Peierls barrier

The effect of driving shear stresses on the dislocations are studied by superimposing a corresponding homogeneous shear strain on the whole model before relaxation. By repeating these calculations with increasing shear strains, the Peierls barrier is determined from the superimposed strain at which the dislocation starts moving. 

As a consequence edge and mixed (111) dislocations move with relative ease, whereas the Peierls barrier for screw dislocations is as high as 2 GPa. These results are in contrast to previous calculations [6], which have shown a splitting for the screw dislocations and also a much lower Peierls barrier. However, our results can perfectly explain most of the experimental results concerning (111) dislocations which will be discussed in the following section. 

For the deformation of NiAl in a soft orientation our calculations give by far the lowest Peierls barriers for the (100) 011 glide system. This glide system is also found in many experimental observations and generally accepted as the primary slip system in NiAl [18], Compared to previous atomistic modelling [6], we obtain Peierls stresses which are markedly lower. The calculated Peierls stresses (see table 1) are in the range of 40-150 MPa which is clearly at the lower end of the experimental low temperature deformation data [18]. This may either be attributed to an insufficiency of the interaction model used here or one may speculate that the low temperature deformation of NiAl is not limited by the Peierls stresses but by the interaction of the dislocations with other obstacles (possibly point defects and impurities). 

Figure 11.6 illustrates the energy that must be supplied by thermal activation. The curve of ab vs. A shows the force that must be applied to the dislocation (per unit length) if it were forced to surmount the Peierls barrier in the manner just described in the absence of thermal activation. The quantity A is the area swept out by the double kink as it surmounts the barrier and is a measure of the forward motion of the double kink. A = 0 corresponds to the dislocation lying along an energy trough (minimum) as in Fig. 11.5a. A2 is the area swept out when maximum force must be supplied to drive the double kink. A4 is the area swept out when the saddle point has been reached and the barrier has been effectively surmounted. The area under the curve is then the total work that must be done by the applied stress to surmount the barrier in the absence of thermal activation. When the applied stress is a a (and too small to force the barrier), the swept-out area is A, and the energy that must be supplied by thermal activation is then the shaded area shown in Fig. 11.6. The activation energy is then...

We know that dislocations in Ge move on 111 planes, but they too can also move on 001 and 011 planes. Is the choice of glide plane due to the Peierls barrier or is it determined by the need to break bonds ... 

In the case of borides, the production of pure dense materials is more difficult because TiB2 does not deform plastically even at very high temperatures due to its intrinsically high concentration of Peierls barriers to dislocation movement. Recent investigations on borides have been totally devoted to the synthesis of composites either metal-ceramic or ceramic-ceramic. Woodger et al. [94,95]... 

The high strength of most ceramics is due to the difficulty of moving dislocations through the lattice that is, most ceramics have a high Peierls stress. Dislocations move from one Peierls valley to the next by the nucleation of a kink pair, under the action of applied stress and temperature. The kinks are abrupt and their further motion is controlled by a secondary Peierls barrier. Mitchell, Peralta and Hirth [22] have adapted the standard treatment of Hirth and Lothe [23] to show that the resulting strain-rate is given by ... 

For those ceramics with a high Peierls stress, the CRSS can be understood consistently in terms of a model of kink pair nudeation and motion on dislocations. The steep temperature dependence is governed by an activation energy that is the sum of the elastic energy for kink pair formation and the energy for the kinks to overcome their secondary Peierls barriers. 

Hartford J, von Sydow B, Wahnstrom G, Lundqvist BI. Peierls barriers and stresses for edge dislocations in Pd and A1 calculated from first principles. Phys. Rev. B 1998 58 2487-2496. 

In 1996, Duesbery and Jobs [45] determined that in usual stress conditions, dislocations should belong to the glide set. Using Peierls barriers deduced from atomistic computations, these authors calculated the kink pair activation energies... 

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