Frenkel Defect: Definition, Characteristics & Calculation

Frenkel Defect is the defect in the formation of lattice crystals, where an ion or atom occupies a usually vacant site. It is named after the Russian Physicist, Yakov Frenkel. The defect in the crystal is caused by the voluntary spacing out of an atom, which creates a vacancy. The defect is also called dislocation defect which clearly depicts both valency and self-interstitial defects.

The crystal lattice comprises of small cations that get displaced from the original positions and thus create a vacant site in the crystal lattice. 

Key Terms: Frenkel Defect, Crystal, Crystal Lattice, Dislocation Defect, Vacancy, Solid State, Crystallographic Defect, Imperfection, Electrical Neutrality

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Frenkel Defect: Definition & Examples

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Frenkel Defect is an imperfection in the formation of crystals. In solid crystals, many units have fewer atoms than the ideal units of crystals. This is called a defect. In crystalline solids, the interruption in the regular pattern is called a crystallographic defect. There are many types of defects, each signifying a significant lapse in the internal formation of crystals.

The different types of defects are as follows:

• Stoichiometric Defect,
• Schottky Defect
• Frenkel Defect
• Impurity Defects  

Examples of Frenkel Defect

Some examples of Frenkel Defect are:

1. Silver (I) Chloride
2. Silver (I) Iodide
3. NaCl (Sodium Chloride)
4. Zinc sulfide
5. Silver (I) Bromide

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Frenkel Defect Formation

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Following is the way in which a Frenkel defect gets formed in the crystal lattice:

1. A cation leaves its own lattice side and becomes interstitial.
2. A vacancy is created in the lattice.
3. The uprooted cation lodges itself in a nearby location between the other cations and anions.

Frenkel Defect in NaCl Crysta

Reason for Frenkel Defect Formation

Defects are common in solid-state structures, as the positions of molecules or atoms are determined by the unit cell parameters in crystals at repeated fixed distances. Frenkel defects are primarily engineered during particle irradiation. A crystal structure is mostly imperfect and subjected to change. In particle irradiation, the enthalpy at the time of formation is higher than at any other point, and thus the equilibrium does not touch the detection limit. Frenkel defect can also occur spontaneously in structures where the cation (smaller ion) is dislocated.

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Characteristics of a Frenkel Defect

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The Frenkel Defect is a unique defection, where the crystal remains neutral and the number of cations and anions remains the same. Owing to the distinction in the size of cations and anions, the smaller atoms occupy the interstitial sites.

Here are some characteristics of the Frenkel Defect:

1. The lattices formed in a Frenkel Defect are relatively open.
2. The Frenkel Defect occurs when the size of cations is smaller in comparison to the anions.
3. The coordination number of a solid-state in the Frenkel Defect is low.
4. The Frenkel Defect does not change the chemical properties of a substance.
5. Frenkel Defect has no impact on the density of the structure, therefore it preserves the mass and volume of the solid.
6. Substances maintain their electrical neutrality in the undertaking of the Frenkel Defect.

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Number of Frenkel Defect Calculation

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Following are the important parameters to calculate thenumber of frenkel deffect in a crystal:

1. Normally Occupied Positions
2. Number of Available Positions
3. Enthalpy Released by the defect
4. Temperature of the spot

The formula for calculating the Frenkel defect is given by: 

\(\sqrt{NN'} e^\frac{\Delta H}{2RT}\)

Where,

N= Normally occupied positions

N’= Number of available positions

ΔH= One Frenkel Defect's enthalpy formation

R = Gas constant

T = Temperature

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Impact of Frenkel Defect on Density

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The Frenkel defect has no impact on the density and stability of the crystal. Although the migration of the ion is directly impacted by the defect, the volume and density of the solid-state structure do not change. In close-packed structures, the interstitial atoms induce strains that expand the lattice. This expansion dominates the contraction of lattice due to incurred vacancy.

Consequences of Frenkel Defect

The Frenkel defect causes a displacement in ions. This defect is also known as the dislocation defect, as the smaller ion being cation is displaced from its original site and is placed into an interstitial site. Although the density remains unchanged, the compounds have low coordination numbers and a vast difference in the size of anions and cations.

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Frenkel and Schottky Defect

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The methods of defections in solid-state crystals lie in their formations and seclusion. Schottky Defect points out the defect in crystalline solids, whereas, Frenkel Defect denotes the formation of crystalline ionic compounds.

Frenkel and Schottky Defect Illustration

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Things To Remember

• Frenkel defect occurs when an ion or atom occupies a vacant site in a crystal lattice. 
• When a cation leaves its position, a vacancy gets created, and the cation moves to a position close by.
• Particle-irradiation is the cause of the Frenkel defect to occur.
• The chemical properties do not undergo any change as part of the Frenkel defect.
• Density or the electrical neutrality of the crystal is not imparted in the Frenkel defect.
• Number of Frenkel defects is calculated based on the number of occupied and available positions and the temperature. 
• Due to displacement of ions, Frenkel defect is also called dislocation defect. 

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