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Calcium crystallizesin fcc unit cell wit...

Calcium crystallizesin `fcc` unit cell with `0.556 nm`. Calculate the density if
a. It contains `0.2%` Frenkel defects
b. It contains `0.1%` Schottky defects

Text Solution

Verified by Experts

a. Frenkel defects do not change the value of the theoretical density because the atom is occupying an interstitial position instead of a lattice position.
b. `Z_(eff)` of `Ca = 4` atom/unit cell (since it is `fc c` type)
Since there are `0.1%` Schottky defects,
So `Z_(eff) = (4 - (0.1)/(100) xx 4) = 3.996`
`:. rho = (Z_(eff) xx Aw)/(N_(A) xx a_(3)) ( :' 1nm = 10^(-9) m = 10^(-7) cm)`
`= ((3.996) xx 40 g)/((6 xx 10^(23) mol^(-1))(0.556 nm xx 10^(-7) cm)^(3))`
`= 1.547 g cm^(-3)`
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