes to ice-I + H2SO4⋅4H2O (“HS4”) at T <
198.6 K (Hornung et al. 1956). This system also has a peritectoid
(solid-state) reaction where ice-I + H2SO4⋅6.5H2O (“HS6.5”) →
H2SO4⋅8H2O (“HS8”) as T is lowered below 200.37 ± 0.36 K
(Beyer et al. 2003).
These systems demonstrate “simple” eutectic reactions in
that the solids exhibit no mutual solubility. This behavior is not
surprising based on some of the Hume-Rothery (1944) empirical
rules, which state, for example, that crystal structures of constituent phases need to be identical for signiÞcant solid solubility. As
indicated in Table 1, the crystal structures for these constituents
are grossly different. Ice-I has a hexagonal close-packed symmetry with four H2O molecules arranged near the vertices of a
tetrahedron centered about a Þfth. No solubility of S6+ ions into
the ice-I structure exists, to Þrst order. The structures of the
hydrates, on the other hand, hinge on the geometry of polymerization of (SO4)2– tetrahedra and are ordered sufÞciently to allow
only limited solubility (i.e., in excess or in deÞcit) of H2O.
The difference in crystal structure of the two phases comprising each of these binaries also means that the boundaries between
the phases are incoherent. This boundary incoherence means that
not only is solidiÞcation of a eutectic aggregate quite different in
many respects to solidiÞcation of a single-component solid, its
mechanical properties are anticipated to be very different as well.
In that the microstructure—that is, the spatial scale and textural
state of constituent phases in a polyphase solid—affects to Þrst
order the mechanical response, a sound Þrst step in characterizing the rheology of polyphase ice-I/hydrate aggregates is to
examine the microstructures of potential chemical systems, i.e.,
as suggested by Europan NIMS analysis. The present work is an
experimental study to characterize the solid-state morphologies
of the binary systems H2O-Na2SO4, H2O-MgSO4, H2O-NaCl,
and H2O-H2SO4 prepared by eutectic solidiÞcation from initially
homogeneous liquid solutions. We demonstrate that microstructures so produced for all the systems share almost all qualities of
those seen for similar eutectic solidiÞcation reactions in binary
metallic and metalloid systems. By analogy with the behavior
of eutectic metals, then, we can speculate on the mechanical
responses of the ice-I/sulfate-hydrate aggregates.
EXPERIMENTAL APPROACH
Liquid solution preparation
Following the published phase diagrams (Figs. 1–4), homogeneous liquid
solutions were prepared at the stable water-rich eutectic compositions, or at other
compositions, depending on the goal of a given solidiÞcation experiment. The
critical issue in preparing homogeneous liquid solutions of a desired composition
is measuring the mass of components accurately, which is a nontrivial task when
one component reacts strongly and rapidly with atmospheric moisture. Different
protocols were followed for the sulfates. For the sodium sulfate, Na2SO4⋅10H2O,
reagent-grade granular crystals were heated to ~80 °C under vacuum to remove the
water of hydration. The anhydrous Na2SO4 powder was subsequently weighed at
milligram resolution. For magnesium sulfate, MgSO4⋅7H2O, reagent-grade granular
crystals were used. At laboratory temperatures (~298 K) the reaction
MgSO4⋅7H2O(s) (epsomite) = MgSO4⋅6H2O(s) (hexahydrite; “MS6”) + H2O(g)
(1)
has an equilibrium relative humidity (RH) of ~50% (Chou and Seal 2003); this
means that as the RH of the lab ßuctuates, the granular crystals as received from
the manufacturer could have some undetermined fraction of MS6. To ensure proper
mass measurements by having solely MS7, the epsomite crystals were placed in
a sealed vessel containing a separate, open container of liquid water (i.e., RH =
100%) for 24 h prior to the procedure.
Reagent-grade NaCl crystals were used for the system H2O-NaCl. For the
system H2O-H2SO4, reagent-grade concentrated sulfuric acid was used. All reactants
were mixed at room temperature with water that was triply distilled. Prior to use
in a solidiÞcation experiment, liquid solutions were stored at room temperature
within sealed test tubes.
SolidiÞcation protocol
Approximately 40 mL of prepared solution was placed in 25 mm ID test tubes
and immersed in a low-temperature ßuid bath (Hart ScientiÞc, Model 7081-SCI),
the temperature of which was maintained to within ±0.006 K as measured by a Pt
resistance probe. A constant temperature (TC) below the eutectic temperature (TE)
was maintained for each sample run. We performed several experiments for each
system varying the degree of undercooling (∆T = TE – TC ≈ 1–5 °C). A small chunk
(roughly 2 mm3) of polyphase crystalline material of the same bulk composition as
the solution (retained from a previous experiment) was placed in a second test tube
in the bath and allowed to reach thermal equilibrium with the bath and the sample.
The chunk was then added to the test tube containing the undercooled solution. Using this seed material, then, we were able to circumvent the thermodynamic barrier
to nucleation and in so doing control the growth rate as a function of ∆T. Seeding
also allowed us to determine precisely when and where growth initiated.
The density of the eutectic solid in each of the systems studied was less than
the density of the eutectic liquid, so that seeds of eutectic composition ßoated to
the top of the liquid in the test tube. In some instances, the test tubes containing
the solidifying samples were removed from the bath temporarily (<20 s duration),
photographed, and then returned to the bath. By repeating this process, growth
rate was approximated by examining the change in thickness of the solid phase
in the time-sequence series of photographs. In instances when the growth front
was non-uniform, the thickness was approximated by averaging the thickest and
thinnest portions of the solid.
