Chapter 5
Solid State Physics
5.1 Basic Concepts and Formulae
Crystal Structure
There are seven crystal systems Cubic, Tetragonal, Orhtorhombic, monoclinic, triclinic, Rhombohedral, Hexagonal. They are distinguished by the axial lengths and
axial angles. The lengths are taken as a, b and c. In the cubic system a = b = c and
the angle between any two axes is a right angle.
Bragg’s equation
2d sin θ = nλ
(5.1)
where d is the distance between parallel diffraction planes, θ is the angle between
the incident beam and the diffraction plane and n is the order of diffraction. The
distance d can be related to the lattice parameters of the crystal cell. In the simple
cubic cell the distance between (100) planes is “a”, the lattice parameter. The distance between parallel (110) planes passing through lattice points is a/
√
2; for (111),
it is a/
√
3. In general distance between parallel planes of indices (hkl) in terms of
the parameter “a” for the cubic system is
d
2
=
a
2
h 2 + k 2 + l 2
(5.2)
Electrical properties of crystals
The principal attractive force between ions of opposite sign is an electrostatic force.
The repulsive force arises from the interaction of the electron clouds surrounding an
atom. This force arises because of the exclusion principle and is not electrostatic in
nature. Empirically this is represented by b/r
n , where b and n are constants, and r
is the anion-cation distance.
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