Voids in Solid State and Their Role in Crystal Structure

Definition

The vacant space that is left unfilled by the constituent particles of a crystalline solid is called void in the solid state.

Matters can have three forms - solid, liquid and gaseous. Solid matters have a definite mass and the atoms or molecules in them cannot have a free flow. Hence they are rigid. As per the arrangement of the constituent particles, matters can be categorized into two categories - Crystalline and amorphous. When we talk about voids in solid state we generally mean voids in crystalline solids. So our focus will be on the study of the structure of crystalline solids, its constituent particles and how these constituent particles are arranged.

Crystal Lattice

A crystal solid is made up of small constituent particles. These particles are arranged in a particular pattern. The crystal solid is made up of the repetition of this pattern. Now when we make a diagram of this pattern to show how the crystal solid is made up, we call that diagram a lattice. The diagram is three dimensional. Their constituent particles are indicated in the form of points.

Unit Cell

We know that a crystal lattice is made up of small constituent particles. In other words, the main crystal solid is made up of many small crystal solids. The smallest part of this crystal solid is called a unit cell. You cannot divide the unit cell into further smaller parts.

Unit Cells are of Three Kinds -

1. Primitive Unit Cells - When the cube-shaped unit cells have constituent particles at their corner or the meeting point of two edges we call those the primitive unit cells.

2. Centred Unit Cell - When in addition to the corners, one or more constituent particles are present inside the centre of the cube-like unit cell or in the middle of the face of the unit cell, we call that centred unit cell. Centred unit cells are of two types - 1. Body Centred Unit Cells where the extra particle resides at the centre of the inner portion of the cube-like cell and 2. Face Centred Unit Cell where the extra particle(s) is/are placed in the middle of the face(s) of the cube-like cell.

3. End Centred Unit Cells - This unit cell has extra constituent particles placed in the middle of the faces that are opposite to one another. The usual corner particles are also present.

What Do We Mean By Voids in Solid State

Now that we know what the features of the solid matters are, let us now focus on the voids in these matters.

We all know that matters are made up of molecules and atoms. In the case of crystalline solids, these matters are packed together closely. There is a strong intermolecular force in work between these atoms and molecules. This kind of tightly packed structure is known as the close pack structure.

Voids in the solid state are that small space in between the molecules/atoms in a close-packed crystalline solid. No matter how packed the molecules are, there will be small spaces in between them that can't be filled because of the shape of the molecules and the way they are packed.

Dimensions

Across the internet, you will see people are saying that there are three modes of closed packing of constituent particles. However, in reality, practical sense, the constituents are packed in the three-dimensional modes. In order to easily understand the concept of void, we visualise this three-dimensional model as one dimensional or two-dimensional model.

Close Packing of Spheres in One Dimension

One dimension means, you only have to mind about one type of measurement. There is no breadth - only length. A line can be considered one dimensional. Close packing of spheres in one dimension means the constituents are arranged as one single line.

In the one dimensional model, each constituent particle is in contact with two neighbouring particles. The number of particles that are nearest to a particle that is not at the extreme start or extreme end is called the coordination of the particle.

Close Packing of Spheres in Two Dimension 

When the one-dimensional line of constituent particles is placed above another one-dimensional line of close-packed constituent particles, it is called close packing of spheres in two dimensions. The particles of each of the dimensions touch their counterparts, they are placed on top of their counterparts. There are two kinds of close packing of spheres in two dimensions:

1. Square Close Packing 

When the spheres or particles of the second row are placed directly on top of their first row counterparts. The spheres are aligned horizontally as well as vertically because of the identical way of putting these spheres. The two rows are exactly the same - that is why the spheres remain aligned. Since the rows are identical, both the first and second rows are known as the A-type rows. The structure is known as the AAA structure. There are four neighbouring spheres that each sphere is connected with. So the coordination number is 4.

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Those empty spaces between the spheres are voids.

2. Hexagonal Close Packing  

In hexagonal close-packing, the second row of the constituent spheres are not placed directly above the first row - they are placed on top of the depressions that are present between two spheres of the first row. As a result, the spheres of the second row are not aligned with those of the first sphere. The first line can be called line A, while the second line can be called line B

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As you can see each sphere (apart from those at the end) is in touch with 6 other spheres. So the coordination number is 6.

Note: Square close packing creates more voids than the Hexagonal close packing.

Close Packing of Spheres in Three Dimension 

Now, if we make a layer by stacking lines of square close-packed spheres and keep on adding such layers above the other, we will get a figure like this - 

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Look at the picture. The spheres of each layer are directly on top of the other. Here too, each sphere is connected with 6 other spheres. Hence the coordination number is 6.

Voids 

While voids form in 1D and 2D structures too, in order to understand the real form of voids, we need to examine how voids look like in 3d structures. There are two types of voids when it comes to 3D structure:

1. Tetrahedral Void 

Look at the hexagonal close-packed structure. Can you see the triangular voids? What happens if the spheres of the second layer of the same hexagonal structure cover these voids. The voids remain there, but they are now surrounded by four spheres. Joining the centre of these spheres will give you a tetrahedral. That is why these voids are called Tetrahedral voids.

2. Octahedral Void 

Instead of covering the triangular voids of the first layer, the triangular voids from the second layer at certain positions do not cover them and live side by side. This type of void is called an octahedral void. This void is surrounded by six spheres and connecting the centre of the spheres will give you an octahedron.

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Calculating the Number of Voids

The number of tetrahedral voids can be found by doubling the number of spheres. So if the number of spheres is n, then the number of voids will be n+n or 2n. Whereas the numbers of spheres and voids are equal in the case of octahedral voids.

Why exactly do we need to study about voids? Voids tell us how strong or how weak a solid is. Too many void places lead to less mass. As your textbook says, we use solids more than liquids and gas. Solid materials like semiconductors, polymers, magnets will play a huge role in the coming years. It is, therefore, necessary to study solids thoroughly.