Field, dipolar

There are higher multipole polarizabilities tiiat describe higher-order multipole moments induced by non-imifonn fields. For example, the quadnipole polarizability is a fourth-rank tensor C that characterizes the lowest-order quadnipole moment induced by an applied field gradient. There are also mixed polarizabilities such as the third-rank dipole-quadnipole polarizability tensor A that describes the lowest-order response of the dipole moment to a field gradient and of the quadnipole moment to a dipolar field. All polarizabilities of order higher tlian dipole depend on the choice of origin. Experimental values are basically restricted to the dipole polarizability and hyperpolarizability [21, 24 and 21]. Ab initio calculations are an imponant source of both dipole and higher polarizabilities [20] some recent examples include [26, 22] ... 

Adsorption of a neutral (n ) onto a metal surface leads to a heat of adsorption of Q, as the electrons and nuclei of the neutral and metal attract or repel each other. Partial positive and negative charges are induced on each with the formation of a dipolar field (Figure 7.4). 

Schematic diagram showing the development of a dipolar field and ionization on the surface of a metal filament, (a) As a neutral atom or molecule approaches the surface of the metal, the negative electrons and positive nuclei of the neutral and metal attract each other, causing dipoles to be set up in each, (b) When the neutral particle reaches the surface, it is attracted there by the dipolar field with an energy Q,. (c) If the values of 1 and <() are opposite, an electron can leave the neutral completely and produce an ion on the surface, and the heat of adsorption becomes Q,. Similarly, an ion alighting on the surface can produce a neutral, depending on the values of I and <(), On a hot filament the relative numbers of ions and neutrals that desorb are given by Equation 7.1,which includes the difference, I - <(), and the temperature, T,...

Schematic diagram showing how placing a thin layer of highly dispersed carbon onto the surface of a metal filament leads to an induced dipolar field having positive and negative image charges. The positive side is always on the metal, which is much less electronegative than carbon. This positive charge makes it much more difficult to remove electrons from the metal surface. The higher the value of a work function, the more difficult it is to remove an electron. Effectively, the layer of carbon increases the work function of the filament metal. Very finely divided silicon dioxide can be used in place of carbon.

In large applied magnetic fields at low temperatures, the ionic spins in a paramagnetic sample are to a large extent aligned and this leads to a field-dependent narrowing of the distribution of dipolar fields, i.e. and (Air ) decrease with... 

As mentioned before, for a bare lattice 11. CEI made the apparently reasonable assumption that screening of the dipolar field by the conductive plates of the MC should decrease below this value, thus insuring that Eq. (32) is satisfied, leading to the... 

Lekner J (1989) Summation of dipolar fields in simulated liquid vapor interfaces. Physica A 157(2) 826-838... 

The B-N distances in as-described borane-amine adducts were found to be shorter in the solid state (156.4 161.6pm) than in the gas phase (167.2 163.7pm). Moreover, it was found that the B-N distance of such adducts in solution is strongly affected by the polarity of the solvent the more polar the solvent the shorter the B-N bond. Both findings indicate the strong influence of a dipolar field, either within a crystal or in polar solvents, on dative B-N bond distances. 

Here p is the stellar dipole magnetic moment and M is the mass accretion rate through the disk. For this formula we assume a purely dipolar field higher multipoles weaken the dependence on M because the field is effectively stiffen... 

Three characteristics of the MRD profile change when the protein is hydrated with either H2O or D2O. Both terms of Eq. (6) are required to provide an accurate fit to the data. The second or perpendicular term dominates once the transverse modes become important. The power law for the MRD profile is retained, but the exponent takes values between 0.78 and 0.5 depending on the degree of hydration. A low frequency plateau is apparent for samples containing H2O which derives from two sources the field limitation of the local proton dipolar field as mentioned above, and from limitations in the magnetization transfer rates that may be a bottleneck in bringing the liquid spins into equilibrium with the solid spins. 

In general the line shape caused by dipolar fields deviates somewhat from the pure Gaussian shape due to the ordered arrangement of the dipoles on a lattice. In the case that two nuclei are relatively close together, with... 

An interesting application of the motional narrowing concept arises in the double NMR technique BS). In this technique the contribution to the NMR line width of nuclei (A) in a solid by the dipolar fields of dissimilar nuclei (B) may be removed by application of a sufficiently strong rf field at the resonance frequency of the B nuclei. With Hib A/Ib, A/Ia where AH is the line width, flipping of B nuclei by the Hib field will cause fluctuations in the dipolar fields of B nuclei at the A nuclei which are rapid compared to T2a and hence cause narrowing of the NMR line of the A nuclei. This effect has been observed in several different solids of the AB type 5S,6A). 

Spin-spin fluctuations can compete with spin-lattice effects an energy hwic can be supplied by a phonon as well as by a spin fluctuation in the dipolar field. A simple thermodynamic view is shown in Fig. 8. For convenience only two distinct carbon... 

The dipolar field, created by all other spins, at the position r, of the spin is given by... 

An essential element of the expressions derived for %, c, and the dipolar fields are the following lattice sums ... 

Sample shape refers to the shape of the whole ensemble of nanoparticles, not to the shape of the individual particles. The linear susceptibility exhibits a sample shape dependence, while the zero-field specific heat and the dipolar fields do not. 

Because of the long-range nature of the dipolar interaction, care must be taken in the evaluation of the dipolar field. For hnite systems the sums in Eq. (3.12) are performed over all particles in the system. Eor systems with periodic boundary conditions the Ewald method [57-59], can be used to correctly calculate the conditionally convergent sum involved. However, in most work [12,13] the simpler Lorentz-cavity method is used instead. 

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