Long range elastic deformation

In the three-dimensional (3D) simulations, the substrate contained as many as 36 layers or 72,576 atoms. Hence long-range elastic deformations were included. The surface yielded plastically after an indentation of only 1.5 layers, through the creation of a small dislocation loop. The accompanying release of... 

It is important to note that Slitcher and Drickamer s model does not provide any information on the mechanism leading to the cooperativity term yfnns)- In order to give microscopic physical meaning to the interaction term, several approaches have been proposed [27-32]. The so-called lattice expansion and elastic interaction model appears as the most successful to interpret the available data [27-29]. In this approach the difference in volume between HS and LS molecules is assumed to cause long-range elastic deformations, leading to the cooperative spin-transition mechanism. 

X-ray diffraction and IR dichroism studies suggest that the long-range elasticity of wool is related to a reversible molecular transformation of the alpha-keratin to an extended beta form (66). No convincing evidence supports this mechanism in stratum corneum viscoelasticity. In fact, the available evidence suggests that the elastic behavior of corneum is primarily entropic in origin. At low deformations, the mechanical properties of hydrated stratum corneum is best described as the behavior of a lightly-crosslinked rubber. 

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]. 

This interaction arises from the overlap of the deformation fields around both defects. For weakly anisotropic cubic crystals and isotropic point defects, the long-range (dipole-dipole) contribution obeys equation (3.1.4) with a(, ip) oc [04] (i.e., the cubic harmonic with l = 4). In other words, the elastic interaction is anisotropic. If defects are also anisotropic, which is the case for an H centre (XJ molecule), in alkali halides or crowdions in metals, there is little hope of getting an analytical expression for a [35]. The calculation of U (r) for F, H pairs in a KBr crystal has demonstrated [36] that their attraction energy has a maximum along an (001) axis with (110) orientation of the H centre reaching for 1 nn the value -0.043 eV. However, in other directions their elastic interaction was found to be repulsive. 

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