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The metal calcium crystallises in a face...

The metal calcium crystallises in a face centred cubic unit cell with a = 0.556 nm. Calculate the density of the metal if
(i) it contains `0.2%` Frenkel defects
(ii) it contains `0.1%` Schottky defects.

Text Solution

Verified by Experts

Frenkel defects do not change the theroetical value of density because the atoms is only occupying an interstitial position instead of lattice position. But in case of Schottky defect
`z = 4xx(1-(0.1)/(100))=3.996`
Density `(rho)=(z xxM)/(N_(o)xx a^(3))`
(i) `a=0.556 nm = 0.556xx10^(-9)m = 0.556xx10^(-7)cm`
`rho` (with Frenkel defect) `= (4xx40)/(6.023xx10^(23)xx(0.556xx10^(-7))^(3))`
`= 1.5463 g//cm^(3)`
(ii) `rho` (with Schottky defect) `= (3.996xx40)/(6.02xx10^(23)xx(0.556xx10^(-7))^(3))`
`= 1.5448 g//cm^(3)`.
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