Crystal Voids
A complete guide to tetrahedral and octahedral voids in crystal structures — location, radius ratio, and significance in materials engineering.
The Spaces Between: Crystal Voids
Even in the most efficient close-packed structures (HCP and FCC), atoms only occupy 74% of the available volume. The remaining 26% consists of empty spaces called Interstitial Voids.
In materials engineering and chemistry, these voids are critical. They are where we put carbon atoms into iron to make steel, or lithium ions into battery cathodes!
The Two Primary Voids
1. Tetrahedral Void (T-Void)
Formed when a sphere of the second layer rests directly over a triangular depression of the first layer. It is surrounded by 4 atoms.
- Coordination Number: 4
- Ideal Radius Ratio ():
- Location in FCC: On the body diagonals (2 per diagonal, 8 total per unit cell).
2. Octahedral Void (O-Void)
Formed at the intersection of two triangular voids from adjacent layers (one triangle pointing up, one pointing down). It is surrounded by 6 atoms.
- Coordination Number: 6
- Ideal Radius Ratio ():
- Location in FCC: At the body center (1) and edge centers (12 edges × 1/4 = 3), making 4 total per unit cell.
Interactive Void Explorer
Use the tool below to isolate these voids. Adjust the "Guest Atom Size" slider to see the exact moment the guest atom forces the host lattice to expand.
Teacher's Insight: Notice that the Octahedral void is significantly larger than the Tetrahedral void. If an impurity atom has a radius ratio of , it is too big for a T-void but too small to perfectly fit an O-void. It will likely occupy the O-void and "rattle" slightly, or distort the lattice!