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Agl crystallises in cubic close-packed ZnS structure. What fraction of tetrahedral sites are occupied by Ag+ ions?

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Question

Agl crystallises in cubic close-packed ZnS structure. What fraction of tetrahedral sites are occupied by Ag+ ions?

Numerical
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Solution

In the ZnS (zinc blende) structure, the anions (I) form a cubic close-packed (ccp) lattice, and the cations (Ag+) occupy the tetrahedral voids.

In a ccp arrangement the number of tetrahedral voids is twice the number of anions present.

If the number of I ions is n, then the number of tetrahedral voids is 2n and Number of Ag+ ions is n.

Fraction of tetrahedral voids occupied:

= `n/(2n)` 

= `1/2`

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