Tetrahedral Void

A tetrahedral void is an important concept in crystallography and solid-state chemistry. It refers to the space within a crystal structure surrounded by four atoms (or ions) arranged as a tetrahedron. 

1.0What Is a Tetrahedral Void?

In the context of the close packing of spheres, the arrangement of atoms (or ions) leaves specific spaces, or vacancies, known as interstitial voids or interstitial sites. These voids are critical in determining the structure and properties of the crystal. The two primary types of interstitial voids are tetrahedral voids and octahedral voids.

A tetrahedral void is the space found in substances with tetrahedral crystal structures. Voids are the empty spaces in a crystal system arising from different atomic arrangements. Tetrahedral voids are located between four spheres arranged in a tetrahedral manner.

2.0Structure of Tetrahedral Void

In a cubic close-packed (CCP) or face-centred cubic (FCC) configuration:

• Spheres (atoms or ions) are arranged close-packed, creating triangular voids between them.
• The spheres in the second layer are placed so that each sphere is above the triangular voids of the first layer.
• Each sphere in the second layer touches three spheres from the first, forming a tetrahedral arrangement.
• The space formed by the centres of these four spheres (three from the first layer and one from the second layer) is a tetrahedral void.

3.0Characteristics of Tetrahedral Void

A tetrahedral void is a type of interstitial space found within three-dimensional close-packed structures. Understanding its characteristics is essential for predicting and explaining the behaviour and properties of various crystalline materials.

• Four atomic spheres surround the space or void, creating a tetrahedral arrangement. As a result, the tetrahedral void’s coordination number is 4.
• A tetrahedral void is created when a triangular void of three coplanar atoms comes into contact with a fourth atom positioned above or below this plane.
• The volume of the tetrahedral void is substantially smaller than that of the spherical particles that form the structure.
• If R is the constituent spherical particle's radius, the tetrahedral void's radius is 0.225R.
• The number of tetrahedral voids equals 2N, where N is the number of close-packed spheres.

4.0Calculating the Number of Tetrahedral Voids in a Lattice

The number of tetrahedral voids in a crystal lattice can be directly related to the number of close-packed spheres within the structure. Here's a step-by-step method to understand and calculate these voids:

• In a closed-packed crystal structure, such as face-centred cubic (FCC) or hexagonal close-packed (HCP), each unit cell consists of a certain number of spheres (atoms or ions).
• For every close-packed sphere in the lattice, there are two tetrahedral voids.
• Therefore, if the number of close-packed spheres (or unit cells) is denoted as n, the number of tetrahedral voids is given by: number of tetrahedral voids = 2n

Example

If there are 200 close-packed spheres in a crystal lattice: 

Number of tetrahedral voids = 2 × 200 = 400

5.0Relative Radius of the Tetrahedral Void and the Radius of the Atoms in Close Packing

The relationship between the Radius of the tetrahedral void and the Radius of the atoms in close packing is essential for understanding the packing efficiency and structure of crystalline materials.

In a closed-packed structure, the Radius of the tetrahedral void (R) is related to the Radius of the atoms or ions in the structure (R). Specifically, the Radius of the tetrahedral void is approximately 0.225 times the radius of the constituent particles in the lattice.

Mathematically, this relationship is expressed as:

r=  0.225R

Where:

• r is the radius of the tetrahedral void.
• R is the radius of the atoms or ions in close packing.

This relationship indicates that the tetrahedral voids are significantly smaller than the atoms or ions in the close-packed structure. It also implies that the size of the tetrahedral void is fixed relative to the size of the constituent particles in the lattice.

6.0Octahedral void 

An octahedral void is a space or void that occurs at the centre of six spheres. Each octahedral void is created by combining the triangular voids of the first and second layers. This void is surrounded by six spheres positioned at the vertices of a regular octahedron. In a crystal lattice, there is typically one octahedral void per atom.

7.0Comparison between tetrahedral and octahedral voids

Understanding the differences between tetrahedral and octahedral voids helps characterise crystalline materials' structural properties and behaviour.