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Question

Calcium crystallizes in face-centred cubic unit cell with a=0.556 nm. Calculate density
(i) if contained 0.1% Frenkel defect
(ii) it contained 0.1% Schottky defect.

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Solution

Theoretical density of the crystal is ρ=nMNoa3 g/cm3

Now, since in Frenkel Defect, there is no change in the theoretical density of the crystal because, in this defect, the only atom switches its position from lattice site to interstitial site.

So, ρ (with 0.1% Frenkel defect) =nMNoa3 g/cm3

a=0.056×107 cm ; M=40 g ; n=4 (For FCC)

ρ=40×46.022×1023×(0.056)3×(107)3=1.5455 g/cm3

Now, in case of Schottky defect, the density of the crystal changes because the atom leaves the crystal. So, in general for FCC, n=4

But, because o 0.1% Schottky defect, the value of n will change.

So, n=44×0.1100=3.996

ρnew=nMNoa3=3.996×406.022×1023×(0.556)3×(107)3=1.5440 g/cm3


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