Dislocations energy

An elastic continuum model, which takes into account the energy of bending, the dislocation energy, and the surface energy, was used as a first approximation to describe the mechanical properties of multilayer cage structures (94). A first-order phase transition from an evenly curved (quasi-spherical) structure into a... 

Strictly speaking, we should include a core energy term in the expression for the dislocation energy, but this term is negligible in the limit so it can be omitted for the purposes of this discussion. 

Because of the large effective mass of a dislocation, the shape of the lattice potential often is not important which allows the lattice potential to be approximated by rectangular potential barriers. For modest shear stress levels, where the dislocation energy is less than the lattice potential, c < U, the probability that a dislocation of energy z will tunnel through a rectangular potential barrier of height U is [19]... 

Dislocation Energies Calculated for Sodium Chloride Assuming a Burgers Vector of Unit Strength along <110> and an Outer Badius (R) of 10 ... 

The fold "a" becomes a fold dislocation with growth of the folds "b" and "c " On completion, the dislocation energy is regained and an energetically favored state of double the fold length results. 

To resolve these problems, a so-called semidiscrete variational P-N (SVPN) model was developed [31] that allows the study of narrow dislocations, a situation that the standard P-N model cannot handle. Within this approach, the equilibrium structure of a dislocation is obtained by minimizing the dislocation energy functional... 

It is known that, in materials, the dislocation Une s direction and the Burgers vector are neither perpendicular nor parallel, being mixed dislocations, consisting of both screw and edge characteristics. Therefore, it is appropriate to sum up the dislocation energies given in Eqs. (3.36) and (3.41), while neglecting the contribution of the core. This may be expressed as ... 

In Eq. (3.35), ro was replaced by 5b, assumed to represent the core of the dislocation. The line tension, T, is acting tangentially to shorten the dislocation line and, thus, to reduce the dislocation energy. The curving of the dislocation line segment, due to its normal force, rbl, as a result of the applied shear stress, is shown in Fig. 3.45. For force equilibrium in the y direction, since it is balanced by the line tension, it is possible to write ... 

The start of heteroepitaxy on porous sdieon was initiated by a Luryi and Suhir paper in 1986 (Luryi and Suhir 1986). They theoretieaUy predicted a possible approach for growing dislocation-fi-ee lattice-mismatched heteroepitaxial layers on small seed pads of lateral dimension L, having a uniform crystal orientation over the entire substrate wafer. It was proposed that when L is smaller than a specific length Lmm, which depends on the lattice misfit as well as the dislocation energy, the entire elastic stress in the epitaxial films will be accommodated without dislocations. Porous Si, studied at that time for dielectric isolation purposes (Imai 1981), was named as a suitable substrate. 

Van der Merwe, J. H. and van der Berg, N. G. (1972), Misfit dislocation energy in epitaxial overgrowths of finite thickness. Surface Science 32, 1-15. 

Fig. 23. Variation of dislocation energy (top), its first derivative, that is, the force exerted on the dislocation by the lattice (middle), and dislocation core width (bottom) as a function of the position of a non-dissociated shuffle screw dislocation. The calculations are performed along two possible paths that are indicated in the middle figure. After PizzagaUi et al. [85].

The dislocation energy is proportional to b . This is a very important property of dislocations because it means that two dis-... 

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