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Calculate packing efficiency in ccp structure.

Calculate packing efficiency in ccp structure.

Grade:11

2 Answers

Gaurav
askIITians Faculty 164 Points
7 years ago
For cubic close packed :

a = 2R√(2)

Since the radius of a sphere is given by 4πR³/3, the total volume of all the atoms in the unit cell is simply

4*[ 4πR³/3 ] = 16πR³/3
volume of the cube in terms of R is (2R√(2))³ = 16R³√(2).

Therefore, the efficiency of the ccp crystal structure is given by
(16πR³/3) / (16R³√(2)) = 0.74078... ≈0.74
volume of all spheres = 2*(4πR³/3) = 8πR³/3

The length of the edge of one of the cubes is related to R by
a = 4R/√(3)
So the volume of the cube in terms of R is

(4R/√(3))³ = 64R³/(3*√(3))

So the efficiency is
(8πR³/3) / [ 64R³/(3*√(3))] = 0.68017... ≈0.68
Amishan
14 Points
4 years ago
Let unit cell edge length be ‘a' and face diagonal AC =b.
AC2= b2= BC2+AB2
                = a+a2
               = √2 aa
If r is the radius of the sphere ,
b = 4r= √2r
a = 4r/2
   = 2√2r
We know that unit cell in CCP structure has 4/spheres.
Total vol. of four sphere in unit cell = 4*(4/3)πr2
Vol. Of cube  = (2√2r)^3.
 
Therfore,
   Packing efficiency = vol. Occupied by four spheres *100% /(2√2r)^3
                                      = 4(4/3)πr^3 * 100%/(2√2r)^3
                                     = (16/3)πr^3 *100%/16√2r^3
                                     = 74% 

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