the reciprocal cell volume

Just as the real unit cell encloses a volume V (say, in cubic angstroms), the reciprocal unit cell encloses a volume too, written V*. Because reciprocal lengths are inverse lengths, this volume is measured in inverse-cubic units (angstrom^-3), and it turns out to be one of the simplest, most memorable relations in the whole subject.

The relation is V* = 1/V (in the crystallographers' 1/d convention). That is it: the volume of the reciprocal cell is the reciprocal of the real cell's volume. A roomy real cell of 100 angstrom^3 has a cramped reciprocal cell of 0.01 angstrom^-3; a tiny real cell has a sprawling reciprocal cell. This falls straight out of the star definitions, because V* = a* . (b* x c*) = 1/[a . (b x c)] = 1/V. (In the 2 pi physics convention the same result reads V* = (2 pi)^3/V, since each star vector carries a factor 2 pi.)

This little formula is the sharpest statement of the inverse-size relationship, and it has teeth. A crystal with a large unit cell — a protein, a zeolite, a complex intermetallic — has a small reciprocal cell, meaning its reciprocal lattice points are packed close together, so its diffraction spots crowd tightly and you need fine angular resolution to separate them. A simple metal with a tiny cell throws its spots far apart. The reciprocal volume also appears as a normalising factor in electron-density calculations and in counting states per unit volume of reciprocal space, so it is not just a curiosity — it is a working constant.