1.17 Which of the following lattices has the highest packing efficiency
(i) simple cubic
(ii) body-centred cubic and
(iii) hexagonal close-packed lattice?
(i) Simple cubic:- In a simple cubic lattice the atoms are located only on the corners of the cube.
Thus, the edge length or side of the cube ‘a’, and the radius of each particle, r are related as a = 2r
Volume of cubic unit cell = =
And Volume of 1 atom :
(ii) Body centred cubic:- In body centred cubic, we have atoms at all corners and at body centre.
Clearly, the atom at the centre will be in touch with the other two atoms diagonally arranged.
Also, the length of body diagonal is equal to 4r.
The volume of the cube :
In BCC, a total number of atoms is 2.
(iii) Hexagonal close-packed:- We know that both types of (hcp and ccp) are equally efficient. We also know that the packing efficiency of ccp is 74 percent.
(i) Simple cubic = 52.4%
(ii) Body centred cubic=68%
(iii) Hexagonal close-packed=74%
Thus among all, packing efficiency of hcp is the highest.
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