Chapter 7, Problem 72A

Interpretation Introduction

Interpretation: The number of neighboring atoms of cobalt in a hexagonal close-packed structure needs to be determined.

Concept Introduction:

A matter can have mainly three states; solid, liquid, and gas. The matter is composed of atoms and in the solid state, these atoms are closely packed giving the solid a rigid shape.

Solids can be crystalline or amorphous. In crystalline form, the atoms, molecules, and ions are in a symmetrical form. On the other hand, amorphous solids are not symmetrical. A crystal lattice is formed by unit cells that combine to form the network. Also, the two types of packing in solids are cubic close packing and hexagonal close packing.

In hexagonal close packing, there are alternating layers of packed spheres. Here, spheres are atoms, molecules, or ions.

Answer to Problem 72A

6

Explanation of Solution

In a hexagonal close packing structure unit cell, middle atoms are not shared with other unit cells but atoms in the upper and bottom layers are shared. Here, in the top layer, the central atom is shared with 1 other unit cell and contributes ½ to one unit cell. In vertices of top and bottom layers, the atoms are shared with 5 unit cells and contribute to 1/6 to one unit cell.

Considering the above arrangement, the number of atoms completely contributing to a unit cell will be 3 (from the middle layer).

Also, 2 atoms (1 from the top layer and one from the bottom layer) contribute ½ to the unit cell. 12 atoms (6 from top and 6 from bottom) contributing 1/6 to the unit cell. The total number of atoms in a unit cell can be calculated as follows:

  $\begin{array}{c}N=3+\frac{1}{2}\left(2\right)+\frac{1}{6}\left(12\right)\\ =3+1+2=6\end{array}$

Therefore, in a hexagonal close packing structure, one unit cell has 6 atoms.

Conclusion

The number of neighboring atoms of cobalt in a hexagonal close-packed structure is 6.