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Question

Compute the percentage void space per unit volume of unit cell in zinc-fluride structure. In zinc fluoride, anions occupy

fcc positions and half of the tetrahedral holes are occupied by cations.


A

25%

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B

30%

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C

40%

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D

20%

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Solution

The correct option is A

25%


Since anions occupy fcc positions and half of the tetrahedral holes are occupied by cations. Since there are four anions and 8 tetrahedral holes per

unit cell, the fraction of volume occupied by spheres/unit volume of the unit cell is

=4×(43πr3a)+12×8×(43πr3c)162r3a = π32{1+(rcra)3}

for tetrahedral holes,
=rcra=0.225
=π32{1+(0.225)3}=0.7496
Void volume = 1-0.7496 = 0.2504/unit volume of unit cell % void space = 25.04%


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