Elastic dipole moment

Alefeld and co-workers (24, 25) have discussed the hydrogen-hydrogen attractive interaction by using the elasticity theory developed for defects in solids by Eshelby and others (46). The strength of the elastic dipole moment is related to the volume expansion resulting from the interstitial hydrogen (25) (Equation 10), where P is the strength of the elastic dipole caused by the interstitial species... 

It is useful to compare the values of hydrogen transfer listed in Table 6.5. Shore and Sander [1972] showed that 3>0 can be calculated using the elastic dipole moments. The results indicate that the aforementioned exponential dependence of the splitting on a0 is associated with an approximately linear growth of 0 with interionic distance. 

It should be noted that an emphasized distinction concerns at room temperature the elastic dipole moment p, fitted for heavy and ordinary water. In view of Table II, pq is in HW three times as much as pq in OW. Moreover, the association factor (24) is noticeably greater in OW than in HW (OW) V20 4.5, while ((HW) y/2A 1.3. It is also interesting that the spread8 S is about twofold... 

In view of Table II the main difference of the parameters, fitted for HW, from those, fitted for OW, concerns (i) some increase of the libration amplitude / , (ii) decrease of the form factor /, (iii) decrease of the frequency vq (the center frequency of the T-band) and increase of the moment nq, responsible for this band, and (iv) decrease of the intensity factor gj, which strongly influences the THz band. Comparison of curves 3 in Figs. 4h and 5h shows that the partial dielectric loss peak g"max of HW, located at v near 150 cm-1 and stipulated by harmonic longitudinal vibration of HB molecules, substantially exceeds such a peak of OW, since the elastic dipole moment / (D20) 8.8 D exceeds the moment / (H20) 3.5 D. 

Figure Bl.25.12. Excitation mechanisms in electron energy loss spectroscopy for a simple adsorbate system Dipole scattering excites only the vibration perpendicular to the surface (v ) in which a dipole moment nonnal to the surface changes the electron wave is reflected by the surface into the specular direction. Impact scattering excites also the bending mode v- in which the atom moves parallel to the surface electrons are scattered over a wide range of angles. The EELS spectra show the higlily intense elastic peak and the relatively weak loss peaks. Off-specular loss peaks are in general one to two orders of magnitude weaker than specular loss peaks.

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

The electric properties of polymers are also related to their mechanical behavior. The dielectric constant and dielectric loss factor are analogous to the elastic compliance and mechanical loss factor. Electric resistivity is analogous to viscosity. Polar polymers, such as ionomers, possess permanent dipole moments. These polar materials are capable of storing... 

Dipolar ions like CN and OH can be incorporated into solids like NaCl and KCl. Several small dopant ions like Cu and Li ions get stabilized in off-centre positions (slightly away from the lattice positions) in host lattices like KCl, giving rise to dipoles. These dipoles, which are present in the field of the crystal potential, are both polarizable and orientable in an external field, hence the name paraelectric impurities. Molecular ions like SJ, SeJ, Nf and O J can also be incorporated into alkali halides. Their optical spectra and relaxation behaviour are of diagnostic value in studying the host lattices. These impurities are characterized by an electric dipole vector and an elastic dipole tensor. The dipole moments and the orientation direction of a variety of paraelectric impurities have been studied in recent years. The reorientation movements may be classical or involve quantum-mechanical tunnelling. 

FERROELECTRIC EFFECT. The phenomenon whereby certain crystals may exhibit a spontaneous dipole moment twhich is called ferroelectric by analogy with ferromagnetic—exhibiting a permanent magnetic moment). The effect in the most typical case, barium manate. seems to he due to a polarization catastrophe, in which the local electric fields due lo the polarizuiion itself increase faster than die elastic restoring forces on the ions in Ihe crystal, thereby leading to an asymmetrical shift in ionic positions, and hence lo a permanent dipole moment. Ferroelectric crystals... 

The model predicts that for the typical elastic parameters the polarization splay is small, just a few degrees. This was also confirmed experimentally as only a small change of birefringence under the electric field is detected for the Blrev phase. The electric field eliminates the spontaneous splay by aligning the dipole moments along the electric field direction. 

Form factor of the hat-curved model Normalized concentration of molecules Kirkwood correlation factor Steady-state energy (Hamiltonian) of a dipole Dimensionless energy of a dipole Moment of inertia of a molecule Longitudinal and transverse components of the spectral function Complex propagation constant Elasticity constant (in Section IX)... 

The relation between p and E is linear when E is small, but becomes nonlinear as E acquires values comparable with interatomic electric fields (typically, 105 to 108 V/m). This may be explained in terms of the simple Lorentz model in which the dipole moment is p = —ex, where x is the displacement of a mass with charge —e to which an electric force — eE is applied. If the restraining elastic force is proportional to the displacement (i.e., if Hooke s law is satisfied), the equilibrium displacement x is proportional to E P is then proportional to E, and the medium is linear. However, if the restraining force is a nonlinear function of the displacement, the equilibrium displacement x and the polarization density P are nonlinear functions of E and, consequently, the medium is nonlinear. 

IR absorptions involve elastic or Rayleigh45 or constant-energy scattering of light in more detail, the electric field vector E of the input light must couple with the transition electric dipole moment fi,f as E fi,f. If E Lp,if, then no IR transition is seen. Allowed IR transitions require that the transition moment vector fii be nonzero—i.e., that is, that the static electric dipole moment fi of the molecule change during the IR absorption. 

Table 3.10 Transition temperatures (°C). elastic constant ratio kjj/kj ). birefringence (A j, dipole moment (pD), Kirkwood-Froehlich factor (g) and dielectric anisotropy (As) for the compounds (106-109)... 

De Boer and coworkers ° °" parameterized the shell model for silica polymorphs on the results of ab initio calculations of the potential energy surfaces, polarizabilities, and dipole moments of Si(OH)4 and (0H)3Si-0(H)-Si(OH)3 clusters. The structural characteristics and elastic moduli calculated with this set of parameters for three structures compared well with results computed with the use of both the rigid ion and the empirical shell models. ... 

Similar problems are encountered in a description of elastic or rotationally inelastic collisions of the electrons with molecules that have permanent dipole moment. However in this case K is never zero because k0 and ki have different norms due to an energy transfer to the vibrational excitation. 

It is instructive to take as a first example the general expression for molecular polarizability, the response tensor that formally mediates elastic light scattering in the electric dipole approximation. The result is obtained by application of Eq. (74) with m = 2 (one photon is annihilated and another of the same frequency is created). Here there are only two time orderings, or state-sequence pathways, as illustrated in Figs. 5 and 6, respectively. Each generates a term whose numerator is a product of transition dipole moment components. For... 

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