Question

In hexagonal close packing of Sphere in three dimensions.
A.In a one-unit cell there are 12 octahedral voids and all are completely inside the unit cell.
B.In one-unit cell there are 6 octahedral voids & 12- tetrahedral voids, and all are completely inside the unit cell.
C.In a one-unit cell there are six octahedral voids and of which three are completely inside the unit cell and other three are partially inside the unit cell.
D.In one-unit cell there are twelve tetrahedral voids, all are completely inside the unit cell

Answer 1

The arrangement of constituent units as demonstrated is that the forces of attraction amid the constituent particles is highest and the constituents occupy the utmost available space is called Packing.

Complete step by step answer:
There are square close packing and hexagonal close packing in two dimensions and there is hexagonal close packing, cubic close packing and body – centered cubic packing in three dimensions.
Unit Cell is the smallest frequently occurring unit in the space lattice. When we repeat a unit cell in all dimensions, we obtain a structure of the crystal. The properties of the unit cell are measured by length of edges and the angles Joining the edges.
In Body Centred Cubic, every layer is balanced from the layer preceding it. Arrangements copy themselves from each other layer.
Cubic close packing: When the third layer is placed above the second layer in such a way that its spheres cover the octahedral voids and the spheres of the third layer are not aligned with the first or the second layer, arrangement is called “C’ type.
hcp: AB ABABAB .... arrangement
Coordination no. = 12
$\%$ occupied space = 74
ccp: ABC ABC.... arrangement
coordination no. = 12
$\%$ occupied space = 74
bcc:
coordination no.= 8
$\%$ occupied space = 68

Hence option B is correct. In a one-unit cell there are 6 – octahedral voids and 12 – tetrahedral voids.

Note:
Hexagonal close packing is more closely packed than cubic close packing because Hexagonal close packing has a coordination number of 12 whereas cubic close packing has a coordination number of 8.