3.2.1  Crystalline Ices

Figure 3.1   Phase diagram of H2O from 0.01 to 10000 GPa and 0 to 500 K, showing stable water phases and their space group when crystalline. Proton disordered phases are written in bold, and proton-ordered phases are written in italics. Phase boundaries are plotted with a thick black line and predicted phase boundaries predicted at ultra-high pressures using computational simulations in dotted lines. (Courtesy of Baptiste Journaux, coauthor of this chapter.)

The phase diagram shown in Figure 3.1 depicts the stability fields of liquid and solid phases of water. That is, the phase diagram merely shows the one phase that is thermodynamically most stable at a specific combination of pressure P and temperature T. Some ice phases, namely ices IV, IX, XII, XIII, XIV, and XVI, cannot be found in Figure 3.1 because they are never the thermodynamically most stable phase. In spite of this metastable nature, such phases readily form and can be isolated and characterized. They do not convert to more stable ice phases at laboratory time scales, and probably also not at astrophysically relevant time scales, provided the temperature and pressure conditions do not change. Crystalline phases can be stable in a P–T field or metastable at all P–T conditions. Some stable ice phases share a phase boundary with liquid water (ices I_h, III, V, VI [e.g., Choukroun and Grasset, 2007 and references therein] and ice VII [Pistorius et al., 1963; Mishima and Endo, 1978; Datchi et al., 2000]), and are disordered [Kuhs, 2007]. Other ice phases are proton ordered and only exist in thermodynamic equilibrium with other ice polymorphs, namely ices II [Kamb, 1964; Kamb et al., 1971; Arnold et al., 1968; Fortes et al., 2003, 2005], VIII [Whalley et al., 1966; Kuhset al., 1984; Jorgensen et al., 1984, 1985; Pruzan et al., 1990, 1992; Besson et al., 1994, 1997; Pruzan et al., 2003; Song et al., 2003; Singer et al., 2005; Knight et al., 2006; Yoshimura et al., 2006; Somayazulu et al., 2008; Fan et al., 2010], XI [Singer et al., 2005; Knight et al., 2006; Fan et al., 2010; Tajima et al., 1984; Matsuo et al., 1986; Fukazawa et al., 1998, 2002; Kuo et al., 2005], XII [Kuhs et al., 1998; Lobban et al., 2000; Salzmann et al., 2006a, 2006b, 2008; Knight and Singer, 2008], XIV [Salzmann et al., 2006a, 2006b; Tribello et al., 2006], and XV [Kuhs et al., 1984; Fan et al., 2010; Knight and Singer, 2005; Kuo and Kuhs, 2006; Salzmann et al., 2009]. Such high-pressure ice phases may be found in the mantles of the icy moons, for example, Ganymede, which is covered by an 800-km-thick layer of water ice [Vance et al., 2014], as well as Callisto [Schubert et al., 2004] and Titan [Tobie et al., 2005; Fortes et al., 2007] (Figure 3.2). It is also expected that high-pressure ices play a key role in ocean planets [Leger et al., 2004; Sotin et al., 2007; Grasset et al., 2009], roughly Earth-sized exoplanets with deep oceans that constitute an interesting analog to the icy satellites (Figure 3.2).

Figure 3.2   Pressures in exoplanet oceans span the multi-GPa range of pressures where liquids are possible. A Europa-depth ocean on Earth would behave like Ganymede’s ocean in terms of having high-pressure ices. This figure shows profiles of pressure (GPa) and temperature (°C) in the upper mantles of selected objects (modified from Vance, S. et al., Astrobiology, 7(6), 2007), beginning at the estimated depth of the seafloor. The overlying ocean is assumed to be at a constant temperature; in general, seafloor temperature will be elevated by more than 40°C in deep oceans. Known exoplanets, albeit very hot ones, are modeled as super Europa objects with seafloor depths like Earth’s (10 km), Europa’s (100 km), and Ganymede’s (800 km). (Courtesy of Steve Vance, principal author of this chapter.)

The distinction between proton-ordered and proton-disordered ice phases is shown in Figure 3.3. In all ice phases, the oxygen atoms occupy lattice positions, that is, the oxygen atoms are ordered over long ranges. The hydrogen atoms occupy lattice positions only in the case of the proton-ordered ice phases. For a given network of oxygen atoms, in principle a larger number of ordered proton configurations are possible. Experimentally, however, only a single type of ordering has been observed so far. Ice I_h, the most common form of ice on Earth, is a proton-disordered form of ice. The hydrogen atoms obey the Bernal–Fowler ice rules [Bernal and Fowler, 1933], but they are randomly distributed within the ice crystal. As a result, ice I_h represents a frustrated crystal, which does not have zero configurational entropy at 0 K. The residual entropy at 0 K has become famous as the Pauling entropy ΔS_P [Pauling, 1935] and amounts to approximately 3.41 J K^–1 mol^–1. This entropy can be released if one successfully achieves the transformation to the proton-ordered state. The ordered counterpart of ice I_h is known as ice XI, and its possible ferroelectric nature is currently being questioned [Parkkinen et al., 2014]. Order–disorder pairs can be easily recognized in the phase diagram in Figure 3.1 because the pair is separated by a phase boundary parallel to the pressure axis. This is so because there is barely any volume difference between proton-ordered and proton-disordered form, that is, ΔV ≈ 0, but the two ices differ by the Pauling entropy, that is, ΔS ≈ ΔS_P. The slope of the phase boundary dP/dT then goes to infinity, that is, parallel to pressure axis, according to the Clausius–Clapeyron equation dP/dT= ΔS/ΔV.

