Chapter 10.8, Problem 10.14CP

Interpretation Introduction

Interpretation:

The smallest repeating unit has to be identified.

Concept Introduction:

Simple cubic unit:

A simple cubic unit cell is the simplest form of a cubic unit cell.  A cube has eight vertices, twelve edges and six faces.  Similarly a cubic unit cell has eight vertices, twelve edges and six faces.  If in a cubic unit cell, the components occupy only the eight vertices, then the unit cell is known as simple cubic unit cell.

Figure 1

A simple cubic unit cell has its all the eight vertices arranged with atoms in it.  Thus eight atoms are arranged in a simple cubic unit cell in eight vertices.  Each atom in a vertex is shared by eight neighboring unit cells.  Each layer of a lattice has four unit cells and the upper or lower to that layer has four unit cells.  So, each simple cubic unit cell has $\frac{\text{1}}{\text{8}}\text{th}$ of an atom at each vertex.  So 8 vertices have $\text{8}\text{×}\frac{\text{1}}{\text{8}}=1\text{atom}$ per unit cell.