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Unformatted text preview: mobile ions can conduct current.
Once the cation and anion have formed, there is an electrostatic attraction between them. This
attractive force increases as the ions come closer to each other. However when the ions get too
close to each other, their electronic clouds start to overlap and a repulsive force arises. At any
given distance apart, there is a net force between the ions that is the sum of the attractive and
4.5 Crystalline Solids
Atoms of a solid will arrange into a configuration that has the lowest free energy, which is
determined by many factors including atomic radius, and electron configuration. Often the
equilibrium configuration is a crystal. In a crystalline solid the atoms are arranged in a repeating
unit that has long-range order. The crystal structure of a material is based on the crystal lattice,
which is an array of points in space. This array of points is not arbitrary but has repeating angles
and dimensions between points and must fill three-dimensional space with no gaps. Each lattice
point may have one or more atoms, ions or molecules associated with it, called a basis.
The smallest group of lattice points that that repeats in space is called the unit cell. The unit cell
has all the properties found in the bulk crystal. The geometry and the arrangement of lattice
points define the unit cell. By translating the unit cell in three dimensions the entire crystal
structure is formed.
The geometry of a unit cell can be represented by a parallelepiped with lattice parameters a, b,
and c and angles α, β, and γ. By varying the lattice parameters and angles, seven distinct crystal
systems can be formed. The seven crystal systems are cubic, tetragonal, orthorhombic,
hexagonal, rhombohedral, monoclinic, and triclinic. There are 14 ways to place the lattice points
in these systems to create Bravais lattices. Most of the metals, ionic salts, and semiconductors
studied in this course are members of the cubic crystal system.
The cubic crystal system has lattice parameters a = b = c and angles α = β = γ =90°. Therefore,
the lattice parameter is referred to as a, and the angles are ignored. The three Bravais lattices
associated with the cubic system are simple cubic (SC - sometimes called primitive cubic), body
centered cubic (BCC), and face centered cubic (FCC). SC has a lattice point (basis) at each of the
cube corners. BCC has lattice points at its corners and one in the center of the cube. FCC has
lattice points at the corners and one point on each of the cube face centers.
The basis is the atoms that are at each lattice points to build the crystal structure. Every lattice
point has the exact same basis. Many of the metallic elements form solids that have one atom per
lattice point. Some structures have more than one atom or ion associated with a lattice point.
Typical examples of this are CsCl, NaCl, Si, and GaAs.
For a crystal system with one atom per basis an important value is the a/r ratio, which is the cube
side (a) divided by the atomic radius (r). It can be determined from the geometry of the crysta...
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- Spring '08