Figure 3.3   Six different proton configurations (white circles) allowed by the Bernal–Fowler ice rules. In proton-ordered ices, only one of these is observed, whereas in proton-disordered ices, all of these configurations are observed with equal probability. The tetrahedral coordination around a central oxygen atom (filled circles) is the motif found in all crystalline and amorphous ices (except for the ultrahigh-pressure phases at >100 GPa, ice X and the post-ice X phases). (Adapted from Fuentes-Landete, V., Proceedings of the International School of Physics “Enrico Fermi,” Volume 187: Water: Fundamentals as the Basis for Understanding the Environment and Promoting Technology, IOS and Bologna: SIF, Amsterdam, 2015.)

Solid–solid transitions between polymorphs are possible by either a rearrangement of the O-lattice (density-driven, e.g., by pressurization) or H-ordering/disordering while preserving the geometry of the O-atoms (entropy-driven, e.g., by cooling a disordered phase to form an ordered one). In the case of density-driven transitions, there is a finite volume change ΔV, but the entropy change may be close to zero ΔS ≈ 0 if the transition is from a proton-disordered to a proton-disordered phase. Such phase boundaries can be identified easily in Figure 3.1, since they are almost parallel to the temperature axis. With increasing pressure, the transition sequence I_h → III → V → VI → VII → X can be identified. All these ice phases, except for ice X, are proton-disordered and of increasing density, starting at 0.92 g cm^–3 and ending at 2.50 g cm^–3. High density is accommodated by improving packing, bending hydrogen bonds, and forming new hydrogen-network topologies. The oxygen networks differ in terms of topology and ring structure. While ices I_h and I_c consist entirely of six rings, ice V has 4-, 5-, 6-, 8-, 9-, 10-, and 12-ring structures [Herrero and Ramírez, 2013]. Some structures show ring threading; for example, ice IV and others show two interpenetrating ice networks (self-clathrates), for example, ices VI, VII, VIII, and X. For the latter ultrahigh-pressure ice X (>100 GPa [Benoit et al., 1996; Pruzan et al., 2003]), the molecular nature disappears due to the symmetrization of hydrogen position between the oxygen atoms.

Three low-density variants of crystalline ice can be produced at ambient pressure: hexagonal ice I_h, cubic ice I_c, and ice XI. While ice I_h is the abundant polymorph of solid H₂O on Earth, ice I_c can occasionally be found in clouds [Murray et al., 2005; Mayer and Hallbrucker, 1987; Whalley, 1983]. Ice I_c forms upon heating of amorphous ice in a vacuum or at ambient pressure. It may thus be present on comets after they have experienced temperatures above the crystallization temperature of ~150 K. It also forms upon heating of high-pressure forms of ice at/below ambient pressure and upon condensation of water vapor on particles at ~140–200 K. Both are very similar in density at P_atm, also appearing to be identical when probing the short-range molecular environment (e.g., Raman or mid-infrared). However, they can be distinguished when examining the long-range order (e.g., x-ray diffraction or neutron diffraction) [Kuhs et al., 1987]. Ices I_h and I_c are polytypical relative to each other: identical layers—differing stacking order (hexagonal rings, ABCABC with hexagonal symmetry for I_h, ABAB with fcc symmetry for I_c) [Kuhs and Lehmann, 1986; Kuhs et al., 1987; Guinier et al., 1984; Röttger et al., 1994]. I_c is not obtained as a single crystal, but only in the form of small crystallites with roughly hexagonal stacking faults (quantified by “cubicity index”) [Kuhs et al., 1987; Kohl et al., 2000; Hansen et al., 2007]. Ice XI, the proton-ordered form of ice I_h, is only stable at T < 72 K. A proton-ordered form of cubic ice I_c might also exist, as has been suggested by in situ IR experiments and ab initio simulations [Geiger et al., 2014].

