Ice Ih

Last updated September 06, 2023

Ice I_h (hexagonal ice crystal) (pronounced: ice one h, also known as ice-phase-one) is the hexagonal crystal form of ordinary ice, or frozen water.^[1] Virtually all ice in the biosphere is ice I_h, with the exception only of a small amount of ice I_c that is occasionally present in the upper atmosphere. Ice I_h exhibits many peculiar properties that are relevant to the existence of life and regulation of global climate. For a description of these properties, see Ice , which deals primarily with ice I_h.

The crystal structure is characterized by the oxygen atoms forming hexagonal symmetry with near tetrahedral bonding angles. Ice I_h is stable down to −268 °C (5 K; −450 °F), as evidenced by x-ray diffraction^[2] and extremely high resolution thermal expansion measurements.^[3] Ice I_h is also stable under applied pressures of up to about 210 megapascals (2,100 atm) where it transitions into ice III or ice II.^[4]

Physical properties

The density of ice I_h is 0.917 g/cm³ which is less than that of liquid water. This is attributed to the presence of hydrogen bonds which causes atoms to become closer in the liquid phase.^[5] Because of this, ice I_h floats on water, which is highly unusual when compared to other materials. The solid phase of materials is usually more closely and neatly packed and has a higher density than the liquid phase. When lakes freeze, they do so only at the surface while the bottom of the lake remains near 4 °C (277 K; 39 °F) because water is densest at this temperature. No matter how cold the surface becomes, there is always a layer at the bottom of the lake that is 4 °C (277 K; 39 °F). This anomalous behavior of water and ice is what allows fish to survive harsh winters. The density of ice I_h increases when cooled, down to about −211 °C (62 K; −348 °F); below that temperature, the ice expands again (negative thermal expansion).^[2]^[3]

The latent heat of melting is 5987 J/mol, and its latent heat of sublimation is 50911 J/mol. The high latent heat of sublimation is principally indicative of the strength of the hydrogen bonds in the crystal lattice. The latent heat of melting is much smaller, partly because liquid water near 0 °C also contains a significant number of hydrogen bonds. The refractive index of ice I_h is 1.31.

Crystal structure

The accepted crystal structure of ordinary ice was first proposed by Linus Pauling in 1935. The structure of ice I_h is the wurtzite lattice, roughly one of crinkled planes composed of tessellating hexagonal rings, with an oxygen atom on each vertex, and the edges of the rings formed by hydrogen bonds. The planes alternate in an ABAB pattern, with B planes being reflections of the A planes along the same axes as the planes themselves.^[6] The distance between oxygen atoms along each bond is about 275 pm and is the same between any two bonded oxygen atoms in the lattice. The angle between bonds in the crystal lattice is very close to the tetrahedral angle of 109.5°, which is also quite close to the angle between hydrogen atoms in the water molecule (in the gas phase), which is 105°. This tetrahedral bonding angle of the water molecule essentially accounts for the unusually low density of the crystal lattice – it is beneficial for the lattice to be arranged with tetrahedral angles even though there is an energy penalty in the increased volume of the crystal lattice. As a result, the large hexagonal rings leave almost enough room for another water molecule to exist inside. This gives naturally occurring ice its rare property of being less dense than its liquid form. The tetrahedral-angled hydrogen-bonded hexagonal rings are also the mechanism that causes liquid water to be densest at 4 °C. Close to 0 °C, tiny hexagonal ice I_h-like lattices form in liquid water, with greater frequency closer to 0 °C. This effect decreases the density of the water, causing it to be densest at 4 °C when the structures form infrequently.

Hydrogen disorder

The Wurtzite structure. In Ice Ih, the oxygen atoms are arranged on the lattice points, and the hydrogen atoms are on the bonds between lattice points. Each oxygen atom has 4 neighboring ones. Note that the lattice bipartites into two subsets, here colored black and white. Wurtzite-boat-chair.png — The Wurtzite structure. In Ice I_h, the oxygen atoms are arranged on the lattice points, and the hydrogen atoms are on the bonds between lattice points. Each oxygen atom has 4 neighboring ones. Note that the lattice bipartites into two subsets, here colored black and white.

