  Volume integrals over the radial pair-distribution function, so-called
Kirkwood-Buff integrals (KBI) play a central role in the theory of solutions,
by linking structural with thermodynamic information. The simplest example is
the compressibility equation, a fundamental relation in statistical mechanics
of fluids. Until now, KBI theory could not be applied to crystals, because the
integrals strongly diverge when computed in the standard way. We solve the
divergence problem and generalize KBI theory to crystalline matter by using the
recently proposed finite-volume theory. For crystals with harmonic interaction,
we derive an analytic expression for the peak shape of the pair-distribution
function at finite temperature. From this we demonstrate that the
compressibility equation holds exactly in harmonic crystals.
