Clausius-Mossotti local field

Can ferroelectric behavior be described in terms of the polarization catastrophe in the Clausius-Mossotti equation Use Equation 23.42 to relate the Clausius-Mossotti local field to the polarization in the medium. Then use Equation 23.28 to relate the temperature to the polarization assuming as the local field. Now use a procedure similar to that used to develop the Curie-Weiss law (Equation 23.55) to obtain the Curie temperature and the Curie constant for BaTiOs. Does the result agree with observed behavior ... 

If we consider the optical response of a molecular monolayer of increasing surface density, the fomi of equation B 1.5.43 is justified in the limit of relatively low density where local-field interactions between the adsorbed species may be neglected. It is difficult to produce any rule for the range of validity of this approximation, as it depends strongly on the system under study, as well as on the desired level of accuracy for the measurement. The relevant corrections, which may be viewed as analogous to the Clausius-Mossotti corrections in linear optics, have been the... 

This equation is not valid for liquids or crystals, but only for substances for which the dielectric constant is very close to unity, as for gases. For other substances an equation derived by consideration of the effect of the induced moments of neighboring molecules upon the molecule undergoing polarization must be considered. In a polarized medium each molecule is affected by the electric field in the region occupied by the molecule, called the local field. For many substances the local field is satisfactorily represented by the Clausius-Mossotti expression, derived in 1850. Each molecule is considered to occupy a spherical cavity. The part of the substance outside the spherical cavity undergoes polarization in the applied field. A simple calcula-... 

This equation, called the Lorenz-Lorentz equation, was derived in 1880 by combining the Clausius-Mossotti expression for the local field with the idea of molecular polarizability. 

To describe local field effects associated with a crystalline environment, e.g. Cso arranged in a lattice of cubic symmetry, we use the Clausius-Mossotti relation [93] in the form... 

H. A. Lorentz, Theory of Electrons, Teubner, Leipzig, 1909 (reprinted by Dover, New York, 1952). O. F. Mossotti, Bibl. Univ. Modena, 6, 193 (1847) Mem. Math. Fis. Modena, 24 11, 49 (1850). R. Clausius, Die mechanische Warmetheorie Vol. 11, Braunschweig, 1879. In Ann. Phy., 49, 1 (1916), Ewald showed that for a lattice of polarizable atoms of cubic symmetry, the local field is essentially that of the continuum considered by Lorentz. 

Accounting for the CMLL local field Clausius-Mossotti relation [9-13, 22, 43]... 

Local Field, Clausius-Mossotti and Onsager Equations... 

The Clausius-Mossotti equation is based on the simplest (Lorentz) form of the local field. In reality, the induced dipole in the selected molecule also creates an additional, reaction field that modifies the cavity field. On account of these factors Onsager has obtained the following equation for dielectric permittivity... 

Lorenz-Lorentz theory addressed the issue by extending the approach of Clausius-Mossotti to optical frequency fields (12,13). This extension relies on a spherical cavity (compare with the need for a needle-shaped cavity) and takes into account the effect of other charges. The only thorny issue is that a spherical cavity is not the best choice for anisotropic molecules. Nevertheless, the Lorenz-Lorentz approach has been widely used in studying optical properties of polymers (14). The expression of the local field is given by... 

It can be concluded that remanent polarization and hence the piezoelectric response of a material are determined by Ae this makes it a practical criterion to use when designing piezoelectric amorphous polymers. The Dielectric relaxation strength Ae may be the result of either free or cooperative dipole motion. Dielectric theory yields a mathematical approach for examining the dielectric relaxation Ae due to free rotation of the dipoles. The equation incorporates Debye s work based on statistical mechanics, the Clausius-Mossotti equation, and the Onsager local field and neglects short-range interactions (43) ... 

Lorentz was the first to consider such problems for a reasonably defensible model of induced dipoles derive the local Lorentz field j and from this obtain the venerable Clausius Mossotti (or perhaps more properly Lorentz-Lorenz) formula. As shown schematically in Figure 1 (a) the molecules are assumed to be at sites on a cubic lattice with uniform macroscopic along the z axis. 

Figure 5.2 reports the absorption cross section of a small silicon nanocrystal. It is clear that the tight-binding approach with inclusion of local field effects (calculated by inversion of the dielectric matrix) compares very well to the formulation with a classical model of the surface polarization, based on the Clausius Mossotti equa-... 

Construct a model for the local magnetic field in a magnetic material similar to the Clausius-Mossotti model for the local electric field in a dipolar field. Can such a model explain the ordering in a ferromagnetic material (Compare the predicted Weiss constant against the observed Weiss constant for Fe.)... 

---