FLOW IN POLYCRYSTALLINE ICE

Part 2 - Background information

By Chris Wilson and Brett Marmo

2.3 Dislocations

The mechanical properties of ice are controlled by the presence and movement of dislocations. The movement of dislocations allows ice crystals to deform under applied stresses. In ice , dislocations move on the () plane and in the <> and equivalent directions allowing isotropic slip on the basal plane (Fig. 2.3.1). Within the ice lattice there are two sets of basal planes; the shuffle plane, or S-plane, and the glide plane, or G-plane (Whitworth 1978) (Fig. 2.3.1).

Figure 2.3.1: The crystal structure of ice Ih, showing the arrangement of molecules projected onto the plane.

The propagation of dislocations results in the re-arrangement of protons (Glen 1968). When a dislocation moves along a slip plane, material above the plane moves relative to the material below by an amount equal to the Burgers vector. This movement does not affect the arrangement of oxygen atoms as they remain in tetrahedral coordination with the surrounding oxygens. However, the dislocation increases the disorder of the hydrogen atoms (Fig. 2.3.2). The disorder of protons is an infringement of the Bernal-Fowler rule. This disorder of protons is referred to as a Bjerrum defect (Bjerrum 1951), and is specific to the ice structure. As the dislocation propagates it creates a pair of Bjerrum defects: L-defects, which are bonds with no protons; and D-defect, which are bonds with two protons (Fig. 2.3.2).

Figure 2.3.2: The propagation of a dislocation through the basal plane of an ice lattice. Oxygen atoms remain in tetrahedral co-ordination after the dislocations have passed. However, Bjerrum defects are produced by the passage of a dislocation leading to disordering in the co-ordination of the hydrogen atoms. L-defects are produced if the inter-molecular bonds contain no protons, and D-defects are produced if the bonds contain two protons (Adapted from Poirier, 1985).

Another possible re-arrangement of protons that avoids the creation of Bjerrum defects will occur if the hydrogen atom crosses the bond and joins the neighbouring oxygen before the dislocation disconnects the bond. This will result in the creation of a cation and a anion. The energy required to create a pair of ionisation defects is greater than that required for a Bjerrum defect so that ionisation defects are less likely to be created.

The yield stress observed in shear experiments is more than three orders of magnitude less than the theoretical value. An explanation for this may be the migration of Bjerrum defects through the lattice (Glen 1968). Goodman et al. (1981) considered the way proton rearrangement controls the drift velocity of a dislocation propagating through the lattice as a pair of kinks. Kink pairs nucleate at sites adjacent to areas where no proton rearrangement is required. A kink is held up at any point where a pair of defects is needed to be created to break the bond between molecules. Re-orientation of the protons by migrating point defects allows the dislocation to continue its journey.

Dislocation motion studies using in situ experiments have been performed by Ahmad et al. (1986) and Shearwood & Whitworth (1991) using a synchrotron X-radiation technique. Single crystals of ice where mounted in a compression jig and loads, up to 65 N, were applied at ~23° to the basal plane. The loads were applied between 20s and 180s then an X-ray defraction topograph was taken. The stress was then re-applied and another topograph exposed. A series of topographs were taken in this manner and the evolution of dislocation loops recorded. Dislocations with 60° orientations and screw dislocations were recognised in the basal planes of the deformed samples.

This is similar to the observations of Jia et al. (1996) and Liu et al. (1995) who also employed dynamic in situ x-ray topographic deformation studies. They were able to show that the basal slip system with the highest Schmid factor was found to be the most active in polycrystalline ice. Whereas, grain boundaries act both as effective sources of lattice dislocations and as strong obstacles to dislocation motion. To act as a source the basal slip is transmitted through a grain boundary, i.e. dislocation impingement on one side of a grain boundary leads to dislocations being emitted from the other side of the grain boundary.

Dynamical straining experiments (Shearwood & Whitworth 1991) of stressed single crystals of ice have determined the velocity of dislocation motion increased linearly with stress; for crystals between -4°C and -39°C. The velocity of screw dislocations for any stress resolved on to the basal plane, at -20°C is with an activation energy for motion of 0.95±0.05 eV. The 60° dislocations has a velocity of for any stress resolved on to the basal plane, with an activation energy of 0.87±0.04 eV. However, in situ straining of polycrystalline ice has shown that grain boundary regions always deform before the grain interiors (Baker 1997). Where dislocations are emitted in order to accommodate grain boundary sliding this leads to stress concentrations at the grain boundary facets. Eventually, the dislocations which have been emitted traverse the grain and pile-up at the opposite grain boundary-and lead to nucleation of new recrystallised grains.