Chapter 12.4, Problem 3PPC

Interpretation Introduction

Interpretation:

The diagram of an edge-centered unit cell of an ionic compound in which ions are in $\text{1:1}$ratio is shown below.

Figure 1

The number of ions per edge-centered cubic unit cell has to be determined.

Concept Introduction:

A cube has $12$edges, $6$faces and $8$corners.  In edge-centered cubic unit cell, each atom/molecule in the corner is shared by eight unit cells. Each atom/molecule in edge is shared by four unit cells. Thus, the number of atoms or molecules per edge-centered cubic unit cell is,

$8\times \frac{1}{8}\text{ atoms/molecules in corners + 12 }\times \frac{1}{4}\text{ atoms/molecules in edges = 1 +3 = 4 atoms/molecules}$