Question

Identical spheres undergo two-dimensional packing to give square close packing (scp) and hexagonal close packing (hcp). Which of the following statement(s) is/are correct?

• A. The ratio of coordination number for a sphere in scp to that of hcp is 2 : 3.
• B. The ratio of coordination number for a sphere in scp to that of hcp is 3 : 2.
• C. The centres of the neighboring spheres in hcp join to form a hexagon
• D. The centres of the neighboring spheres in scp form a simple cubic structure

Answer 1

Answer: (A), (C)

The centres of the neighboring spheres in hcp join to form a hexagon

In 2-D, the arrangement of spheres can be done by stacking the rows of closely packed spheres in two possible ways:

1. Square close packing:
Here, the second row of spheres is placed adjacent to the first row so that he spheres in the two rows are aligned horizontally, as well as, vertically. Thus, it gives AAA.. type arrangement.
Each sphere touches 4 other neighbours. Thus, its coordination number is 4.
The centres of the neighbouring spheres joins to form a square.​​ So, the packing is known as square close packing in 2-D.​
Thus, statement (d) is incorrect.

2. Hexagonal close packing:
Here, the second row of spheres is placed in the interstices or depressions of the first-row spheres. Thus, it gives ABAB.. type arrangement.
Each sphere touches 6 other neighbours. Thus, its coordination number is 6.
The centres of the neighboring spheres join to form a hexagon.​ So, the packing is known as hexagonal close packing in 2-D.
Thus, statement (c) is correct.
In cubic close packing, coordination number = 4
whereas in hcp, coordination number = 6
So, the ratio is 2 : 3
Thus, statement (a) is correct.