As mentioned, a crystalline phase may be transformed into another by ordering/ disordering the protons while almost entirely preserving the O-atom topology. These order– disorder pairs will be found in the same P region of the phase diagram (I_h–XI [Singer et al., 2005; Knight et al., 2006; Fan et al., 2010; Tajima et al., 1984; Matsuo et al., 1986; Fukazawa et al., 1998, 2002; Kuo et al., 2005], III–IX [Fan et al., 2010; Kuhs et al., 1998; Lobban et al., 2000; Whalley et al., 1968; LaPlaca et al., 1973; Nishibata and Whalley, 1974; Minceva-Sukarova et al., 1984; Londono et al., 1993; Knight et al., 2006], V–XIII [Kuhs et al., 1998; Lobban et al., 2000; Salzmann et al., 2006a, 2008; Knight et al., 2008; Martin-Conde et al., 2006; Noya et al., 2008], VI–XV [Kuhs et al., 1984; Fan, 2010; Knight and Singer, 2005; Kuo and Kuhs, 2006; Salzmann et al., 2009], VII–VIII [Whalley et al., 1966; Kuhs et al., 1984; Jorgensen et al., 1984, 1985; Pruzan et al., 1990, 1992, 2003; Besson et al., 1994, 1997; Song et al., 2003; Singer et al., 2005; Knight et al., 2006; Yoshimura et al., 2006; Somayazulu et al., 2008; Fan et al., 2010], and XII–XIV [Salzmann et al., 2006a, 2006c; Tribello et al., 2006; Martin-Conde et al., 2006; Noya et al., 2008; Köster et al., 2015]), the ordered phase at lower and the disordered phase at higher temperatures (as the transition connected to the process of disordering an ordered phase is of entropic nature). Six configurations are allowed by the Bernal–Fowler ice rules in the local tetrahedral hydrogen-bond geometry known as Walrafen pentamer. In a fully disordered phase, all six are populated with the same probability (averaged over space/time) [Bernal and Fowler, 1933], whereas in an ordered phase, only one configuration is found. Often, the ordered low temperature phase cannot be accessed due to geometric constraints and kinetic limitations at such low temperatures. Point defects (Bjerrum L/D or ionic defects) in the ice lattice may enhance the reorientational mobility in the ice lattice. By using dopants incorporated into the ice lattice in ice I_h (e.g., HCl, HBr, HF, NH₃, KOH, etc. [Tajima et al., 1984; Matsuo et al., 1986; Hobbs, 1974; Gross and Svec, 1997]) and also at a higher pressure in ice VII (e.g., NaCl, LiCl, RbI [Frank et al., 2006, 2013; Klotz et al., 2009; Journaux et al., 2015]), such point defects may be introduced deliberately. These extrinsic defects may enhance the mobility related to rearrangement of protons and/or rotation of H₂O molecules, thereby overcoming kinetic limitations and allowing access to the proton-ordered low temperature phase [Köster et al., 2015]. However, this may also slow down the dynamics. Empirically it has been found that KOH doping accelerates dynamics in ice I_h whereas HCl doping has been found to accelerate the dynamics in the high-pressure ices V, VI, and XII [Salzmann et al., 2006a, 2006b, 2009]. The reasons why one dopant is effective and the other is not are still unclear, but are certainly related to the dynamics of pairs of point defects within the ice lattices [Burton and Oliver 1935; Mayer and Pletzer 1986]. Some ice phases do not form an order–disorder pair; new ice phases related to them through an order–disorder transition may be found in the future. For example, the ordered counterparts of I_c and IV, as well as the disordered one of II, still await discovery [Lokotosh and Malomuzh, 1993; Zabrodsky and Lokotosh, 1993].

The solubility of dopants in ice is generally assumed to be low. Ice I_h tends to reject any impurities during freezing [Gross and Svec, 1997]. For concentrated solutions, for example, freezing aqueous solutions present during sea ice formation, rejected salts may be incorporated in the bulk ice sheet at the grain boundaries as liquid brine inclusions [Weeks and Akley, 1986]. For the H₂O–NaCl system, the partition coefficient K_d (NaCl) is estimated around 2.7 × 10^–3 and 3.2 (±0.2) × 10^–3 [Gross et al., 1977, 1987]. This incompatible behavior of salts in ice I_h has a notable exception with ammonium fluoride, which forms a solid solution by substituting with H₂O molecules up to 5.2 mol% [Gross and Svec, 1997], most likely due to the isomorphism between the crystal lattices of NH₄F and ice I_h. Such incorporation should be distinguished from that occurring in clathrate hydrates as the ice solid solution keeps the crystallographic structure of the pure H₂O phase. While most substances are completely insoluble in ice, some dopants can be incorporated in the ice crystal by replacing water molecules. In cases of HCl, KOH, NH₃, HBr, or HF, the solubilities are in the ppb and ppm range. In spite of the low solubility, the influence on H-dynamics can be huge.

Figure 3.4   (a) Proton-disordered ice VII crystallographic structure in one possible proton configuration with the octahedral interstitial face-centered void. (b) Snapshot of a possible configuration of “salty” ice VII (LiCl·6H2O) derived from ab initio calculations illustrating the lattice distortion and H2O misorientation induced by the incorporation of Li+ (large circle) and Cl– (medium circle) ions. (Modified from Klotz, S., Nat. Mater., 8, 2009.)

