 The (hkl)
plane can be drawn as shown here. The (hkl)
plane makes intercepts a/h, b/k and c/l
on the x, y
and z axes as shown. Since another plane in
the family passes through the origin, the interplanar spacing dhkl is the length of the normal OP to the plane. Since the reciprocal
vector ghkl is
also normal to the plane (hkl), it is
parallel to OP. A unit vector in this
direction, p, is therefore given by:
- p = g
/ |g|
The length of OP is the projection
of OX in the direction of p, so:
Since a*. a = l and b*. a
= c*. a = 0:
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