Solid State Chemistry
Solid State Chemistry: Solids may be classified into different types such as crystalline, amorphous, glassy and so on. At low temperatures and high pressures, most substances condense into a solid state. The formation of a solid is a consequence of a variety of intermolecular forces such as ionic, covalent as well as non-covalent (such as van der Waals forces). In this lecture we will classify crystalline solids into various types of lattice structures and give examples of each type. We will also estimate lattice energies of ionic crystals.
The variety and beauty of patterns in crystals is due to the presence of repeating units. The repeating units extend periodically in three dimensional space giving a space filling structure. The structurally repeating unit may be a group of one or more atoms, molecules or ions. If each one of these units is represented by a point, a space filling pattern can be obtained by regularly repeating this unit in three dimensions. This space filling pattern is called a space lattice or a crystal lattice or a Bravais lattice. Bravais showed in 1875 that there can be only 14 distinct lattices in three dimensions. Each point of a Bravais lattice can be associated with a unit cell, which is an imaginary parallelopiped (i.e., a figure with parallel sides) that contains one unit of the translationally repeating pattern.
The fourteen Bravais lattices can be grouped into seven crystal systems by using the symmetry properties of unit cells, as well as by the relations between the sides and angles of the unit cell. Consider two unit cells as shown below.
Figure 1 Unit cells. Sides are a, b and c and the angles are (between b and c in the bc plane), (in the ac plane,between a and c) and (between a and b in the ab plane. (a) cubic unit cell, (b) non-cubic unit cell
In a cubic crystal system (formed from cubic unit cells placed at the lattice points) there are four C3 axes placed in a tetrahedral arrangement. In Fig 1(a) the line joining the points 3 and 5, for example is a C3 axis. What this means is that if the unit cell/crystal is rotated by 120o, 240o and 360o (three angles, multiples of 120o), we get an arrangement which is indistinguishable from the original arrangement. Having only a C1 axis is as good as having no symmetry at all because every object has a C1 axis of symmetry, i.e., if you rotate it with respect to any axis by 360o, you will recover the original arrangement. A triclinic crystal has no symmetry or has only a C1 symmetry axis.
The symmetry elements of the seven crystal systems are given in Table 1
Table 1 Essential symmetries of the seven crystal systems.
Table 1 seven crystal systems or Bravais unit cells.