1. IntroductionIce is the solid crystalline form of water (a polymorph of ice), the most essential and

abundant material on planet Earth. In fact, the word crystal that is used in mineralogy came

from the Greek word for ice, Krystallos (Suga, 1997). Depending on the Earth’s position in orbit

around the sun and angle of declination, ice covers anywhere from 10%-15% of its surface

which occurs dominantly at the north and south poles (Petrenko et al., 1999; Dunaevea et al.,

2010). Ice also plays an intricate role in the formation of other minerals throughout the solar

system (Fortes et al., 2010). Currently, there are 15 known species of ice that occur throughout

the solar system in places such as Uranus, Neptune, and satellites of Jupiter and Saturn

(Dunaevea et al., 2010). On Earth, terrestrial conditions only permit one species to exist, known

as ice I in hexagonal and cubic form (iceh and icec respectively), but scientists are able to

produce the other remaining species in various laboratory experiments (Dunaevea et al., 2010).

The elements present in ice are hydrogen and oxygen (H2O) which take on different forms

throughout the 15 species as temperature and pressure conditions change (Fig. 1). As per

www.mindat.org, the IMA (International Mineralogical Association) classification of ice is “Valid -

first described prior to 1959 (pre-IMA) - "Grandfathered" “(mindat.org 2012).

The purpose of this paper is to discuss the physical properties, chemistry, crystallography

(of phases I – XII), deformation (basal glide), dislocation (point, line, and planar defects) of ice

(with emphasis on ice I hexagonal and cubic) and its role in the formation of the solar system

and occurrence.

2. Physical Properties of Ice The information gathered in this section was from www.mindat.org unless otherwise noted.

2.1 Density propertyPerhaps the most distinguishing physical property of ice I is the specific gravity, which is

measured at 0.9167 g/cm3. This aspect of ice is noteworthy because the solid form of water is

less dense than the liquid form (measured at ~ 1.000 g/cm3) a property which is not very

common in nature with an exception of silicon and germanium (Petrenko et al., 1999).

However, the species of ice known as ice III, V, and VI, do not exhibit this property as the ice

molecules compress at different pressures at a rate greater than water, known as geometrical

compression (Bernal et al., 1933).

2.2 Physical properties

An easily noticeable feature of ice is the vitreous luster and it’s transparent to translucent

diaphaneity. The color of ice ranges from colorless to white (which is most common when

1

observed in snowflakes and in lacustrine environments), and from pale blue to greenish blue

when pressurized in a glacial environment. Ice is a very soft mineral that has a Mohs hardness

scale rating of 1.5, which can be scratched by a fingernail. If one were able to scratch ice on a

streak plate, they would observe a white streak. The fracture and tenacity of ice is conchoidal

and brittle respectively.

2.3 Classification

The classification of ice in the Strunz 8th edition ID is 4/A. 1-10 and the Nickel-Strunz 10th

edition ID is 4.AA.05 (4 : OXIDES (Hydroxides, V[5,6] vanadates, arsenites, antimonites,

bismuthites, sulfites, selenites, tellurites, iodates) A : Metal: Oxygen = 2:1 and 1:1 A :

Cation:Anion (M:O) = 2:1 (and 1.8:1), this classification is noted as “pending” on mindat.org. Ice

is referred to as falling under the “Simple Oxides” in the Dana 8th edition ID 4.1.2.1, 4 : SIMPLE

OXIDES, 1 : A 2 X.

2.4 Optical Properties

In terms of the optical mineralogy of ice, the type is listed as uniaxial and the refractive index

(RI) values are nalpha= 1.320 and nbeta= 1.330, with a maximum birefringence value measured at

1.320, which is considered to be low (Petrenko et al., 1999), and shows moderate surface relief

when viewed in thin section.

3. Crystallography The sections that discuss the crystallography of the various phases of ice from ice II – ice

XII was extracted from text and tables found in chapter 11 titled “The other phases of ice” (pg.

252 – 276) of Physics of Ice published in 1999 by Victor Petrenko and Robert Whitworth unless

otherwise cited within the paragraph. Each section ends with a Petrenko et al. citation.