We also examined solidiÞcation rate using differential temperature analysis
(DTA) following a similar protocol to Zanotello et al. (1998). This method employs
thermocouples to detect the recalescence that occurs when undercooled liquid solution is heated by the latent heat of crystallization. A peak in the temperature reading
represents the playoff between the latent heat of crystallization and the ability of
the surrounding material to dissipate such heat, which is a convolution of its heat
capacity and its thermal conductivity. (Dynamic conditions, thus, are between
adiabatic and isothermal.) In controlled, directional growth, the recalescence front
can be used as a Þrst-order approximation of the growth rate. Four Type-K (Ni-10
wt% Cr vs. Ni-2 wt% Al-2 wt% Mn) thermocouples, sheathed in stainless steel, were
TABLE 1. Phases of interest in this study and their properties*
Compound
Crystal
Space
Molecular weight
Tm (K)
Density
Molar volume
Eutectic comp.†
Eutectic
(cm3)
(wt% salt)
T† (K)
system
group
(g/mol)
(g/cm3)
hexagonal
P63/mmc
18.01
273.15
0.917
19.64
–
–
H2O (ice-I)
monoclinic
P21/c
322.19
305.55
1.46
219.80
4.03
271.99
Na2SO4⋅10H2O
orthorhombic
P212121
246.47
321.55
1.67
146.71
19.55‡
268.15‡
MgSO4⋅7H2O
triclinic
P1
318.48
273.75
1.51
210.92
17.28
269.55
MgSO4⋅11H2O
monoclinic
P21/c
94.47
273.3
1.61
58.68
23.3
252.35
NaCl⋅2H2O
monoclinic
I1m1
215.17
219.38
1.54
154.86
35.65
211.28
H2SO4⋅6.5H2O
* After Calleri et al. (1984); Lide (1992); Marion and Farren (1999); Marion (2002); Mighell (2003); Mootz and Merschenz-Quack (1987); Peterson and Wang (2006).
† In binary reaction with ice-I.
‡ Metastable equilibrium.
MCCARTHY ET AL.: EUTECTIC SOLIDIFICATION IN ICE-I/HYDRATE SYSTEMS
1553
positioned within the solution-containing test tube with their junctions equidistant
(~3 cm spacing) such that the Þrst thermocouple junction (“TC1”) was just at the
top of the liquid column in the test tube and the last (“TC4”) was resting on the
bottom. A Þfth Type-K thermocouple rested in the bath. Thermocouple readings
were collected by a data acquisition system (National Instruments LabVIEW) and
stored on a computer.
Microscopy: specimen preparation, imaging, and analysis
Once crystallization was complete, the samples were removed from test tubes
and cut into 3–5 mm thick slabs with a band saw, all while remaining in a freezer at
~253 K. Specimens were then transported in contact with liquid nitrogen (77 K) to
the microscopy lab. While submersed in liquid nitrogen, samples of roughly 5 mm3
were cut with a razorblade and Þt onto a specially made brass sample holder. Screws
were tightened to hold the specimen in place. Imaging was performed on a Leo 982
Macro, Þeld-emission cryogenic scanning electron microscope (CSEM) Þtted with
a Gatan Alto 2100 preparation and coating station. Once in the pre-chilled (below
100 K) preparation/coating station, a fresh surface was created on the specimen
by nicking it with a cold blade (which is incorporated into the station). In some
cases, samples were sputter-coated with AuPd using a non-heat-emitting sputter
head. This procedure produces a layer of AuPd of ~1 nm thickness to improve the
electrical conductivity of the specimen. Imaging was performed at temperatures
≤105 K and a vacuum below 10–3 Pa (10–8 bar), using a low acceleration voltage
(1–3 kV) to minimize sample alteration or beam damage of the sample surface. The
primary mode of imaging employed secondary electrons (SEI). Energy dispersive
X-ray spectrometry (EDS) was also employed; although resolution is limited by the
long focal distance (~15 mm) of the spectrometer, the chemical information thus
provided helped to distinguish between the ice-I and hydrate phases. Cryogenic
X-ray diffraction (XRD) enabled us to verify the phases present.
Image analysis was conducted using Adobe Photoshop CS. Digital SEM images that were representative and in which, when possible, the plane of view was
orthogonal to lamellae were loaded and thresholded to assign each phase as either
black or white. The histogram tool in the Image menu generated a graph in which
each vertical line represents the number of pixels associated with a brightness level.
In some instances the images had to be manually adjusted to correct for shadows
and brightness due to surface orientation and roughness. Low-magniÞcation images
were analyzed to discern an areal fraction of the primary ice-I phase in relation to
the eutectic. High-magniÞcation images were analyzed to identify areal fraction
of hydrate phase within the eutectic microstructure.
FIGURE 5. Results of a thermal study of 4 wt% Na2SO4 held in a cold
bath at 269 K (–4.16 °C; ∆T = 3 ºC). No seed material was employed
and thus nucleation took a considerable amount of time. At the onset
of crystallization (t = 0 s), all thermocouples positioned in the sample
simultaneously recorded an increase in temperature above that of the
eutectic temperature, TE, indicating that a primary phase crystallized Þrst.
Temperature values were captured at a frequency of 0.3 Hz.
