INVESTIGATION OF THE CRYSTAL STRUCTURE OF ICE USING NEUTRON DIFFRACTION

The crystal structure of ice has been investigated by many authors over a fairly long period of time (the first works date back to 1921).

As a result of work carried out by the method of X-ray structural analysis, it was found that an ice single crystal possesses hexagonal symmetry, with the oxygen atoms located at the vertices and at the center of a tetrahedron (the distance between neighboring oxygen atoms is 2.76 Å). As for the hydrogen atoms, their position obviously could not be established by X-ray diffraction. In connection with this, several hypotheses were proposed concerning the possible localization of the hydrogen atoms in the crystal lattice of ice. In 1929 Barnes¹ proposed that the hydrogen atoms are located in the middle of a straight-line segment connecting two neighboring oxygen atoms (see Fig. 1, A), and that the unit crystal cell consists of four H₂O molecules. In 1933 Bernal and Fowler² expressed the idea that in an ice crystal the H₂O molecules have approximately the same structure as water-vapor molecules. The structure of “free” H₂O molecules can be judged from

...to the data obtained from spectroscopic measurements, and to the magnitude of the dipole moment. It is found that the distance O—H is approximately \(0.96\) Å, and the angle between the “bond lines” of the hydrogen atoms with the oxygen atom is about \(105^\circ\).

Oxygen
Hydrogen

A  B  C  D

Fig. 1.

If the same structure is adopted for the molecules of an ice crystal, and if it is assumed that each unit crystal cell consists of 12 molecules of \(H_2O\), then we obtain the scheme shown in Fig. 1, B. However, the Bernal and Fowler hypothesis does not agree with the experimental fact that the entropy of the crystal does not tend to zero when it is cooled to very low temperatures. This contradiction is removed if one assumes that there are several stable states of the crystal, in which the hydrogen atom may occupy different positions along the straight line joining two oxygen atoms (conventionally represented by the shaded circles in Fig. 1, C), with the maxima of the probability amplitude corresponding to a distance of \(0.96\) Å from either of the oxygen atoms. Finally, a fourth variant is possible—the rotation of hydrogen atoms around oxygen atoms (Fig. 1, D).

Fig. 2.

In the May issue of The Physical Review for 1949 an experimental paper\(^4\) was published, the results of which make it possible to choose unambiguously among the structural schemes listed above. The structure of the crystal lattice of ice was investigated by means of diffraction of slow monochromatic neutrons, the source of which was a uranium slab (see review\(^5\)). The measurements were made with samples of heavy ice \((D_2O)\), the temperature of which during the experiments was lowered to \(-90^\circ\)C by means of a special cooling mixture. Heavy ice was used instead of ordinary ice \((H_2O)\) for two reasons: first, the effective coherent-scattering cross section, calculated per one deuterium nucleus \((= 5 \cdot 10^{-24}\ \text{cm}^2)\), is greater than that for hydrogen \((= 2 \cdot 10^{-24}\ \text{cm}^2)\); second, the ratio of the effective coherent and incoherent scattering cross sections for \(D_2O\) is greater than for the \(H_2O\) molecule. The results

of these experiments and their comparison with various theoretical curves are presented in Fig. 2.

On the abscissa axis is plotted the quantity \(\frac{\sin \vartheta}{\lambda}\) (\(\vartheta\) is the diffraction angle, \(\lambda = \mathrm{const} = 1.06\ \text{Å}\) is the neutron wavelength); on the ordinate axis, the beam intensity (in arbitrary units) corresponding to the given \(\vartheta\).

As can be seen from the graph, the results obtained convincingly testify in favor of the scheme shown in Fig. 1, C.

I. Sh.

CITED LITERATURE

1. W. H. Barnes, Proc. Roy. Soc. A 125, 670 (1929).
2. J. D. Bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933).
3. L. Pauling, J. Chem. Soc. 57, 2680 (1935).
4. E. O. Wollan, W. L. Davidson and C. G. Shull, Phys. Rev. 75, 1348 (1949).
5. R. P. Ozerov, UFN, 38, 413, (1949).