# Frenkel Defect

Yakov Frenkel, a Russian physicists 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

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.

### Characteristic of Frenkel Defect

This defect occurs only when cations are smaller in size when compared to the anions. There are also no changes in chemical properties. There is also no significant impact of 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.

### Examples

In order for the Frenkel defect to occur in an atom, it requires a low coordination number as well as have 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 of the 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 Schottky defects.

### Calculation

Frenkel Defects can be calculated using the equation given below:

$\sqrt{NN^{\ast }} \: e^{\delta \frac{H}{2RT}}$

Where,

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 materials experiences 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.