Читать книгу Solid State Physics - Philip Hofmann - Страница 37

Two different forces must be present to establish bonding in a solid or in a molecule. An attractive force is necessary for any bonding. Different types of attractive forces will be discussed in the following sections. A repulsive force, on the other hand, is required in order to keep the atoms from getting too close to each other. A simple expression for an interatomic potential can thus be written as

(2.1)

where is the distance between the atoms and – that is, the repulsive part has to prevail for short distances (sometimes, this is achieved by assuming an exponential repulsion potential). Such a potential and the resulting force are shown in Figure 2.1. The reason for the strong repulsion at short distances is the Pauli exclusion principle. For a strong overlap of the electron clouds of two atoms, which will occur at short distances, the wave functions have to change in order to become orthogonal to each other, because the Pauli principle does not allow more than two electrons to exist in the same (spatial) quantum state. This orthogonalization requires much energy, hence the strong repulsion.

Figure 2.1 (a) Typical interatomic potential for bonding in solids according to Eq. (2.1) with and . (b) Resulting force, that is, .