Universal compressibility behaviour of ions in ionic crystals

The theory of atoms in molecules leads to a convenient partition of the crystalline space into atomic regions that are space filling and allow a decomposition of the bulk compressibility of a crystal as a volume-weighted sum of local compressibilities. Using available ab initio calculations for the complete alkali halides (AX) family in the rock salt phase and some selected spinels, we find that the pressure at the limit of stability of the crystal matches exactly those of the individual ions (or group of ions), pointing to the conclusion that the ionic volumes at the equilibrium define the relative compressibilities of the ions (or group of ions) in the crystal at all pressures. We also analyse the functional dependence between the ionic compressibilities and volumes for the AX family. We show that these ions exhibit universal behaviour when the local bulk moduli are correlated with the pressure referred to the spinodal pressure value, instead of volume. This fact allows us to define a generalised equation of state for the individual ions based on the spinodal instability hypothesis.