EXPERIMENTAL RESULTS
Thermal results
Figures 5 and 6 show multi-thermocouple temperatures vs.
time proÞles for solidifying eutectic solutions in the H2O-Na2SO4
and H2O-MgSO4 systems, respectively. Using this method,
combined with visual inspection of the solidifying solutions,
we identiÞed two modes of crystallization. Samples from the
H2O-Na2SO4 system produced simultaneous peaking above TE
for all four thermocouples (Fig. 5). Examination of test tubes just
following the initial thermal spike revealed large, feathery crystals branching throughout the sample. The H2O-H2SO4 system
produced both similar thermal behavior and appearance.
The H2O-MgSO4 system (Fig. 6), on the other hand, produced a thermal signature of “top-down” crystallization, which
was conÞrmed by visual inspection, where an almost planar
solidiÞcation front was seen. The thermocouple positioned at
the top of the column recorded the Þrst and largest peak, the
temperature of which was near, but not as high, as TE. Each additional thermocouple in succession experienced a temperature
spike, the amplitude of which decreased with distance from the
top of the sample.
The H2O-NaCl system demonstrated a combination of both
of these modes. In some cases simultaneous peaking (with
visible crystals throughout), as in the H2O-Na2SO4 system,
F IGURE 6. Thermal results representative of “top-down”
crystallization of 17.28 wt% MgSO4 at a constant bath temperature of
–5 °C, representing a ∆T = 1.4 °C. Seed material was employed at t = 0
s. The time differences separating the peak temperatures can be used to
approximate the crystallization (grain-growth) rate in the sample (where
distance between thermocouple junctions is 2 cm). Thermal history
periods A, B, and C are addressed in the Discussion.
occurred; in other cases the top two thermocouples recorded
simultaneous temperature peaks that was followed by top down
crystallization.
Microstructure of the as-grown eutectics
All of the systems exhibited classic eutectic microstructure,
that is, unlike a random dispersion of individual grains, these
systems form a Þne intergrowth of two phases in a regular, repeating pattern throughout the sample. The local arrangement of
the phases tends to have directionality. A region with common
MCCARTHY ET AL.: EUTECTIC SOLIDIFICATION IN ICE-I/HYDRATE SYSTEMS
1554
orientation is described as a “colony” (Croker et al. 1975); where
it has impinged on another colony during growth constitutes a
colony boundary. Such a boundary is evident in many of the
micrographs. We found that the pattern, or morphology, the
intergrowth takes within a colony is unique to each ice-I/hydrate
system, regardless of its bulk composition. Samples with offeutectic bulk compositions have individual crystals of whichever
phase is in excess—called the primary phase—surrounded by
the eutectic structure attributable to that system.
As nominally identical structures have been long identiÞed in
metallurgy, we borrow their terminology in classifying the type
of eutectic morphology exhibited by each system (Croker et al.
1973; cf. Elliot 1977). We refer to the Croker et al. (1973) terminology as “CFS.” Table 2 describes in brief the microstructure
observed in each system and the volume and areal fractions of
the hydrate phases. Aided by EDS, we determined that the darker,
mottled phase in the SEM/SEI micrographs (to be presented by
chemical system below) is ice-I and the lighter phase that stands
in relief in all images is the hydrate phase. In the table, volume
fraction of the hydrate (VF) is presented as calculated from the
(batched) bulk chemistry; image analysis performed on multiple
SEM/SEI micrographs for each system provides a mean areal
fraction of primary ice-I and of hydrate phase in the eutectic.
The signiÞcance of the disparity between these measurements
will be discussed further below.
to isothermal. Large, rounded grains of primary ice-I are present
in all samples, in places covering up to 20% of the surface area of
low-magniÞcation images. Further analysis of the eutectic microstructure (i.e., the remaining 80%) in high-magniÞcation images
reveals that in all samples, regardless of undercooling or composition, the observed areal fraction of the hydrate phase ranges
from 0.46–0.56, which is much greater than the volume fraction
calculated from the batched bulk chemistry for the eutectic.
H2O-Na2SO4 eutectic
The morphology of the H2O-Na2SO4 eutectic is characterized by uniform blade-like grains of mirabilite, 1–3 μm wide,
arranged in roughly parallel columns within an ice-I matrix
(Fig. 7). CFS described this morphology as “broken lamellar.”
In this system, regions of eutectic microstructure alternate with
elongate grains of primary ice-I in a somewhat regular pattern,
giving the appearance of alternating eutectic and ice-I lamellae.
Analysis of low magniÞcation images reveals that, despite the
bulk composition being equal to that of the eutectic, ~30% of the
surface area is primary ice-I. High magniÞcation images indicate
local areal fraction of mirabilite to be 0.1–0.2. This result deviates from the 0.06 volume fraction of mirabilite predicted by the
batched bulk chemistry.
H2O-MgSO4 eutectic
Figure 8 shows the typical microstructure of the H2O-MgSO4
system, which consists of an array of interconnected ice-I and
MS11 phases (phases conÞrmed by XRD) that in some regions
exhibits classical “regular” lamellae and in others a labyrinthine
pattern that is described by CFS as “complex regular.” In both
images, the specimens were taken from the bottom half of the
sample where thermal results suggest that crystallization is close
FIGURE 7. SEM/SEI images of a fresh fracture surface revealing the
“broken lamellar” microstructure (CFS index 3) for the system H2ONa2SO4. The samples in these two images have a bulk composition of 4
wt% Na2SO4 (the eutectic composition). (a) Low-magniÞcation image:
primary ice-I grains (single-phase regions showing conchoidal fracture
morphology) are separated by regions of two-phase eutectic. (b) Detail
of eutectic: the lighter phase in relief (blade morphology) is mirabilite
and the darker phase is ice-I. Although the volume fraction of hydrate
calculated for a sample at the eutectic composition is 0.06, the areal
fraction on local scales is closer to 0.10.
