Cross slip

Another important class of three-dimensional dislocation configurations are those associated with the cross slip process in which a screw dislocation passes from one glide plane to another. The most familiar mechanism for such cross slip is probably the Friedel-Escaig mechanism, which is illustrated schematically in fig. 8.37. The basic idea is that an extended dislocation suffers a local constriction at some point along the line. This dislocation segment, which after constriction is a pure screw dislocation, can then glide in a different slip plane than that on which is gliding the parent dislocation. This mechanism, like those considered already, is amenable to treatment from both continuum and atomistic perspectives, and we take them each up in turn. 

Since it is presumed that the process of cross slip is thermally activated, to the extent that we are trying to explicate the unit processes that make up plasticity it is of great interest to come up with an estimate for the activation energy for cross slip. In broad terms, what this implies is a comparison of the energies between the unconstricted and constricted states. The simplest continuum estimate 

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The NEB method has been applied successfiilly to a wide range of problems, for example studies of diffusion processes at metal smfaces, multiple atom exchange processes observed in sputter deposition simulations, dissociative adsorption of a molecule on a smface, diffusion of rigid water molecules on an ice Di siuface, contact formation between metal tip and a smface, cross-slip of screw dislocations in a metal (a simulation requiring over 100,000 atoms in the system, and a total of over 2,000,000 atoms in the MEP calculation), g d diffusion processes at and near semiconductor smfaces (using a plane wave based Density Fimctional Theory method to calculate the atomic forces). In the last two applications the calculation was carried out on a cluster of workstations with the force on each image calculated on a separate node. 

An edge dislocation is confined to move on its slip plane (conservative motion), and the slip due to the motion of the dislocation is also confined to the slip plane. Movement of a screw dislocation can capture on the plane where it started or else move to any other, parallel to the dislocation line (cross slip). If an edge dislocation were to move... 

Fig. 14. Schematic representation of cross-slip in a hexagonal metal ia> slip on CRYSTAL FIELD THEORY. A theory developed in the early 1930s...

At temperatures above 500°C, dislocation climb becomes apparent, and extensive cross slip of undissociated screw dislocations from 1012 to (0001) takes place. 

Preliminary Dislocation Dynamics (DD) simulations using the model developed by Verdier et al. provide a plausible scenario for the dislocation patterning occuring during the deformation of ice single crystals based on cross-slip mechanism. The simulated dislocation multiplication mechanism is consistent with the scale invariant pattemings observed experimentally. 

Figure 5 represents a typical evolution of the dislocation pattern during the deformation. The simulation was performed in a 20 mm diameter crystal, with 2 initial basal planes activated (one system in each plane) at the beginning of the deformation. It clearly appears that the double cross-slip mechanism propagates the plasticity in many other basal planes. One can also notice the asymmetry in the plane expansion due to the dislocation interactions. 

Figure 5 Thickening of slip planes due to the double cross-slip of basal dislocations.

The double cross-slip mechanism can then be considered as the most probable deformation process, complementary to the basal slip. Indeed, dislocation climb can hardly be invoked in this torsion loading conditions since most of the dislocations are of screw type. 

Usually, creep deformation of ice single crystals is associated to a steady-state creep regime, with a stress exponent equal to 2 when basal glide is activated . In the torsion experiments performed, the steady-state creep was not reached, but one would expect it to be achieved for larger strain when the immobilisation of the basal dislocations in the pile-ups is balanced by the dislocation multiplication induced by the double cross-slip mechanism. 

In summary, torsion creep tests on well-oriented ice single crystals appear to be a pertinent experiment to try to understand and represent the fundamental mechanisms of deformation in ice single crystals. The presented evidence for the occurence of cross-slip as a rate-limiting process questions the role of dislocation climb as suggested by Louchet (2004) I... 

Fig. 8.37. Schematic of the Friedel-Escaig cross slip mechanism (adapted from Bonneville et al. (1988)).

Fig. 8.38. Series of intermediate configurations during the cross slip process as computed using atomistics (adapted from Rasmussen et al. (1997b)).

Fig. 8.39. Experimental image of the cross slip process (courtesy of I. Robertson).

Bonneville J., Escaig B. and Martin J. L., A Study of Cross-Slip Activation Parameters in Pure Copper, Acta Metall 36, 1989 (1988). 

Li J. C. M., Cross Slip and Cross Climb of Dislocations Induced by a Locked Dislocation, /. Appl. Phys. 32, 593 (1961). 

Rasmussen T., Jacobsen K. W., Leffers T. and Pedersen O. B., Simulations of the Atomic Structure, Energetics and Cross-Slip of Screw Dislocations in Copper, Phys. Rev. B56, 2977 (1997). 

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