Question

How many number of atoms are present in the unit cell of HCP structure?

• A. 2
• B. 4
• C. 6
• D. 12

Hint:

The HCP structure has a packing efficiency of approximately 74%, similar to FCC, and is one of the most efficiently packed crystal structures.

Answer 1

The Correct Option is C

The Hexagonal Close-Packed (HCP) structure features atoms arranged in a hexagonal pattern, with two layers stacked alternately. The number of atoms in an HCP unit cell can be calculated as follows: Step 1: Contribution of atoms - 12 corner atoms are shared by 6 adjacent unit cells, contributing \( \frac{1}{6} \) per unit cell. - 2 atoms inside the unit cell are entirely contained, contributing fully. - 3 face-centered atoms are shared between 2 unit cells, contributing \( \frac{1}{2} \) per unit cell.

Step 2: Total atoms in HCP unit cell \[ \left( 12 \times \frac{1}{6} \right) + \left( 2 \times 1 \right) + \left( 3 \times \frac{1}{2} \right) = 2 + 2 + 2 = 6. \] Thus, the total number of atoms in the unit cell of an HCP structure is 6.