The hydrogen atoms in the crystal lattice lie very nearly along the hydrogen bonds, and in such a way that each water molecule is preserved. This means that each oxygen atom in the lattice has two hydrogens adjacent to it, at about 101 pm along the 275 pm length of the bond. The crystal lattice allows a substantial amount of disorder in the positions of the hydrogen atoms frozen into the structure as it cools to absolute zero. As a result, the crystal structure contains some residual entropy inherent to the lattice and determined by the number of possible configurations of hydrogen positions that can be formed while still maintaining the requirement for each oxygen atom to have only two hydrogens in closest proximity, and each H-bond joining two oxygen atoms having only one hydrogen atom.^[7] This residual entropy $S 0$ is equal to 3.4±0.1 J mol⁻¹ K⁻¹ $=R\ln(1.50\pm 0.02)$ .^[8]

There are various ways of approximating this number from first principles. The following is the one used by Linus Pauling.^[9]^[10]

Suppose there are a given number $N$ of water molecules in an ice lattice. To compute its residual entropy, we need to count the number of configurations that the lattice can assume. The oxygen atoms are fixed at the lattice points, but the hydrogen atoms are located on the lattice edges. The problem is to pick one end of each lattice edge for the hydrogen to bond to, in a way that still makes sure each oxygen atom is bond to two hydrogen atoms.

The oxygen atoms form a bipartite lattice: they can be divided into two sets, with all the neighbors of an oxygen atom from one set lying in the other set. Focus attention on the oxygen atoms in one set: there are $N /2$ of them. Each has four hydrogen bonds, with two hydrogens close to it and two far away. This means there are ${\textstyle {\tbinom {4}{2}}=6}$ allowed configurations of hydrogens for this oxygen atom (see Binomial coefficient). Thus, there are $6 N /2$ configurations that satisfy these $N /2$ atoms. But now, consider the remaining $N /2$ oxygen atoms: in general they won't be satisfied (i.e., they will not have precisely two hydrogen atoms near them). For each of those, there are $24 = 16$ possible placements of the hydrogen atoms along their hydrogen bonds, of which 6 are allowed. So, naively, we would expect the total number of configurations to be

6^{N/2}(6/16)^{N/2}=(3/2)^{N}.

Using Boltzmann's principle, we conclude that

S_{0}=Nk\ln(3/2)=nR\ln(3/2),

where $k$ is the Boltzmann constant and R is the molar gas constant. So, the molar residual entropy is $R\ln(3/2)=3.37\mathrm {J} \cdot \mathrm {mol} ^{-1}\mathrm {K} ^{-1}$ .

Another estimate first orients each water molecule randomly in each of the 6 possible configurations, then check that each lattice edge contains exactly one hydrogen atom. Assuming that the lattice edges are independent, then the probability that a single edge contains exactly one hydrogen atom is 1/2, and since there are 2N edges in total, we obtain a total configuration count $6^{N}\times (1/2)^{2N}=(3/2)^{N}$ , as before.

This estimate is 'naive', as it assumes the six out of 16 hydrogen configurations for oxygen atoms in the second set can be independently chosen, which is false. More complex methods can be employed to better approximate the exact number of possible configurations, and achieve results closer to measured values. Nagle (1966) used a series summation to obtain $R\ln(1.50685\pm 0.00015)$ .^[11]

As an illustrative example of refinement, consider the following way to refine the second estimate method. According to the second estimation, six water molecules in a hexagonal ring would allow $6^{6}\times (1/2)^{6}=729$ configurations. However, by explicit enumeration, there are actually 730 configurations. Now in the lattice, each oxygen atom participates in 12 hexagonal rings, so there are 2N rings in total, giving a refined result of $R\ln(1.5\times (1+1/729)^{2})=R\ln(1.504)$ .^[12]

By contrast, the structure of ice II is hydrogen-ordered, which helps to explain the entropy change of 3.22 J/mol when the crystal structure changes to that of ice I. Also, ice XI, an orthorhombic, hydrogen-ordered form of ice I_h, is considered the most stable form at low temperatures.

Related Research Articles

In chemistry, a hydrogen bond is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a lone pair of electrons—the hydrogen bond acceptor (Ac). Such an interacting system is generally denoted Dn−H···Ac, where the solid line denotes a polar covalent bond, and the dotted or dashed line indicates the hydrogen bond. The most frequent donor and acceptor atoms are the period 2 elements nitrogen (N), oxygen (O), and fluorine (F).

In thermodynamics, the enthalpy of vaporization, also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. The enthalpy of vaporization is a function of the pressure at which the transformation takes place.

<span class="mw-page-title-main">Crystal structure</span> Ordered arrangement of atoms, ions, or molecules in a crystalline material

In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.

