The Solid State

Tetrahedral and Octahedral Voids

The crystalline solids are characterized by their space lattices and close packing of atoms. However, these structures have some gaps in their arrangement we call voids. Many scientists believe that this spacing between atoms is of crucial importance to the properties of the substance. So let us study tetrahedral voids and octahedral voids.

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Three Dimensional Structure of Crystal Lattice

Now we have previously seen the closet packing in crystal structures. This packing happens at three different levels, one dimensional, two dimensional and three dimensional. Now we must realize those constituent particles have a spherical shape. And the unit cells of a crystal lattice is a cube. So when these atoms or ions are packed into a cube there will be space between the atoms. These spaces are known as voids.

We see these voids in the two-dimensional structures as well. Here there are two types of closet packing, and two types of voids. One is a square shape void and the other is a triangle shape void. But here we will be focusing on the voids in the three-dimensional structure.

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Tetrahedral Voids

Tetrahedral voids and octahedral voids(Source: Chemistrystackexchange)

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 “n”, then the number of voids will be twice as many. So the number of tetrahedral voids will be “2n”.

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.

 Tetrahedral and Octahedral Voids

Octahedral Voids

If you observe a three-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.

So 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. So we say the coordination number of an octahedral void is six.

To calculate octahedral void, if the number of spheres in a structure is “n”, then the number of octahedral voids will also be the same. i.e. “n”.

Solved Question for You

Q: If Z is the number of atoms in the unit cell that represents the closest packing sequence ABCABC, the number of tetrahedral voids in the unit cell is equal to:

  1. Z
  2. 2Z
  3. Z/2
  4. None of the above

Ans: The correct option is “B”. As we know the number of tetrahedral voids in a closed packed ccp or fcc is double the number of atoms forming the crystal lattice (Z). So the number of voids will be 2Z.

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