Recent high-pressure experiments have shown that ice VII can incorporate up to 1.6 mol% of NaCl, 5 mol% of CH₃OH [Frank et al., 2006, 2013], and up to 16.7 mol% of LiCl [Klotz et al., 2009]. Using DFT ab initio calculations, Klotz et al. [2009] predict incorporation in ice VII at interstitial (face-centered) and lattice sites (H₂O substitution) for Li⁺ and Cl^–, respectively (Figure 3.4). The presence of 16.7 mol% of Li⁺ and Cl^– solutes in the ice VII cubic Pn-3m lattice increases the volume of the phase by 8%, increasing the density by 0.2 g cm^–3. At low temperatures, the presence of Li and Cl ions inhibits the transition to proton-ordered ice VIII down to 80 K. Strong electrostatic interactions between the incorporated ions and the polar water molecules seem to disadvantage long-range ordering of the H₂O orientations, as it may generate “crystal plasticity”^* even at very low temperature. At present, the effect of neutral solutes on the transition to a proton-ordered phase remains unknown.

Incorporating substantial amounts of ionic and molecular solutes may affect the conductivity, volume, density, and thermodynamic stability of water ice. Such modifications of the physical properties of the solid are of interest for planetary scientists, as large water-rich planetary bodies may contain high-pressure ice mantles with thicknesses of hundreds of kilometers. As far as we know, no studies exist of solutes incorporated into other high-pressure ice phases of interest for icy moons and large H₂O-rich planets (e.g., ice III, V, VI, and X).

In the negative pressure regime, phases resembling the geometries of naturally occurring, cage-like clathrate structures are predicted to be thermodynamically stable [Stevenson et al., 1999]. Experiments have not yet been possible on ice at negative pressures. However, one empty clathrate structure could be prepared experimentally and is now known as ice XVI [Kuhs et al., 2014].

At ultrahigh pressures exceeding a few Mbar, currently not accessible experimentally, simulations predict new phases of ice [Wang et al., 2011; Militzer and Wilson, 2010; Hermann et al., 2012; Umemoto and Wentzcovitch, 2011; Sanloup et al., 2013].

3.2.2  Amorphous Ices

Just as polymorphism is regarded to be one of H₂O’s anomalous properties, so is polyamorphism: the existence of more than one amorphous solid phase [Mishima et al., 1984, 1985].

One of solid water’s amorphous low-density variants, most likely the most abundant form of water in the universe (amorphous solid water, ASW), is produced by the deposition of gaseous water or chemical reaction of atomic H, O, and OH on a very cold solid substrate. Experimentally ASW was produced by deposition of H₂O_(g) on a cooled copper rod in early experiments [Ioppolo et al., 2010]. ASW naturally occurs on comets, satellites, interstellar dust, and in cold dark star-forming clouds in space [Mayer and Pletzer, 1986; Ehrenfreund et al., 2003; Ioppolo et al., 2010]). Depending on the conditions of formation (e.g., the temperature and general character of the substrate or the flow rates of the deposit gases [Stevenson et al., 1999; Cartwright et al., 2008; Bossa et al., 2012], the produced ASW may be highly microporous, resulting in specific surface areas of several hundred and even more than 1000 m²/g [Baragiola, 2003]. These micropores will collapse when temperatures are raised, forming a much more compact variant of ASW with a specific surface area of less than 1 m²/g [Baragiola, 2003; Mitterdorfer, 2014]. During formation of microporous noncollapsed ASW and in the presence of trace gases (e.g., in the cold regions of dense interstellar clouds), gas molecules can be trapped inside the pores [Ehrenfreund et al., 2003; Mitterdorfer et al., 2011]. Chemical reactions of trapped molecules in the micropores are promoted, and ASW may thus play a pivotal role in the very early stages of planet building [Ehrenfreund et al., 2003]. Furthermore, when pore collapse is induced while guest molecules are trapped, clathrate hydrates may form as a result [Mitterdorfer et al., 2011; Faizullin et al., 2014].

Molecular crystal with dynamical disorder in the orientation of its constituent molecules, in which flip rates range from picoseconds to nanoseconds.

As shown in Figure 3.5, low-density forms of amorphous H₂O_(s) are experimentally obtainable in three ways: cryo-deposition of gaseous H₂O (ASW) [Burton and Oliver, 1935], cryo-deposition of micrometer-sized droplets (also on a cooled substrate; hyper-quenched glassy water, HGW) [Mayer, 1985; Kohl et al., 2005] and decompression of higher-density forms of amorphous solid water at elevated temperatures (low-density amorphous ice, LDA) [Mishima et al., 1985]. All of them behave like glassy solids and seem to transform to a deeply supercooled, ultraviscous liquid upon heating, which is known as low-density liquid (LDL) water. The temperature of this transformation, known as glass-to-liquid transition, depends on the heating rate, found to be 124 K for slow heating (10 K/h) [Handa et al., 1986], 136 K for “common” heating (10 K/min), and 170 K for very fast heating rates (10⁵ K/s) [Sepúlveda et al., 2012]. ASW/HGW/LDA have been shown by DSC at “common” rates to exhibit very similar glass transition temperatures (T_g) of 136–137 K [Hallbrucker et al., 1989; Johari et al., 1987; Elsaesser et al., 2010]. Mechanical indentation experiments have indicated softening and penetration of the material at about 143 K [Johari, 1998].

