Continuum elastic model

The Debye s elastic continuum model for solids [1-9] gives for cph ... 

Still, the strain enthalpy is of particular importance. An elastic continuum model for this size mismatch enthalpy shows that, within the limitations of the model, this enthalpy contribution correlates with the square of the volume difference [41,42], The model furthermore predicts what is often observed experimentally for a given size difference it is easier to put a smaller atom in a larger host than vice versa. Both the excess enthalpy of mixing and the solubility limits are often asymmetric with regard to composition. This elastic contribution to the enthalpy of mixing scales with the two-parameter sub-regular solution model described in Chapter 3 (see eq. 3.74) ... 

An elastic continuum model, which takes into account the energy of bending, the dislocation energy, and the surface energy, was used as a first approximation to describe the mechanical properties of multilayer cage structures (94). A first-order phase transition from an evenly curved (quasi-spherical) structure into a... 

Doublets of folded longitudinal acoustic (LA) phonons due to the superlattice periodicity [143] can also be seen in the Raman spectra of the SLs (indicated by arrows in Fig. 21.2). The positions of the doubled peaks agree well with the first doublet frequencies calculated within the elastic continuum model [144]. The observation of the LA phonon folding suggests that these superlattices possess the requisite structural quality for acoustic Bragg mirrors and cavities to be used for potential coherent phonon generation applications [145-147]. 

The harmonic-oscillator and elastic-continuum models can be used to explain the presence of surface phonons (Rayleigh waves and localized surface modes of vibration) and the larger mean-square displacement of surface atoms compared to that of atoms in the bulk. 

It is instructive to consider reasons for the nonisotropic, irradiation-induced expansion and the implications for the type of disorder produced. Eshelby showed that within the elastic-continuum model of a solid the strain fields caused by distortional defects produce expansion (or contraction) and further that the fractional change in macroscopic dimensions. A///, is equal to the fractional change in lattice parameter, AJ/d, if there is no change in the number of unit cells [156]. The latter was verified experimentally, and information about the radiation-induced disorder was obtained by comparing A/// with Ad/d, and by comparing these quantities with defect concentrations detected by techniques such as optical absorption [150-152,157]. It is possible to distinguish between... 

More-over the vibration analysis of MWCNTs were implemented by Aydogdu [73] using generalized shear deformation beam theory (GSD-BT). Parabolic shear deformation theory (PSDT) was used in the specific solutions and the results showed remarkable difference between PSDT and Euler beam theory and also the importance of vdW force presence for small inner radius. Lei et al. [74] have presented a theoretical vibration analysis of the radial breathing mode (RBM) of DWCNTs subjected to pressure based on elastic continuum model. It was shown that the frequency of RBM increases perspicuously as the pressure increases under different conditions. 

Even better agreement is observed between calorimetric and elastic Debye temperatures. The Debye temperature is based on a continuum model for long wavelengths, and hence the discrete nature of the atoms is neglected. The wave velocity is constant and the Debye temperature can be expressed through the average speed of sound in longitudinal and transverse directions (parallel and normal to the wave vector). Calorimetric and elastic Debye temperatures are compared in Table 8.3 for some selected elements and compounds. 

Arridge, R. C. and Barham, P. J. Polymer Elasticity. Discrete and Continuum Models. Vol. 46,... 

Polymer Elasticity - Discrete and Continuum Models R. C. Arridge and P. J. Barham. 67... 

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