3.1 Crystallography of terrestrial ice Terrestrial ice is known as Ice I, of which there are two sub-species referred to as iceh (h=

hexagonal) and icec (c = Cubic). Both structures form at low pressures and have similarities to

the quartz polymorphs tridymite and cristobalite respectively (Fortes et al., 2010). The polar

hexagonal lattice of Iceh has a space group of Cmc21 or mm2 (Fig. 2), while the apolar

hexagonal lattice has a space group of Pna21 (Fig. 3), both of these structures are commonly

referred to as the wurtzite lattice (Morrison et al., 1999; Casassa et al., 2005). Icec also

possesses both polar and apolar cubic lattice structures with space groups of I41md and P41212

respectively (Fig. 4 and Fig. 5) (Morrison et al., 1999; Casassa et al., 2005). The chemical

arrangement of atoms (or unit cell) in the crystalline structure of iceh is fixed and known as the

4-coordinated tetrahedral (Fig. 6) (Petrenko et al., 1999; Bernal et al. 1933; Fortes et al., 2010).

2

This coordinated structure contains four oxygen atoms which are covalently bonded to adjacent

H2O molecules by disordered hydrogen atoms, in a length that is equal to 2.76 Å (Petrenko et

al., 1999). The tetrahedral unit cell of iceh yields a density of molecules measured at

3.074X1028 molecules/m3 (Petrenko et al., 1999). This arrangement of atoms was found by

Bernal and Fowler in 1933 and is regarded as the “ice rules” which states that two hydrogen

atoms are always adjacent to one oxygen (making an H2O molecule), and each bond shall only

contain one hydrogen atom (Petrenko et al., 1999; Bernal et al. 1933; Fortes et al., 2010). The

coordinated tetrahedra of iceh has the following axes measurements a = 4.4923 Å, b = 7.7808 Å

and c = 7.3358 Å, these values vary slightly as the temperature decreases (Petrenko et al.,

1999). The structure of iceh can also be ferroelectric and anti-ferroelectric (Fan et al., 2010).

Pauling found in 1935, that unlike most minerals which are classified as having long-range

order, the arrangement of oxygen and hydrogen atoms in the tetrahedra do not exhibit such

long range order (Fortes et al., 2010; Petrenko et al., 1999; Louchet, 2004). The reason for the

lack of long-range order in the ice crystal structure is due to H2O molecules of one unit cell

becoming oriented differently than the molecules in adjacent cells (Petrenko et al., 1999). Iceh

is the most abundant species of ice on Earth as it is the common type that is produced when

liquid water is frozen at 0º C and 1 atmosphere of pressure (1 atm) (Fortes et al., 2010;

Petrenko et al., 1999). When iceh is formed in the atmosphere from water vapor, it nucleates

around ambient dust and/or clay particles (Gravner et al., 2008). As the crystal begins to gather

more vapor and mass, needlelike arms begin to protrude from a platelet with hexagonal

symmetry in single crystal snowflakes in an orientation that is perpendicular to the c-axis (Fig. 7)

(Gravner et al., 2008). Also oriented perpendicular to the c-axis are multiple layers of oxygen

atoms that result from the buildup of hexagonal rings (Petrenko et al., 1999). As a result, each

ring contains an independent center of symmetry along with an additional center of symmetry

equidistant and flanked by oxygen bonds (Petrenko et al., 1999). The hexagonal rings are

connected in a manner that produces sheets where every fourth sheet is oriented directly

overhead the initial sheet in the series, known as HCP (hydrogen close packing) (Fortes et al.,

2010). The Miller-Bravais notation of these single crystals are designated [0001] with the c-axis

termed as the hexagonal axes (Petrenko et al., 1999). The hexagonal symmetry and orientation

of atoms in Iceh that has been accepted was determined in 1929 by single-crystal diffraction

experiments carried out by W.H. Barnes (Petrenko et al., 1999). These findings have been

further reinforced by the synchrotron radiation method employed in 1994 by Rottger et al.

(Petrenko et al., 1999).