TABLE 2. Eutectic microstructures
Eutectic phases
Calculated VF
of hydrate
0.06
0.34
0.25
0.51–0.87†
Areal Fraction:
primary ice-I
~0.3
~0.2
<0.05
0.08
Areal Fraction:
hydrate in eutectic
0.1–0.2
0.45–0.56
0.30
0.7–0.8
Eutectic
Microstructure
Broken lamellar
Regular and Complex regular lamellar
Complex regular and irregular lamellar
Regular rod
CFS index*
3
Na2SO4⋅10H2O/ice-I
1, 5
MgSO4⋅11H2O/ice-I
4, 5
NaCl⋅2H2O/ice-I
2
H2SO4⋅qH2O/ice-I†
* Croker et al. (1973).
† The stable hydrate for this system is H2SO4⋅6.5H2O. The close proximity of metastable equilibria H2SO4⋅4H2O/H2O and H2SO4⋅8H2O/H2O make it unclear which
hydrate is present. The range of VF from 0.51–0.87 constitutes this uncertainty.
MCCARTHY ET AL.: EUTECTIC SOLIDIFICATION IN ICE-I/HYDRATE SYSTEMS
FIGURE 8. SEM/SEI images of fresh surfaces of H2O-MgSO4 at
bulk composition equivalent to the stable eutectic liquid, i.e., ~17.3 wt%
MgSO4. (a) Sample solidiÞed at ∆T = 3.3 °C. (b) Sample solidiÞed at
∆T = 1.05 °C. The darker phase that is recessed in the structure and in
the large grains in a is ice-I. Cryogenic XRD analysis of the eutectic
material conÞrms that the lighter phase in relief is MgSO4⋅11H2O (cf.
Peterson and Wang 2006). Although the volume fraction of the batched
composition is ~0.27, areal fraction of the eutectic microstructure is
~0.50. Both specimens show a “complex regular lamellar” microstructure
(CFS index 5). Colony boundaries can be seen in both images.
H2O-NaCl eutectic
Many of the samples observed in the H2O-NaCl system have
“complex regular” morphology that is nearly identical to that seen
in the H2O-MgSO4 system. Phase boundaries in these materials,
however, appear to have less curvature, i.e., are more faceted,
than the MgSO4-hydrate/ice-I eutectic materials. Furthermore,
some samples in this system exhibit branching (dendritic form)
in the hydrate phase (hydrohalite, conÞrmed by XRD) indicative of a CFS “irregular” eutectic morphology (Fig. 9). There is
very little primary ice-I found in the samples and the calculated
areal fraction is very near to that expected from the batched
bulk composition.
FIGURE 9. SEM/SEI images of system H2O-NaCl. (a) Sample with a
composition of ~24 wt% NaCl that was solidiÞed at ∆T = 3.6 °C. Under
these conditions the morphology formed is “Complex regular lamellar”
(CFS index 5). (b) Sample with bulk composition of ~23.3 wt% NaCl,
which corresponds to that of the eutectic, solidiÞed at ∆T = 4.0 °C. The
lighter phase in relief is hydrohalite (conÞrmed by cryogenic XRD) and
is exhibiting the branching behavior characteristic of “irregular” eutectic
morphology (CFS index 4).
Type 2 consists of large (5–200 μm in diameter) ice-I grains in
patterns crisscrossing through the sample. It is unclear whether
the ice-I in Type 2 is primary ice-I or part of a separate eutectic
morphology. Type 2 morphology comprises ~8% of the surface
area and appears to be conÞned to planes. The intricacy and
curvature of the patterns in the planes is suggestive of cross-sectional (i.e., nominally trace) views of snowßakes (cf. Bentley and
Humphreys 1931); this observation strengthens the case for these
features being primary ice-I. In the H2O-H2SO4 system, ice-I is
the minority species, as is clearly conÞrmed in the micrographs.
Image analysis reveals that the ice-I rods in Type 1 microstructure
have an areal fraction of approximately 0.20 whereas the ice-I
in Type 2 amounts to closer to 0.30.
DISCUSSION
H2O-H2SO4 eutectic
Two distinct morphologies are present in all specimens of
the H2O-H2SO4 system (Fig. 10): Type 1 is characterized by
very small (<1 μm in diameter) rods of ice-I in a sulfate hydrate
matrix that is consistent with the CFS “rod-like” morphology;
1555
Eutectic solidiÞcation
The observed intricacy and beauty of the eutectic microstructures are part of that tendency of nature to form complex
1556
MCCARTHY ET AL.: EUTECTIC SOLIDIFICATION IN ICE-I/HYDRATE SYSTEMS
FIGURE 11. Schematic of eutectic solidiÞcation in which crystalline
lamellae of phases α and β grow side-by-side—with a periodicity
λ—from a homogeneous (A,B) liquid (L) solution of composition
CE. Fluxes of A and B (JA,JB) in the liquid phase are required. The
compositional gradients that occur in this narrow (approximately
λ/2) region diminish in magnitude with distance from the solidliquid interface. These compositional gradients dictate an effective
undercooling, ∆Tx (inset), that contributes to the undercooling overall
(i.e., it adds to another effective undercooling described by the Gibbs
Energy/curvature-“Gibbs-Thomson”—relationship at the α-β-L triple
junctions); the total undercooling dictates both λ and the growth velocity,
v (cf. Eqs. 2 and 3).
