Frenkel defects arise when an ion occupies an interstitial position between the lattice points.
It is shown in the figure that the crystal of AgBr. One of the Ag+ ions occupies a position in the interstitial space rather than its appropriate site in the lattice. As shown, a vacancy is created in the lattice. It may be noted that the crystal remains neutral since the number of positive ions is the same as the number of negative ions.
Frenkel defects in a crystal of AgCl
The presence of Ag+ ions in the interstitial space of AgBr crystals is responsible for forming a photographic image on exposure of AgBr crystals to light.
Frenkel defects appear in another crystal Zns. Zn+2 ions are entrapped in the interstitial space leaving vacancies in the lattice.
Mostly these defects show in crystals where the negative ions are much larger than the positive ions. Like Schottky defects, the Frenkel defects are also responsible for the conduction of electricity in crystals and the phenomena of diffusion in solids.
NUMBER OF FRENKEL DEFECTS
An ionic crystal has N ions and Ni interstitial spaces in its structures. The number of ways in which n Frenkel defects can be formed is given by,
The energy required to displace an ion from its position to an interstitial position is ε. Then the energy needed to produce n Frenkel defects would be nε. This energy is designated by E.
Using the Boltzmann entropy equation, S=klnW, the free energy equation, ∆A=E-T∆S and the Stirling approximation for evaluating factorial terms, we conclude that,
Equation (2) gives the number of Frenkel defects in a crystal.
It is evident from the Schottky and Frenkel defects equation that the number of Schottky and Frenkel defects would increase exponentially with an increase in temperature.
It is observed by X-rays diffraction of NaCl that at room temperature, there is only one Schottky defect for 105 lattice sites, increasing to 106 at 500◦C and 1011 at 800◦C for the same number of lattice sites.
