Problem 17 - Entrance Test

Let's analyze the effect of each defect on crystal density: - **Schottky defect**: This defect involves an equal number of cations and anions missing from their lattice sites, essentially creating vacancies. Since ions (mass) are removed from the crystal lattice, the overall mass of the crystal decreases for a given volume, leading to a *decrease* in the density of the crystal. - **Frenkel defect**: This defect involves an ion leaving its lattice site and occupying an interstitial position within the same crystal. No ions leave the crystal lattice. Therefore, the overall mass and volume remain essentially constant, and thus, the density *does not change*. - **Interstitial defect**: This is a non-stoichiometric defect where extra atoms/ions occupy interstitial sites. This increases the total mass within the same volume, leading to an *increase* in density. - **Metal excess defect (due to interstitial cation)**: This is a specific type of interstitial defect. An extra cation occupies an interstitial site, and an electron occupies another interstitial site or is delocalized to maintain electrical neutrality. Since extra atoms (cations) are added, the mass increases for the same volume, leading to an *increase* in density. Therefore, the Schottky defect is the one most likely to decrease the density of an ionic crystal.