Presentation on theme: "Miller indices and crystal directions"— Presentation transcript:
1 Miller indices and crystal directions How to describe a particular crystallographic plane and direction?not necessarily of equal lengthPrimitive translation vectors a1, a2, a3 :not necessarily right anglesDetermine the intercepts of the face along the crystallographic axes,in terms of unit cell dimensionsn1,n2,n3here 1,3,1Miller indices (h,k,l)specify set ofequivalent planesTake the reciprocals1/n1,1/n2,1/n3here 1,1/3,1Clear fractions with the smallest possible integerhere 3,1,3
5 Set of four Miller indices for hexagonal crystals first three Miller indices add up to zero
6 Crystal directionsLattice vector:T=n1a1+n2a2+n3a3direction defined by[n1 n2 n3]If[n1 n2 n3]have a common factor, the latter is removedE.g.,  instead of Note: [hkl] is in general not normal to the (hkl) plane
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