Frenkel Defect

Frenkel defect, also known as the Frenkel pair, is a type of point defect in crystal lattice structures. It was named after the Russian physicist Yakov Frenkel, who first proposed the concept in 1926. This defect involves the displacement of an atom from its normal lattice site to an interstitial site, creating both a vacancy at the original site and an interstitial atom elsewhere in the crystal lattice. It is commonly observed in ionic solid due to difference between size of cations and anions.

In this article, we will learn what is Frenkel Defect, its properties, causes, and effects, and how to calculate the number of Frenkel defects in a compound. We will also compare and learn difference between Frenkel and Schottky defects.

What is Frenkel Defect?

Frenkel defect is a Point Defect commonly observed in ionic crystals, where the cation (positively charged ion) is much smaller than the anion (negatively charged ion). When a cation migrates to an interstitial site, leaving behind a vacancy, it can maintain charge neutrality with the anions, frenkel defect is created.

This type of defect is more likely to occur in crystals with high coordination numbers, where each ion has many neighbouring ions. Common examples of materials exhibiting Frenkel defects include silver halides (AgCl, AgBr, AgI) and alkali metal halides (such as NaCl, KBr).

Frenkel defects do not significantly affect the overall electrical neutrality of the crystal and can have implications for the material’s electrical and optical properties. They are one of the several types of point defects that can occur in crystalline structures, including vacancies, interstitials, and Schottky defects.

Frenkel Defect Definition

Frenkel defect is a type of point defect that occurs when an atom or cation leaves its initial position in the lattice structure to create a void and moves to a different interstitial position within the solid crystal. It is a type of point defect in crystals, commonly found in ionic crystals.

The image for the frenkel defect is shown below:

How is Frenkel Defect Formed?

A Frenkel defect It occurs when an ion is displaced from its regular lattice site to an interstitial position. This type of defect is often observed in ionic compounds where there is a large difference in size between the cations and anions.

The formation of a Frenkel defect involves two main steps:

• Ion Displacement: One of the ions, usually a cation, is displaced from its regular lattice site to an interstitial site (a space between lattice points). This displacement can be caused by thermal vibrations or external factors such as radiation.
• Creation of Interstitial Ion: The ion that is displaced becomes an interstitial ion, occupying a position between the lattice points. This results in a vacant site at the original lattice position.

For example, consider a crystal of silver iodide (AgI), where silver ions (Ag⁺) are smaller than iodide ions (I⁻). The smaller silver ions may be displaced from their regular lattice sites and occupy interstitial positions within the crystal lattice. This creates a vacancy at the original silver ion site and an interstitial silver ion.

Reasons for Frenkel Defects

Frenkel Defect involves the displacement of an ion from its lattice site to an interstitial site within the crystal structure. They are often observed in ionic compounds where there is a large difference in size between the cations and anions. Here are some reasons for the formation of Frenkel defects:

• Size Mismatch: Frenkel defects are more likely to occur in crystals where there is a significant size difference between the cations and anions. If the cation is much smaller than the anion, the cation may move to an interstitial site to reduce the strain caused by the size difference.
• Highly Polarizable Ions: Ions with high polarizability are more likely to form Frenkel defects. Polarizability refers to the ability of an ion to deform its electron cloud in response to an external electric field. More polarizable ions may be more easily displaced from their lattice sites.
• High Coordination Number: Crystals with high coordination numbers, where each ion is surrounded by many neighbouring ions, are more prone to Frenkel defects. The increased number of neighbouring ions provides more opportunities for an ion to move to an interstitial site without disrupting the overall structure significantly.
• Temperature: High temperatures increase the chances of Frenkel defects. As temperature rises, the ions gain thermal energy, making it easier for them to overcome the energy barriers and move to interstitial positions.
• Ionic Mobility: Ions with higher mobility are more likely to form Frenkel defects. This is related to the ability of ions to move within the crystal lattice. Higher ionic mobility increases the chances of an ion moving from its regular lattice site to an interstitial site.
• Electrostatic Forces: The strength of electrostatic forces between ions plays a role in Frenkel defect formation. If the electrostatic forces are not strong enough to hold the ions in their lattice positions, ions may more easily move to interstitial sites.

