Faces and directions joining atoms in crystals can be best described by Miller Indices (in the names of W. H. Miller ) ascribed to determine various planes and directions. While planes are determined little empirically, directions are nothing but vectors.
1.1.8.1 Crystallographic Planes
Identification of various faces seen on the crystal
( h.k.l ) for a plane or {h..k.l} for identical set of planes
A crystallographic plane in a crystal satisfies the following equation
(1.1)
h/a, k/b, and c/l are the intercepts of the plane on x, y, and z axes.
a, b, c are the unit cell lengths
h, k, l are integers called Miller indices and the plane is represented as (h, k, l)
Any negative indices in Miller indices of a plane is written with a bar on top such as .
1.1.8.2 Directions
These are basically atomic directions in the crystal.
Miller indices are [ u , v , w ] for a direction or < u , v , w > for identical set of directions where u , v , w are integers
Vector components of the direction resolved along each of the crystal axis reduced to smallest set of integers
Figure 1.8(a) Planes and Directions in Crystals
Crystal Directions
How to locate a direction:
Example: [231] direction would be
1/3 intercept on cell a-length
1/2 intercept on cell b-length and
1/6 intercept on cell c-length
Directions are always denoted with [ uvw ] with square brackets and family of directions in the form < uvw >
Figure 1.8(b) Planes and Directions in Crystals
We will not go into too much details of this assuming that you would know about planes and directions in a crystal. If you are not sure, then refer to any elementary materials science text book on structure of materials (see bibliography) or else refer to other NPTEL modules.
.