In condensed matter physics, the term geometrical frustration refers to a phenomenon where atoms tend to stick to non-trivial positions or where, on a regular crystal lattice, conflicting inter-atomic forces lead to quite complex structures. As a consequence of the frustration in the geometry or in the forces, a plenitude of distinct ground states may result at zero temperature, and usual thermal ordering may be suppressed at higher temperatures. Much studied examples are amorphous materials, glasses, or dilute magnets.

<span class="mw-page-title-main">Cyclohexane conformation</span> Structures of cyclohexane

Cyclohexane conformations are any of several three-dimensional shapes adopted by molecules of cyclohexane. Because many compounds feature structurally similar six-membered rings, the structure and dynamics of cyclohexane are important prototypes of a wide range of compounds.

A tetrahedral intermediate is a reaction intermediate in which the bond arrangement around an initially double-bonded carbon atom has been transformed from trigonal to tetrahedral. Tetrahedral intermediates result from nucleophilic addition to a carbonyl group. The stability of tetrahedral intermediate depends on the ability of the groups attached to the new tetrahedral carbon atom to leave with the negative charge. Tetrahedral intermediates are very significant in organic syntheses and biological systems as a key intermediate in esterification, transesterification, ester hydrolysis, formation and hydrolysis of amides and peptides, hydride reductions, and other chemical reactions.

Residual entropy is the difference in entropy between a non-equilibrium state and crystal state of a substance close to absolute zero. This term is used in condensed matter physics to describe the entropy at zero kelvin of a glass or plastic crystal referred to the crystal state, whose entropy is zero according to the third law of thermodynamics. It occurs if a material can exist in many different states when cooled. The most common non-equilibrium state is vitreous state, glass.

In chemistry and physics, cohesion, also called cohesive attraction or cohesive force, is the action or property of like molecules sticking together, being mutually attractive. It is an intrinsic property of a substance that is caused by the shape and structure of its molecules, which makes the distribution of surrounding electrons irregular when molecules get close to one another, creating electrical attraction that can maintain a microscopic structure such as a water drop. Cohesion allows for surface tension, creating a "solid-like" state upon which light-weight or low-density materials can be placed.

In chemistry, a non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The chemical energy released in the formation of non-covalent interactions is typically on the order of 1–5 kcal/mol. Non-covalent interactions can be classified into different categories, such as electrostatic, π-effects, van der Waals forces, and hydrophobic effects.

<span class="mw-page-title-main">Tetrahedral molecular geometry</span> Central atom with four substituents located at the corners of a tetrahedron

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<span class="mw-page-title-main">Spin ice</span>

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Ice I_c is a metastable cubic crystalline variant of ice. Hans König was the first to identify and deduce the structure of ice I_c. The oxygen atoms in ice I_c are arranged in a diamond structure and is extremely similar to ice I_h having nearly identical densities and the same lattice constant along the hexagonal puckered-planes. It forms at temperatures between 130 and 220 kelvins upon cooling, and can exist up to 240 K (−33 °C) upon warming, when it transforms into ice I_h.

Ice XI is the hydrogen-ordered form of I_h, the ordinary form of ice. Different phases of ice, from ice II to ice XIX, have been created in the laboratory at different temperatures and pressures. The total internal energy of ice XI is about one sixth lower than ice I_h, so in principle it should naturally form when ice I_h is cooled to below 72 K. The low temperature required to achieve this transition is correlated with the relatively low energy difference between the two structures. Water molecules in ice I_h are surrounded by four semi-randomly directed hydrogen bonds. Such arrangements should change to the more ordered arrangement of hydrogen bonds found in ice XI at low temperatures, so long as localized proton hopping is sufficiently enabled; a process that becomes easier with increasing pressure. Correspondingly, ice XI is believed to have a triple point with hexagonal ice and gaseous water at.

Ice VII is a cubic crystalline form of ice. It can be formed from liquid water above 3 GPa (30,000 atmospheres) by lowering its temperature to room temperature, or by decompressing heavy water (D₂O) ice VI below 95 K. (Different types of ice, from ice II to ice XVIII, have been created in the laboratory at different temperatures and pressures. Ordinary water ice is known as ice I_h in the Bridgman nomenclature.) Ice VII is metastable over a wide range of temperatures and pressures and transforms into low-density amorphous ice (LDA) above 120 K (−153 °C). Ice VII has a triple point with liquid water and ice VI at 355 K and 2.216 GPa, with the melt line extending to at least 715 K (442 °C) and 10 GPa. Ice VII can be formed within nanoseconds by rapid compression via shock-waves. It can also be created by increasing the pressure on ice VI at ambient temperature. At around 5 GPa, Ice VII becomes the tetragonal Ice VII_t.

