Question

What is the coordination number of an atom in an FCC unit cell?

• A. \(6\)
• B. \(8\)
• C. \(12\)
• D. \(4\)

Hint:

Common coordination numbers in cubic crystal structures:
• Simple Cubic (SC): \(6\)
• Body-Centered Cubic (BCC): \(8\)
• Face-Centered Cubic (FCC): \(12\) FCC structures are highly packed and therefore have the highest coordination number among the three.

Answer 1

The Correct Option is C

Concept: The coordination number of an atom in a crystal lattice is the number of nearest neighbouring atoms that surround that atom. In a Face-Centered Cubic (FCC) unit cell:
• Atoms are present at the 8 corners of the cube.
• Atoms are also present at the center of each of the 6 faces. Each atom in this structure is closely surrounded by several nearest neighbours arranged symmetrically.

Step 1: Understanding neighbour arrangement in FCC. Consider an atom located at the center of a face or at a corner of the cube. In the FCC structure, the nearest atoms lie along the face diagonals.
• The atom touches 4 atoms in its own plane.
• It touches 4 atoms in the plane above.
• It touches 4 atoms in the plane below. Therefore, the total number of nearest neighbours is \[ 4 + 4 + 4 = 12 \]

Step 2: Determining the coordination number. Since each atom has 12 nearest neighbouring atoms, the coordination number of an atom in an FCC lattice is \[ \boxed{12} \]