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Octahedral Voids: Geometry, Location, and Crystal Chemistry

Understand octahedral voids in close-packed crystal structures. Learn where they form, their coordination, size ratio, and how they determine ionic crystal structures like NaCl and corundum.

V
Vectora Team
STEM Education
7 min read
2025-10-11

What Are Octahedral Voids?

An octahedral void is an empty space in a close-packed crystal structure that is surrounded by 6 atoms arranged at the corners of an octahedron — 3 from the layer above and 3 from the layer below.

In any close-packed structure (CCP or HCP), there is exactly 1 octahedral void per atom.

Learning Goals: By the end of this guide, you should be able to:

  1. Identify the location of octahedral voids in a close-packed structure.
  2. State the number of octahedral voids per atom.
  3. Use the radius ratio to predict when smaller ions fill octahedral voids.
  4. Apply this to real crystal structures.

Properties of Octahedral Voids

PropertyValue
Coordination number6
Number per atom1 (equal to the number of atoms)
Radius ratio (rvoid/ratomr_{void}/r_{atom})0.414
ShapeOctahedron

Radius Ratio

The maximum radius of a sphere that fits in an octahedral void is 0.414R0.414R, where RR is the radius of the close-packed atoms. This is called the critical radius ratio for octahedral coordination.

If 0.414≤r+/r−≤0.7320.414 \leq r^+/r^- \leq 0.732, the smaller ion typically occupies octahedral voids.

Location in the FCC Unit Cell

In a face-centred cubic cell, octahedral voids are located at:

  • 1 at the body centre of the cube
  • 12 at the edge centres (each shared among 4 cells → 12×14=312 \times \frac{1}{4} = 3)

Total: 4 octahedral voids per FCC unit cell (matching the 4 atoms per cell → ratio 1:1).

Octahedral Void Explorer

Visualise octahedral voids in 3D within CCP and HCP structures. See how 6 surrounding atoms create the octahedral coordination geometry.
Explore Octahedral Voids

Crystal Structures Using Octahedral Voids

NaCl (Rock Salt) Structure

Cl−Cl^- ions form a CCP arrangement. Na+Na^+ ions occupy all octahedral voids.

  • 4 Cl−Cl^- per cell, 4 Na+Na^+ per cell → ratio 1:1 → formula NaClNaCl ✓
  • Na+Na^+ coordination number: 6

Corundum (Al2O3Al_2O_3)

O2−O^{2-} ions in HCP. Al3+Al^{3+} occupies ⅔ of the octahedral voids (to achieve charge balance).

Worked Example

Question: In a CCP arrangement of X atoms, all octahedral voids are filled by Y atoms. What is the formula?

Solution: CCP has 4 X atoms per cell and 4 octahedral voids per cell. If all are filled: 4 Y atoms. Formula: XY (1:1 ratio).

Common Mistakes

  1. Confusing octahedral and tetrahedral voids — Octahedral voids have CN = 6 and there's 1 per atom. Tetrahedral voids have CN = 4 and there are 2 per atom.

  2. Wrong radius ratio — Octahedral: 0.414. Tetrahedral: 0.225. Don't mix them up.