Consider an ionic solid MX with the standard NaCl structure. Construct a new unit cell structure (Z) — Solid State Chemistry Question
Question
Consider an ionic solid MX with the standard NaCl structure. Construct a new unit cell structure (Z) following these sequential instructions: (i) Remove all anions (X) except the central one. (ii) Replace all face-centered cations (M) by anions (X). (iii) Remove all corner cations (M). (iv) Replace the central anion (X) with a cation (M). What is the ratio of (number of anions) / (number of cations) in Z?
💡 Solution & Explanation
Standard NaCl: M at corners(1) & faces(3) [Total M=4]; X at edges(3) & center(1) [Total X=4]. Step (i): Remove all X except central $\implies$ X only at center (1). Step (ii): Replace face M by X $\implies$ M at faces=0, X at faces=3. Now X is at center(1) + faces(3). Step (iii): Remove corner M $\implies$ M=0 entirely. Step (iv): Replace central X with M $\implies$ Center is now M(1), faces remain X(3). Final Z: M=1, X=3. Ratio X/M = 3/1 = 3.