Voids in Close Packed Structures — Core Principles
Core Principles
Close-packed structures, like HCP and CCP (FCC), are the most efficient ways to arrange spheres, yet they inherently contain empty spaces called voids. These voids are critical interstitial sites that can be occupied by smaller atoms or ions, especially in ionic solids.
The two main types are tetrahedral voids (TVs) and octahedral voids (OVs). Tetrahedral voids are surrounded by four spheres, forming a tetrahedron, and have a coordination number of 4. Octahedral voids are surrounded by six spheres, forming an octahedron, and have a coordination number of 6.
For 'N' spheres in a close-packed arrangement, there are 'N' octahedral voids and '2N' tetrahedral voids. In an FCC unit cell, there are 4 effective atoms, 4 octahedral voids (at body center and edge centers), and 8 tetrahedral voids (along body diagonals).
The stability of ions occupying these voids is governed by the radius ratio rule, which specifies the ideal values for stable coordination ( for tetrahedral, for octahedral). Understanding voids is essential for predicting the stoichiometry and crystal structure of many inorganic compounds.
Important Differences
vs Octahedral Voids
| Aspect | This Topic | Octahedral Voids |
|---|---|---|
| Geometry | Tetrahedral (surrounded by 4 spheres) | Octahedral (surrounded by 6 spheres) |
| Coordination Number | 4 | 6 |
| Relative Size | Smaller | Larger |
| Number per 'N' spheres (close-packed) | 2N | N |
| Location in FCC unit cell (4 effective atoms) | 8 voids, along body diagonals (1/4th and 3/4th from corners) | 4 voids, at body center and edge centers |
| Ideal Radius Ratio ($r_+/r_-$) | $0.225$ | $0.414$ |