3

3.2 Crystallography of ice phases II - XIIIce II is a high pressure, proton ordered phase of water ice with a symmetry space group of

R3̄ , and belongs to the trigonal class of crystals. The formation of ice II continues from Iceh

after the pressure threshold of approximately 0.2GPa is reached. The temperature range of

formation is -60º C to -80ºC, but dissimilar to terrestrial ice, ice II does not melt. Unlike some of

the other phases of ice such as I, ice II does not have a disordered counterpart in which it

transitions to. The unit cell structure of ice II is rhombohedral that contains 12 molecules per

cell, which yields a density of 1.170 Mg/m3. The cell parameters of the 12 molecule structure

are a = 7.78 Å. These parameters are the more commonly observed, but Ice II can also have a

larger unit cell that contains 36 molecules which produces the following parameters a = 12.97 Å

and c = 6.25 Å. Unlike Ice I, Ice II contains hexagonal tubes coupled together by hydrogen

bonds instead of rings (Fortes et al., 2010; Fortes et al., 2003; Petrenko et al., 1999). The tubes

are ordered in a manner parallel to the c-axis and the six sides of the tubes are oriented at an

angle of approximately 16º in relation to the adjacent parallel columns (Fortes et al., 2010;

Fortes et al., 2003; Petrenko et al., 1999). The placement is more convolute which yields the

greater density as stated above. Within these hexagonal rings, there can also be helium and

neon inclusions (2 helium atoms), thus producing a structure that is similar to both but altering

the physical properties (Fortes et al., 2010; Fortes et al., 2003; Petrenko et al., 1999).

Ice III is a proton disordered, high pressure phase that lives in a very confined region of the

water-ice phase diagram (Fig. 1). The crystal structure of ice III belongs to the tetragonal class

and has a space group of P41212. Contained within each tetrahedral unit cell are 12 molecules

of H2O, this packing of molecules causes ice III to be less dense than the other higher pressure

species of ice such as IV, V, and VI. Because of the pressure that Ice III forms at (0.28 GPa),

the density is measured at 1.165Mg/m3, this also causes the cell parameters to be shorter at a =

6.666 Å and c = 6.936 Å. The five oxygen’s that construct the rings within the lattice are bonded

by hydrogen atoms that vary in angle and length (Petrenko et al., 1999).

Ice IV is also a proton disordered, high pressure phase that forms at pressures equal to 0.50

GPa. Ice IV belongs to the Rhombohedral crystal system and has a space group of R3̄ c.

Within each unit cell, there are 16 H2O molecules which yields a density measured at 1.272

Mg/m3. The cell parameters of ice IV is measured at a = 7.60 Å. The rhombohedral symmetry

contains a hexagonal axis as the c-axis, which is threefold. Oriented perpendicular to the c-

axis, are 6 H2O molecule membered rings that approach planar. Through the center of these

rings are hydrogen bonded molecules that have a bond length measured at 2.92 Å (Petrenko et

al., 1999).

4

Ice V is another phase that is naturally proton disordered, but experiments such as neutron

diffraction and Raman spectroscopy have revealed that partial ordering is possible at lower

temperatures. This phase belongs to the monoclinic crystal class and has a monoclinic unit cell

that contains 28 H2O molecules within the cell and forms at high pressures. As a result of the

number of molecules in each cell, the density is 1.231 Mg/m3. The space group for this crystal

is A2/a with cell parameters measured at a = 9.22 Å, b = 7.54 Å, and c = 10.35 Å, a complicated

structure that contains a 4 membered oxygen ring (Petrenko et al., 1999).

Ice VI is a proton disordered, high pressure phase as well. The crystal class of this phase is

tetragonal with a space group of P42/nmc and each unit cell contains 10 molecules of H2O with

the following cell parameters measured at a = 6.181 Å and c = 5.698 Å. Contained within the

crystal structure is an overlapping series of hydrogen bonded H2O molecules which are oriented

parallel to [001], a fourfold axis. The hydrogen bond sequences that lay centered on the edges

of the cell are oriented parallel to [100] and [010]. The arrangement of atoms does not possess

homogeneity in terms of bond angles, and some lengths are varied, which is a consequence of

proton disordering (Petrenko et al., 1999).

Ice VII is another phase of ice that does not have proton ordering (Fan et al., 2010). This

phase belongs to the cubic crystal system and has the space group Pn3M (Hirsch et al., 1984).