FIGURE 10. SEM/SEI images of H2O-H2SO4 with a bulk composition
of ~36 wt% H2SO4 (eutectic composition) crystallized at a rate of 8.3
× 10–2 cm/s. The “regular rod” eutectic microstructure (CFS index 2)
consists of a matrix of sulfuric acid hydrate, within which the ice-I phase
forms rods. (a) Large recessed grains are primary ice-I and are found
in intricate patterns crisscrossing through the sample in planes. (b) The
ice-I rods in the eutectic [found in the inter-primary regions of a], when
cut orthogonally, appear as small holes.
patterns in its (dynamic) response to gradients in free energy.
In the case of a solidifying binary system, the patterns initiate
from thermal perturbations at the interface between the growing
two-phase solid and the liquid. The eutectic solid phases grow
cooperatively, side by side in what are often lamellae (Fig. 11).
The velocity of crystal growth, v, is correlated with the extent
of undercooling below the equilibrium eutectic temperature, ∆T,
and is limited by chemical diffusion (component ßuxes, Ji) in the
liquid near the solid-liquid interface; the diffusion is required for
the coupled growth of two crystalline phases of distinctly different compositions. Compositional variations along the interface
result in an effective undercooling, ∆Tx, that has its maximum at
the center of each lamella. Concentration gradients in the liquid
diminish in magnitude with distance from the interface. Curvature at the triple junction among the two solid phases and the
liquid phase (which arises from the requirement of equilibrium of
the interfacial energies) creates, too, an additional undercooling
that has its maximum at the triple junction (∆Tc). Despite these
microscopic thermal variations, the sum of the composition and
curvature undercoolings is constant (∆T = ∆Tx + ∆Tc) so that the
solid/liquid interface is nearly isothermal and growth proceeds in
a macroscopically planar fashion, perpendicular to the interface
(Flemings 1974; Kurz and Fisher 1998).
The scale of the eutectic layering (λ) is a function of the eutectic temperature (TE), the liquid undercooling, the phase-boundary
energy (γαβ), and the enthalpy of fusion (melting; ∆fusH) of the
two-phase solids mixture. A minimum eutectic interlamellar
spacing is calculable from thermodynamics:
λ min =
2 γαβTE
Δ fus H ΔT
(2)
where, here, ∆fusH is in units of energy per volume. SolidiÞcation
is a dynamic process, of course, and while driven by the undercooling, the lamellar spacing and the solidiÞcation velocity (v ∝
∆T/λ) are optimized to maximize the overall energy dissipation
rate; one result is that the eutectic interlamellar spacing is λ =
2λmin and the product vλ2 is discovered to be a materials-system
constant:
~
Dγ T
(3)
vλ 2 = L αβ E
Δ fus H
~
where D L is the chemical diffusion coefÞcient for components
in the liquid. For many materials systems, the right-hand side
of Equation 2 is ≈10–16 m3/s.2 Clearly, higher solidiÞcation velocities, wrought by greater liquid undercooling (i.e., steeper
temperature gradients), produce Þner lamellar eutectic spacing
(Porter and Easterling 1992; cf. Hunt and Jackson 1966; Croker
et al. 1973).
The model described above, which is ascribed to Jackson
MCCARTHY ET AL.: EUTECTIC SOLIDIFICATION IN ICE-I/HYDRATE SYSTEMS
and Hunt (1966) (referred to hereafter as “JH”), is complicated
by the dynamics of the solid-liquid interfaces of the constituent phases, in particular whether a crystalline phase grows (1)
rounded and unrestricted (unfaceted) into the liquid, or (2)
preferentially along speciÞc crystallographic directions (faceted).
Distinct eutectic textures have been observed depending on
the combination of the behavior of the two crystalline phases:
non-faceted/non-faceted (nf/nf), faceted/non-faceted (f/nf), or
faceted/faceted (f/f). Nf/nf combinations were observed to yield
“regular” structures of rod-like or lamellar eutectics that follow
closely the JH model. In f/nf combinations, the growth overall
is controlled by the faceting phase, but because its growth is
restricted to particular directions, the system cannot make the
rapid adjustments of phase spacing that are needed to produce a
regular lamellar structure; thus, “anomalous” eutectic structures
result (Elliott 1977). F/f combinations also produce “anomalous”
morphologies and often spatially independent crystals of the two
phases (e.g., Stubican and Bradt 1981). The range of anomalous
eutectic microstructures that a binary can adopt—e.g., isolated
plates, irregular branched plates, arrays of interconnected Þbers,
or maze-like networks—are, in part, a result of the various ways
that the system structurally accommodates growth incongruity
of the two solid phases.
Another contributing factor to microstructure development is
the relative volume fraction (VF) of the crystalline phases. Volume
fraction of phases in a eutectic region of the microstructure is
generally calculated at the eutectic composition. VF can deviate
from bulk composition on local scales, however, particularly in
f/nf combinations: the disparity in growth kinetics of the two
phases can cause the non-faceting phase to overgrow the faceting phase. The manifestation of this behavior is a dendrite of the
primary phase. As Figure 12 demonstrates, when dendrites of one
phase grow, the composition of the nearby liquid moves away
from that phase down the metastable extension of its liquidus.
