12.87P - Chemistry: Molecular Nature Of Matter And Change

Question

As molten iron cools to 1674 K, it adopts one type of cubic unit cell; then, as the temperature drops below 1181 K, it changes to another, as depicted below:

1. What is the change in unit cell?
2. Which crystal structure has the greater packing efficiency?

Step-by-Step Solution

Answer

1. When molten iron cools to 1674 K, it has face-centered cubic unit cell; whenever the temperature comes below 1181 K, it changes to body-centered cubic unit cell.
2. Face-centered crystal structure has greater packing efficiency.

Step 1: Phase transformation of cooling

When the molten iron cools to a low temperature of 1674 K, it changes its crystal lattice to face-centered cubic unit cell. Now, again when the temperature further decreases to 1181 K, the face-centered cubic unit cell disrupts and gets converted into a body-centered cubic unit cell.

Step 2: Packing efficiency

Considering the two phases, the face-centered (left) and body-centered (right) cubic lattice has the following structure:

             

     Figure (a) Body centered cubic unit cell and (b) Face centered cubic unit cell

The face centered has the packing efficiency of 74% whereas the body-centered has the packing efficiency of 68%.Hence, the face-centered has higher packing efficiency.