Inter-atomic force

With the assumption of pairwise additive, conservative inter-atomic forces that are only a function of the pair separation, the force that particle j exerts on particle i is fij — Here = ri - r jl is the pair separation. The total... 

In this review, the term elastic is applied to inter-atomic forces of chemical bonding treated in harmonic approximation, to be distinguished from bulk elasticity in solids (see Kanamori [27]). 

Pauling L (1938) The nature of inter-atomic forces in metals. Phys Rev 54 899... 

Only a relatively small number of polymers have sufficient mobility to be rubbery at room temperature. The molecular mobility depends heavily on the composition of the polymer backbone, which often contains a significant proportion of simple hydrocarbon species, such as those derived from ethylene, butadiene or isoprene. These species are small and are able to undergo bond rotation with relative ease, since they do not suffer problems due to steric hindrance [2] or the presence of strong dipoles. The rubber molecule is also able to undergo extension easily because the forces acting on the material are relatively weak secondary intermolecular forces, i.e., those acting between molecules, and not the primary inter-atomic forces, i.e., those existing within a molecule [3]. 

The problem was that science was still asking the wrong questions. Materials strengths are not determined only by inter-atomic forces, they are largely determined by the existence of micro- and macro-defects in the materials. 

Using the inter-atomic force model given by Eq. 11.1 and shown in Fig. 2.22 can be used to estimate the tensile strength of a material to be of the same order of magnitude as the elastic modulus. 

A more subtle issue is that the interaction between atoms is often a group behaviour while the simplistic inter-atomic force depends only on the pair of atoms under... 

Theoretically, the elasticity theory of continuous media may be used to study the long-wavelength modes. To determine the microscopic modes, numerical approaches are necessary. Most of them have used Born s model to estimate the inter-atomic forces. The semi-infinite crystals are modelled by thin films, whose thickness must be larger than the attenuation length of the surface modes. The complete MgO(OOl) phonon spectrum has been calculated, neglecting (Chen et al, 1977 Barnett and Bass, 1979) or taking into account (Lakshmi and de Wette, 1980) the surface relaxation. The same has been done for SrTiO3(001) (Prade et al, 1993). 

P. Debye modified the Einstein s model by introduction of inter-atomic forces in a crystal model. This is equivalent as to take phonons into account (refer to Section 9.3.1). To each elastic wave (phonon) the Bom-Karman atomic chain was attracted spread out in a three-dimensional array (Figure 9.13 and 9.15). As a result of reflection from external crystal borders, standing waves with various values co and k (refer to Section 2.9.2 and 2.9.3) are formed. There is the certain relationship between the wavelength of standing waves X and the size of the crystal L expressed by the eqn (2.9.8). Phase speed of running... 

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