This liquid then crystallizes in the space around the dendrites
with a local volume fraction that deviates from that expected at
the eutectic. Local areal fraction calculations and results from
the thermal analysis on system H2O-Na2SO4 (Fig. 5) indicate that
ice-I/hydrate systems are prone to this behavior. Regardless of
the initial bulk composition, then, it is the local composition of
the liquid (after primary phases have been removed) that will
inßuence the microstructure of the eutectic solid that forms.
Taylor et al. (1971) found that the morphology of the eutectic
microstructure for a given system at a given set of thermodynamic and physical conditions can be predicted. They focused on
interface roughness, or f/nf behavior: morphology would depend
on both the absolute values of the entropy associated with the
2
One can, additionally, calculate vλ2 based on solid-liquid interfacial energies, assuming a constant curvature of each lamella
into the liquid (cf. Fig. 11) and employing the Gibbs-Thomson
relationship (cf. Kurz and Fisher 1998). Interfacial energy data
are hard to come by. Nevertheless, if one employs the solidliquid interfacial energy for the anhydrous Mg2SO4-aqueous
solution interface [~0.08 J/m2 (Lide 1992)] and λ measured here
from high-resolution SEM images of the ice-I/MS11 eutectic
specimens, we calculate a value for vλ2 of ~8 × 10–17 m3/s, fully
consistent with the plethora of data in the metals and ceramics
literatures for planar-front eutectic solidiÞcation.
1557
solidiÞcation of each eutectic phase as well as on the relative
values between the phases. The critical thermodynamic variables,
then, are the degree of undercooling (as it affects solidiÞcation
velocity) and the partial molar entropy of solution of each solid
phase into the eutectic-composition liquid, ∆solSi (where i is used
to denote the phase). ∆solSi is signiÞcantly different physically
(and often numerically, depending on the eutectic liquid composition) from the entropy of fusion of a pure constituent phase
as demonstrated in the entropy vs. composition plot in Figure
13. Croker et al. (1973) used the value from the phase with the
higher ∆solSi , which we here denote as ∆solSh , weighted against
the effects from the volume fraction of that phase, VF,h, and the
FIGURE 12. Portion of a simple-eutectic, binary phase diagram
demonstrating the path of liquid composition if relative crystal-growth
kinetics cause one phase to overgrow another. In this case, dendrites of
the α phase grow more easily, causing the composition of the nearby
liquid solution to follow the metastable extension of the α liquidus and
so result locally in a more B-rich liquid composition (C1). The eutectic
microstructure thus formed has a VF,β exceeding that predicted from
eutectic composition, CE.
FIGURE 13. Schematic diagram for determination of ∆solSh . The
points at either end of the tangent represent the ∆solSi for each of the two
solid phases in equilibrium with the liquid at the eutectic composition, XE.
Assuming the solids at their respective liquidus temperatures represent
the standard states, the ∆fusSi values (per mole of solution formed) deÞne
points on the liquid solution curve; thus the values of the partial molar
entropy of solution for compounds at XE are straightforwardly determined
via the tangent/intercept technique. In this case, phase β (A2B) has the
higher ∆solSi and so will dictate the eutectic morphology.
1558
MCCARTHY ET AL.: EUTECTIC SOLIDIFICATION IN ICE-I/HYDRATE SYSTEMS
crystal growth velocity, v, to develop a classiÞcation scheme for
eutectic morphology.
Using published thermodynamic data (Telkes 1980; Beyer et
al. 2003) for entropies of fusion for the appropriate compound
phases, we apply the CFS analysis to the ice-I/hydrate systems.
Calculated values of ∆solSh for each system at the eutectic (or
metastable-eutectic) composition and temperature are provided
in Table 3. Using this method we found that in two of the systems
studied (H2O-Na2SO4 and H2O-NaCl), the hydrate is the highentropy phase, whereas in the other two systems (H2O-MgSO4
and H2O-H2SO4) ice-I has the higher ∆solSh . Some of the main
features of the CFS analysis are featured in Figure 14, where we
plot the value of ∆solSh against the observed, local VF,h for each
of the ice-I/hydrate systems studied. The vertical line in the plot
at ∆solSh = 23 J/(mol·K), dividing regular (nf/nf combinations)
and anomalous (f/nf and f/f) structures, corresponds to the onset
of faceting in a variety of materials due to thermal and crystal
growth anisotropy. Diagonal and dashed lines mark boundaries
of distinct regions (numbered) within which CFS found that a
system favors a speciÞc eutectic morphology. (These numbers
constitute the CFS index notation incorporated in our description of microstructures within this text and in Table 2.) The line
separating regions 1 and 2 is diagonal, for example, because it
was observed that the heterophase boundary energy between the
eutectic solids increases with ∆solSh , thus displacing the transition
from rod to lamellar structures to smaller VF,h as ∆solSh increases.
That the microstructures we observed are essentially identical
to those presented in such regions by CFS suggests that the underlying dynamics involved in the growth of metal and ceramic
eutectics holds true for ice-I/hydrate systems.
