Lattice Defect Phenomena and Diffusion Processes in Ionic, Covalent, and Metallic Crystals

Abstract

Chemists have known for a long time that many inorganic chemical compounds, e.g., the oxides (Cu2O, FeO, NiO, etc.) and sulfides (Cu2S, Ag2S, NiS, etc.) and intermetallic phases in alloy systems do not have a stoichiometric composition, but rather exhibit a more-or-less large excess or deficit of one or another of the constituent components of the crystal. In such cases, the fact that the crystal lattice is not ideally filled is easily understandable. However, there are also compounds with stoichiometric composition, e.g., the alkali and silver halides, which can exhibit considerable disorder in their lattice site occupation, as we shall see later. It can be said, in general, that these lattice building blocks (atoms and ions) leave their lattice sites with increasing frequency as the temperature increases and go either to an interstitial lattice site or, if this is not possible for spatial energetic reasons, “break out” to the surface and leave behind an unoccupied lattice site, which serves again as an empty site, which can be occupied, in turn, by particles lying deeper in the interior. Thus, the unoccupied lattice site (vacancy) moves toward the interior, while the ions migrate to the surface. A condition of equilibrium is obtained when the particle and vacancy currents, which are in opposite directions, are of equal magnitude. At constant pressure or volume and constant crystal composition, the concentration of the lattice defects is determined solely by the temperature. In succeeding sections, we group the above events following Frenkel1, Jost2, and Schottky and Wagner3,4 under the term lattice defect phenomena.