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In chemistry, ice rules are basic principles that govern arrangement of atoms in water ice. They are also known as Bernal–Fowler rules, after British physicists John Desmond Bernal and Ralph H. Fowler who first described them in 1933.

A Bjerrum defect is a crystallographic defect which is specific to ice, and which is partly responsible for the electrical properties of ice. It was first proposed by Niels Bjerrum in 1952 in order to explain the electrical polarization of ice in an electric field. A hydrogen bond normally has one proton, but a hydrogen bond with a Bjerrum defect will have either two protons or no proton. D-defects are more energetically favorable than L-defects. The unfavorable defect strain is resolved when a water molecule pivots about an oxygen atom to produce hydrogen bonds with single protons. Dislocations of ice Ih along a slip plane create pairs of Bjerrum defects, one D defect and one L defect.

Solid nitrogen is a number of solid forms of the element nitrogen, first observed in 1884. Solid nitrogen is mainly the subject of academic research, but low-temperature, low-pressure solid nitrogen is a substantial component of bodies in the outer Solar System and high-temperature, high-pressure solid nitrogen is a powerful explosive, with higher energy density than any other non-nuclear material.

References

↑ Norman Anderson. "The Many Phases of Ice" (PDF). Iowa State University. Archived from the original (PDF) on 7 October 2009.{{cite journal}}: Cite journal requires |journal= (help)
1 2 Rottger, K.; Endriss, A.; Ihringer, J.; Doyle, S.; Kuhs, W. F. (1994). "Lattice Constants and Thermal Expansion of H₂O and D₂O Ice I_h Between 10 and 265 K". Acta Crystallogr. B50 (6): 644–648. doi:10.1107/S0108768194004933.
1 2 David T. W. Buckingham, J. J. Neumeier, S. H. Masunaga, and Yi-Kuo Yu (2018). "Thermal Expansion of Single-Crystal H₂O and D₂O Ice Ih". Physical Review Letters. 121 (18): 185505. Bibcode:2018PhRvL.121r5505B. doi: 10.1103/PhysRevLett.121.185505 . PMID 30444387.{{cite journal}}: CS1 maint: multiple names: authors list (link)
↑ P. W. Bridgman (1912). "Water, in the Liquid and Five Solid Forms, under Pressure". Proceedings of the American Academy of Arts and Sciences. 47 (13): 441–558. doi:10.2307/20022754. JSTOR 20022754.
↑ Atkins, Peter; de Paula, Julio (2010). Physical chemistry (9th ed.). New York: W. H. Freeman and Co. p. 144. ISBN 978-1429218122.
↑ Bjerrum, N (11 April 1952). "Structure and Properties of Ice". Science. 115 (2989): 385–390. Bibcode:1952Sci...115..385B. doi:10.1126/science.115.2989.385. PMID 17741864.
↑ Bernal, J. D.; Fowler, R. H. (1 January 1933). "A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions". The Journal of Chemical Physics. 1 (8): 515. Bibcode:1933JChPh...1..515B. doi:10.1063/1.1749327.
↑ Berg, Bernd A.; Muguruma, Chizuru; Okamoto, Yuko (2007-03-21). "Residual entropy of ordinary ice from multicanonical simulations". Physical Review B. 75 (9). doi:10.1103/PhysRevB.75.092202. ISSN 1098-0121.
↑ Pauling, Linus (1 December 1935). "The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement". Journal of the American Chemical Society. 57 (12): 2680–2684. doi:10.1021/ja01315a102.
↑ Petrenko, Victor F.; Whitworth, Robert W. (2002-01-17). "2. Ice Ih". Physics of Ice. Oxford University Press. doi:10.1093/acprof:oso/9780198518945.003.0002. ISBN 978-0-19-851894-5.
↑ Nagle, J. F. (1966-08-01). "Lattice Statistics of Hydrogen Bonded Crystals. I. The Residual Entropy of Ice". Journal of Mathematical Physics. 7 (8): 1484–1491. doi:10.1063/1.1705058. ISSN 0022-2488.
↑ Hollins, G. T. (December 1964). "Configurational statistics and the dielectric constant of ice". Proceedings of the Physical Society. 84 (6): 1001. doi:10.1088/0370-1328/84/6/318. ISSN 0370-1328.

Ice Ih

Contents

Physical properties

Crystal structure

Hydrogen disorder

See also

Related Research Articles

References

Further reading

Ice Ih

Contents

Physical properties

Crystal structure

Hydrogen disorder

Refinements

See also

Related Research Articles

References

Further reading