Figure 3.5   Preparation routes for amorphous ices, starting from water vapor (leading to ASW), from liquid water (leading to HGW) and from crystalline ice (leading to HDA). Note that the acronyms ASW, HGW, and LDA represent the same structural state (commonly called “LDA”) after annealing at >110 K for a few minutes. This is indicated by the dashed arrows. The three polyamorphic forms LDA, HDA, and VHDA can reversibly be interconverted by compression/decompression experiments. (Modified from Fuentes-Landete, V., Proceedings of the International School of Physics “Enrico Fermi,” Volume 187: Water: Fundamentals as the Basis for Understanding the Environment and Promoting Technology, IOS and Bologna: SIF, Amsterdam, 2015.)

To date, two higher-density amorphous solid phases are known: high-density amorphous ice (HDA) and very high-density amorphous ice (VHDA), with sub-states of HDA differing in the degree of structural relaxation (unannealed HDA = uHDA [Mishima et al., 1984; Nelmes et al., 2006], expanded HDA = eHDA [Winkel et al., 2008; Salzmann et al., 2006d], and relaxed HDA = rHDA [Salzmann et al., 2006d]). HDA (uHDA) was the first high-density amorphous ice to be produced (in 1984) by compressing I_h to P > 1 GPa at 77 K [Mishima et al., 1984] (see Figure 3.5). VHDA can be formed by heating uHDA to temperatures below crystallization at pressures >0.8 GPa [Loerting et al., 2011]. eHDA behaves like a glassy solid and transforms upon heating into a deeply supercooled ultraviscous liquid—HDL water. The glass-to-liquid transition temperature was determined to be 116 K (10 K/min) at ambient pressure [Amann-Winkel et al., 2013].

Isotope substitution neutron diffraction experiments have shown ASW/HGW/LDA to be of highly similar structure [Bowron et al., 2006], as is also the case for uHDA–eHDA [Loerting et al., 2011]. However, uHDA and eHDA differ in their thermal stability (connected to their intrinsic states of relaxation), with uHDA transforming to LDA at approximately 110 K and eHDA at about 132 K at ambient pressure [Winkel et al., 2011].

However, the general question of whether HDA may be considered glassy (or possibly rather an assembly of nanoscaled polycrystallites) has remained [Loerting et al., 2009]. Studies have shown uHDA to first relax and then transform to LDA at P_atm [Handa et al., 1986]. At 1 GPa however, there appears to be a reversible glass–liquid transition at about 140 K [Andersson, 2011]. High-pressure experiments have presented dielectric relaxation times of VHDA of 100 s as early as 122 K at 1 GPa [Andersson, 2006]. Dilatometric analysis in the range of 0.1–0.3 GPa has located the onsets of reversible volume changes (attributed to possible glass transitions) to be between 134 and 142 K (at 0.1 and 0.3 GPa, respectively) [Seidl et al., 2011]. DSC measurements on eHDA at P_atm have indicated an onset of a glass transition at 116 K, presented as an endothermic feature that could not be found in the case of uHDA [Amann-Winkel et al., 2013]. All these findings suggest transformation of amorphous ices to ultraviscous, deeply supercooled liquids prior to crystallization at <160 K. At 140 K and 0.07 GPa, experimental evidence for spontaneous liquid–liquid phase separation and the formation of an interface between two ultraviscous liquids differing by 25% in density was obtained [Winkel et al., 2011]. At higher temperatures, these deeply supercooled liquids crystallize inevitably and rapidly, and so the thermodynamic connection between amorphous ices/deeply supercooled water and stable/supercooled water above 230 K remains unclear. At astrophysical time scales, water between about 160 and 240 K will always be crystalline.

3.2.3  Rheological Considerations

Durham and Stern [2001] reviewed the rheological properties of water ices, which influence planetary geology, including tectonics, crater formation and relaxation, and global thermal evolution.

Other low temperature materials produce frozen volatiles that are thought to be abundant on icy satellites and hypothesized exoplanets. Ammonia has been identified as a likely constituent in icy bodies beyond Jupiter, which implies a lower ice temperature and a strongly temperature-dependent viscosity [Croft et al., 1988; Durham et al., 1993; Arakawa and Maeno, 1994; Hogenboom et al., 1997; Leliwa-Kopystynski et al., 2002; Fortes et al., 2003]. The thermal conductivity of ammonia-rich (10%–30%) ice is two to three times lower than that of pure water ice, and the loss tangent is about 100 times greater [Lorenz and Shandera, 2001]. Intrinsic absorption in the ice matrix might be responsible for the latter. A recent study of the rheology of ammonia-water slurries as a function of temperature and strain rate show the development of yield stress-like behaviors, shear-rate dependence, and thixotropic behavior, even at relatively low crystal fractions [Carey et al., 2015]. Light and heavy alkanes familiar to the petroleum industry cover the surface of Titan and populate its atmosphere. Formation of methane and ethane clathrates may play a critical role in the evolution of Titan’s atmosphere [Choukroun et al., 2010]. Such work has implications for icy satellites where cryovolcanism may exist, such as Triton and Titan.