Within each unit cell, there are only two H2O molecules. The H2O molecules are bonded to

neighboring unit cells by half-hydrogen bonds with the following cell parameters measured at a

= 3.344 Å. The oxygen atom in each of these molecules is oriented near eight adjacent

molecules, but bonds are only made with four of them which produce a tetrahedral structure.

Within the crystal structure, there are cubic sublattices (same symmetry as icec) that

interpenetrate (Petrenko et al., 1999).

Ice VIII is the proton ordered phase of ice VII. Both phases have large coverage areas in

the ice-water phase diagram (Fig. 1). The crystal class of ice VIII is tetragonal and has a

symmetry space group of I41/amd. The cell parameters are measured at a = 4.656 Å and c =

6.775 Å. Within each unit cell, there are eight H2O molecules and similar to its disordered

counterpart, two interpenetrating sublattices. Unlike the structure of ice VII, these sublattices

are not connected. The tetragonal lattice has a fourfold axis labeled as the c-axis, while the a

and b axes are oriented on <11̄ 0> (Petrenko et al., 1999).

Ice IX is the proton ordered phase of ice III that belongs to the tetragonal crystal class and

has a symmetry space group of P41212. Each unit cell contains 12 H2O molecules (Petrenko et

al., 1999; Reis et al., 2001). The cell parameters of ice IX are measured at a = 6.692 Å and c =

6.715 Å (Petrenko et al., 1999).

5

Ice X belongs to the cubic crystal system with a symmetry space group of Pn3m. Within

each unit cell there are two H2O molecules and the cell parameters measured at a = 2.78 Å

(Petrenko et al., 1999).

Ice XI is the ordered phase of terrestrial iceh where the hydrogen atoms are ordered

alongside the c-axis (Fukazawa et al., 2005). This phase belongs to the orthorhombic crystal

class and has the symmetry space group Cmc21. Each unit cell contains eight H2O molecules

and has the following cell parameters measured at a = 4.465 Å, b = 7.858 Å, and c = 7.292 Å

(Petrenko et al., 1999).

Ice XII is a fully disordered phase of ice that belongs to the tetragonal crystal class and has

a symmetry space group of I4̄ 2d. This phase contains 12 H2O molecules within each unit cell

and has the following cell parameters a = 8.304 Å and c = 4.024 Å (Petrenko et al., 1999).

4. Chemistry – elements, bonding, Currie points, orbits The chemistry of ice is very similar to its liquid polymorph counterpart, water. Both contain

molecules of two hydrogen atoms covalently bonded to one oxygen atom (Louchet, 2004), but

the difference arises in the bond angles which are 104º-106º for water and 109º for ice I (Bernal

et al., 1933; Petrenko et al., 1999). Each water molecule is hydrogen bonded to adjacent

molecules and this causes the ferroelectric property of ice (Cubiotti et al., 1967). Hexagonal Ice

I (ice h) has a Curie point of approximately -173º C (Cubiotti et al., 1967) and can be found

stable at 0º C to -200º C (Louchet, 2004), while icec has one measured at approximately -80º C

(Cubiotti et al., 1967). The oxygen atoms in the water molecule exhibit dual behavior as they

can either act as a proton donor or proton acceptor (Suga, 1997). The oxygen accomplishes

this feature by the fact that it has a hybrid electron orbit sp3 (Suga, 1997). This hybridization

allows oxygen to utilize two of the orbitals to make lone-paired electrons available and

interconnect with two hydrogen atoms (Suga, 1997).

4.1 Enthalpy, lattice and bond energies In 1957, Whalley calculated the enthalpy that is required to dissociate the hexagonal lattice

structure of iceh at 0K and 0atm (Petrenko et al., 1999). This value was measured at 47.34 ±

0.02 kJ/mol and in 1976, he also calculated the lattice energy that would transform the crystal

structure to molecules measured at 58.95 kJ/mol which is equivalent to 0.6110 eV per H2O

molecule (Petrenko et al., 1999). The value of this energy is caused by hydrogen bonds which

are measured at 0.306 eV per bond (Each H2O molecule has two of them for a total of 0.6110

eV) and van der Waals activity (Petrenko et al., 1999). The observed bonding energy of iceh is

actually lower than its terrestrial counterpart icec by approximately 0.0005 eV and has an

6

ordering energy of 0.0025 eV (Petrenko et al., 1999). The problem with calculating the total

energy of a sample of ice is disordering, which prohibits accurate observations from summation

of the individual hydrogen bond energies (Petrenko et al., 1999).

