A theoretical model is suggested, which describes generation of misfit dislocations in film/substrate composites of wire form. In the framework of the model, the ranges of the geometric parameters (wire radius, film thickness, misfit parameter) of a wire composite are calculated at which the generation of misfit dislocations is energetically favourable. The specific features of generation of misfit dislocations in wire composites are discussed and compared with those in conventional platelike composites.

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Misfit dislocations in wire composite solids

A representation is developed that allows the stresses due to an arbitrary dislocation in an isotropic, homogeneous half-space to be expressed as a line integral around that dislocation For the special case of a dislocation half-line the integral is evaluated analytically to yield closed form solutions for the stresses The given formulae allow the study of three-dimensional dislocation configurations to be carried through with much greater computational simplicity than has hitherto been possible As an example, two approximations are assessed that are commonly used in the literature to infer the energies of dislocation loops in a half-space from infinite-body results: the energy of a buried loop in a half-space is commonly taken to be the same as the energy of the corresponding loop in a whole-space; the energy of a surface half-loop is commonly taken to be half the energy of the completed loop in a whole-space It is demonstrated that simple correlation factors may be evaluated, which modify the approximate formulae, yielding exact results The case is considered of formation of a dislocation with Burgers vector 1 2 [101] on a (111) glide plane in a strained layer with (100) surface normal; such a loop would lead to the formation of a misfit dislocation of the commonly observed 60 type at the substrate-layer interface Simple correction factors are presented for the energies of a square loop buried in the layer, and of rectangular and semicircular half-loops forming at the free surface It is found that the approximation for the energy of a buried loop yields accurate activation energies for loop formation unless the layer thickness is small, corresponding to the early stages of layer growth, in which case the approximation may over-estimate the activation energy by a factor of one and a half Moreover, in some cases the approximation yields as the critical loop dimension a side length for which the loop would no longer be contained within the layer In such a situation it is not clear what significance can be attached to the obtained activation energy By contrast, the results presented here allow the critical loop dimension and activation energy to vary with layer thickness, yielding physically reasonable results in all cases The approximation for the energy of a surface half-loop is found to be more seriously in error, yielding over-estimates by as much as factors of two and three of, respectively, the activation energies of rectangular and semicircular surface half-loops

A line-integral representation for the stresses due to an arbitrary dislocation in an isotropic half-space

A theoretical model is suggested which describes the generation and evolution of misfit dislocations in composite solids containing nanowires with rectangular cross-section. In the framework of the model, the ranges of the geometric parameters (nanowire sizes, misfit parameter, interspacing between the nanowire and the free surface of the composite) are calculated at which the generation of various misfit dislocation configurations (loops, semi-loops and dipoles) is energetically favourable. Transformations of these dislocation configurations and their specific features are discussed.

http://mp.ipme.ru/ipme/labs/ltdm/JPCM_2003_Gutkin_et_al.pdf

Misfit dislocations in composites with nanowires

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach–Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in {110} planes are more stable than those gliding in {112} planes.

/pdf/elastic-energy-of-a-straight-dislocation-and-contribution-7p97jf69z9.pdf

Elastic energy of a straight dislocation and contribution from core tractions

High density nanotwins with average twin thickness varying from 3 to 6 nm are formed in sputtered highly (111) textured Cu/Ni multilayers, when individual layer thickness is 25 nm or less. Twin interfaces are normal to growth direction. Both maximum twin thickness and volume fraction of twins vary with the individual layer thickness. Coherency stress plays an important role in tailoring the formation of nanotwins. Nanotwins compete with misfit dislocations in accommodating elastic strain energy in epitaxial Cu/Ni multilayers.

A formation mechanism for ultra-thin nanotwins in highly textured Cu/Ni multilayers

Exact closed-form solutions are obtained for the energy of arrays of dislocations lying at the interface between a strained epitaxial layer and substrate that are elastically anisotropic and have the same elastic constants. Closed-form solutions are obtained both when all dislocations in an array have the same Burgers vector and when the sign of one or more of the components of the Burgers vector alternates within an array. The method of solution makes the consideration of multiple arrays particularly simple (i.e. sets of more than one array in the interface, each inclined to the others at some non-zero angle, e.g. a pair of orthogonal arrays). Also, an approximate treatment is given of the case in which the elastic constants of the substrate differ from those of the layer by a small perturbation. The method is based on performing a perturbation expansion about the solution for the homogeneous body. A correction term, accurate to first order in the perturbation, is thus obtained to account for th...

J. R. Willis

Papers

The energy of arrays of dislocations in an anisotropic half-space