Figure 14 assumes a constant growth rate. The slopes of the
diagonal boundary lines, for instance, ßatten at faster growth
rates; one result is that the stable microstructure can change with
local conditions. Because growth rate is a function of the undercooling (Eqs. 2 and 3), as the temperature of samples evolves
during solidiÞcation—as is the case, e.g., when the latent heat
of crystallization warms the surrounding liquid—so too will
the growth rate ßuctuate. Such a process is seen in the thermal
analysis for the system H2O-MgSO4. In Figure 6, growth rate is
approximated by distance between thermocouples divided by
the time between observed peaks (the left—low time—edges
of the regions marked A, B, and C). At the top of the sample
(TC1, region A) there was a large undercooling; the growth
rate here is fast. After the onset of crystallization, recalescence
warms up the surrounding liquid so that material deeper within
the sample (TC2, region B) experiences a smaller ∆T; thus, the
crystal growth rate slows. As crystallization extends to lower
portions of the sample (TC3, region C), the growth rate is slower
yet. There could be a difference in scale within the sample by a
factor of four with thermal results such as these. Furthermore,
the observation that many of our systems appear on or near the
shifting (with cooling rate) boundaries in Figure 14 explains why
variations in type of microstructure are observed within a given
system, and even within a given sample.
Thermal conditions additionally affect the phases present in a
sample. In the system H2O-H2SO4, there is a peritectoid reaction
that occurs at 200.37 K. For the samples in this study, which were
initially solidiÞed at ~211 K, a reaction potentially occurred while
they were stored in the freezer (~187 K) awaiting microscopic
analysis, speciÞcally, ice-I + HS6.5 → HS8. The ∆solS curve
for this system is nearly linear in this composition range, with
ice-I as the high-entropy phase (∆solSice-I = ∆solSh ; Table 3), so a
change in ∆solSh due to this phase change would be minimal. The
volume fraction change, however, would be signiÞcant, so much
so that the two assemblages plot on either side of a boundary line
(points D and E in Fig. 14). The signiÞcance of this is that two
morphologies could be present in the sample as it transitioned
FIGURE 14. ClassiÞcation of eutectic microstructures by VF,h and
∆solSh at constant growth rate based on Croker et al. (1973). Key to regions
of morphology: (1) regular lamellar; (2) regular rod; (3) broken lamellar;
(4) irregular; (5) complex regular; (6) quasi-regular. Lettered notations
are for the materials characterized in this study: (A) H2O-Na2SO4; (B)
H2O-MgSO4; (C) H2O-NaCl; (D) and (E) H2O-H2SO4.
TABLE 3. Molar entropies of fusion (∆fusS) and of solution at the eutectic composition (∆solSh ) for water/salt-hydrate eutectic reactions
Phases
Mole fraction hydrate
at eutectic composition
Entropy of fusion of
hydrate ∆fusS (J/mol/K)
per mole of hydrate
per mole of solution
0.005
265.43
24.13
Na2SO4⋅10H2O/ice-I
0.035
154.40
19.30
MgSO4⋅7H2O/ice-I
0.030
252.36*
21.03*
MgSO4⋅11H2O/ice-I
0.086
70.17*
23.39*
NaCl⋅2H2O/ice-I
0.044
145.80
19.44†
H2SO4⋅6.5H2O/ice-I
0.041
158.49
17.61†
H2SO4⋅8H2O/ice-I
ice-I
–
–
22.0
* Calculated using approximation from Telkes (1980).
† Beyer et al. (2003).
Phase with highest ∆solS at
the eutectic (thus ∆solSh )
Partial molar Entropy of
Solution ∆solSh (J/mol/K)
NS10
ice-I
ice-I
NC2
ice-I
ice-I
–
25.9
22.0
22.0
23.1
21.6
21.5
–
MCCARTHY ET AL.: EUTECTIC SOLIDIFICATION IN ICE-I/HYDRATE SYSTEMS
through the solid-state reaction. Thus, it is unclear whether the
snowßake-like patterns found crisscrossing through the sample
in Figure 10a are a form of primary ice-I phase crystallization
(though, morphologically, this is the model we favor), or remnants of an ice-I/HS6.5 eutectic morphology.
As the examples and analysis above demonstrate, a system’s
thermal history during solidiÞcation (and, in the case of H2OH2SO4, its post-solidiÞcation history) is critical to the eutectic
microstructure that results, both in morphology and in scale:
small ßuctuations in (local) temperature can produce signiÞcant differences in microstructure. Nevertheless, the criteria of
∆solSh and VF,h dominate the microstructure for the modest
undercoolings explored in these experiments, which are, too,
the solidiÞcation conditions anticipated in many planetary settings, e.g., at the interface between a planetary ice shell and an
underlying liquid ocean.
Not explored in these experiments are the physics of static,
high-temperature annealing and its effect on the microstructure
of these aggregates. Such a study will constitute a part of our
continuing research.
Mechanical response
As a potential constituent of the icy shell, it is important
to understand how ice-I/hydrate eutectic aggregates respond
to deviatoric stress at Europa-like conditions. The addition of
other phases can greatly affect the rheology of polycrystalline
aggregates. The microstructures of many eutectic binary metals are nearly identical to those seen, e.g., in the MS11/ice-I
samples, including the absolute scale of the phases. There is
a panoply of studies on the low-strain-rate rheology of these
analogous engineering materials. For example, Chatterjee et al.