Effects of Frenkel defect

Frenkel defect is common in ionic crystals, where there is a significant size mismatch between cations and anions. The consequences of Frenkel defects can have several effects on the properties of the material:

• Electrical Conductivity: Frenkel defects can contribute to electrical conductivity in materials. When an ion moves to an interstitial site, it creates a vacancy at its original site, and the interstitial ion is free to move through the crystal lattice. This movement of charged particles can enhance the electrical conductivity of the material.
• Optical Properties: Frenkel defects can influence the optical properties of a material. For example, they can cause colour centres, which are responsible for the colour of certain crystals. The presence of these defects can lead to the absorption or emission of specific wavelengths of light.
• Mechanical Properties: The movement of ions to interstitial sites can affect the mechanical properties of a material. The presence of defects can alter the crystal lattice structure and, consequently, influence properties such as hardness, brittleness, and elasticity.
• Thermal Properties: Frenkel defects can affect the thermal conductivity of a material. The increased vibrational motion of atoms around the defects can influence the overall thermal properties of the crystal.
• Stability of the Crystal Structure: The creation of defects introduces strain into the crystal structure, and this strain can affect the overall stability and integrity of the material.
• Diffusion: The movement of ions to interstitial sites and the subsequent migration of these ions through the crystal lattice can impact the diffusion properties of the material. This can be relevant in various applications, such as in solid-state diffusion processes.

It is important to note that the specific consequences of Frenkel defects can depend on the type of material, the nature of the ions involved, and the conditions under which the material is used. In some cases, Frenkel defects may be intentionally introduced to tailor the properties of a material for specific applications.

Characteristics of Frenkel Defect

Frenkel defect is a type of point defect that can occur in crystalline solids, particularly in ionic compounds. It involves the displacement of ions within the crystal lattice. Here are the characteristics of Frenkel defect:

• Ion Displacement: Frenkel defect occurs when an ion is displaced from its normal lattice site to an interstitial site within the crystal structure. Typically, the cation (positively charged ion) is displaced.
• Ionic Solids: Frenkel defects are commonly observed in ionic solids, where there is a significant size mismatch between the cations and anions. This size mismatch makes it easier for smaller cations to move into interstitial sites.
• High Charge Ratio: The likelihood of Frenkel defects increases with a higher charge ratio of cations to anions. A higher charge ratio means that cations are relatively smaller compared to anions, facilitating their movement into interstitial sites.
• Temperature Dependence: Frenkel defects are often more pronounced at higher temperatures. Elevated temperatures provide the thermal energy required for ions to overcome the lattice energy and move into interstitial positions.
• Minimal Impact on Density: Frenkel defects do not significantly affect the overall density of the crystal lattice since the displaced ion remains within the lattice.
• Common in ionic compounds with small cations: It is more commonly observed in crystals where the cations are smaller and can easily fit into interstitial spaces without causing a significant distortion in the lattice.
• Stability: Frenkel defects are generally more stable in compounds where the cation-anion interactions are strong, as the displaced cation can remain within the lattice without being easily displaced by external forces.
• No Change in Electrical Neutrality: The crystal structure maintains its electrical neutrality despite the presence of Frenkel defects, as the displaced cation is still part of the crystal.

Examples of Frenkel Defect

Frenkel defect is a type of point defect that occurs in crystal structures, where an atom or ion is displaced from its lattice site to an interstitial site. This type of defect is commonly observed in ionic crystals. Here are a few examples of Frenkel defects:

• Silver Halides (AgCl, AgBr, AgI): In these ionic crystals, silver ions (Ag⁺) may occupy interstitial sites instead of their regular lattice positions. The displaced silver ion creates a vacancy at its original lattice site.
• Zinc Sulfide (ZnS): Frenkel defects can occur in zinc sulfide where zinc ions (Zn²⁺) move to interstitial positions, leaving behind a vacancy at the original lattice site.
• Cesium Chloride (CsCl): Cesium chloride has a simple cubic structure, and cesium ions (Cs⁺) may undergo Frenkel defects by moving to interstitial positions.
• Silver Iodide (AgI): Silver iodide exhibits Frenkel defects where silver ions may migrate to interstitial sites, creating vacancies in the lattice.
• Copper(I) Chloride (CuCl): In copper(I) chloride, copper ions (Cu⁺) may experience Frenkel defects by moving to interstitial positions, causing vacancies in the crystal lattice.

