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  Lattice Vectors     13 of 18
Any lattice vector r in a real lattice can be written as:
r = n1a + n2b + n3c  

where ni are integers and a, b and c are the unit vectors describing the lattice.

These real space lattice vectors correspond to directions in the crystal. The lattice vector can also be written as:

r = ua + vb + wc

where u, v and w are the components of the direction index [uvw].

Lattice vector image
Reciprocal lattice vectors image A reciprocal lattice vector can be defined in the same way:
r* = m1a* + m2b* + m3c*  

where mi are integers and a*, b* and c* are the reciprocal unit vectors.

This is more commonly written:

ghkl = ha* + kb* + lc*  

where h, k, l are the Miller indices of the plane (hkl).

Questions imageWhich one of the statements about real and reciprocal  lattice vectors below is true?

The components u, v, and w of a vector ruvw in real space give the plane index (uvw).

The components h, k and l of the reciprocal vector ghkl in reciprocal space give the direction index [hkl].

The reciprocal vector ghkl in the reciprocal lattice is always perpendicular to the plane (hkl) in the real lattice.



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