Question

write the packing efficiency of SC BCC and fcc

Answer 1

The packing efficiency of both types of close packed structure is 74%, i.e. 74% of the space in hcp and ccp is filled. The hcp and ccp structure are equally efficient; in terms of packing. The packing efficiency of simple cubic lattice is 52.4%. And the packing efficiency of body centered cubic lattice (bcc) is 68%.

Answer 2

Packing Efficiency of Close Packed Structure - 1
Both ccp and hcp are highly efficient lattice; in terms of packing. The packing efficiency of both types of close packed structure is 74%, i.e. 74% of the space in hcp and ccp is filled. The hcp and ccp structure are equally efficient; in terms of packing.

The packing efficiency of simple cubic lattice is 52.4%. And the packing efficiency of body centered cubic lattice (bcc) is 68%.

Calculation of pacing efficiency in hcp and ccp structure:

The packing efficiency can be calculated by the percent of space occupied by spheres present in a unit cell.

Solid state 4
Let the side of an unit cell = a

And diagonal AC = b

packing efficiecny of hcp and ccp
Now, in ∆ ABC,

AB is perpendicular, DC is base and AC is diagonal

Solid state 5
Solid state 6
Thus,packing efficiency of hcp or ccp structure=74%

Packing efficiency of body centered cubic (bcc) structure:

packing efficiecny of bcc
In body centered cubic unit cell, one atom is present in body center apart from 4 atoms at its corners. Therefore, total number of atoms present in bcc unit cell is equal to 2.

Let a unit cell of bcc structure with side a.

Let FD (diagonal) = b and diagonal AF = c

Let the radius of atom present in unit cell = r

Now, in ∆EFD

Solid state 7
After subtituting the value of a from equation (vi) we get

Solid state 8
Thus,packing efficiency of bcc structure=68%