The corundum crystal structure, found for Al2O3, consists of an HCP arrangement of O2- ions; the Al3+ ions occupy octahedral positions.
(a) What fraction of the available octahedral positions are filled with Al3+ ions?
(b) Ketch two close-packed O2–planes stacked in an AB sequence, and note octahedral positions that will be filled with the Al3+ ions.
The correct answer and explanation is :
(a) Fraction of Octahedral Positions Filled by Al³⁺ Ions
The corundum (α-Al₂O₃) structure consists of an hcp (hexagonal close-packed) arrangement of O²⁻ ions. In an hcp unit cell, there is one octahedral site per anion (O²⁻). Given the chemical formula Al₂O₃, for every 3 oxygen ions, there are 2 aluminum ions. Therefore:
- Number of O²⁻ ions: 3
- Number of octahedral sites: 3 (one per O²⁻)
- Number of Al³⁺ ions: 2
So, the fraction of octahedral sites filled is:
$$
\text{Fraction} = \frac{\text{Number of Al}^{3+}}{\text{Number of octahedral sites}} = \frac{2}{3}
$$
Answer: (a) 2/3 of the octahedral positions are filled.
(b) Diagram Description and Explanation
In the hcp structure, oxygen anions form a hexagonal close-packed arrangement, with alternating layers labeled A and B. Each oxygen layer is a flat sheet of spheres (O²⁻ ions), and the stacking sequence alternates ABAB…
Octahedral positions are located:
- Between two oxygen layers, coordinated by three O²⁻ from layer A and three from layer B.
- Each octahedral site sits in the void created by these two staggered triangular layers.
In corundum:
- Only 2/3 of these interlayer octahedral voids are occupied by Al³⁺ ions.
- The placement of Al³⁺ ions is ordered, not random, leading to a distortion from ideal close-packing and rhombohedral symmetry (not hexagonal).
Explanation (300 words)
Corundum (α-Al₂O₃) adopts a crystal structure based on a hexagonal close-packed (hcp) lattice of O²⁻ ions. In this configuration, the oxide ions form alternating layers of close-packed spheres (A and B layers). Between these layers, there are interstitial voids, specifically octahedral and tetrahedral sites, where cations can reside. The Al³⁺ ions in corundum occupy only the octahedral positions.
Each O²⁻ ion in an hcp lattice contributes one octahedral site, so in total, there are as many octahedral sites as there are O²⁻ ions. Given the stoichiometry of Al₂O₃, for every three O²⁻ ions, two Al³⁺ ions are needed to maintain charge neutrality. Therefore, only 2/3 of the available octahedral sites are occupied by Al³⁺ ions. This partial occupancy is crucial because it determines the overall symmetry and physical properties of the crystal.
The arrangement of the Al³⁺ ions is not random; instead, it follows an ordered pattern, which minimizes electrostatic repulsion and ensures structural stability. This results in the distortion of the ideal hcp lattice and leads to the rhombohedral unit cell characteristic of the corundum structure.
When sketching the structure, two O²⁻ layers in AB sequence can be drawn as alternating triangles. Between these layers, some of the octahedral voids formed by the staggered triangles are filled with Al³⁺ ions, specifically 2 out of every 3 available voids. This selective filling and ordered placement of Al³⁺ ions are key features that define the unique mechanical hardness and chemical stability of Al₂O₃.