Frenkel defects are more common in compounds where there is a large difference in size between cations and anions. The smaller ion tends to occupy interstitial sites, leading to the displacement of the larger ion and the creation of vacancies.

Number of Frenkel Defect

The number of Frenkel defects in a crystal depends on various factors, including the temperature, pressure, and the type of material. In general, as the temperature increases, the likelihood of Frenkel defects occurring also increases. The exact number of Frenkel defects can be challenging to determine precisely without specific information about the conditions. However there exist a formula to estimate the numbers of Frenkel defects in crystal.

Calculation of Number of Frenkel Defect

Frenkel Defect can be calculated using following formula:

n = √(NN*)e^-ΔH/2RT

where,

• n= Number of Frenkel defect
• N* = Number of occupied positions.
• N = Number of available positions.
• ΔH = Enthalpy formation of one Frenkel defect.
• R = Gas constant

Difference Between Schottky and Frenkel defects

Schottky and Frenkel defects are two types of point defects that can occur in crystal lattices, especially in ionic solids. These defects affect the arrangement of atoms or ions in a crystal lattice and can influence the material’s properties.

Criteria	Schottky Defect	Frenkel Defect
Type	Schottky defect is a vacancy-type defect.	Frenkel defect is a combination of interstitial and vacancy-type defect.
Nature	It involves the loss of equal numbers of cations and anions from their lattice sites, creating vacancies.	It involves the dislocation of an ion from its regular lattice site to an interstitial site, creating a vacancy at the original site.
Charge Neutrality	Schottky defects maintain charge neutrality, as the number of positive and negative charges lost are equal.	Frenkel defects maintain charge neutrality, as the displaced ion occupies an interstitial site, and there is no net loss of charge.
Stoichiometry	The stoichiometry of the crystal remains unchanged because the same number of cations and anions are missing.	The stoichiometry of the crystal remains unchanged, as there is no loss of ions; rather, an ion is displaced from its regular position.
Common in	Schottky defects are more common in compounds with a high coordination number, such as ionic compounds with a large size difference between cations and anions.	Frenkel defects are more common in compounds where there is a significant size difference between cations and anions, and the cation can easily occupy interstitial sites.

Conclusion: Frenkel Defect

In summary, Schottky defects involve the creation of vacancies with an equal number of missing cations and anions, maintaining charge neutrality. On the other hand, Frenkel defects involve the displacement of an ion to an interstitial site, creating a vacancy at the original site, while still maintaining charge neutrality. Both types of defects can influence the electrical, optical, and mechanical properties of materials.

Frenkel Defect Frequently Asked Questions

What is the Frenkel defect?

A Frenkel defect is another form of a point defect which is created when an atom or cation leaves its original place in the lattice structure to create a vacancy while occupying another interstitial position within the solid crystal.

What is the Frenkel pair defect?

The Frenkel defect (also known as the Frenkel pair/disorder) is a defect in the lattice crystal where an atom or ion occupies a normally vacant site other than its own. As a result the atom or ion leaves its own lattice site vacant.

What is the difference between the Frenkel and Schottky defect ?

Schottky defect and Frenkel defect are two types of point defects found in crystal lattices. The main difference between Schottky defect and Frenkel defect is that Schottky defect reduces the density of the crystal whereas Frenkel defect does not have any impact on the density of the crystal.

What Colour is AgBr?

Silver bromide (AgBr) is a soft, pale-yellow, water-insoluble salt well known (along with other silver halides) for its unusual sensitivity to light.

Which example shows both Schottky and Frenkel defects?

AgBr shows both Schottky and Frenkel defect.