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Miller indices and crystal directions. ?. How to describe a particular crystallographic plane and direction. not necessarily of equal length. Primitive translation vectors a 1 , a 2 , a 3 :. not necessarily right angles. Determine the intercepts of the face along the crystallographic axes,
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Miller indices and crystal directions ? How to describe a particular crystallographic plane and direction not necessarily of equal length Primitive translation vectors a1, a2, a3 : not necessarily right angles • Determine the intercepts of the face along the crystallographic axes, • in terms of unit cell dimensions n1,n2,n3 here 1,3,1 Miller indices(h,k,l) specify set of equivalent planes • Take the reciprocals 1/n1,1/n2,1/n3 here 1,1/3,1 here 3,1,3 • Clear fractions with the smallest possible integer
example for a plane that cuts the a-axis at • negative intercept is denoted by a bar : • the symbol denotes all planes equivalent to (h,k,l)
Set of four Miller indices for hexagonal crystals first three Miller indices add up to zero
T=n1a1+n2a2+n3a3 Lattice vector: [n1 n2 n3] If have a common factor, the latter is removed Crystal directions [n1 n2 n3] direction defined by E.g., [111] instead of [222] Note: [hkl] is in general not normal to the (hkl) plane
