Ice. II. A proton-ordered form of ice

Abstract

Ice II, one of the high-pressure polymorphs of ice, d. 1.17, has 12H2O mols. in a rhombohedral unit cell with a 7.78 A., and alpha = 113.1 Deg. According to the Laue symmetry shown in single-crystal photographs, the space group should be either R.hivin.3m, R3m, or R32. Centrosymmetry is indicated by a statistical test with essentially 3-dimensional intensity data. However, the Patterson function indicates a pseudostructure in space group R.hivin.3c. The true structure must be appreciably distorted from this because of moderately strong violation of the c-glide extinction condition. The distortion could degrade the space group to R32, but the resulting structure has unsatisfactory features and does not conform well with the exptl. data. Structural reasoning indicates space group R.hivin.3. The observed R.hivin.3m Laue symmetry must therefore be the result of intimate twinning of R.hivin.3 individuals. The structure in R.hivin.3 can be refined, under the assumption of twinning, and with the inclusion of H atoms, to R = 0.08. The basic R.hivin.3c structure contains ice-I-like units built out of puckered "6-rings" of H2O-mols. These units are linked together in a more compact way than in ice I. Each O atom is bonded to 4 nearest neighbors at 2.80 +- 0.04 A. and has in addn. a nextnearest neighbor at 3.24 A. The distortion of the true structure from the pseudostructure leaves the bond lengths essentially unaltered but changes the bond angles appreciably. It constitutes evidence that the H atoms are in ordered arrangement in the crystal, rather than disordered, as in ice I. The particular ordered arrangement actually realized can be deduced from detailed features of the structure. This arrangement gives better agreement with the x-ray data than any other, although the x-ray distinction among various arrangements is necessarily marginal. The ordering energy in ice II, formulated in terms of the H.sbd.bond strain, must involve significantly the effects of both donor and acceptor misorientation. The acceptor strain energy contribution depends primarily not on deviation from tetrahedral bond orientation relative to the accepting H2O, but on deviation from the "accepting plane" that bisects the H.sbd.O.sbd.H angle of the mol. The H2O environment in ice II deviates greatly from an ideal tetrahedral one, yet the H.sbd.bond strain energy, although greater than in ice I, is small enough to be offset by the extra van der Waals energy, so that the energy of ice II is only 0.01 kcal./mole greater than that of ice I. The measured entropy difference between I and II is a direct reflection of the entropy of proton disorder in ice I. [on SciFinder (R)]