Dipole-moment density

The magnetic field seen by the probe neutron is solely due to the magnetic dipole moment density of the unpaired electrons. In other words, the magnetisation density is simply related to the electron spin density by a multiplicative factor, and there is no ambiguity in its definition. 

P polarisation, nett dipole moment densities per unit volume... 

The unique piezoelectric and pyroelectric properties of semicrystalline films of PVDF arise from changes in the polarization imparted to the overall film by the crystalline P-phase. The polar nature of the P-phase is, in turn, a direct result of the parallel alignment of the dipole moment of the repeat units in the unit cell (Figure 11.1). The crystal polarization is defined as the dipole moment density of the crystal ... 

Figure 1.1. Scheme of dipole-moment densities utilized in the method of Ewald (A) Distribution of point dipoles whose field is calculated at the origin 0. (B) distribution of gaussians centered at each point, point 0 included. (C) distribution of dipoles plus gaussians ... 

The dipole-moment density of the gaussian centered at each point x is... 

According to Eq. (25), the equilibrium radius R of the island is the product of two factors one of them is the equilibrium radius in the absence of other islands (C = 0), and the other one increases exponentially with the area fraction of the islands. R is determined by the line tension (2) and the difference Ap between the two-dimensional dipole moment densities of the LC islands and the LE molecules. Both X and Ap depend on the molecular surface area difference (jAd — Ac) between the LC and LE phases. Since Ac is assumed to be constant and is considered to... 

A. Surfactant Adsorption. The surface density of surfactant has a relevant role for both the double-layer (via the surface charge density) and the hydration interaction (via the dipole moment density of the ion pairs formed). It will be computed using the Frumkin adsorption isotherm ... 

Dielectric constant, dipole moment, density, refractive index liquid fatty acids G2-G18, 25-120 C. 

S. Soundararajan and S. V. Ananta-krishnan. Proc. Indian Acad. Sci. 38A, 176-83 (1953). Dipole moment, density, refractive index furoin, hydrofuramidc. 

Dipole moment density occurs as a result of very small translational displacements of the electronic cloud with respect to the nucleus, whether in single atoms or in molecules. Displacement of electrons is very fast (picosecond), and the dispersion is in the gigahertz region. Induced dipoles will have the direction of the local E-field and undergo no rotation. 

Equation (3.5) shows the relationship between polarization and permittivity. High polarization means high permittivity, E = 0 means P = 0 and no polarization. Permittivity is a measure of the amount of dipole moment density created (induced) by an electric field. Bound charges that can be displaced a long distance L, cause a larger dipole moment,... 

A similar expression exists for the ft component. The i atom moves along the trajectory x-xj +v t where x and v are the components of position and velocity along the direction of the laser pulses. The dipole moment density is obtained by summing over all atoms and is proportional to... 

TSP current is the sum of two components one is of dipolar origin, the other is ascribed to conduction. The dipolar part is proportional to the time derivative of the polarization (dipole moment density), which can be described as follows, assuming a single relaxation time (t) and an exponential dielectric response function [1] ... 

FIGURE 4.6 Water dipole moment density distribution along LiCl (a), NaCl (b), KCl (c), and RbCl (d) salt surface normal. (From Du, H. and Miller, J. D. J. Phys. Chem. C, 111 10013, 2007c. With permission.)... 

The polarization vector P ro) appearing in equation (6.1b) is defined as the dipole moment density in a small region V as the volume V is taken to zero. Using equation (6.181b), we write... 

Macroscopic electric field Let us consider a slab of equi-distant layers, bearing positive and negative charge densities equal to + cr (Fig. 3.7a). The repeat unit has a dipole moment density equal to aR. As for an association of capacitors. Gauss theorem allows an estimation of the electric field S perpendicular to the layers and of the electrostatic potential V. The field S turns out to be equal to zero between two double-layers and equal to 47rcr inside a double-layer. Its mean value in the slab is, therefore, non-zero ... 

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