Calculate the number of paricles per unit cell of FCC .

Explanation

In `Delta ABG_3`
`b^2= a^(2) +a^(2)` therefore `b^(2) = 2a^(2)`,
In, `Delta AGD`,
`C^(2) = a^(2)+b^(2)` = `a^(2) + 2a^(2)` therefore `C= sqrt(3a)`
Radius of the atom =r
Length of thee body diagonal `C= 4r`
`sqrt3a `= `4r`, a= `(4r)/sqrt3`
Edge length of the cube = a = `(4r)/sqrt3`
volume of the cubic unit cell. = `a^3 =((4r)/sqrt3)`
Volume of one particle (sphere ) = `4/3pir^(3)`
The number of particle per unit cell of a BCC=2
The volume occupied by two spheres = `2xx4/3 pir^(3)`
packing efficiency = `("Total volume occupied by the two spheres")/ ("volume of a cubic unit cell" ) xx100`
`(4/3pir^3xx2)/(4/sqrt3r)^3xx100 = (8/3pi r^3)/((64)/((3)sqrt3) r^3 )xx100= 68%`
(1) A face centerd cube contains 8 lattice points at the eight coner and 6 lattice point at the center of six faces.
(2) A particle present at the centre of a face provides a share of 1/2 of that particle to each unit cell .
(3) A particle present at the centre of a face provides a share of 1/2 of that particle to each unit cell .
(4) The number of particles presemnt in unit cell of fee = `1/8xx 8+ 1/2 xx6= 1+3 =4`.