First slide

Crystal lattices and unit cells

Question

In a CPS (Closed Packed Structure) of mixed oxides, it is found that lattice has O^2- (oxide ions) and one-half of octahedral voids are occupied by trivalent cations (A³⁺) and one-eight of tetrahedral voids are occupied by divalent cations (B²⁺). Based on derived formula of the mixed oxide the correct statements will be

Moderate

A

number of trivalent cations = ½
B

composition of oxide is A₂BO₄
C

number of dipositive cations = ¼
D

no. of tetrahedral voids are 4

Solution

Number of octahedral voids per ion in lattice = 1
Hence, number of trivalent cations (A³⁺)=1× $\frac{1}{2} = \frac{1}{2}$
Number of tetrahedral voids per ion in lattice = 2
Hence, Number of divalent cations (B²⁺) = 2 × $\frac{1}{8} = \frac{1}{4}$
Thus, formula is $A_{1 / 2} B_{1 / 4} O$ or $A_{2} {BO}_{4}$ .

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