Dissociated dislocation

Dd (dissoc) diffusivity along a dissociated dislocation core (i.e., a cylinder, or a pipe of diameter, <5)... 

The diffusivity in free surfaces is larger than that in general grain boundaries, which is about the same as that in undissociated dislocations. Furthermore, the diffusivity in undissociated dislocations is greater than that in dissociated dislocations, which is greater than that in the crystal 5... 

Using the result of Exercise 9.1 and data in Fig. 9.1, estimate the density of dissociated dislocations necessary to enhance the average bulk self-diffusivity by a factor of 2 at Tm/2, where Tm is the absolute melting temperature of the material. Note typical dislocation densities in annealed f.c.c. metal crystals are in the range 106-108 cm-2. 

Both types of microstructure found in olivine are indicative of a significant component of dislocation climb during deformation. The dissociated dislocations present in the low-temperature microstructure have not been reproduced in any experiments nor have they been found in other naturally deformed olivines. The climb-dissociation may affect the type... 

In this section, our aim is to compute the core geometry associated with a dissociated dislocation in an fee material. Our model will be founded upon a... 

Figure 9.7 (a) Kink pair nucleation on the leading partial of a dissociated dislocation (b) Kink pair... 

Fig. 3.71 Dissociated dislocation node in nonstoichiometric MgO-3.5 AI2O3 spinel. Node of three 1/2 (110) dislocations has dissociated by climb to produce two partial nodes each consisting of three 1/2 (110) dislocations [38]. With kind permission of John Wiley and Sons...

Fig. 3.85 Slip bands in the intermediate region of the indented volume, a Slip band planarity and evidence of profuse pile-ups. The dislocations exhibiting paired lines in the boxed area are not dipoles but dissociated dislocations since the distance between partials is constant whether the dipole is imaged with the g or -g reflecting plane, b Intersecting slip bands, c The slight misalignment and differences in pile-up projected widths indicate that the slip bands are parallel to at least two crystallographically distinct planes [31]. With kind permission of Elsevier...

Figure 67. Dissociated dislocations in silicon viewed along the 110 zone in the high-resolulion inode (Courtesy of H. Bender)...

Images of dissociated dislocations (i.e.. dislocation ribbons) have been used extensively as a means to deduce the stacking fault energy [125]. 

From the observation of the dissociation of dislocations, both at rest and moving, it was concluded that dissociated dislocations belong to the ghde set. In principle, TEM examinations of edge-on dislocation lines at high resolution and of the associated simulated contrasts should allow one to distinguish the dissociation modes. 

Attempts to determine experimentally the values of and Wm were carried out using various techniques internal friction [36,37], deformation under load pulse sequence [38], and TEM. There are very few internal friction experiments on semiconductors. The reason is the brittleness of these materials and the need to work at very low frequencies in order to get a relaxation peak at moderate temperatures. The direct observation of kink motion was realized by TEM, either by studying the relaxation of out-of-equilibrium dissociated dislocations [39], by in situ deformation [40], or by using forbidden reflections in the high-resolution mode [41,42]. These various experiments were analyzed within the framework of the kink-diffusion model of Hirth and Lothe [12], which does not take into account... 

Although the deformation microstructures are different in these two orientations, the analysis of surface source nucleation mechanisms in silicon led to the conclusion that the activation energies for the movement of decorrelated partials and of dissociated dislocations should be the same at high stresses, in agreement with the apparent macroscopic response [57]. 

These experiments under hydrostatic pressure allowed the study of silicon plasticity under high stresses in the absence of a phase transition. However, although stresses as high as 2 GPa were reached in the plastic regime, the dislocation microstructures were not found to significantly differ from those found in usual low-stress deformation conditions where dissociated dislocations control plasticity. This may relate to the prestrain that was needed to increase substantially the range of experimental conditions leading to plastic behavior (see Ref. [57] for more detail and discussion). 

The nature of the dislocations not depends only on the applied stress but also on other thermomechanical conditions imposed to the material. Indeed, the same resolved shear stress (about 2 GPa) induces the formation of largely dissociated dislocations when reached after a prestrain ([54] see Section 2.1.1) and of perfect dislocations when applied to virgin crystals below 400 °C. In these two cases, the dislocations were submitted to stresses larger than the stress for partial decorrelation, since decorrelated partials were observed after a prestrain. This is in agreement with the fact that the perfect dislocations found at high stresses and low temperatures are not glide set dislocations. 

