E3 Ionic Point Defects

Topic

The ionic crystal of this ceramic intrinsically exhibits two types of point defects: the Schottky defect and the Frenkel defect. The fact that both defects appear intrinsically—that is, as part of the crystal structure itself at thermal equilibrium, rather than due to external impurities or introduced defects—means that their combined concentration ultimately determines the ceramic's ionic conductivity. We begin by discussing the Schottky defect.

The Schottky defect consists of the simultaneous absence of a cation and an anion, each missing from its respective lattice site; both ions leave the crystal—typically migrating to the surface—leaving behind two vacancies: one cationic and one anionic. Because both vacancies appear together, the Schottky defect preserves the crystal's electrical neutrality at all times.

In contrast, the Frenkel defect does not involve any ion leaving the crystal; instead, an ion—usually the cation, due to its smaller size—shifts from its regular lattice site to a nearby interstitial site, leaving a vacancy behind while simultaneously creating an occupied interstitial site. Since the ion moves within the crystal without exiting it, the Frenkel defect also maintains electrical neutrality, albeit through a mechanism different from that of the Schottky defect.

The simultaneous and independent occurrence of Schottky and Frenkel defects within the same ionic crystal means their concentrations combine into a single total concentration of intrinsic defects; the more Schottky and Frenkel defects coexist in the crystal, the higher this total concentration becomes. A higher total concentration of intrinsic defects results in higher ionic conductivity in the ceramic: each vacancy—whether cationic, anionic, or left by an ion that has migrated to an interstitial site—acts as an empty site into which a neighboring ion can jump; the more such empty sites exist within the crystal, the more easily ions can move through the lattice. Conversely, a lower total defect concentration results in lower ionic conductivity. It is precisely this ionic conductivity that is described in detail by another model in this set.

For this reason, the present model—which began by considering the intrinsic point defects of an ionic crystal—differs from the equivalent model for metals, where point defects do not involve cations or anions because metallic crystals are not composed of ions of opposite charge. Instead, this model informs the other model in the set that describes ionic conductivity: the ion transport through the crystal described by that other model depends precisely on the total concentration of Schottky and Frenkel defects established here.

ID:4386