Dislocations In Cubic Crystals Research Articles

Dislocations in cubic crystals described by discrete models

Discrete models of dislocations in cubic crystal lattices having one or two atoms per unit cell are proposed. These models have the standard linear anisotropic elasticity as their continuum limit and their main ingredients are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the dislocation size. For these models, conservative and damped equations of motion are proposed. In the latter case, the entropy production and thermodynamic forces are calculated and fluctuation terms obeying the fluctuation-dissipation theorem are added. Numerical simulations illustrate static perfect screw and 60 ∘ dislocations for GaAs and Si.

The contrast factors of dislocations in cubic crystals: the dislocation model of strain anisotropy in practice

It has been shown recently that in many cases strain anisotropy in powder diffraction can be well accounted for by the dislocation model of the mean square strain. The practical application assumes knowledge of the individual contrast factorsCof dislocations related to particular Burgers, line and diffraction vectors or to the average contrast factorsC¯. A simple procedure for the experimental determination ofC¯has been worked out, enabling the determination of the character of the dislocations in terms of a simple parameterq. The values of the individualCfactors were determined numerically for a wide range of elastic constants for cubic crystals. TheC¯factors andqparameters were parametrized by simple analytical functions, which can be used in a straightforward manner in numerical analyses, ase.g.in Rietveld structure refinement procedures.

Step heights associated with grain boundary dislocations in cubic crystals

The step vectors associated with perfect grain boundary dislocations in cubic crystals are determined for coincidence systems up to Σ37a. These determine the step heights which may be associated with the dislocations. Certain trends in the data are identified and rationalized : in particular, it is predicted that non-primitive grain boundary dislocations will be relatively stable in lower-coincidence boundaries. Structural and kinetic consequences of this prediction are discussed, and comparisons are drawn with available data.

The interaction force between tetragonal defects and screw dislocations in cubic crystals

The force-distance profiles for the interaction of straight screw dislocations with tetragonal defects are calculated for several different cubic crystals. The calculations are based on Eshelby's “transformation strain” method for treating the problem of the misfitting sphere. Three different tetragonal defect problems are posed and solved. 1. (1) 〈110〉 defect in the rock salt structure with 〈110〉 {110} slip; 2. (2) 〈111〉 defect in an f.c.c. metal with 〈110〉 {111} slip and 3. (3) 〈100〉 defect in a b.c.c. metal with 〈111〉 {110} slip. It is shown that anisotropy has a large effect on both the shape and magnitude of the force-distance profiles. In addition each tetragonal defect presents two different obstacles to dislocation motion, depending on the relative motion of the dislocation with respect to the defect. Finally, it is shown that neither Fleischer's original calculation of the force-distance profile for a tetragonal defect in the rock salt structure nor Tyson's later modification is correct, even for the case of isotropic elasticity.