Water 3

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3 - Ice and crystalline water

All ice is not crystalline

not all crystalline water is ice

H2O solid phases

(From Savage)

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Some general comments on the phasediagram

All crystalline ice is tetrahedrically coordinated,and the polymorphs differ primarily in H-bond an-

gles and next-nearest neighbour separations.

Ice II, VIII and IX cannot be obtained directly from

liquid water.

Only ice I has a lower density than liquid water.

The rich phase diagram is a consequence of the

pressure sensitivity following from the open tetra-hedral structure of water.

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Ice Ih ordinary ice

Atomic arrangement in ice

Ih. H2 positions are half

occupied, and H1 positions

(filled) indicate positions in

the bent hydrogen model.

(From Kuhs)

Ice Ih is a thoroughly disordered crystalline material,

whose translational symmetry is not retained at theunit cell-level. In a time- and space-averaged sense

however, the symmetry of ice Ih is very high.

Although the oxygen atoms on average forms aregular lattice, this is not the case for the H atoms.

Along each OO-axis, there are two equivalent sites,

resulting in proton disorder.

Averaged molecular geometry (at 223 K for ice)

O H OO HOH OOO (A) (A) (deg) (deg) (g/cm3)

Ice Ih 1.00 2.76 107 109 0.931

Liquid 0.97 2.82 106 0.997

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Proton order and configurational degeneracy

Bernal & Fowler (1933) and Pauling (1935) arguedthat the similarites between ice and water esp. the

vibrational spectrum is evidence that H2O moleculesare intact in ice. This implies the Bernal and Fowler

conditions on the arrangement of hydrogen atoms:

(1) Each OO line has one and only one H atom.

(2) Each O has two H at about 1 A from its center,

and two at about 1.76 A.

Out of the 16 possible ways of arranging H atoms nearone particular O atom, there are only 6 consistent with

these conditions.

The five possible arrangements of hydrogens around a given oxygen. Num-

bers in brackets indicate the degeneracy. (Adapted from Ben-Naim)

Assuming all arrangements are equally likely, how manyconfigurations are there in ice containing N water

molecules?

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The residual entropy

With N water molecules, there are N oxygens, 2Nhydrogens and 2N OO bonds.

Ignoring condition (2), each hydrogen may be placedat either of two sites in each OO bond, thus 22N pos-

sible arrangements.

Some of these are inconsistent with (2); for each oxy-

gen, there is a 6/16 probability of finding an acceptablearrangement, so the total number of possible configu-

rations is

= 6

16

N

22N = (3/2)N

This can be used to calculate the residual entropy ofice:

S0 = k ln = 3.38 J/mol K

in good agreement with the observed 3.41 J/mol K.

A classical example of a successful prediction based

on an elementary statistical argument!

Proton order in ice Ih and disorder in ice VIII. (From Savage)

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Vibrational constants for water and ice(cm1)

Symmetric Asymmetricstretch, 1 stretch, 2 Bend, 3

H2O (g) 3657 3756 1595H2O (l) 3490 3450 1645

Ice Ih 3085 3220 1650Ice II 3194 3280 1690

Ice VIII 3359 3448

Denser ice forms become liquidlike? Loss of the ro-

bust tetrahedral hydrogen bonding (relative to Ih)partially recovers the water-like vibrational nature in

denser (high pressure) forms of ice.

H-bonded Closest non- OOOIce O O H-bonded OO (g/cm3) angles

Ih 2.74 4.5 0.931 109II 2.77-2.84 3.24-3.60 (9) 1.18 81-128

VIII 2.88 2.74-3.14 (5) 1.50 109.5

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The crystalline ice polymorphs

H-bonded Closest non- OOO HydrogenIce O O H-bonded OO (g/cm3) angles order

Ih 2.74 4.5 0.931 109 DisorderedIc 2.74 4.5 0.93 109.5 DisorderedII 2.77-2.84 3.24-3.60 (9) 1.18 81-128 Ordered

III 2.76-2.80 3.47 (1) 1.16 87-144 DisorderedIV 2.79-2.92 3.14-3.29 (9) 1.27 88-128 DisorderedV 2.76-2.87 3.28-3.49 (7) 1.23 84-128 Disordered

VI 2.81 3.44-3.46 (17) 1.31 76-128 DisorderedVII 2.90 2.90 (4) 1.50 109.5 Disordered

VIII 2.88 2.74-3.14 (5) 1.50 109.5 OrderedIX 2.75-2.79 3.45 (1) 1.16 87-144 OrderedX Properties largely unknown

(Adapted from Robinson and Savage)

All forms have 4 H-bonded nearest neighbours

Although denser, most structures have longer nearest-

neighbour OO distances than ice Ih, due to weak-ening of the hydrogen bonds.