5. Dislocations, deformation, point and line defects5.1 Dislocation and plastic deformation

Terrestrial ice deforms in an inelastic and non-linear fashion (Choi et al., 1996). The

magnitude and range in which polycrystalline ice deforms is contingent upon temperature, load,

and internal microcrystalline assembly (Choi et al., 1996; Montagnat et al., 2011). The manner

in which ice deforms depends heavily on the mechanical properties of singular crystals, which

are anisotropic (Choi et al., 1996). Noteworthy however is that when stress is applied

perpendicular or parallel to the c-axis of an individual ice crystal, it will not deform (Petrenko et

al., 1999). Dislocation behavior of ice is also affected by locking of grain boundaries, basal

sliding, orientation of single crystals, changes in the density dislocations, and propagation of

structural weaknesses triggered by micro-cracks (Choi et al., 1996).

Plastic deformation in polycrystalline terrestrial hexagonal ice (iceh) ensues

heterogeneously (Louchet, 2004) which proceeds as “dislocation glide along the basal plane”

(Montagnat et al., 2011) that produces shear stress subject to the rate of loading, known as

viscoplasticity (Fig. 8) (Montagnat et al., 2011). Basal slip commences once the stress

threshold of an aggregate is reached and the grains that are oriented in the slip direction will

begin the initial deformation (Petrenko et al., 1999). The deformation can come to a standstill

when the slip oriented grains come in contact with ones of opposing directions and internal

stress begins to prosper as a result (Petrenko et al., 1999). The stress field that accumulates

can be released by recrystallization, where the newly formed grains often orient themselves in

the direction of basal slip, or cracks may propagate in areas where the stress builds at a rate

faster than recrystallization can occur (Montagnat et al., 2011; Petrenko et al., 1999).

5.2 Point and line defects

The proton disordered nature of ice allows for point defects to arise which contributes to the

macroscopic plastic behavior (Louchet, 2004; Petrenko et al., 1999). The types of point defects

that occur in ice are molecular vacancies and interstitials, of which the latter are foremost

(Louchet, 2004), protonic defects, impurity atoms, electronic defects, and combined defects

(Petrenko et al., 1999). The dominant interstitial point defects, in which an additional H2O

molecule is placed between others in the lattice, are hypothesized as not hydrogen bonding to

other molecules within the original lattice structure (Petrenko et al., 1999). The protonic defects

7

arise when one of two bonding anomalies arise, such as a bond created with no protons known

as an “L-defect”, or when two protons bond while facing each other known as a “D-defect”

(Louchet, 2003; Petrenko et al., 1999). Substitution of atoms can occur in the hexagonal lattice

and accounts for the impurity atom defects (Petrenko et al.,1999). An example of such is when

a fluorine atom can replace an oxygen, or when a potassium can inhabit an interstitial site

defect (Petrenko et al., 1999).

When a dislocation occurs in ice, it is referred to as a line defect (Petrenko et al., 1999).

This happens when a plane of atoms glides past another within a lattice space, and the amount

of slippage is denoted as a Burgers vector (Petrenko et al., 1999). The region that is parallel to

the Burgers vector is termed the screw orientation, and the perpendicular region is the edge

(Petrenko et al., 1999). The lattice becomes elastically distorted at the screw orientation, and

found at the edge orientation, are bonds that “dangle” (Petrenko et al., 1999). The displacement

of the screw region (Fig. 9) glides at a rate that is dependent on the amount of stress caused by

the load (Fukuda et al., 1981). The gliding of these planes can also produce a step in the plane

known as a kink, which is located in the edge region (Petrenko et al., 1999).

