Displacement of ions

ZnS(llO) surface consists of parallel zigzag chains with equal numbers of zinc and sulphur ions (see Fig. 9.12(a)). It is a charge neutral surface. Relaxation of the ZnS (110) surface has been performed using GGA with CASTER Some pioneering works show that there is a negligible displacement of ions below the second and third atomic layer. Therefore, in relaxation calculation, only the atoms on the first layer of the surface are allowed to move. The surface structure and ionic displacement vectors for the (110) surface are shown in Fig. 9.12(b). Ionic displacements due to surface relaxation are presented in Table 9.5. 

Figure 8.4—Influence of net charge, field, viscosity and species size on the migration velocity vector of an electrolyte assumed to he immobile. The general term cataphoresis corresponds to the displacement of ions towards the cathode whereas anaphoresis corresponds to the displacement of ions towards the anode.

Firstly the thermal displacement of ions from lattice sites to interstitial site is considered and then the motion of the interstitial ions treated. 

In lattice structure calculation the crystal lattice parameters are obtained by the optimization of crystal energy with respect to displacements of ions that do not change crystal lattice symmetry. The crystal energy is calculated in the framework... 

Static dielectric constant depends on the displacement of ions from their regular positions in an applied electric field. 

Iodine, iron, and zinc increased in wells over the concentrations in the brine or local groundwater, represented by the private (PVT) well. The researchers hypothesized that chemical displacement of ions coating the sand grains took place. This explanation is plausible for the iron alone. Hence, another explanation was... 

From the data listed in Table 3, it may be noted that the polarization values of the ceramics are lower than that of the single crystal [7,8] whereas the coercive field is higher. This may be attributed to the existence of the non-ferroelectric layers at the metal-ferroelectric interfaces and grain boundaries. In other way, when the anisotropy of the crystal get stronger, the displacement of ions, which is demanded by polarization inversion, get larger, the coercive field will be stronger. 

In seeking an atomic view of the process of conduction, one approach is to begin with the picture of ionic movements as described in the treatment of diffusion (Section 4.2.4) and then to consider how these movements are perturbed by an electric field. In the treatment of ionic movements, it was stated that the ions in solution perform a random walk in which all possible directions are equally likely for any particular step. The analysis of such a random walk indicated that the mean displacement of ions is zero (Section 4.2.4), diffusion being the result of the statistical bias in the movement of ions, due to inequalities in their numbers in different regions. 

Fig. 5.18. The formation of a hole in a liquid by the relative displacement of ions in contact.

In conventional MD, employing PBC, there are no surface effects. Thus, any process involving the generation or removal of species from the surface cannot be simulated. An example is provided by the generation of Schotty disorder in crystals, which requires displacement of ions to the surface. This cannot be simulated by conventional MD studies. 

ESD shows consistently the displacement of ions of the substrate by ion species of the surface carboxylate, although to maintain stability of adsorbate... 

Dielectric The static dielectric constant of a solid arises from the displacement of ions in an electric field... 

This matrix element is associated with the CDW occurring on the lattice sites of the crystal, i. e. we neglect here the presumably small displacements of ions accompanying the CDW. In Equ. (3), V0 is the on-site Coulomb interaction, while... 

This is described as electrodynamic coupling, central to this approach. The induced dipole moment is given by, />2(0 = e.X2(t), where e is the charge on ion 2, and X2(t) is the time-dependent displacement of ion 2. The equation of motion governing the displacement of ion 2 corresponds to that of a forced damped oscillator and is given by... 

In calculating the repulsive interaction energy between colloidal particles [Eq. (22)] it is usually assumed that a complete equilibrium exists between the particle surface and the dispersion medium at any separation between the particles. This is not necessarily correct, however, because the adjustment of equilibrium takes a finite time and this time may be longer than the time involved in a collision or longer even than the coagulation time. The time needed for adjusting the structure of the diffuse double layer (the relaxation time of the double layer) is equal to the average time needed for the displacement of ions across the double layer. 

Thongh IMS and ion mobility spectrometry/mass spectrometry (IMS/MS) methods may not be recognized widely for determining values for enthalpy, entropy, and kinetic constants, significant experience in the study of reactions at ambient or elevated pressures exists. In the discnssion below, examples are drawn from gas-phase reactions for associations and displacements of ions using either combined mobility-mass spectrometry or, in some instances when the chemistry was well known, a drift tube alone. The order of presentation follows that used in the prior section. In a later discussion, reactions with electrons are described. 

This is displacement of positive ions with respect to negative ions. To clarify the division between electronic and ionic polarization electronic polarization is the displacement of the electron cloud with respect to the nucleus ionic polarization is the displacement of ions relative to each other. The hydrated sheath around an ion at rest is symmetrical (not really at rest, everything is bumping around at room temperature, we are talking statistically). When current flows, the sheath will lag behind the migrating ion, and the sheath is no longer symmetrical to the ion, cf. the Wien effect (Section 8.4.1). This is local polarization of charges bound to each other. 

Figure 1.6. Displacements of ions in ionic cubic crystal in (a) transverse and (b) longitudinal waves.

Figure 3.5. Displacements of ions inside ultrathin film of ionic cubic crystal in transverse polarization wave propagating along film. Below is shown polarization field due to ion displacement.

Eq. (4.12) can be deduced from the assumption that the broadening of the edge is proportional to the mean square displacement of ions which in turn is proportional to the mean potential energy of their oscillations, and therefore to their total energy. In the classical case das kT in the quantum-mechanical case,... 

Fig, 11. Comparison of Ca(II)-Na(I) equilibrium quotients for exchange between aqueous CaCl2 NaCl solutions, otal " and montmorillonite, measured by different isotope-dilution techniques. Comparison of ion-exchange capacities measured by isotope dilution and by displacement of ions. 

The displacements of ions from tiie equilibrium positions at static and dynamic deformations of the lattice may be presented as... 

Displacements of ions in the LiTmF crystal near impurity Ntf" and Lu ions ... 

Displacement of ions is common in ionic solids such as ceramic materials. Under the influence of an electric field, dipole moments are created by the shifting of these ions toward the opposing polarity. The displacement of the dipoles can be relatively large in comparison to the electronic displacement, and the contribution to the relative permittivity is high in certain ceramics. The ionic polarization resulting from this behavior is given by the relation below, where n is the atom density, in m o the ionic polarizability in CmV or the absolute ionic polarizability, in m and the local electric field in the atom, in V.m ... 

---