Rheologies of other frozen volatiles have been studied in connection with other planets and a few locations on Earth: methane clathrate [Stern et al., 1996; Durham et al., 2003], CO₂ [Durham et al., 1999], and N2 and CH4 [reviewed by Eluszkiewicz and Stevenson 1990]. Both brittle and ductile behaviors were observed for solid nitrogen and methane; the maximum strengths were determined to be 9 and 10 MPa, respectively, in the brittle failure mode [Yamashita et al., 2010]. These low strengths suggest that H₂O ice or other stronger materials may underlay solid N₂ and CH₄ to generate the topography observed on Triton.

The interaction of materials with different rheologies, melting points, and mixing behaviors has led planetary scientists to consider cryovolcanism as a class of geological process not found on Earth (Figure 3.6) [e.g., Kargel, 1994; Gaidos, 2001; Fagents, 2003; Sotin et al., 2005; Porco et al., 2006; Fortes et al., 2007; Desch et al., 2009; Cooper et al., 2009].

Figure 3.6   Amorphous solid water at various low temperatures. (Courtesy of AIP. With permission.)

3.3.1  Structure of Liquids

Low temperature liquids display a range of viscosity, density, and thermal expansion. These properties determine the efficiency of thermal and material transport of extraterrestrial oceans [e.g., Vance and Goodman 2009; Vance et al., 2014].

Related to the existence of more than one amorphous phase of solid water is the hypothesis of there being more than one liquid phase of water in the supercooled region [Finney et al., 2002]. The liquid phases would be thermodynamically continuously connected to the amorphous solid phases and would correspondingly be of different density (LDL and HDL). At about 0.2 GPa, these two liquids may exist in thermodynamic equilibrium, that is, with a sharp interface between the two liquids of pure H₂O. So, the one-component system water at ambient conditions might in fact be a fluctuating mixture of two liquids, which may separate under low temperature and high pressure conditions. This, in turn, may indicate the possibility of a second critical point in the regime of these two different liquid phases [Stanley et al., 2000]. This second critical point cannot be accessed experimentally because of fast crystallization at its predicted location, and so has remained a virtual point up to now.

3.3.2  Properties of Water and Aqueous Systems

Aqueous solutions are stable in liquid form at an elevated pressure (250 MPa) to temperatures as low as 160 K [Mishima, 2011]. In the pure phase, liquid water exhibits ordering behavior that causes a maximum density at 4°C anomalous to the behavior of other simple fluids (Figure 3.7). The anomalous nature of water becomes more pronounced in the supercooled state below 0°C. Response functions such as heat capacity or isothermal compressibility show a power-law increase, where a singular temperature of about 228 K was identified [Speedy and Angell, 1976]. These anomalies can be rationalized if the single-component system water experiences a spontaneous liquid–liquid separation into a HDL and LDL [Debenedetti, 2003]. The occurrence of polyamorphism (see Section 3.2.2) and the experimental evidence for spontaneous phase separation at 140 K and 0.07 GPa into the two ultraviscous liquids LDL and HDL [Winkel et al., 2011] support this theory. In the presence of sufficient amounts of solutes, the anomalies of water disappear and concentrated aqueous solutions behave as simple liquids.

Figure 3.7   Compressibility, heat capacity, and density versus temperature. (Adapted from http://www.lsbu.ac.uk/water.)

Low temperature eutectic brines, the last occurring phase in freezing aqueous systems, represent a likely ocean composition in the ice-covered worlds [e.g., Zolotov and Kargel, 2009]. The array of possible compositions comprises a multicomponent space of low temperature liquids that requires a systematic and extensible representation of possible thermodynamic states. Such a systematic framework for computing thermodynamics of aqueous systems has been available for decades, based on the theoretical formulation of Kenneth Pitzer [1991]. The FREZCHEM implementation of the Pitzer thermodynamic framework (e.g., Marion et al., 2012) balances the activity of water (excess chemical potential) of aqueous solutions to compute the properties of aqueous systems in the presence of ice I. The underlying Gibbs energy is computed as the sum of contributions from dissolved cations (c) and anions (a), with pressure- and temperature-dependent coefficients describing the cation–anion interactions (B_ca and C_ca). Higher-order interactions become relevant for higher concentrations.

