Crystal Structure 1 3.1 Some Basic Concepts of Crystal Structure ...

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Crystal Structure Bragg Diffraction and Reciprocal Lattice Vectors 10
Crystal Structure Next we discuss the physical meaning of reciprocal lattice vectors as defined in eqn. 3.6. Consider the primitive vectors, a, b and c of a lattice as depicted below. We first focus on the plane (100) as marked in the figure. One may observe that the area of this plane is |a b| and the cross product a b is normal to the plane and directed away from the origin. In addition, the volume of the parallelepiped generated by a, b and c, which we label by V abc is a (b c) (= b (c a) = c (a b)). It follows that the distance between this plane the one next and parallel to it is: Vabc a b c d100 . b c b c (3.7) Therefore, the reciprocal lattice vector, A, as defined in eqn. 3.6 can be rewritten as: b c 1 A 2 2 nˆ 100 d (3.8) a b c 100 where n 100 is the unit vector normal to (100) (and directed away from the origin.) By repeating the argument for the other two planes, i.e., (010) and (001), we have: B C 1 2 nˆ d 010 1 2 nˆ d 001 010 001 (3.9) where n 010 and n 001 is the unit normal to (010) and (001), respectively. 11
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Crystal Structure 1 3.1 Some Basic Concepts of Crystal Structure ...

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