In a close packed face-centred unit cell, are all lattice positions occupied by 'A' atoms and body-centred octahedral hole is occupied by atom 'B' having appropriate size. Choose the correct statement(s) regarding such crystal.

Options

A. void percentage is 24.6
B. percentage space occupied is 80.3
C. formula of the compound is `A_(2)B_(3)`
D. formula of the compound is AB

Answer

A

Explanation

Radius of octahedral voids=`0.414r_(A)`, where `r_(A)` is the radius of atom A.
Only the octahedral void at the body centre is occupied by sphere.
Hence, volume of sphere occupying void=`(4)/(3)pi(0.414r_(A))^(3)=(4)/(3)pixx0.071r_(A)^(3)`
Total volume of sphere forming the unit cell`=4xx(4)/(3)pir_(A)^(3)`
Packing fraction`=(4xx(4)/(3)pir_(A)^(3)+(4)/(3)pixx0.071r_(A)^(3))/(a^(3))(sqrt(2)a=4r,a=(4r)/(sqrt2))`
On solving we get packing fraction=0.754=75.4%.