# What Do We Mean by Voids in Solid State? Packing of Spheres in 2 Dimensions (For CBSE, ICSE, IAS, NET, NRA 2022)

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## What Do We Mean by Voids in Solid State?

• Voids literally mean gaps between the constituent particles. Voids in solid states mean the vacant space between the constituent particles in a closed packed structure. Close packing in solids can be generally done in three ways: 1D close packing, 2D close packing and 3D close packing.
• In 2 dimensional structures when the atoms are arranged in square close packing and hexagonal close packing, we see empty spaces called as voids and in the case of hexagonal packing, these voids are in triangular shapes and are known as the triangular voids.

## Packing of Spheres in 2 Dimensions

• These triangular voids in hexagonal packing are shown in two orientations. We can see that in one row, the apex of the triangle points in an upward direction and in the other row it points in the downward direction.
• In the three-dimensional structure, both in CCP and HCP close packing in solids, about 26 % of total space is vacant and is not covered by spheres. These empty spaces are known as the interstitial voids, interstices or holes. The above voids in solids depend on the number of spheres.
• There are two types of interstitial voids in a 3D structure:

### Tetrahedral Voids

• In cubic close packed structure, spheres of the second layer lie above the triangular voids of the first layer. Each sphere touches the three spheres of the first layer. By joining the centre of these four spheres, it forms a tetrahedron and the empty space left over by joining the centre of these spheres forms a tetrahedral void.
• In closed packed structure the number of tetrahedral voids is two times the number of spheres.
• Let the number of spheres be n.
• Then the number of tetrahedral voids will be .

### Octahedral Voids

• Adjacent to tetrahedral voids you can find octahedral voids. So now, what are Octahedral Voids? When the triangular voids of the first layer coincide with the triangular voids of the layer above or below it, we get a void that is formed by enclosing six spheres.
• This vacant space formed by combining the triangular voids of the first layer and that of the second layer are called Octahedral Voids.
• If the number of spheres in a close-packed structure is n, then the number of octahedral voids will be n.

Tetrahedral and octahedral void

## Tetrahedral Voids

• Now there are two types of three-dimensional close packing in crystals. One such type is Cubic Close packing. Here the two-dimensional structures are stacked in a specific alignment. The layers alternate with each other. So, the second layer will be located in the depression of the first layer.
• You will notice that a triangle-shaped void is seen in this type of alignment. The sphere which is in the depression will leave a void between itself and the sphere in the layer above. This void is the Tetrahedral Void.
• There is a simple way to calculate the number of Tetrahedral Voids in a lattice. Here if the number of spheres (i.e.. , unit cells) is said to be ānā , then the number of voids will be twice as many. So, the number of tetrahedral voids will be ā2nā
• The void is much smaller than the sphere, i.e.. , it has a smaller volume. And the coordination number of a tetrahedral void is four because of the void forms at the center of four spheres.

## Octahedral Voids

• 3-dimensional structure of a crystal lattice you will observe the gaps in between the spheres. These are the voids. As you see that tetrahedral voids are triangular in shape. When two such voids combine, from two different layers they form an octahedral void.
• When the tetrahedral void of the first layer and the tetrahedral void of the second layer align together, they form an octahedral void. Here the void forms at the center of six spheres. Coordination number of an octahedral void is six.
• To calculate octahedral void, if the number of spheres in a structure is ānā , then the number of octahedral voids will also be the same. i.e.. ānā .

## Questions

### How Many Types of Voids Are Present in a Solid Crystal?

Two types

The size and distribution of voids in materials plays a role in determining in the close packed crystals (FCC, HCP) there are two types of voids - tetrahedral and octahedral voids (identical in both the structures as the voids are formed between two layers of atoms) .