(2002) conducted creep tests on Ti-Al materials consisting of
a fully lamellar microstructure of α2 (Ti3Al; hexagonal) and γ
(TiAl; face-centered tetragonal) phases. Additionally, Argon et
al. (2001) examined the creep response of a eutectic ionic aggregate, Al2O3(corundum)/c-ZrO2 (ßuorite structure), which also
exhibits colonies of aligned lamellae. In both these studies, the
eutectic morphology was found to be remarkably creep resistant,
more so than either phase alone. Furthermore, in the Chatterjee
et al. (2002) study, the creep resistance (strength) was found to
be affected positively by decreased lamellar spacing.
Initial, constant-load mechanical tests on specimens with compositions corresponding to the eutectic (and metastable eutectic) in
the system H2O-MgSO4 have demonstrated that, like their counterparts in engineering materials, the polyphase aggregates have
a more complex rheology than does pure ice-I (McCarthy et al.
2006, 2007). The steady state creep results show that the eutectic
aggregates have an effective viscosity that is at least an order of
magnitude greater than that of polycrystalline ice-I at the same
conditions of pressure, temperature, and differential stress (cf.
Durham et al. 2001; Goldsby and Kohlstedt 2001). In a previous
study of the same phases that were instead formed via solid-state
mixing, Durham et al. (2005) found no difference between the
strength of the mixture and that of pure ice because the randomly
dispersed hydrate grains behaved as virtually undeformable inclusions. Clearly, it is the unique nature of the eutectic microstructure
that causes the increase in strength.
Yielding plasticity in crystalline material follows the Hall-
1559
Petch relation, which predicts that the ßow strength of polycrystalline materials increases with decreasing grain size (speciÞcally,
strength is proportional to the inverse square-root of grain size).
Applied to lamellar, heterophase solids like the ones described
above, the critical constraint is the spacing of lamellae, λ (e.g.,
Kaya et al. 2004). This inverse relationship is posited to be
related to the pile-up of lattice dislocations on a glide plane due
to the barrier to slip (dislocation glide) presented by the grain
or heterophase boundary. Modeling of the dislocation physics
shows that the spatial density of the barriers increases the average stress for continued motion of dislocations (Hall 1951; Petch
1953). The incoherent nature of the heterophase boundaries in
the eutectic materials makes the barrier strength signiÞcantly
greater than that attributed to grain (homophase) boundaries.
Thus it is reasonable to propose that if an icy satellite has a crust
wholly or even partially made of a Þne-grained binary eutectic
intergrowth, that crust would be much stronger than is currently
estimated for a pure-ice rheology.
A further, and possibly more signiÞcant, implication is that
the unique lamellar microstructure of these aggregates offers far
more sites for absorption (dissipation) of mechanical energy than
would single-phase materials. Lakes (1999), Lakes and Quackenbush (1996), and McMillan et al. (2003) performed torsional
attenuation experiments on the β-In3Sn/γ-InSn4 eutectic as well
as on each of the phases alone. The data were collected on a
broadband viscoelastic spectrometer over nine decades of frequency (ƒ = 10–4 to 105 Hz) at room temperature (approximately
0.76 TE); they found that the torsional attenuation (QG–1) follows
a power law, i.e., QG–1 ∝ ƒ–m with m ≅ 0.3 and approaching m =
0 at increasing frequencies. The behavior is far more absorbing
than any inversion of a Maxwell-solid rheology would predict
(QG–1 ∝ ƒ–1; cf. Cooper 2002). Furthermore, at low frequencies,
the β-γ eutectic is distinctly more absorbing than either of the
phases β or γ independently. Additionally, as the eutectic microstructure thermally ages, speciÞcally by having the minority
phase γ (~35 vol%) coarsen so as to lower the total area of β-γ
phase boundaries, the attenuation diminishes. Clearly the role of
phase boundaries is indicated as signiÞcant in mechanical absorption: it is the high volume of heterophase boundaries present in a
eutectic aggregate that is responsible for the non-intuitive combination of high stiffness and high attenuation. Indeed, an initial
experimental study of the transient (anelastic; Young’s modulus)
response of the H2O-MgSO4 eutectic aggregates shows that, with
transformation to the frequency domain, they too demonstrate
a power-law frequency dependence with m ≅ 0.5 (McCarthy et
al. 2007). An icy crust on Europa made of ice/hydrate eutectic
material is thus anticipated to be both stronger and distinctly more
absorbing of mechanical energy than would be anticipated for a
pure-ice rheology; in addition, the capability of dissipating tidal
energy, i.e., converting it to heat, would be enhanced beyond that
presently postulated in Maxwell-solid rheology models of the
Europa crust (e.g., Moore and Schubert 2000).
Our continuing research consists of both creep and attenuation experiments on aggregates of ice-I with the non-ice phases
presented here. Information gleaned from such experiments will
constrain models of crustal thickness for the icy satellites, as
well as explain morphological features on the surface that are,
at present, poorly understood.
1560
MCCARTHY ET AL.: EUTECTIC SOLIDIFICATION IN ICE-I/HYDRATE SYSTEMS
ACKNOWLEDGMENTS
Support for this research was provided, in part, by NASA order W-19,868 (to
S.H.K.) and NSF grant EAR-0405064 (to R.F.C.). We thank J. Pinkston (USGS, Menlo
Park) for his technical support, R. Peterson (Queen’s University, Kingston, ON) for
sharing XRD data for the MS11 phase, A.D. Fortes (University College London) for
helpful comments and discussions concerning physicochemical properties of magnesium sulfate, and W.B. Durham for fruitful discussions on mechanical response.
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MANUSCRIPT ACCEPTED MAY 4, 2007
MANUSCRIPT HANDLED BY RHIAN JONES