a reciprocal lattice point

Every dot in the reciprocal lattice is a reciprocal lattice point, and each one carries a three-integer name (hkl). Here is the single most important thing to hold onto: one point does NOT stand for one atom, or one plane, or one direction. It stands for a whole FAMILY of parallel, equally spaced crystal planes — the (hkl) planes — squeezed down into a single dot. The reciprocal lattice is, in effect, a catalogue in which every entry is one family of planes.

The dot encodes two facts about that family of planes, and it does so geometrically. First, the DIRECTION from the origin out to the point (hkl) is the direction of the plane normal — the way the planes face. Second, the DISTANCE from the origin to the point is 1/d_hkl, the reciprocal of the interplanar spacing. So a family of tightly packed planes (small d) is represented by a far-out point, and loosely packed planes (large d) by a point close in. Reading a reciprocal lattice point is therefore reading, at a glance, both the orientation and the spacing of a set of real planes.

This is exactly why a diffraction pattern is so informative: each recorded spot IS a reciprocal lattice point, so its position on the film tells you the orientation and spacing of the planes that produced it. Be careful about one thing, though — a reciprocal lattice point and a real-space direction can share the numbers (hkl) and (uvw) yet mean different things, and only in the cubic system does the direction [hkl] happen to be perpendicular to the plane (hkl). The reciprocal lattice makes the plane-normal relationship true in EVERY crystal system, which is a large part of its power.