Dislocations self energy

In a given material, the selection of the aaive dislocation system is based on competitions in both the dislocation self-energy and dislocation mobility. The reduction in the self-energy due to APB dissociation is given by... 

Sub-GBs are expected to be formed during a high-temperature growth process by the stabilization of dislocations, to form array-like configuration that minimizes the self-energy. To form dislocations, the existence of a source with a discontinuous crystal lattice is required, because extremely large stress, typically in the order of the modulus of transverse elasticity, is necessary to form a dislocation from a perfect crystal lattice. In the case of Si multicrystal growth, possible sources are the inner wall of the crucible, inclusions and GBs. 

Whereas the line tension was invoked as a way to capture the self-energy of dislocations from an elastic perspective, there are also ways of capturing core effects on the basis of locality assumptions. Recall that in our treatment of dislocation cores we introduced the Peierls-Nabarro model (see section 8.6.2) in which the misfit energy associated with slip displacements across the slip plane is associated with an energy penalty of the form... 

A noteworthy aspect of the above solution is that it does not involve either lattice dilatation du/dz or layer undulation V n. Therefore, within the approximations of the linear theory considered here, screw dislocations in smectic A have no self energy (apart from the core), nor do they interact amongst themselves. In this respect they are entirely different from screw dislocations in crystals. 

At the center of a dislocation the crystal is highly strained with atoms displaced from their normal sites and we cannot use linear elasticity so we again exclude this region from the calculation by making the inner limit Tq. There must be a contribution to the self-energy of the dislocation from this core, but we need atomistic modeling to estimate the value it is usually assumed to be about 10%... 

The strain energy (or self energy) of a dislocation actually depends on the character of the dislocation, but setting E = aGb is a good estimate, where a is -0.5. 

To estimate believe that loop of misfit dislocation is the equatorial location on the spheroidal precipitate Rp = the self-energy prismatic loop (Kolesnikova et al., 2007)... 

The self-energy of the dislocation at the interface is then the total work which must be done in overcoming this image force as the dislocation is moved from the surface of the substrate to the interface, which is... 

Elastic constants are fundamentetl physical constants that are measures of the interatomic forces in materials, and are often used for the estimation of an interatomic potential that is applied in a computer simulation. They give information about the stiffness of the material and are used for understanding of mechanical properties. For example, the properties of dislocations like Peierls stress, self-energy, interaction between dislocations, etc., are explained by elastic theory. The Peierls stress rp is given by the following equation (Peieris, 1940 Nabarro, 1947) ... 

In his early survey of computer experiments in materials science , Beeler (1970), in the book chapter already cited, divides such experiments into four categories. One is the Monte Carlo approach. The second is the dynamic approach (today usually named molecular dynamics), in which a finite system of N particles (usually atoms) is treated by setting up 3A equations of motion which are coupled through an assumed two-body potential, and the set of 3A differential equations is then solved numerically on a computer to give the space trajectories and velocities of all particles as function of successive time steps. The third is what Beeler called the variational approach, used to establish equilibrium configurations of atoms in (for instance) a crystal dislocation and also to establish what happens to the atoms when the defect moves each atom is moved in turn, one at a time, in a self-consistent iterative process, until the total energy of the system is minimised. The fourth category of computer experiment is what Beeler called a pattern development... 

Dislocations can attract a population of impurities, vacancies, or self-interstitials that are bound to the dislocation core by a binding energy Agb. These will be liberated and become free to contribute to the overall diffusion at higher temperatures, so that it is possible to write... 

Figure 9.1 presents self-diffusivity data for DD(dissoc), DD(undissoc), DB, DS, DXL, and DL, for f.c.c. metals on a single Arrhenius plot. With the exception of the surface diffusion data, the data are represented by ideal straight-line Arrhenius plots, which would be realistic if the various activation energies were constants (independent of temperature). However, the data are not sufficiently accurate or extensive to rule out some possible curvature, at least for the grain boundary and dislocation curves, as discussed in Section 9.2.3. 

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