Validity of the compressibility equation and Kirkwood-Buff theory for crystalline matter

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