(a) Calculate the packing efficiency in body centered cubic lattice.
(b) What is Schottky defect?

Explanation

(a) In `Delta ABC`
`b^(2) = a^(2) + a^(2) :. b^(2) = 2a^(2)`,
In `Delta AGD`
`C^(2) = a^(2) + b^(2) = a^(2) + 2a^(2) :. C = sqrt(3)a`
Radius of the atom = r
Length of the body diagonal C = 4r
`sqrt(3)a = 4r, a = 4r/sqrt(3)`
Edge length of the cube = `a = 4r/sqrt(3)`
Volume of the cubic unit cell = `a^(3) = (4r/sqrt(3))^(3)`
Volume of one particle per unit cell of a BCC = 2
Total volume occupied by two spheres = ` 2 xx 4/3 pir^(3)`
Packing Efficiency = ` (4/3 pir^(3) xx 2)/(4/sqrt(3)r)^(3) xx 100 = (8/3 pir^(3))/(64/3sqrt(3)r^(3)) xx 100 = 68%`
(b)When equal number of cations and anions are missing from their lattice.sites, the defect is called Schottky defect.