Molecular diffusion and spatial symmetry of the arrangement of the HF molecules in crystalline solvates

Conclusion

If diffusion brings about the successive occupation, by the HF molecule, of all nonequivalent positions in the crystal, the intramolecular interaction of the nuclei, averaged by the motion, is a characteristic of the crystal as a whole. In accordance with Neumann's principle, the symmetry of the local field tensor should include the elements of symmetry of the point group of the crystal. From the nonaxial character of the tensor (η≠0), detected experimentally for the crystalline solvates studied, it follows that the symmetry of the three crystals examined belongs to one of the lower classes and cannot be higher than orthorhombic.

From the preservation of one of the axes of the tensor with the development of the diffusion process, and published data [7], it follows that all the HF molecules lie in parallel (possibly slightly “corrugated”) planes.

The symmetry of the arrangement of the HF molecules in the layers does not have axes of order higher than 2. Otherwise, on diffusion, the local field tensor would have remained axial even in a crystal of low symmetry. If one structure contains not more than two nonequivalent positions for HF molecules, the angle γ between the directions of the H−F vectors can be determined. The value of γ is related to the value of the asymmetry parameter by the expression

$$\gamma = arccos (\eta /3).$$

From this we obtain γ=106° for Cs₂GeF₆·4HF and 109° for Cs₂SnF₆·4HF. For comparison it may be noted that for solid hydrogen fluoride, γ=119°.

Data on the temperatures of activation of the diffusional mobility were used to find the activation energies of diffusion of HF: 9.7 kcal/mole in Cs₂GeF₆·4HF, 10.8 kcal/mole in Cs₂SnF₆·4HF, and 11.2 kcal/mole for the diffusion of HF molecules in K₂SnF₆·4HF.