Induced polarisation

At these high frequencies, the retarding effect of the ion-atmosphere on the movement of a central ion is greatly decreased and conductance tends to be increased. The capacitance effect is related to the absorption of energy due to induced polarisation and the continuous re-alignment of electrically unsymmetrical molecules in the oscillating field. With electrolyte solutions of low dielectric constant, it is the conductance which is mainly affected, whilst in solutions of low conductance and high dielectric constant, the effect is mostly in relation to capacitance. 

Another example of the coupling between microscopic and macroscopic properties is the flexo-electric effect in liquid crystals [33] which was first predicted theoretically by Meyer [34] and later observed in MBBA [35], Here orientational deformations of the director give rise to spontaneous polarisation. In nematic materials, the induced polarisation is given by... 

Figure 11.43 Induced polarisation as a function of time, (a) Linear, (b) nonlinear and (c) graphical representation as a function of applied field.

The fundamental component (aE) is linear in E and represents the linear optical properties discussed above. The second (jfiE-E) third ( yE-E-E) and subsequent harmonic terms are nonlinear in E and give rise to NTO effects. The / and values are referred to, respectively, as the first and second hyperpolarisabilities. The second harmonic term gives rise to second harmonic generation (SHG), the third results in frequency tripling effects, and so on. Importantly, since only the time-averaged asymmetrically induced polarisation leads to second-order NLO effects, the molecule and crystal must be non-centrosymmetric, otherwise the effects will cancel one another. Third-order effects, however, may be observed in both centrosymmetric and non-centrosymmetric materials. 

The use of SP surveys as an exploration tool has waned since the 1950s with the increasing sophistication of other electrical geophysical techniques such as induced polarisation (IP) and ground resistivity. Part of the reason is that the interpretation of these non-passive techniques is easier because electrical theory and electronics theory can be applied. Since the causes of natural SP above mineralisation are still widely misunderstood (Hamilton, 1998), the interpretation of the results of SP surveys is difficult. 

Since K depends on the wavefunction density at the nucleus, the effect is dominated by s-electrons which is certainly true in metals with unpaired s-electrons. If the Pauli susceptibility and electron density can be independently measured then the Knight shift will give an independent measure of the s-component of the conduction electron spin density. These shifts are positive and are much larger than chemical shift effects, some typical values being Li — 0.025%, Ag — 0.52% and Hg — 2.5%. In other metals the situation is more complicated when the s-electrons are paired but there are other electrons (e.g. p but especially d). As only s-electrons have significant density at the nucleus the effects of these other electrons are much smaller. The hyperfine fields of these electrons induce polarisation in the s-electrons that subsequently produce a shift, termed core polarisation. 

In the case of dinitrogen and dioxygen, the multiple bonds were homoatomic, and so there is no permanent polarisation across the central bond. In the case of diimide, exactly the same atoms appear on each side of the central bond, and so again there is no permanent charge separation. However, temporary and induced polarisations may occur in each of these cases as may occur in homoatomic single bonds. 

For most purposes the induced polarisation of the H-C bond can be ignored, while in H-O, H-F and H-Cl bonds it is significant. One consequence of this polarisation is that lone pairs can interact with the 8+ hydrogens by forming a hydrogen bond, which is a weak Coulombic interaction. This bond can be either intermolecular or intramolecular. 

The induced polarisations within a molecule can be summed together as vectors, to give the overall dipolar motion of the molecule. For some molecules, like methane and boron trichloride, the result is zero while for others, like water and ammonia, the result is non-zero. 

The polarisations resulting from inductive and mesomeric effects are in the same direction in pyridine, resulting in a permanent dipole towards the nitrogen atom. This also means that there are fractional positive charges on the carbons of the ring, located mainly on the a- and y-positions. It is because of this general elecuon-deficiency at carbon that pyridine and similar heterocycles are referred to as electron-poor , or sometimes jt-deflcient . A comparison with the dipole moment of piperidine, which is due wholly to the induced polarisation of the o-skeleton, gives an idea of the additional polarisation associated with distortion of the tr-electron system. 

The transfer of momentum from the beam to an absorbing particle is therefore straightforward compared to other cases, such as transparent particles and atoms. For transparent particles, refraction and induced polarisation must be taken into account. For an atom, the frequency dependence of the absorption and spontaneous emission must be considered, while for an absorbing particle, the absorption can be assumed to be independent of frequency, and inter-atomic collision rates within the particle can be assumed to be high enough to cause deexcitation without re-emission. 

Above 130 kbar there is a phase change to a non-magnetic hexagonal phase which has a chemical isomer shift 0-17 mm s more negative than for the body-centred cubic a-iron [13, 15]. The relative line intensities are also affected by pressure due to a pressure-induced polarisation of the iron foil... 

In the phase xMgaSn04-(l — x)MgFca04, magnetic interaction is seen in both the Fe and Sn resonances for x > 0-3 (in the case of tin as a result of an induced polarisation by the magnetic cations) [100]. However, in both instances randomisation effects prevent the appearance of a unique magnetic field, and the resonance lines are broadened. Similar effects are found in the system MgFe204-MnFc204 when doped with Sn [101]. 

Magnetic field orientation is analogous to the induced-polarisation effect for electric-field orientation. Here it is the anisotropy of the magnetic susceptibility of the molecule that leads to a lowest interaction energy for a particular orientation of the molecule in the field. 

Interfacial strain in the superlattice series formed by m unit cells of ferroelectric PbTiOj and n unit cells of dielectric SrTiOj also produces curious behaviour. Normal ferroelectric behaviour is found when the layers are relatively thick. This diminishes as layer thicknesses fall but surprisingly, at the lowest values, ferroelectricity recovers. In bulk PbTiOj octahedral tilt is suppressed and in SrTiOj octahedral rotation is suppressed. However, in superlattices these distortions become possible, creating a strain between the two perovskite slices. As the slabs become thin, the strain component of the interfaces becomes relatively greater and ultimately, in the thinnest layers, is able to induce polarisation and an increased ferroelectric response. 

Raman scattering arises from the interaction between radiation induced oscillating electric dipoles and molecular vibrational modes. In general, the induced polarisability is not necessarily in the direction of the incident beam, and they are related by a second range tensor, a, thus ... 

Second Order Non-Linear Effects. In order to probe second-order effects, materials normally must be subjected to electric fields of high enough intensity to polarise the material substantially, so that the induced polarisation becomes a non-linear function of the field strength. The relationship between the two common parameters which characterise bulk materials, viz. dielectric constant e and refractive index r, is shown in the following relationships ... 

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