Defect dynamic interaction

It is clear that defect interactions must play an important role in their stability and transformations. Along with the generally-known Coulomb attraction 

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 1 ) (X [04] (i.e., the cubic harmonic with / = 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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Thus, the kinematical theory is valid only for very thin crystals that are not diffracting strongly. To interpret the details of the images observed from the much thicker crystals commonly used in TEM (particularly when s = 0), we require a theory that includes the dynamical interaction of the many beams excited in such crystals. The dynamical theory, which is developed in the next chapter, overcomes the critical limiations of the kinematical theory and provides the basis for the interpretation of the images due to crystal defects, which are discussed in detail in Chapter 5. 

In chap. 8 we developed many of the fundamental tools needed to examine the behavior of one or several dislocations. However, an equally challenging and important problem is the statistical problem posed by a collection of large numbers of dislocations. We made a certain level of progress in confronting the statistical questions that attend the presence of multiple interacting dislocations in the previous chapter, and now revisit these questions from the standpoint of the hierarchical approaches being described here and in particular in terms of the variational approaches to defect dynamics introduced in section 12.3.2. 

Overall, these molecular dynamics crystal simulations showed that random, uncorrelated conformational disorder was governed by three processes (1) the intramolecular dynamics leading to local isomeric transition (2) the number of intermolecular collisions and (3) the restrictiveness of the crystal environment [5b]. These initial conformational defects do not corr pond to a potential energy minimum and thus cannot easily be predicted by molecular mechanics calculations. They are the result of the dynamic interaction of skeletal vibrations... 

Detailed calculations are presented in the articles (V.I. Talanin I.E. Talanin, 2010b).Our results somewhat differ from those obtained in (Kulkarni et al., 2004). These differences are as follows (i) the nucleation rate of microvoids at the initial stage of their formation is low and weakly increases with a decrease in the temperature and (ii) a sharp increase in the nucleation rate, which determines the nucleation temperature, occurs at a temperature T 1333 K. These differences result from the fact that the recombination factor in our calculations was taken to be kjy = 0. For kjy 0, consideration of the interaction between impurities and intrinsic point defects in the high-temperature range becomes impossible, which is accepted by the authors of the model of point defect dynamics (Kulkami et al., 2004). In this case, in terms of the model, there arises a contradiction between the calculations using the mathematical model and the real physical system, which manifests itself in the ignoring of the precipatation process (Kulkami et al., 2004). 

Using this scaled spectrum, Eq. 11 predicts an H oscillator energy of 72.8 meV, in excellent agreement with the peak observed at (73 1) meV for 10 H. The obsei ved "defect peak is broadened beyond instrumental resolution, since defects at this concentration are far from isolated. The comparison demonstrates that the complex spectrum for the H overlayer on Pt is primarily due to dispersion of a vibrational mode associated with a single type of site on the Pt surface (which in turn reflects strong dynamic interaction of H atoms), and not to the existence of different surface H sites or surface impurities. 

In principle, we could find the minimum-energy crystal lattice from electronic structure calculations, determine the appropriate A-body interaction potential in the presence of lattice defects, and use molecular dynamics methods to calculate ab initio dynamic macroscale material properties. Some of the problems associated with this approach are considered by Wallace [1]. Because of these problems it is useful to establish a bridge between the micro-... 

A very similar technique is atomic force microscope (AFM) [38] where the force between the tip and the surface is measured. The interaction is usually much less localized and the lateral resolution with polymers is mostly of the order of 0.5 nm or worse. In some cases of polymer crystals atomic resolution is reported [39], The big advantage for polymers is, however, that non-conducting surfaces can be investigated. Chemical recognition by the use of specific tips is possible and by dynamic techniques a distinction between forces of different types (van der Waals, electrostatic, magnetic etc.) can be made. The resolution of AFM does not, at this moment, reach the atomic resolution of STM and, in particular, defects and localized structures on the atomic scale are difficult to see by AFM. The technique, however, will be developed further and one can expect a large potential for polymer applications. 

The linear and nonlinear optical properties of the conjugated polymeric crystals are reviewed. It is shown that the dimensionality of the rr-electron distribution and electron-phonon interaction drastically influence the order of magnitude and time response of these properties. The one-dimensional conjugated crystals show the strongest nonlinearities their response time is determined by the diffusion time of the intrinsic conjugation defects whose dynamics are described within the soliton picture. 

The linear and nonlinear optical properties of one-dimensional conjugated polymers contain a wealth of information closely related to the structure and dynamics of the ir-electron distribution and to their interaction with the lattice distorsions. The existing values of the nonlinear susceptibilities indicate that these materials are strong candidates for nonlinear optical devices in different applications. However their time response may be limited by the diffusion time of intrinsic conjugation defects and the electron-phonon coupling. Since these defects arise from competition of resonant chemical structures the possible remedy is to control this competition without affecting the delocalization. The understanding of the polymerisation process is consequently essential. 

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