SKEDSOFT
Description:
Many physical properties of crystalline solids are dependent on the direction of measurement or the planes across which the properties are studied. In order to specify directions in a lattice, we make use of lattice basis vectors a, b and c.
In general, any directional vector can be expressed as
R= n1a n2b n3c
where n1, n2 and n3 are integers. The direction of the vector R is determined by these integers. If these numbers have common factors, they are removed and the direction of R is denoted as [n1 n2 n3]. A similar set of three integers enclosed in a round bracket is used to designate planes in a crystal.
Lattice planes and Miller indices:
The crystal lattice may be regarded as made up of a set of parallel, equidistant planes passing through the lattice points. These planes are known as lattice planes and may be represented by a set of three smallest possible integers. These numbers are called βMiller indicesβ named after the crystallographer W.H.Miller.
Determination of Miller indices:
Consider a crystal plane intersecting the crystal axes as shown:
The procedure adopted to find the miller indices for the plane is as follows:
1. Find the intercepts of the plane with the crystal axes along the basis vectors a, band c. Let the intercepts be x, y and zrespectively.
2. Express x, y and z as fractional multiples of the respective basis vectors. Then we obtain the fractions,
x/a, y/b, z/c .
3. Take the reciprocal of the three fractions to obtain π/π±, π/π², /π³.
