Question

{"given":"Four types of crystal defects are provided: Frenkel defect, Schottky defect, metal excess defect due to excess cation, and interstitial defect. We need to determine which defect lowers the crystal density when present.","key_observation":"Crystal density is defined as mass per unit volume (ρ = m/V). To lower density, either the mass must decrease while volume stays constant, or volume must increase while mass stays constant. Among the given defects, only Schottky defect involves the removal of ions from the crystal lattice, which reduces the total mass while maintaining approximately the same lattice volume, thereby decreasing the overall density.","option_analysis":[{"label":"(A)","text":"Frenkel","verdict":"incorrect","explanation":"In Frenkel defect, an ion moves from its normal lattice site to an interstitial position. No ions are removed from the crystal, so the total mass remains constant while volume may slightly increase. This typically has minimal effect on density."},{"label":"(B)","text":"Schottky","verdict":"correct","explanation":"In Schottky defect, equal numbers of cations and anions are removed from their lattice sites, creating vacancies. This reduces the total mass of the crystal while the volume remains approximately the same, resulting in lower density."},{"label":"(C)","text":"Metal excess defect due to excess cation","verdict":"incorrect","explanation":"This defect involves addition of extra cations to interstitial sites or creation of anionic vacancies with excess electrons. The presence of extra cations increases the total mass, which increases the density rather than decreasing it."},{"label":"(D)","text":"Interstitial defect","verdict":"incorrect","explanation":"Interstitial defect involves placing extra atoms or ions in the interstitial spaces of the crystal lattice. This adds extra mass to the crystal without proportional volume increase, resulting in higher density rather than lower density."}],"answer":"(B)","formula_steps":[]}