6. Ice in the solar system and beyond6.1 Ice moons and planets in the solar system

Ice is a chief mineral constituent in the solar system in terms of the formation of rock

minerals and the dominant component of the icy satellites Europa (Fig. 10), Ganymede (ice VI

and VII), Callisto (Ice VI and VII), Titan (Ice VI) (Fig. 11), Enceladus, as well as the make-up of

Jupiter’s lithosphere (Dunaeve et al., 2009). The following is a list of planets and their icy

moons, Jupiter (Europa, Ganymede, and Callisto), Saturn (Mimas, Enceladus, Tethys, Dione,

Rhea, Titan, and Iapetus), Uranus (Miranda, Ariel, Umbriel, Titania, and Oberon), and Pluto

(Charon) (Petrenko et al., 1999). Of these planetary bodies, the larger icy satellites Ganymede,

Callisto, and Titan, have mantle structures with concentric layers of ice Ih, II, III, V, and VI that

are approximately 800 km thick (Fortes et al., 2010). Ice is also the primary mineral component

of the planets Uranus and Neptune and is postulated to exist in concentric layers of thousands

of kilometers thick (Dunaeve et al., 2009). Ice also exists in the more miniscule parts of the

solar system such as in grains around the rings of Saturn and enveloping dust particles of

comets (Kouchi et al., 1995). By interpretation of infrared absorption spectra, ice has also been

identified in various parts of the Milky Way near low temperature stars and interstellar gaseous

and molecular clouds (Kouchi et al., 1995).

8

6.2 Role of ice in formation of planetary bodies and starsIce plays an intricate role in the formation of stars, our solar system, and other planetary

bodies (Dunaeve et al., 2009). Throughout the process of stellar evolution, stars such as red

giants and supernovas will emit gases and silicate particles via explosions (Kouchi et al., 1995).

The silicate particles that are dispersed are then encapsulated by ice which forms a mantle

around them at temperatures near 100K (Kouchi et al., 1995; Petrenko et al., 1999). The

particles that have now formed icy mantles begin to coalesce with molecular clouds which are

called “dark clouds” because the temperatures surrounding them are low (Kouchi et al., 1995).

The formation of the solar system is derived from these molecular clouds by means of

gravitational forces causing them to collapse inwards (Kouchi et al., 1995). Once this reduction

takes place, the constituents of the cloud break apart into smaller pieces and begin to coalesce

once again to form planetesimals (Kouchi et al., 1995). Preceding the planetesimal formation,

the grains located toward the center of the cloud sublimed as heat is released from shock

waves caused by the implosion of gas particles toward the center (Fig. 12) (Kouchi et al., 1995).

The dust particles containing icy mantles that were located on the outer perimeter of the cloud

would not have transitioned this way and were then able to form planetesimals that would later

evolve into the planets of our solar system (Kouchi et al., 1995). The comets that line the outer

solar system are the consequence of planetesimals that did not coalesce to form planets

(Kouchi et al., 1995).

9

REFERENCES

Research articles

1. Bernal, J.D., Fowler, R.H., 1933. A Theory of Water and Ionic Solution, with Particular

Reference to Hydrogen and Hydroxyl Ions. Journal of Chemical Physics 1: 515-548.

2. Casassa, S., Calatayud, M., Doll, K., Minot, C., Pisani, C., 2005. Proton ordered cubic and

hexagonal periodic models of ordinary ice. Chemical Physics Letters 49: 110-117.

3. Choi, D.H., Connor, J.J., 1997. A constructive creep model for single crystal ice. Mechanics

of Materials 25: 97-112.

4. Cubiotti, G., Geracitano, R., 1967. Ferroelectric behavior of ice. Physics Letters A 24: 179-

180.

5. Dunaeva, A.N., Antsyshkin, D.V., Kuskov, O.L., 2010. Phase diagram of H2O:

Thermodynamics functions of the phase transitions of high-pressure ices. Solar System

Research 44: 202-222.

6. Fan, X., Bing, D., Zhang, J., Shen, Z., Kuo, J.L., 2010. Predicting the hydrogen bond ordered

structures of ice Ih, II, III, VI and ice VII: DFT methods with localized based sets.

Computational Materials Science 49: S170-S175.

7. Fortes, A.D., Choukroun, M., 2010. Phase behavior of ices and hydrates. Springer Science

& Business Media 153: 185-218.

8. Fortes, A.D., Wood, I.G, Brodholt, J.P., Vocaldo, L., 2003. Ab initio simulation of the ice II

structure. Journal of Chemical Physics 119: 4567-4572.

