Miller Indices For Directions
Determine
the coordinates of the two points (Head and
Tail) in the direction.
Subtract the coordinates: Head Tail
Clear fractions to give lowest integer values for all
coordinates
Indices are written in square brackets wi
Factors that Determine Crystal Structure
1. Relative sizes of ions Formation of stable structures:
maximize the # of oppositely charged ion neighbors.

+



unstable
+


stable
2. Maintenance of
Charge Neutrality :
Net charge in ceramic
should be
a)
b)
c)
The perfect crystal in a) is cut and an extra plane of atoms is inserted
in b). The bottom edge of the extra plane is an edge dislocation in c).
A Burgers vector b is required to close a loop of equal atom spacings
around the edge dislocation.
Ed
Disadvantages in using Threeaxis coordinate system
Miller Indices of Equivalent Directions in Hexagonal Crystal System
z
<100> in Hexagonal = [100], [010], [110]
Not Permutations
y
[100]
[010]
[11 0]
x
Disadvantages in using Threeaxis coordinate system
Miller indices of Plane: Procedure to determine miller indices of plane: (1) Choose origin in
such a way which lies outside the plane of interest (choice of origin is arbitrary) (2) Find the
intercepts of the plane on the three co ordinate axes (3) Take r
One Dimensional Array of Points (Lattice)
a
Smallest Unit: line
Lattice parameter: a (length)
Two Dimensional Array of Points
a
b
Smallest Unit: polygon
Lattice parameter: a, b (length);
and (angle)
Some 2D lattices
Square Lattice
a=b; =90
Rectangular La