Elastic interaction distributions

Examples which show that elastic interactions between particles can stabilize distributions of fine particles against coarsening include the observation by Miyazaki et al. that large particles in aged Ni-Si and Ni-Al alloys split into pairs and even octets of smaller particles as aging proceeds [18], In such cases, the reduction in... 

In conclusion of Section 6.3 we wish to stress that the elastic attraction of similar defects (reactants) leads to their dynamic aggregation which, in turn, reduces considerably the reaction rate. This effect is mostly pronounced for the intermediate times (dependent on the initial defect concentration and spatial distribution), when the effective radius of the interaction re = - JTX exceeds greatly the diffusion length = y/Dt. In this case the reaction kinetics is governed by the elastic interaction of both similar and dissimilar particles. A comparative study shows that for equal elastic constants A the elastic attraction of similar particles has greater impact on the kinetics than interaction of dissimilar particles. 

For textured samples the relation between the peak shifts and sin F becomes nonlinear and analytical expressions can be found only by approximating the texture pole distribution by d functions on some prominent sample directions. This could be a rough approximation, especially if the grain elastic interactions are not of the Reuss type, and numerical calculations of the diffraction stress factors are preferable. 

The driving mechanisms for the island vertical correlation have been the subject of extensive studies over the past years. Because the buried islands produce a nonuniform strain field at the surface of the spacer layer, i.e. the regions above the islands are tensely strained while the regions in between islands remain compressed, exciting models have treated the island distribution at the spacer layer surface by considering the effect of such a strain field on surface diffusion [4] or on island nucleation [3]. Recent calculations have taken into account the effect of the elastic anisotropy of the materials [16], the surface energy [18] or the elastic interaction between the buried islands with newly deposited ones [19]. However, in all of the above models it was assumed that the surface of the spacer layer becomes perfectly flat before the deposition of a new layer. From the experimental point of view, this... 

The self-consistent method is suitable for dealing with systems that contain dilute concentrations of a number of different heterogeneities with different elastic properties, provided that certain conditions are met. The heterogeneities must be of equiaxed shape, must not be clustered in space, and must generally be randomly distributed and present in dilute concentrations, of volume fraction around 0.1 or less, to make elastic interactions between heterogeneities negligible. Plate-like and needle-like heterogeneities are excluded. 

Another effect of elastic deformation is that it causes a long-range interaction between steps. From the continuum elasticity theory, two steps sepa-rated by a distance have a repulsive interaction proportional to l for homo- and to In i for hetero-epitaxial cases, respectively [84]. This interaction plays an important role, for example, in step fluctuations, terrace width distribution, step bunching, and so forth [7,85-88]. 

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