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Miller indices and crystal directions How to describe a particular crystallographic plane and direction ? Primitive translation vectors a 1, a 2, a 3 :

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Presentation on theme: "Miller indices and crystal directions How to describe a particular crystallographic plane and direction ? Primitive translation vectors a 1, a 2, a 3 :"— Presentation transcript:

1 Miller indices and crystal directions How to describe a particular crystallographic plane and direction ? Primitive translation vectors a 1, a 2, a 3 : not necessarily of equal length not necessarily right angles Determine the intercepts of the face along the crystallographic axes, in terms of unit cell dimensions n 1,n 2,n 3 here 1,3,1 Take the reciprocals 1/n 1,1/n 2,1/n 3 here 1,1/3,1 Clear fractions with the smallest possible integer here 3,1,3 Miller indices (h,k,l) specify set of equivalent planes

2 Simplified example for cubic system

3 negative intercept is denoted by a bar : the symboldenotes all planes equivalent to (h,k,l) example for a plane that cuts the a-axis at

4

5 Set of four Miller indices for hexagonal crystals first three Miller indices add up to zero

6 Crystal directions Lattice vector: T=n 1 a 1 +n 2 a 2 +n 3 a 3 direction defined by [n 1 n 2 n 3 ] If [n 1 n 2 n 3 ] have a common factor, the latter is removed E.g., [111] instead of [222] Note: [hkl] is in general not normal to the (hkl) plane


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