J. P. Hirth

Flexible boundary conditions and nonlinear geometric effects in atomic dislocation modeling

A technique is described for applying flexible boundaries to an atomic region in computer simulation of dislocations or other line defects. The method results in continuity of equilibrium, under the chosen interatomic potential, across the interface between the atomic region and the outer region described in terms of anisotropic elastic continuum solutions. The technique has high numerical efficiency. It is shown that when the crystal is initially dislocated according to the Volterra solution for displacements, the finite strains give rise to geometrical nonlinear effects, usually disregarded in linear elasticity, which contribute to a volume change of the crystal. Allowance for this effect, and for elastic nonlinearity in the crystal beyond the boundary region, allows the overall dilatation of a finite body due to the dislocation to be rigorously computed. For illustration of the geometric nonlinear effect, and for comparison with earlier modeling methods, examples of computations are given for the [100]...

Atomic simulation of the dislocation core structure and Peierls stress in alkali halide

Abstract Dislocation core behaviour was studied by determining the equilibrium arrangement of ions surrounding an a/2〈110〉 {110} edge dislocation in potassium chloride. A computer simulation method was used to solve the equations of motion of the ions interacting through a Coulombic potential, with a Born-Mayer repulsive contribution, between nearest neighbours. Two flexible boundary schemes were employed and their application and importance to the results are described. The observed difference between the Volterra description of the ion positions and the calculated equilibrium position constitutes the core field. This core field was examined in detail but its most important feature is a lattice expansion of about 0-5 b2 per unit dislocation length. Shear stresses were also applied to the models using flexible boundary conditions with results indicating a Peierls stress in the range of 12-7 to 32-4 MPa which is in reasonable agreement with experiment. The case of moving the dislocation was quite sensitive...

A new representation of the strain field associated with the cube‐edge dislocation in a model of a α‐iron

The displacement field around an edge dislocation core is examined in an attempt to quantitatively modify the linear elastic Volterra solution. The approach derives from a computer simulation to obtain the equilibrium atomic positions in a dislocated bcc crystallite using Johnsons potential to model α‐iron. Unlike many previous calculations of this nature which employ rigid boundary conditions throughout the relaxation, the elastic media bounding the crystallite is here allowed to adjust in response to atomic readjustments within the crystallite. The procedure used to achieve flexible boundaries and its application to this problem is discussed in detail. This scheme permits linear elastic displacements at distances relatively far from the dislocation center. The difference between the computed strain field and the Volterra prescription results from nonlinear effects in the core, and is found to correspond to a net expansion of 0.25b2 per unit dislocation length. This is in accord with findings of experim...

Damage of coherent multilayer structures by injection of dislocations or cracks

Experimental evidence indicates that coherent multilayer structures (strained superlattices) can be grown in a damage‐free state when the thickness of the layer is less than a critical value. The resistance of such structures to subsequent damage by dislocation or crack injection is examined in the present study. The structures are determined to exhibit damage resistance that decreases as either the layer thickness or the coherency strains increase.

Dissociated and faceted large-angle coincident-site-lattice boundaries in silicon

Abstract The interaction of three large-angle near-coincident-site-lattice grain boundaries ([Sgrave]3, [Sgrave]9 and [Sgrave]27) in a polycrystal of silicon, has been observed both optically and by transmission electron microscopy (TEM). [Sgrave]3 boundaries were found to be formed on {111} and {112} planes, [Sgrave]9 on {122}, {411} and {111}/{115} planes, and [Sgrave]27 on {255} planes. On a macroscopic scale, [Sgrave]9 {122} dissociated repeatedly into two coherent [Sgrave]3 boundaries which, when contacted with a third non-coherent [Sgrave]3 boundary, formed a triangular twin grain with an average size of 0·3 mm. Further TEM observations showed the [Sgrave]27 boundary to dissociate into a series of 100nm triangular grains, consisting of a coherent [Sgrave]3, a {122} [Sgrave]9 and a {111}/{115} [Sgrave]9 boundary. The [Sgrave]9 boundary {111}/{115} dissociated further to form still smaller 10nm twin grains consisting of two coherent and one noncoherent [Sgrave]3 boundaries. The dissociation reactions ...

Stress fields of dislocation arrays at interfaces in bicrystals

Abstract Elastic fields of dislocation walls at the interface of a bicrystal are determined in both the isotropic and anisotropic cases. Singularities at the interface are represented in terms of line force fields. It is shown that the long–range portion of the stress field of the wall can be removed without introducing incompatibilities at the interface.

Elastic fields of line defects in a cracked body

Abstract Elastic fields are presented for line forces and dislocations in the vicinity of a crack tip and of a contained, double-ended planar crack. The fields of line force couples are also derived. The corresponding stress intensity factors are listed. The use of these results as two-dimensional Green functions for more general cases is discussed.

Dislocation structures in In-doped and undoped GaAs deformed at 700-1100°C

Dislocation structures in In-doped and undoped GaAs single crystals deformed at 700-1100°C have been studied by transmission electron microscopy. The results for (Ga, In)As, similar to earlier findings for Si and Ge, provide the basis for a proposed model for recovery processes. The observed structures together with their mechanical properties indicate that the role of In is consistent with an athermal contribution to the frictional stress arising from a solid-solution-hardening effect.

Deformation behavior of undoped and In-doped GaAs in the temperature range 700–1100 °C

Compressive deformation of undoped and In‐doped GaAs single crystals has been carried out in [001] and [123] orientations in the temperature range 700–1100 °C. Indium additions, at levels of 1–2×10^(20) atoms cm^(−3), result in critical resolved shear stress (CRSS) values that are about twice as large as the undoped crystals in the temperature range of 700–1100 °C. The CRSS was weakly dependent on temperature in the temperature range investigated as expected for a model of athermal solid solution hardening. The CRSS value of 3.3 MPa for the In‐doped crystal is sufficient to eliminate profuse dislocation formation in a 75‐mm‐diam crystal on the basis of current theories for the magnitude of the thermal stress experienced during growth. The results also suggest that the process of dislocation climb is slowed appreciably by In doping.

Anisotropic elastic solutions for line defects in high‐symmetry cases

The elastic fields of line‐force couples have been shown to be applicable to the description of dislocation core fields. The conventional anisotropic elastic theory of line defects is extended to include such couples. Explicit results are presented for cases of high‐crystallographic symmetry for which the results can be expressed in simple analytical form.