Reduced (non-H-bonded) second-neighbour OO dis-

tances cause the density differences.

A structural relationship between the phases allow

transformations over relatively small energy bar-riers, which take place primarily by bending, not

breaking, H-bonds.

X Forms at 440 kbar. Believed to contain sym-metric H-bonds with ionic character. Structure un-

certain.

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Temperature dependence

Lattice constants for the a and c axes of ice Ih.

(From Kuhs)

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Ice Ih and ice II

The hexagonal rings inice II are flat, and half

the hexagonal tunnel

structures along the c-

axis are collapsed.

The protons in ice II

are fully ordered, so the

Pauling entropy is ab-sent.

(From Savage)

Ih (top) and II (bottom).

H-bonded Closest non- OOO Hydrogen

Ice O O H-bonded OO (g/cm3

) angles orderIh 2.74 4.5 0.931 109 DisorderedII 2.77-2.84 3.24-3.60 (9) 1.18 81-128 Ordered

Without the (proton) ordering, ice II is only slightlyless energetically stable than Ih, so that absence of

Pauling entropy would likely have led to freezing to

the dense II form in the depths of many waters...

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Ice IX / III

Ice IX / III, viewed along the c-axis. Filled bonds show the

5-membered ring in a unit cell. (From Savage)

IX and III have the same structure, but H is fully ori-

entationally ordered in IX and fully disordered in III.Contains 5- and 7-membered rings, but no hexagonal

rings.


Ih 2.74 4.5 0.931 109 DisorderedIII 2.76-2.80 3.47 (1) 1.16 87-144 DisorderedIX 2.75-2.79 3.45 (1) 1.16 87-144 Ordered

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Ice VI

One of the two interpenetrating lattices, with a structural unit

marked with filled bonds (left). Both lattices along the c axis of

the unit cell (right). (From Savage)

The first phase to form two interpenetrating lattices

as the pressure is increased.


Ih 2.74 4.5 0.931 109 Disordered

VI 2.81 3.44-3.46 (17) 1.31 76-128 Disordered

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Ice VII and ice VIII

VII (left) and VIII (right). (Adapted from Savage)

Ices VII and VIII comprise two interpenetrating

(ice Ic) lattices with all OOO bond angles closeto the tetrahedral value.

VIII is fully proton ordered, while VII is disor-dered.

VII has 8 nearest-neighbours at 2.90 A, of which

only 4 are H-bonded.

If the H-bonds were not extended, the density of

VII would be twice that of Ih.


Ih 2.74 4.5 0.931 109 DisorderedVII 2.90 2.90 (4) 1.50 109.5 Disordered

VIII 2.88 2.74-3.14 (5) 1.50 109.5 Ordered

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Amorphous ice I

Oxygen-oxygen par-tial radial distribu-tion functions of low-density amorphous ice(LDA), high-density

amorphous ice) HDA,liquid water, and iceIh. HDA appears com-pressed in a way sim-ilar to the way wateris collapsed from ice.(From Finney, PRL88, 225503 (2002)).

Phase diagram indicat-ing the LDA and HDAregions. (From Science297, 1289 (2002)).

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Amorphous ice II

Distribution of neighbour water molecules

Spatial density functions showing the distribution of neighbour wa-

ter molecules. Figures in brackets indicate contour levels g(r,).(From Finney, PRL 88, 225503 (2002)).

LDA has 3.9 nearest neighbours, while HDA has 5;

compare with 4 for ice Ih and 4.3-4.4 for liquid water...!

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Non-solid crystalline water

Water structure in coenzyme (Vitamin) B12

(From Savage)

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Primary references

H. Savage, Water structure in crystalline solids, in Water

Science Reviews 2, F. Franks (ed.), Cambridge: CUP 1986. G. Wilse Robinson et al., Water in biology, chemistry and

physics, Singapore: World Scientific 1996.

F. W. Kuhs and M. S. Lehmann, The structure of Ice-Ih, inWater Science Reviews 2, F. Franks (ed.), Cambridge: CUP1986.

D. Eisenberg and W. Kauzmann, The structure and proper-

ties of water, Oxford: OUP 1969. A. Ben-Naim, Water and aqueous solutions, New York: Plenum

1974.

E. Whalley (ed.), Physics and chemistry of ice : papers pre-sented at the symposium on the physics and chemistry of ice

held in Ottawa, Canada, 14-18 August 1972, Ottawa: RoyalSociety of Canada 1973.

Water 3

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