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Chapter 12: 12.87P (page 496)

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?

Short Answer

Expert verified
  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 by step solution

01

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.

02

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.

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