5.1.Molecular Field in a Dielectric
The Molecular field is the electric field at a molecular position in the dielectric, and it is produced by all external sources and by all polarized molecules in the dielectric with the exception of the one molecule at the point under consideration.
Ed =
Let us write the macroscopic electric field in the dielectric without a subscript-that is, E. Since the normal component of the electric displacement D is continous across the vacuum-dielectric interface, and since D = 0Ex in the vacuum just outside the dielectric slab,
E = Ex + Ed
Em = E + Es + E’
The field E, arises from the polarization charge density, p = Pn, on the spherical surface S. Using spherical coordinates and taking the polar direction along the direction of P,
dEs =
where r is the vector from the surface to the center of the sphere. From symmetry, it is evident that only the component of dEs along the direction of P will contribute to the integral equation ebove, over thecomplete surface. Since da = r2sin d d ,
Es =
The ratio of the dipole moment of a molecule to the polarizing field is called the molecular polarizability, α. In other words,
Pm = αEm
α =
which known as the Clausius-Mossotti equation
5.2.INDUCED DIPOLES : A SIMPLE MODEL
The molecules of a dielectric may be clasified as polar or nonpolar. A polar molecule is one that has a permanent dipole moment, even in the absence of a polarizing field Em. In the next section, the response of a polar dielectric to an external electric field will be studied. Here we deal with the somewhat simpler problem involving nonpolar molecules, in which the “centers of grafity” of the positive and negative charge distributions normally coincide. Symmetrical molecules such as H2, N2, and O2 and monoatomic molecules such as He, Ne, and Ar fall into this category.
5.3.POLAR MOLECULES: THE LANGEVIN-DEBYE FORMULA
As mentioned in the preceding section, a polar molecule has a permanent dipole moment. A polar molecule consist of at least two different species of atoms. During molecule formation, some of the electron may be completely or partially transferred from one atomic species to the other, with the resulting electronic arrangement being such that positive and negative charge centers do not coincide in the molecule. In the absence of an electric field, a macroscopic piece of the polar dielectric is not polarized. The polarization has been defined as
P =
Where the summation extends over all molecules in the volume element v. When the Pm are oriented at random, the summation vanishes.
If the polar dielectric is subjected to an electric field, the individual dipoles experience torques that tend to align them with the field. If the field is strong enough, the poles may be completely aligned, and the polarization achieves the saturation value
Ps = NPm
Where N is the number of molecules per unit volume. This orientation effect is in addition to the induced dipole effects, which are usually present also. For the moment, we shall ignore the induced dipole contribution, but its effect will be added in later.
5.4.PERMANENT POLARIZATION: FERROELECTRICITY
When E is set equal to zero
Em = P0
Therefore, if N is the number of molecules per unit volume
P0 = NαEm = P0
This result is satisfied when either
P0 = 0
or
= 1
The polarized state of a ferroelectric material is a relativity stable one and one that can persist for long periods of time. This statment may surprise us to some extent because a polarized specimen is subjected to its own depolarizing field and, defending on the geometry of the speciemen, this the polarizing field may be rather large. The depolarizing field is largest for a speciemen in the shape of a flat slab, polarized in a direction normal to its faces.
Ed = - P
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