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 refers to the total number of neighboring atoms touching a central atom within a crystal lattice structure. It indicates how tightly packed the atoms are in a solid.
Step 1: Understanding the Question:
The question asks for the number of nearest neighbors for any single atom in a Face-Centered Cubic (FCC) lattice. In this structure, atoms are located at the corners and the centers of all six faces of the cube.
Step 2: Key Formula or Approach:
The best way to determine the coordination number is to visualize a central atom and count its neighbors in three dimensions:
1. Neighbors in its own plane.
2. Neighbors in the plane immediately above.
3. Neighbors in the plane immediately below.
Step 3: Detailed Solution:
In an FCC arrangement, if we consider an atom at a face center:
- It is in contact with 4 atoms located at the corners of that specific face (same plane).
- It is in contact with 4 atoms at the centers of the faces in the unit cell above.
- It is in contact with 4 atoms at the centers of the faces in the unit cell below.
Total neighbors = \(4 + 4 + 4 = 12\).
Step 4: Final Answer:
The coordination number of an atom in an FCC unit cell is 12.