Elements of Modern Physics
256
The description of the properties of solids is an important application of the
quantum principles to a collection of a large number of particles arranged in
order. Many of the solids are in a crystalline form, associated with a lattice. A
lattice is obtained by an infinite, regular repetition, in space, of basic units. In a
perfect crystal, the atoms are arranged according to a pattern in each unit, and
the pattern is repeated for all the units. Our concern will be mainly with such
crystals, e.g., sodium chloride, diamond, etc. This leaves out some important
substances, such as amorphous solids which have some short-range order but
no long-range order (e.g., glass, amorphous semiconductors etc.), and others
like wood, plastics, etc. which have huge molecules. Furthermore, most
crystalline materials are usually a collection of small crystals packed together,
and even the single crystals may have some disorder introduced by an impurity
or a missing atom. These disorders play an important role in determining their
properties.
The forces which bind the atoms in solids, and the structure of solids are
considered first. The energy levels in solids are significant and often decisive in
determining their electromagnetic properties, and lead to important applications.
After considering the band structure of energy levels in solids, in particular,
semiconductors, some aspects of magnetic and dielectric properties of solids
are discussed.
8.1 BINDING FORCES IN SOLIDS
The binding forces between the atoms in a solid are electromagnetic in origin.
It is the valence electrons of the constituent atoms and the quantum effects
which are important in determining the details of these forces. The binding
forces are similar to those in molecules though the many-particle effects bring
in some new aspects. We briefly discuss the different types of bonds in solids.
In a real solid, more than one of these bonds may contribute to the binding of
the atoms.
Ionic Bonds
As in the case of molecules, these bonds are formed when it is energetically
favourable for a valence electron to be transferred from one atom to another
resulting in a net electrostatic attraction between the ions. However, in the solid
there are many more ions and the electrostatic interaction of an ion with all the
other ions should be taken into account. This is done by writing the electrostatic
energy per ion pair as
V el =
2
0
4
e
R
α
− πε
(8.1)
256
The description of the properties of solids is an important application of the
quantum principles to a collection of a large number of particles arranged in
order. Many of the solids are in a crystalline form, associated with a lattice. A
lattice is obtained by an infinite, regular repetition, in space, of basic units. In a
perfect crystal, the atoms are arranged according to a pattern in each unit, and
the pattern is repeated for all the units. Our concern will be mainly with such
crystals, e.g., sodium chloride, diamond, etc. This leaves out some important
substances, such as amorphous solids which have some short-range order but
no long-range order (e.g., glass, amorphous semiconductors etc.), and others
like wood, plastics, etc. which have huge molecules. Furthermore, most
crystalline materials are usually a collection of small crystals packed together,
and even the single crystals may have some disorder introduced by an impurity
or a missing atom. These disorders play an important role in determining their
properties.
The forces which bind the atoms in solids, and the structure of solids are
considered first. The energy levels in solids are significant and often decisive in
determining their electromagnetic properties, and lead to important applications.
After considering the band structure of energy levels in solids, in particular,
semiconductors, some aspects of magnetic and dielectric properties of solids
are discussed.
8.1 BINDING FORCES IN SOLIDS
The binding forces between the atoms in a solid are electromagnetic in origin.
It is the valence electrons of the constituent atoms and the quantum effects
which are important in determining the details of these forces. The binding
forces are similar to those in molecules though the many-particle effects bring
in some new aspects. We briefly discuss the different types of bonds in solids.
In a real solid, more than one of these bonds may contribute to the binding of
the atoms.
Ionic Bonds
As in the case of molecules, these bonds are formed when it is energetically
favourable for a valence electron to be transferred from one atom to another
resulting in a net electrostatic attraction between the ions. However, in the solid
there are many more ions and the electrostatic interaction of an ion with all the
other ions should be taken into account. This is done by writing the electrostatic
energy per ion pair as
V el =
2
0
4
e
R
α
− πε
(8.1)