In an in ionic solid AB2O4, the oxide ions form CCP. 'A' and 'B' are metal ions in which one is biva — Solid State Chemistry Question
Question
In an in ionic solid AB2O4, the oxide ions form CCP. 'A' and 'B' are metal ions in which one is bivalent and another is trivalent (not necessarily in given order). If all the bivalent ions occupy octahedral holes and the trivalent ions occupy tetrahedral and octahedral voids in equal numbers, then the fraction of octahedral voids unoccupied is
💡 Solution & Explanation
The unit cell has 4 oxide ions (total charge -8). Charge balance requires positive charge of +8. This is met by one bivalent A2+ ion and two trivalent B3+ ions. The bivalent A2+ ion occupies 1 octahedral void. The two trivalent B3+ ions are equally split: 1 in a tetrahedral void and 1 in an octahedral void. Total octahedral voids occupied = 1 (by A2+) + 1 (by B3+) = 2. Since total octahedral voids = 4, the unoccupied fraction is (4 - 2) / 4 = 1/2.