Elements of crystallography

Simple bodies, inorganic molecules (usually ionic: ClNa, CO₃Ca, etc.) and organic molecules (neutral or in the form of salts) exist in the solid state in the form of crystals characterized by long-range order. This translates into the repetition in three-dimensional space of a pattern of atoms, ions or molecules, which, from a mathematical point of view, translates into a translation operation. A comprehensive understanding of polymorphism and crystal morphology requires an in-depth study of crystallography as the science of the spatial organization of atoms, ions and molecules (see box).