1. MILLER INDICES INTRODUCTION OF MILLER INDICES DETERMINE MILLER INDICES OF PLANES DETERMINE MILLER INDICES SALIENT POINTS OF MILLER INDICES MILLER-BRAVAIS INDICES

4. Two Methods for Determining Miller Indices • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Method 1: Single Plane. • choose plane of interest. • plane intercepts a at 22/3 • intercepts b at 4 • intercepts c at ∞ • invert: 3/8 ¼ 0 • multiply by common denominator (x8) • Miller Index: (3 2 0) b • a origin 4 b 22/3 a

5. Two Methods for Determining Miller Indices • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Method 2: Parallel Planes. • draw unit cell and all parallel planes going through the cell. • a axis cut into 3 equal parts. • b axis cut into 2 equal parts. • c axis not cut at all. • Miller Index: (3 2 0) b a origin

6. DETERMINE THE MILLER INDICES OF PLANES • The given values are ( h k l ). These are the miller indices with respect to x, y, z axes respectively. • Take reciprocal of these Miller Indices and the value will be of Intercepts along x, y and z axes respectively. As : • p = 1 / h q = 1 / k r = 1 / l • Convert them with respect to linear vectors or linear dimensions of unit cell i.e. with respect to a, b, c along x, y and z axes respectively. • Choosing origin, mark the intercepts and join them to draw the plane.

8. Salient Points of Miller Indices ♦ Miller Indices of parallel planes are same. ♦ For parallel planes, Miller Indices value will be zero as they intercepts at infinity and reciprocal of infinity is zero. ♦ The plane passing through origin will have non-zero miller indices. ♦ Any two planes will perpendicular if : h1 . h2 + k1 . k2 + l1 . l2 = 0 ♦ When Miller Indices contains more than single digits, they can be separated by commas or spaces. ♦ All members of a family of planes may not be parallel to each other.

9. MILLER-BRAVAIS INDICES An alternate indexing system, which has four numbers in each set of indices, is often used for hexagonal crystal. The indices are called miller-bravais indices. • Transformation between 3-index [uvw] and 4-index [hkil] notations on solving these equation u=(2h+k) V=(2k+h) W=l

10. a3 a2 a1 Hexagonal crystals → Miller-Bravais Indices Intercepts → 1 1 - ½  Plane → (1 12 0) (h k i l) i = (h + k) The use of the 4 index notation is to bring out the equivalence between crystallographicallyequivalent planes and directions

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