$$\begin{array}{c}\frac{G^{ex}}{w_{w}RT}=f(I)+2{\displaystyle \sum _c{\displaystyle \sum _a{m}_c{m}_a}}\left[B_{ca}+\left({\displaystyle \sum _a{m}_c{z}_c}\right)C_{ca}\right]\\ +{\displaystyle \sum _{c<c^{\prime }}{\displaystyle \sum m_c{m}_{c^{\prime }}}}\left[2{\Phi }_{c{c}^{\prime }}+{\displaystyle \sum _a{m}_c{\psi }_{c{c}^{\prime }a}}\right]+{\displaystyle \sum _{a<a^{\prime }}{\displaystyle \sum m_a{m}_{a^{\prime }}}}\left[2{\Phi }_{a{a}^{\prime }}+{\displaystyle \sum _c{m}_c{\psi }_{ca{a}^{\prime }}}\right]\\ +2{\displaystyle \sum _a{\displaystyle \sum _c{m}_a{m}_c{\lambda }_{ac}}}+2{\displaystyle \sum _n{\displaystyle \sum _a{m}_n{m}_a{\lambda }_{na}}}+2{\displaystyle \sum _{n<n^{\prime }}{\displaystyle \sum m_n{m}_{n^{\prime }}{\lambda }_{n{n}^{\prime }}}}+{\displaystyle \sum _n{m}_n^2{\lambda }_{nn}}+\cdots \end{array}$$

The Pitzer framework is useful for representing the multicomponent thermodynamics of water, but limited in its application to other worlds by Earth-centric data sets as illustrated by available density measurements for MgSO₄ shown in Figure 3.8.

Sound speed and specific heat capacity measurements in solutions at low temperature provide a sensitive probe of thermodynamic behaviors. Both are related to Gibbs free energy through the second derivatives in pressure and temperature, respectively:

$${\left(\frac{\partial \rho }{\partial P}\right)}_{\text{T},\text{m}}=\frac{1}{c^2}+\frac{T{\alpha }^2}{C_{\text{P}}}$$

$${\left(\frac{\partial C_{\text{P}}}{\partial P}\right)}_{\text{T},\text{m}}=-T\frac{{\partial }^{2}V}{\partial T^2}$$

$$V=\frac{m}{\rho }={\left(\frac{\partial G}{\partial P}\right)}_{\text{T},\text{m}}$$

$$C_{\text{P}}=-T\frac{{\partial }^{2}G}{\partial T^2}$$

Sound speed measurements in water [Vance and Brown, 2010; Lin and Trusler, 2012] and aqueous solutions [Chen and Millero 1977; Chen et al., 1978; Millero et al., 1985; Vance and Brown 2013] and nonaqueous systems at low temperatures provide a sensitive measure of water’s thermodynamic properties, which can be used to systematically predict the behavior of multicomponent systems in low temperature settings.

Developing large thermodynamic frameworks is made possible by modern computers that can solve large inverse problems associated with sparse multiproperty thermodynamic data sets [Lemmon et al., 2013] and forward problems associated with ab initio molecular dynamics calculations [e.g., Hassanali et al., 2011].

Figure 3.8   Pressures and temperatures of density measurements in the MgSO4(aq) system illustrate that studies typically explore convenient laboratory conditions and conditions relevant to Earth’s oceans. (Modified from Cosmochim. Acta, 110, Vance, S., J.M. Brown, 176–189, Copyright 2013, with permission from Elsevier.)

3.3.3  Properties of Nonaqueous Systems

Nonaqueous liquids play important roles in the chemistry and transport of materials at cryogenic temperatures. The best example of these interactions can be found on Titan, a moon of Saturn with a thick atmosphere and liquid hydrocarbon lakes. Methane and ethane form the liquid phase and are involved in an active cycle similar to the hydrologic cycle on Earth—these hydrocarbons form clouds, precipitate onto the surface, and pool in lakes at the North and South poles [Brown et al., 2010].

Titan also contains a vast inventory of organic molecules generated by photochemistry in the atmosphere. These species form solid aerosol particles that fall onto the surface, forming dunes in the equatorial regions [Lorenz et al., 2006]. Interactions of liquid hydrocarbons with solid phases include pluvial (via rainfall) and fluvial (via river) transport of particulates into the lakes [Lorenz et al., 2008], and may also generate landforms similar to limestone or gypsum karst structures on Earth [Malaska and Hodyss, 2014; Cornet et al., 2015].

In fact, the conditions present on Titan may be much more ubiquitous throughout the universe than those on Earth. The most common type of stable star in the universe is the M-dwarf (red dwarf), which is smaller and less luminous than the Sun (a G-dwarf). Planets in a safe orbit around such a star (1 AU) would receive a similar amount of radiation as Titan does—just enough to maintain liquid methane and ethane on the planet’s surface. Since M-dwarfs are 10–100 times more abundant than G-dwarfs, it may be the case that Titan-like worlds are much more common than Earth-like worlds [Lunine, 2009]. Studies of the physical properties of nonaqueous liquids such as methane and ethane, therefore, may have implications for the exploration of many worlds.

