A theoretical analysis of the mechanical relaxation of single-crystalline ice

Abstract

Kneser, Magun & Ziegler (1955) have found a mechanical relaxation of single crystals of ice. Torsional vibrations of cylindrical specimens, cut parallel to the c -axis, were employed and the logarithmic decrement showed the characteristic maximum associated with a single relaxation time. Similar results have since beer obtained by Schiller (yet unpublished) for various modes of vibration and various crystallographic orientations. The frequency for maximum loss factor and the energy of activation are approximately equal for the mechanical and dielectric relaxation. It seems obvious to associate both relaxations with movements of the hydrogen atoms. In the mechanical case, this may be done in two different ways. As a first possibility I have assumed that an equilibrium exists between a large number of possible hydrogen arrangements and that this equilibrium is disturbed by and mechanical deformation of the crystal lattice. The rearrangement of the hydrogen atoms throughout the lattice then gives rise to the observed relaxation. A second possible mechanism is connected with the distribution of lattice defects such as doubly occupied and vacant bonds between neighbouring oxygen atoms. Normally the probability of finding a given type of defect on a given bond would be approxi­mately the same for all bonds. In the deformed lattice, bonds with a certain orientation would be preferred and the resulting rearrangement of the defects would cause the observed relaxation. With the first mechanism, lattice defects can serve as catalysts in bringing about configurational changes and their presence (in small numbers) will thus affect the relaxation time, but not the magnitude of the decrement. With the second mechanism, however, the magnitude of the decrement is proportional to the number of defects present. I have calculated the maximum value of the decrement for the first mechanism, which implies a general rearrange­ment of the hydrogen atoms, and shall show that the result agrees well with the measurements. On the other hand, estimates based on the second mechanism are clearly inconsistent with the experimental evidence.