Lattice charge-induced dipole

Figure 1.26 Induced polarization effects arising from a cationic vacancy in a crystal (negative net charge). Arrows mark induced dipoles at various lattice positions. From Lasaga (1981c). Reprinted with permission of The Mineralogical Society of America.

When the free electrostatic charge in phase a turns to zero, = 0 and = X . The surface potential of a liquid phase is dictated by a certain interfacial orientation of solvent dipoles and other molecules with inherent and induced dipole moments, and also of ions and surface-active solute molecules. For solid phases, it is associated with the electronic gas, which expands beyond the lattice (and also causes the formation of a dipolar layer) other reasons are also possible. 

The extent to which the sixth-rank parameters exceeded expectations could only be judged by carrying out an actual calculation. One of the earliest was that of Hutchison and Wong (1958) for the Lads lattice. Charges of 3e and —e were placed at the La and Cl sites, and allowance was made for the induced dipoles on the chlorine ions. In the 1950 s it was none too easy to estimate for the 4i electrons however, a hydrogenic approximation led to values for the products for... 

This phenomenon involves the rotation of permanent electric dipoles under an applied electric field. Although permanent dipoles exist within many ceramic compounds such as SiO, which has no center of symmetry for positive and negative charges, dipole orientation is not found to occur in most cases, as the dipole is restricted from shifting by the rigid crystal lattice of ceramic materials. Reorientation of the dipole is precluded as destruction of the lattice would occur. Dipole orientation is more common in polymers, which by virtue of their atomic structure permit reorientation. Note that this mechanism of permanent dipoles is not the same as that of induced dipoles of ionic polarization. The dipole polarizability is a function of the permanent dipole moment of the molecule as described by the following equation ... 

Typical lattice defects include cation vacancies substitutional or interstitial ions are other types of more complicated structural defects. A cation vacancy behaves like a negative charge. If the temperature is high, ions are sufficiently mobile that an anion could be expelled from the lattice by the Coulomb potential of the cation vacancy. Cation and anion vacancies could form a dipole oriented along one of the six crystallographic axes. This vacancy coupling is then able to induce a crystalline dipole. Similar dipoles can also appear when an ion is substituted for the host ion. 

Image-charge models. These models take into account the discreteness of surface charges, which induces orientation in the adjacent water dipoles [574-577]. Dipoles due to zwit-terionic surface groups, for example, phospholipid headgroups [578], have been also taken into consideration in models of the electrostatic interaction between planar dipole lattices [579-583]. 

The field la then the same for all molecules and parallel to . as are the induced moments m taken to be given by m > o where o is a simple scalar polarizability The gist of the Lorentz argument (7) is that the resultant field at any one molecule i from all the other dipoles j in a sphere, surrounding the one vanishes as it is given by the sumr Tl - 3 cos (R j z)]a over lattice distances which is zero for cubic symmetry (or an isotropic continuum) leaving s the field of charges external to the sphere if it is in a vacuum. The macroscopic in the sphere from Eo and the macroscopic is by electrostatics - - (AtT/3) and the Lorentz field is... 

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