Close Packed Structures — Definition

Definition

Imagine you have a large number of identical marbles and you want to arrange them in a box in the most compact way possible, leaving the least amount of empty space. This is precisely what 'close packing' in chemistry is all about.

It describes how atoms, which we can visualize as hard spheres, arrange themselves in a crystal lattice to maximize their density and stability. This arrangement is crucial because it dictates many physical properties of solids, such as their density, hardness, and melting point.

We can understand close packing by building it up step-by-step, starting from one dimension, then two, and finally three dimensions.

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One-Dimensional (1D) Close Packing: — If you arrange marbles in a single straight line, each marble touches two neighbors (one on its left and one on its right). This is the simplest form of packing, with a coordination number of 2.

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Two-Dimensional (2D) Close Packing: — Now, let's arrange layers of these 1D rows. There are two main ways to do this:

* Square Close Packing (SCP): Imagine stacking the 1D rows directly on top of each other. Each sphere in the interior of the layer touches four other spheres, forming a square pattern. The centers of these four spheres form a square.

The coordination number in 2D is 4. There are relatively large square voids (empty spaces) between the spheres. * Hexagonal Close Packing (HCP): This is a more efficient way. Instead of stacking rows directly, you place the spheres of the second row in the depressions (grooves) of the first row.

If you continue this, each sphere in the interior touches six other spheres, forming a hexagonal pattern. The centers of these six spheres form a hexagon. The coordination number in 2D is 6. This arrangement is much more compact than square close packing and creates smaller, triangular voids.

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Three-Dimensional (3D) Close Packing: — This is where it gets really interesting and relevant for real crystals. We build 3D structures by stacking these 2D close-packed layers (specifically, the 2D hexagonal close-packed layers) on top of each other. When you place a second 2D hexagonal layer (let's call it 'B' layer) on top of a first 'A' layer, the spheres of the 'B' layer sit in the depressions of the 'A' layer. This creates two types of empty spaces or 'voids' in the structure:

* Tetrahedral Voids: These are smaller voids formed when a sphere in the second layer rests on three spheres in the first layer. They are surrounded by four spheres (one from the top layer, three from the bottom), hence 'tetrahedral'.

* Octahedral Voids: These are larger voids formed when a sphere in the second layer rests on three spheres in the first layer, and simultaneously, three spheres in the first layer are directly below a void in the second layer.

They are surrounded by six spheres (three from the top layer, three from the bottom), hence 'octahedral'.

Now, when we add a third layer ('C' layer) on top of the 'B' layer, there are two choices for placing the spheres: * Hexagonal Close Packing (HCP): If the spheres of the third layer are placed directly above the spheres of the first 'A' layer, the stacking pattern becomes A-B-A-B-A-B...

This is called hexagonal close packing. Many metals like Mg, Zn, and Ti adopt this structure. * Cubic Close Packing (CCP) / Face-Centered Cubic (FCC): If the spheres of the third layer are placed in a new set of depressions, not directly above the 'A' layer spheres, the stacking pattern becomes A-B-C-A-B-C...

This is called cubic close packing. This structure is equivalent to the face-centered cubic (FCC) unit cell. Many metals like Cu, Ag, Au, and Al adopt this structure.

Both HCP and CCP are incredibly efficient, with about 74% of the space occupied by atoms. They both have a coordination number of 12, meaning each atom is surrounded by 12 nearest neighbors. Understanding these arrangements helps us predict and explain the properties of a vast array of solid materials.