Packing Efficiency

Concept: In a Face-Centered Cubic (FCC) crystal structure:
• Atoms are present at the 8 corners
• Atoms are also present at the 6 faces Each corner atom is shared by 8 unit cells and each face-centered atom is shared by 2 unit cells.

Step 1: Contribution of corner atoms.

Step 2: Contribution of face-centered atoms.

Step 3: Total number of atoms in the unit cell. Thus,

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

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