Crystallographic Planes Explained

Crystallographic Planes (Miller Indices)

Crystallographic planes describe the orientation of atomic layers in a crystal using Miller indices like (100), (110), and (111).

Note:
(hkl) = one specific plane
{hkl} = family of equivalent planes

🔹 (100) Plane

The (100) plane cuts the crystal along one axis and is parallel to the other two axes.

• Intercepts: x = 1, y = ∞, z = ∞
• Looks like: a flat face of the cube
• Atomic density: Low

   ●──────●
   |      |
   |      |   ← (100) plane (cube face)
   |      |
   ●──────●

🔹 (110) Plane

The (110) plane cuts two axes and is parallel to the third.

• Intercepts: x = 1, y = 1, z = ∞
• Looks like: diagonal rectangle across the cube
• Atomic density: Medium

   ●──────●
   |\     |
   | \    |   ← (110) diagonal cut
   |  \   |
   ●──────●

🔹 (111) Plane

The (111) plane cuts all three axes equally.

• Intercepts: x = 1, y = 1, z = 1
• Looks like: triangular slice
• Atomic density: Highest (most closely packed)

      ●
     / \
    /   \   ← (111) triangular plane
   ●─────●

🔹 Summary

• (100) → cube face (simple cut)
• (110) → diagonal plane
• (111) → triangular, most dense

🔹 Why it matters

• Determines material properties
• Controls defects like stacking faults
• Important in semiconductors (like silicon)

Electronics and Communication Study Material →