(a) Calculate the number of particles in Face Centred Cubic (FCC) lattice.
(b) What is Frenkel defect? What is its effect on the density of a solid?

Explanation

(a) Let .a. : be the edge length of the cube
’b. : be the face diagonal
’r’: is the radius of the sphere b= 4r
In `Delta` ABC
`b^(2) = a^(2) + a^(2)`
`b^(2) = 2a^(2)`
`b = sqrt(2)xx a
`4r= sqrt(2)xx a, a =`4/sqrt(2)r`,a=`2sqrt(2)r`
• Volume of the cube = `a^(3) =(2sqrt(2)r)^(3)`
• Each unit cell of CCP structure contain 4 spheres.
• Volume of the four spheres = `4xx4/3(pir^(2)`
• Packing efficiency = Volume of 4 atoms in the unit cell/( Total volume of the unit cell )`xx100`
`=(4xx4/(3)pir^3()/(2sqrt(2)r)^(3)xx100 `
Packing efficiency= 74%.