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# Frenkel Defect

Yakov Frenkel, a Russian physicist was the person who discovered the Frenkel defect while conducting research on the molecular theory of condensed state. However, this discovery was important as his model explained a defect in the molecule of crystalline solids where an atom or ion moved out of their own lattice site making it vacant while occupying another intermediary vacant site on the same crystal. The defect is also known as dislocation defect and it also clearly depicts both vacancy and self-interstitial defects.

As shown in the figure, the cation has left its own lattice site vacant and it has moved to a new place between the cations and anions.

## Definition of 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.

This defect creates vacancy defect at original site and interstitial defect at new site. The Frankel defect is also called a dislocation defect.

## Characteristic of Frenkel Defect

• This defect occurs only when cations are smaller when compared to the anions.
• There is also no significant impact of the Frenkel defect on the density of the solid and therefore both the volume and mass of the solid is preserved.
• In such cases, substances also maintain their electrical neutrality.
• There is an increase in the dielectric constant as the like charge ions come closer.
• The solids having Frenkel defect show conductivity and diffusion in solid state due to the presence of vacant lattice sites.
• Due to the Frenkel defect, the lattice energy and stability of crystalline solid decreases. This defect influences the chemical properties of ionic compounds.
• The entropy of the solid increases.

## Examples of Frenkel Defect

The main conditions for Frenkel defects are:
(i) Coordination number should be low
(ii) Size of the anion should be bigger than the cation.

The defect is not found in alkali metal halides because cations and anions have almost equal sizes and cations cannot be accommodated in interstitial sites.

In order for the Frenkel defect to occur in an atom, it requires a low coordination number as well as having the crystal lattices open for the molecule. Frenkel defects are mostly exhibited in ionic solids where the smaller ion (usually the cation) is dislocated. Some examples include AgBr, ZnS, AgCl, and AgI.

• Silver Bromide
• Zinc Sulfide
• Silver Chloride
• Silver Iodide

Here the defect occurs mainly due to the smaller size of Zn2+ and Ag+ ions. Meanwhile, Silver Bromide also shows another form of point defect known as the Schottky defect.

## Calculation of the number of Frenkel defects

Frenkel Defects can be calculated using the equation given below:

$$\begin{array}{l}n= \sqrt{NN^{*}}\ e^{-\frac{\Delta H}{2RT}}\end{array}$$

Where,

n= Number of Frenkel defect

N = normally occupied positions.

N∗ = number of available positions.

Delta H = the enthalpy formation of one Frenkel defect.

R = gas constant.

## Key Differences Between Schottky and Frenkel Defect

An ionic material experience both frenkel and schottky defect but there are some differences between them. We have listed the main ones below.

 Schottky Defect Frenkel Defect In Schottky defect the difference in size between cation and anion is small. Frenkel defect contains ionic crystals where the anion is larger than the cation. Both anion and cation leave the solid crystal. Usually the smaller ion cation leaves its original lattice structure. Atoms permanently leave the crystal. Atoms remain within the solid crystal. There is formation of two vacancies. Only one vacancy is created. The density of the solid decreases. Density remains the same.

### 1. What is the Frenkel defect, give an example?

The Frenkel defect is caused if some of the ions of the lattice occupy interstitial sites, leaving a corresponding number of normal lattice sites vacant. The examples of Frenkel defects are AgCl, AgBr, AgI, ZnS etc.

### 2. What is the Frenkel and Schottky defect?

The crystal defect where an equal number of cationic and anionic vacancies are present is called the Schottky defect. The crystal defect where some ions are displaced from normal lattice sites to the interstitial sites is called the Frenkel defect.

### 3. What is the Frenkel defect also called?

The Frankel defect is also called a dislocation defect. Because cations leave its original place in the lattice structure to create a vacancy while occupying another interstitial position within the solid crystal

### 4. Why is the Frenkel defect not found in alkali metal halides?

In order for the Frenkel defect to occur in an atom, it requires a low coordination number as well as having the crystal lattices open for the molecule.The defect is not found in alkali metal halides because cations and anions have almost equal sizes and cations cannot be accommodated in interstitial sites.

### 5. Why does AgBr show both Schottky and Frenkel defects?

AgBr shows both Frenkel and Schottky defects because the radius ratio for AgBr is intermediate. AgBr shows Schottky defects when their anions and cations are both absent from the crystal lattice. Ag+ ions are exceptionally mobile and they have a tendency to move about inside the lattice. So they also show the Frenkel defect.

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