The fraction of voids occupied in the inverse | vedclass

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Question

(A) The general formula for inverse spinel is $B(AB)O_4$,where $O^{2-}$ ions form a $ccp$ lattice.In inverse spinels,the divalent $A^{2+}$ ions occupy

Vedclass · Accepted Answer

$1/8^{th}$ of tetrahedral voids and $1/2$ of octahedral voids.

Vedclass · Answer

(A) The general formula for inverse spinel is $B(AB)O_4$,where $O^{2-}$ ions form a $ccp$ lattice.In inverse spinels,the divalent $A^{2+}$ ions occupy octahedral voids.The trivalent $B^{3+}$ ions are distributed such that half of them occupy tetrahedral voids and the other half occupy octahedral voids.Since there are $2$ tetrahedral voids and $1$ octahedral void per $O^{2-}$ ion in a $ccp$ lattice,for $4$ $O^{2-}$ ions,there are $8$ tetrahedral voids and $4$ octahedral voids.Thus,$B^{3+}$ ions occupy $1/8$ of the $8$ tetrahedral voids (i.e.,$1$ ion) and $1/4$ of the $4$ octahedral voids (i.e.,$1$ ion),while $A^{2+}$ occupies the remaining $1/4$ of octahedral voids (i.e.,$1$ ion).

The fraction of voids occupied in the inverse spinel compounds are

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