Sources Of Polarizability
Sources of polarizability: Now we examine more closely the physical process which gives rise to polarizability. Basically, polarizability is a consequence of the fact that the molecules, which are the building blocks of all substances, are composed of both positive charges (nuclei) and negative charges (electrons). When a field acts on a molecule, the positive charges are displaced along the field, while the negative charges are displaced in a direction opposite to that of the field. The effect is therefore to pull the opposite charges apart, i.e., to polarize the molecule. There are different types of polarization
processes, depending on the structure of the molecules which constitute the solid. If the molecule has a permanent moment, i.e., a moment even in the absence of an electric field, we speak of a dipolar molecule, and a dipolar substance.
Fig.1 (a) The water molecule (b) CO2 molecule.
An example of a dipolar molecule is the H2O molecule in Fig.1a. The dipole moments of the two OH bonds add vectorially to give a nonvanishing net dipole moment. Some molecules are nondipolar, possessing no permanent moments; a common example is the CO2 molecule in Fig.1b. The moments of the two CO bands cancel each other because of the rectilinear shape of the molecule, resulting in a zero net dipole moment.
The water molecule has a permanent moment because the two OH bands do not lie along the same straight line, as they do in the CO2 molecule. The moment thus depends on the geometrical arrangement of the charges, and by measuring the moment one can therefore gain information concerning the structure of the molecule. Despite the fact that the individual molecules in a dipolar substance have permanent moments, the net polarization vanishes in the absence of an external field because the molecular moments are randomly oriented, resulting in a complete cancellation of the polarization. When a field is applied to the substance, however, the molecular dipoles tend to align with the field, and this results in a net nonvanishing polarization. This leads to the so-called dipolar polarizability.
If the molecule contains ionic bonds, then the field tends to stretch the lengths of these bonds. This occurs in NaCl, for instance, because the field tends to displace the positive ion Na to the right (see Fig.2), and the negative ion Cl- to the left, resulting in a stretching in the length of the bond. The effect of this change in length is to produce a net dipole moment in the unit cell where previously there was none. Since the polarization here is due to the relative displacements of oppositely charged ions, we speak of ionic polarizability.
Fig.2 Ionic polarization in NaCl. The field displaces Na and Cl- ions in opposite directions, changing the bond length.
Ionic polarizability exists whenever the substance is either ionic, as in NaCl, or dipolar, as in H2O, because in each of these classes there are ionic bonds present. But in substances in which such bonds are missing - such as Si and Ge - ionic polarizability is absent.
The third type of polarizability arises because the individual ions or atoms in a molecule are themselves polarized by the field. In the case of NaCl, each of the Na and Cl - ions are polarized. Thus the Na ion is polarized because the electrons in its various shells are displaced to the left relative to the nucleus, as shown in Fig.3. We are clearly speaking here of electronic polarizability.
Fig. 3 Electronic polarization: (a) Unpolarized atom, (b) Atom polarized as a result of the field.
Electronic polarizability arises even in the case of a neutral atom, again because of the relative displacement of the orbital electrons.
In general, therefore, the total polarizability is given by