Fig. 14. Dissociated dislocations in the (111) glide plane of a crystal prestrained at 1050 °C and further deformed at 293 °C under 5 GPa. There are two slip systems, A and B. (a) Weak-beam dark field (2.2g, g = 2 2 0) A and B are in contrast, (b) Weak-beam dark field (7.1g, g = 1 1 1) the stacking fault of A is in contrast, B is in contrast, (c) Weak-beam dark field (3.1g, g = 2 0 2) A is out of contrast, B is in contrast. After Rabier and Demenet [77].

Analyzing the core geometry is a first step that can also provide useful information on the low-energy configuration of perfect dislocations. Indeed, this was already performed long ago by Hornstra [10], but these results have to be revisited in view of the new data obtained on high-stress microstructures. Furthermore, most of the work done since the advent of the weak-beam technique (see Section 1) has focused on dissociated dislocations in the glide set. 

Apparently, partial dislocations obtained by high temperature deformation cannot be transformed into perfect dislocations. Conversely, the transformation of perfect dislocations into dissociated dislocations was observed, but only at a limited rate and in specific regions. 

Non-dissociated dislocations can be nucleated from surfaces in the shnffle set under high-stress conditions. The dislocation that is formed the most easily has a 60° orientation. Conversely, at high temperature, partial dislocations are obtained. 

Usually, experiments and numerical simulations are rather complementary and it may be difficult to make meaningful comparisons. Nevertheless, there are two cases where this can be done. The first one is related to the mobility of non-dissociated dislocations. The computed Peierls stress for the non-dissociated shuffle screw dislocation is 4 GPa, in good agreement with the order of magnitude of the extrapolation at OK of flow stress measurements below 300°C (Section 2.3.2). In addition, the extrapolation at OK of yield stress measurements performed in the medium temperature range fits quite well the computed values of the Peierls stress for glide dislocations. Numerical simulations revealed that the thermally activated motion of non-dissociated screw dislocations was possible at 300 °C under an applied stress of 1.5 GPa, as reported from yield stress measurements (Section 2.3.2). The second case concerns the nucleation of dislocations. Molecular dynamics simulations of the dislocation nucleation from surface steps... 

The core of PS and DG dislocations can be transformed from one to the other through several elementary mechanisms. The two basic mechanisms that allow dislocations moving over one atomic distance to switch from one set to the other are cross slip and climb (Fig. 32). Some mechanisms that can be involved in such transformations are similar to those proposed in the frame of composite models of dislocation core structures, in which a dissociated dislocation can move from glide set to shuffle set in its dissociated form (see, e.g., [1]). However, in composite models, the transformation mechanisms are relevant to the movement of partial dislocations from glide to shuffle positions and a constriction of the parent dislocations is not required. In the present case, the transformation mechanism concerns the change from perfect to dissociated dislocations (as well as the reverse transformation), and a different mechanism can also be involved, namely cross slip [57]. 

Cross shp is initiated when a critical part of the parent dislocation deviates in the cross shp plane. If the parent dislocation is a perfect one, this can be achieved through local stress concentrations. In the case of a dissociated dislocation, a local constriction of the stacking-fanlt ribbon is required in a first step to ahow for a deviation. Thns, cross slip may be easier from PS to DG than from DG to PS. 

Are they two different and independent deformation microstructures depending on the thermomechanical conditions Experimentally, no massive transformation was evidenced from preexisting perfect dislocations to dissociated ones. The interpretations proposed by Rabier and Demenet [69] and Saka et al. [76] seem to be very different, that is, there is no transformation but nucleation of dissociated dislocations, apparently with no relation to preexisting perfect defects [69], or there is a core transformation [76]. The two experiments were performed in very different conditions, but a common interpretation could be that a small critical nucleus of transformed core can provide a source for a new dislocation population [86], leaving unaffected most of the parent dislocation microstructure. 

EPR is a technique that has been widely used in the determination of the structure of dissociated dislocations (see Section 1.3) this technique would be of interest for determining whether danghng bonds are present in the core of a perfect dislocation. 

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