Frenkel defect

A Frenkel defect or dislocation defect is a type of point defect in crystalline solids named after its discoverer Yakov Frenkel[1]. The defect forms when an atom or smaller ion (usually cation) leaves its place in the lattice, creating a vacancy, and becomes an interstitial by lodging in a nearby location.[2] Their primary mechanism of generation is by particle irradiation, as their equilibrium concentration according to the Boltzmann distribution is much smaller than the pure vacancinterstitial atoms.

In an ionic crystal, this point defect forms when an ion is displaced from its lattice position to an interstitial site, creating a vacancy at the original site and an interstitial defect at the new location without any changes in chemical properties.[3] This defect appears in an ionic solid which usually possess low coordination number or a considerable disparity in the sizes of the ions. The smaller ion (usually the cation) is dislocated; e.g. in ZnS, AgCl, AgBr, and AgI due to the small size of the zinc ion with charge +2 and the silver ion with charge +1, the cations in the respective cases get dislocated.

AgBr exhibits both Frenkel defect and Schottky defect despite the disparity in the sizes of the constituent ions.

Effect on density

Frenkel defect does not have any impact on the density of the solid as it involves only the migration of the ions within the crystal, thus preserving both the volume as well as mass.[citation needed]

Examples

The Frenkel defect within the NaCl structure

Frenkel defects are exhibited in ionic solids with a large size difference between the anion and cation (with the cation usually smaller due to an increased effective nuclear charge)

Some examples of solids which exhibit Frenkel defects:

These are due to the comparatively smaller size of Zn2+ and Ag+ ions.

For example, consider a lattice formed by Xn and Mn+ ions. Suppose an M ion leaves the M sublattice, leaving the X sublattice unchanged. The number of interstitials formed will equal the number of vacancies formed.

One form of a Frenkel defect reaction in MgO with the oxide anion leaving the lattice and going into the interstitial site written in Kröger–Vink notation:

Mg×
Mg
+ O×
O
→ O${\displaystyle \prime \prime }$
i
+ v••
O
+ Mg×
Mg

This can be illustrated with the example of the sodium chloride crystal structure. The diagrams below are schematic two-dimensional representations.

The defect-free NaCl structure
Two Frenkel defects within the NaCl structure