MILLER INDICES - SIGNIFICANCE

Crystal planes :

Crystal planes are defined as imaginary planes inside a crystal lattice passing through the atoms along x, y and Z directions. 
These planes are represented as XY, YZ, ZX and XYZ planes. We cannot find a single plane in a crystal lattice but set of parallel planes are observed.

Miller indices:

Miller indices are defined as the reciprocals of intercepts of crystal plane. They are used to represent the direction of crystal planes. Miller indices are denoted as the coordinates ( h, k, l ) .
h : k : l = 1/p : 1/q : 1/r
Miller indices represent the structure of unit cell.

Procedure to find Miller indices:

1. Identify the plane intercepts on the x, y and z-axes.
2. Represent intercepts in fractional coordinates as ( p, q, r)
3. Take the reciprocals of the fractional intercepts h : k : l = 1/p : 1/q : 1/r
4. convert the small fractions into integers by multiplying with their least common factor LCM.

Significance of Miller indices :

Miller indices represent a set of parallel planes.
1.They do not represent a single plane.
2.If any plane is parallel to an axis, then the intercept of the plane is infinity on that axis. The reciprocal value is Miller index and it is equal to zero.
3. When a Miller index is smaller, the plane is more parallel to that axis.
4. When a Miller index is bigger, the plane is more perpendicular to that axis.
5. generally Miller index is consider as 1 and if the intercept is infinity ,then the Miller index is equal to 0.

Example. If a plane is parallel to Y axis then the Mille indices are
 ( 1,0,1)
(1,1,0) : plane parallel to Z axis.

(0,0,1) pane passes through Z axis only.

The relation between miller-indices and interplanar spacing is

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