Close Packed Structures
From 1D chains to 3D Lattices: Understanding HCP and CCP.
In solids, constituent particles (atoms, molecules, or ions) are packed as closely as possible to maximize attractive forces and stability. To understand these complex 3D structures, we treat the particles as identical hard spheres and build up the structure dimension by dimension.
1. Close Packing in One Dimension
There is only one way to arrange spheres in a one-dimensional structure: placing them in a single row, touching each other.
(Each interior sphere touches exactly two neighboring spheres).
2. Close Packing in Two Dimensions
Two-dimensional layers are generated by placing 1D rows side-by-side. This can be done in two distinct ways:
- Arrangement: The spheres of the second row are placed exactly above those of the first row. The rows align vertically and horizontally.
- Pattern: AAA... type.
- Coordination Number: 4 (Each sphere touches 4 neighbors, forming a square).
- Efficiency: Less efficient packing with more empty space.
- Arrangement: The spheres of the second row are placed in the depressions of the first row.
- Pattern: ABAB... type.
- Coordination Number: 6 (Each sphere touches 6 neighbors, forming a regular hexagon).
- Efficiency: Maximum packing efficiency in 2D. It leaves smaller, triangular voids.
3. Close Packing in Three Dimensions
Real crystals are three-dimensional. They are formed by stacking 2D layers one over the other. The type of 3D lattice generated depends on the type of 2D layer used as the base.
A. From 2D Square Close Packed Layers (AAA... Pattern)
If 2D square close-packed layers are stacked such that spheres of the upper layer are exactly above those of the lower layer, an AAA... 3D pattern is formed.
- This arrangement generates a Simple Cubic (SC) lattice.
- Its unit cell is the primitive cubic unit cell.
B. From 2D Hexagonal Close Packed Layers
To maximize efficiency, nature builds 3D crystals starting from the highly efficient 2D hexagonal layer.
Placing the Second Layer:
The second layer (Layer B) is placed in the depressions of the first layer (Layer A). This generates two types of 3D voids (empty spaces):
- Tetrahedral Voids (TV): Formed when a sphere of the second layer rests over a triangular void of the first layer (surrounded by 4 spheres).
- Octahedral Voids (OV): Formed when triangular voids of the first and second layers overlap (surrounded by 6 spheres).
Placing the Third Layer (The Crucial Step):
How the third layer is placed determines the final crystal structure. There are two options:
If the third layer is placed over the tetrahedral voids, it aligns exactly with the first layer (Layer A). This generates an ABAB... pattern.
Examples: Mg, Zn
If the third layer is placed over the octahedral voids, it aligns with neither layer A nor B, creating a new Layer C. The pattern is ABCABC...
Examples: Cu, Ag
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