Elastic Models of Crystal Defects

Reconstruction of Martensitic Nucleation Process from Morphological Attributes

“…As was discussed in [5], the dislocations with lines [ l 1 ?l, planes of sliding (01 1) and Burgers vectors b, 11 [ l 1 11, b, (1 [OI 71, b, 11 [loo], b, 11 [ l 711 are the most probable DNC in this alloy. The elastic field of DNC was calculated by the technique [6] for the elastic moduli: CL = 208,15 GPa, C , = 85,50 GPa and C' = 6,35 GPa [7]. The condition S = S , , , Like the orientation of NO, 11 [2 11 121 is averaged among the set of N,, there are orientations located at the left, and to the right of the line N t -[01 l ] (see [8]) and the area of the observable N, to the left of a line NZ -101 l ] appears wider than the area of orientations of NW calculated for infinite dislocations.…”

“…That is, in (3) it is necessary to replace t i by 5; where In (5) Q is an orthogonal matrix correlated with ok Then, in the framework of the simplest model of the crystal growth control (the wave normals n,, n, coincide with the orientations of the vectors E,, , E, , ) the expression for NL is: NL \\ t L * X ' < ; , (6) where X' is the ratio between the wave velocities in the new directions.…”

A Note on Residual Stress, Lattice Orientation and Dislocation Density in Crystalline Solids

“…That the strain energy depends on H via C follows from the symmetry of the Cauchy stress T, related to P by P = TF * (see, for example, [6]). This, of course, is equivalent to (5) 2 .…”

“…In the geometrically linear theory, for which the lattice distortion H is close to the identity (and hence so too the plastic distortion K in the residual stress problem), the dislocation density field is imposed as data and the stress function is obtained by integrating the linear partial differential equations expressing the incompatibility of the lattice strain [1][2][3]. However, we know of no rationale justifying the a priori restriction to rotations that are close to the identity, and thus regard the geometrically linear theory as being of limited relevance.…”

X-ray diffraction line broadening due to dislocations in non-cubic materials. I. General considerations and the case of elastic isotropy applied to hexagonal crystals

“…Steeds, 1973;Teodosiu, 1982) it is always possible to obtain relations of the type (2) with an explicit form of the function ~. For this reason it is not difficult to show that the orientation factor Zp of a polycrystalline material with randomly oriented grains can be conveniently written in the general form gp = ~ (Grt`)Ert` (K,L=l,2,...,6).…”