Question

packing efficiency in hcp and CCP structure​

Answer 1

both types of clothes packing (hcp and ccp) are equally efficient.

from the picture,

let the unit cell edge length a and face diagonal AC = b

In ∆ ABC

AC^2=b^2 =BC^2+AB^2

= a^2+a^2=2a^2

or,b=√2a

if r is the radius of the sphere, we find

we find b=4r=√2a

we find b=4r=√2a or,a=4r/√2 =2√2r (so.r=a/2√2)

we know that each unit cell in CCP structure has effectively four square total volume of four square is equal to 4×(4/3)πr^3 and the volume of the cube is a^3 or (2√2r)^3.

Therefore,

packing efficiency= volume occupied by 4 squares in unit cell/ total volume of the unit cell ×100℅

= 4×(4/3)πr^3/(2√2r)^3 ×100%

=74%