Dislocation Formation Energy

The line energy required for the formation of a dislocation depends on the magnitude of its BV h and on the distance r. It can be calculated on the basis of linear elasticity theory according to [37], 

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Fig. 16. Core and elastic contributions to the screw dislocation formation energies [Eq. (8)] in Ta, Mo, and V as function of pressure, (a) Core formation energy as obtained from GFBC/MGPT atomistic simulations and (b) elastic coefficient AeiasUc determined from MGPT elastic moduli.

Based on the discussion in earlier sections of this chapter, one may expect atomically flat incommensurate surfaces to be superlubric. Indeed the first suggestion that ultra-low friction may be possible was based on simulations of copper surfaces.6,7 Furthermore, the simulations of Ni(100)/(100) interfaces discussed in the previous section showed very low friction when the surfaces were atomically flat and misoriented (see the data for the atomically flat system between 30° and 60° in Figure 21). In general, however, it is reasonable to assume that bare metals are not good candidates for superlubric materials because they are vulnerable to a variety of energy dissipation mechanisms such as dislocation formation, plastic deformation, and wear. 

The (100) split-dumbbell defect in Fig. 8.5d, while having the lowest energy of all interstitial defects, still has a large formation energy (Ef = 2.2 eV) because of the large amount of distortion and ion-core repulsion required for its insertion into the close-packed Cu crystal. However, once the interstitial defect is present, it persists until it migrates to an interface or dislocation or annihilates with a vacancy. The... 

Suppose now that such a source is present in a crystal that is rapidly quenched from a temperature Tq to a temperature Ta to produce supersaturated vacancies. Find an expression for the critical value of the quenching temperature, Tq, which must be used to produce sufficient supersaturation to activate the source so that it will be able to create dislocations loops capable of destroying the supersaturated vacancies by climb. The vacancy formation energy is Ey and the segment length is L. 

The local deformation, cracking and the dislocation formation in the composites1 under the oxygenation treatment, obviously, occur at the expense of the energies of the internal reactions17. 

More recently, Schaarwachter 45, 46) has argued that the formation energy of a nucleus at a dislocation is less than the corresponding formation energy at a perfect surface by a factor which is determined by the ration, [ibja, where a is the specific edge energy of the nucleus. 

The primary one-dimensional or line defects seen in sohds are dislocations. In general, dislocation formation and motion require more energy in ceramics than in metals. This is due to the complex atomic structures of ceramics, which often have large unit cells, and to the typically strong and localized bonding between atoms in... 

In order to examine the mechanics of dislocation formation in a compliant film-substrate system, the energy of a dislocation at an arbitrary position in this structure in the absence of any other stress field is required. This energy is equivalent to the configurational force on the dislocation as a function of position through the thickness of the composite layer. In order to determine an approximate form for the critical thickness condition in Section 6.7.1, an ad hoc assumption on the variation of this force was made in (6.66). While the assumed variation of the force is asymptotically correct near either free surface and it has the obvious virtue of simplicity, the quality of the approximation is not evident. Thus, in this section, the variation of this force with position is examined in greater detail. 

The physical system studied is depicted in Figure 7.1. A thin film of thickness h is epitaxially bonded to relatively thick substrate, and the lateral extent of the interface is assumed to be very large compared to h. The lattice mismatch between the film and substrate materials is represented by the mismatch shear strain 7m. Prior to formation of any dislocations in the film, the elastic strain in the film is uniform and is given by xz = lyz = 0. Dislocation formation occurs at the expense of the energy stored in this strain field. The critical thickness condition for dislocation formation is given in (6.46) for general cut off radius ro, and it is restated here for the particular value Vo= as... 

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