The viscosities and densities of liquid methane, ethane, and propane have been reported at cryogenic temperatures [Haynes, 1973; Diller and Saber, 1981; Goodwin et al., 1973; Diller, 1982; Goodwin, 1977], as these are relevant for the liquefied natural gas industry. Thermal conductivities for these liquid hydrocarbons have also been measured [Younglove and Ely, 1987]. Values relevant to Titan surface conditions are shown in Table 3.1.

A recent study reported the complex dielectric constants of liquid methane and ethane at 90 K [Mitchell et al., 2015]. These loss tangents suggest that the northern lake Ligeia Mare of Titan is almost entirely comprised of methane, while the southern lake Ontario Lacus is more ethane-rich [Brown et al., 2008]. The loss tangent for methane (2.86 ± 1.01 × 10⁻⁵) from Mitchell et al. is considerably lower compared with a previous study (1.14 × 10⁻³) [Paillou et al., 2008], although the authors note that the Paillou et al. sample contained ~5% heavier hydrocarbons and is probably higher due to this contamination. Work with liquid alkane mixtures [Sen et al., 1992] indicates that the dielectric constant varies linearly with volume fraction as predicted by the Clausius–Mossotti equation [Hill et al., 1969]:

$$({\epsilon }_{\text{m}}^{\prime }-1)/({\epsilon }_{\text{m}}^{\prime }+2)={\Sigma }_{i}4\pi {\upsilon }_i{\rho }_i{N}_{\text{A}}{\alpha }_i/3M_i$$

where ε′ _m is the dielectric constant of the mixture, and for the ith component of the mixture, υ _i is the volume fraction, ρ _i is the mass density, α _i is the electric polarizability, and M_i is the molecular weight.

Interactions of liquid hydrocarbons with solid organics at cryogenic temperatures have also been explored. Simulated Titan aerosols, termed “tholins,” have been generated using various energy sources (cold plasma discharge, UV irradiation, etc.) and exposed to liquid hydrocarbons. These complex organics are relatively insoluble in liquid hydrocarbons, although adsorption onto the surface of these particles may enable chemistry at a gas– liquid interface as they fall through the atmosphere of Titan (for a review of Titan tholin formation and reactivity, see Cable et al., 2012).

Although tholins are not very soluble in liquid hydrocarbons, other organic species such as acetylene and HCN are believed to comprise approximately 1% and 2% of the Titan lakes, respectively [Cordier et al., 2009]. Acetylene is capable of polymerization on Titan [Raulin, 1987] and can serve as an energy source for methanogenic bacteria [McKay and Smith, 2005].

Less soluble species also have implications for Titan surface physical properties. Liquid ethane readily forms a co-crystal with solid benzene at 90 K, similar to a hydrated mineral on Earth [Cable et al., 2014; Vu et al., 2014]. These co-crystals may be present in evaporitic deposits around Titan lakes, and can affect evaporite properties such as particle size and dissolution rate. The crystal structure of the benzene–ethane co-crystal has recently been obtained at 90 K using synchrotron powder diffraction [Maynard-Casely et al., 2016].

Understanding the interaction of nonaqueous liquids with spacecraft materials is significant, both for interpreting data from the Huygens lander [Niemann et al., 2005; Lebreton et al., 2005] and for designing future in situ Titan missions. Methane behaves like a viscous non-Newtonian fluid just below its melting point (90.6 K), and adheres to materials such as aluminum, stainless steel, and PTFE with similar affinity [Kirichek et al., 2012]. Exposure of hydrocarbons to materials such as aluminum, steel, and titanium at cryogenic temperatures has been extensively explored in the liquefied natural gas industry, and no chemical reactivity has been reported [Kaufman, 1975].

Lorenz [2015] studied the effects of heat rejection for a Titan lake lander or submersible. For a lander with heat leaks on the order of 100 W/m² into the hydrocarbon liquid, experimental simulations indicate the formation of nitrogen bubbles (exsolvation) that may interfere with scientific measurements. Such heat leaks should be avoided by using thick insulation and rejecting as much heat as possible into the atmosphere.

3.3.3  Phase Transitions

Solid–liquid phase boundaries define multiple curves that are difficult to treat by extrapolation. Details of the melting point as a function of composition and temperature determine where liquids are stable in natural settings on Earth and other planets (e.g., Figures 3.9 and 3.10). Careful measurements of phase boundaries and crystallization kinetics in aqueous systems are enabled by high-resolution Raman spectroscopy [e.g., Bollengier et al., 2013; Cable et al., 2014].

Figure 3.9   Phase diagram for ammonia at atmospheric pressure, showing a eutectic temperature of 170 K at 29 wt% and peritectic transitions separating different hydration states of ice at ~55 wt%, 185 K and 80 wt%, 180 K. (Reprinted from Icarus, 73(2), Croft, S.K., J.I. Lunine, J. Kargel, Equation of state of ammonia water liquid: Derivation and planetological applications, 279–293, Copyright 1988, with permission from Elsevier.)