9. Fukazawa, H., Hoshikawa, A., Yamauchi, H., Yamaguchi, Y., Ishii, Y., 2005. Formation and

growth of ice XI: A powder neutron diffraction study. Journal of Crystal Growth 282: 251-

259.

10. Fukuda, A., Shoji, H., 1981. A dislocation model for the plastic deformation of single crystals

of ice. Cold Regions Science and Technology 4: 175-185.

11. Gravner, J., Griffeath, D., 2008. Modeling snow crystal growth II: A mesoscopic lattice map

with plausible dynamics. Physica D: Nonlinear Phenomena 237: 385-404.

12. Hirsch, K.R., Holzapfel, W.B., 1984. Symmetric hydrogen bonds in ice X. Physics Letters A

101: 142-144.

13. Kouchi, A., Yamamoto, T., 1995. Cosmoglaciology: Evolution of ice in interstellar space and

the early solar system. Progress in Crystal Growth and Characterization of Materials 30:

83-107.

14. Louchet, F., 2004. Dislocations and plasticity in ice. Comptes Rendus Physique 5: 687-698.

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Research articles

15. Montagnat, M., Blackford, J.R., Piazolo, S., Aarnaud, L., Lebensohn, R., 2011.

Measurements and full-field predictions of deformation heterogeneities in ice. Earth and

Planetary Science Letters 305: 153-160.

16. Morrison, I., Jenkins, S., 1999. First principles lattice dynamics studies of the vibrational

spectra of ice. Physica B: Condensed Matter 263: 442-444.

17. Reis, H., Raptis, S.G., Papadopoulos, M.G., 2001. Electrostatic calculation of linear and

non-linear optical properties of ice Ih, II, IX and VIII. Chemical Physics 263: 301-316.

18. Suga, H., 1997. A facet of recent ice sciences. Thermochimica Acta 300: 117-126.

Books

1. Petrenko, V.F., Whitworth, R. W., 1999. Physics of Ice, p. 10-35. In: Ice Ih, p. 126-153. In:

Point Defects, p. 156-180. In: Dislocations and planar defects, p. 184-212. In: Mechanical

properties, p. 252-283. In: The other phases of ice, p. 307-314. In: Ice in nature. Oxford

University Press Inc., NY, NY. 373 p.

11

Figure 1. This figure depicts the phase diagram of the different species of ice in terms of temperature and pressure. From Fortes et al. (2003, p. 4568).

12

Figure 2. Unit cell figure depiction of the polar hexagonal structure. From Casassa et al. (2005, p. 112).

Figure 3. Unit cell depiction of the apolar hexagonal structure. From Casassa et al. (2005, p. 112).

13

Figure 4. Unit cell depiction of the polar cubic structure. From Casassa et al. (2005, p. 112).

Figure 5. Unit cell depiction of the apolar cubic structure. From Casassa et al. (2005, p. 112).

14

Figure 6. The 4-coordinated tetrahedra of terrestrial ice. From Casassa et al. (2005, p. 111).

Figure 7. Various ways hexagonal ice can form in the atmosphere, note the six needle arm hexagonal symmetry. From Gravnar et al. (2008, p. 387).

15

Figure 8. σ represents the stress of the load applied and the dotted lines depict the basal glide planes. The shear stress along the basal planes caused by the load is represented by Ƭ with the directional arrows. From Choi et al. (1996, p. 100).

16

Figure 9. This figure shows the basal plane where screw dislocations arise as a result of basal slippage. From Fukuda (1980, p. 176).

17

Figure10. Europa is a moon of Jupiter which has solid icy layers as well as ones that convect comparable to the mantle beneath the surface of the earth. From NASA/JPL (1999, http://photojournal.jpl.nasa.gov/catalog/PIA01669).

18

Figure 11. The various layers of Titan which is the largest moon orbiting Saturn. Note the 4th layer containing the high pressure phase of ice VI. From Fortes (image credit) NASA (2012, http://www.nasa.gov/mission_pages/cassini/multimedia/titan20120223L.html)

19

Figure 12. An artist’s rendition of icy dust particles dispersing as a shock wave propagates through the molecular cloud. From Ciesla et al. NASA (2011, http://solarsystem.nasa.gov/scitech/display.cfm?ST_ID=748).

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