There are 6 point defects in crystals –

a)  Vacancy –

It is due to the removal of an atom from its regular lattice position. This atom travels to surface of materials.

Diagram –

For low number of vacancies, the following relation exists.

$n =N.exp \left ( \dfrac {-E_{V}}{KT} \right )$

where $n=$ number of vacancies,

$N=$ Total numbers of atoms,

$T=$ temp in $^{\circ}k$

$E_{V}=$ average energy required to create vacancy.

b) Interstitial –

When an extra atom of same type is fitted into the void between the regular occupied sites then this defects occurs.

c)  Substitutional  Impurity –

In this foreign atom is found occupying a regular site in crystal lattice

d) Interstitial Impurities –

Here a foreign atom is found occupying a non-regular site in a crystal lattice   

diagram

e)  Schottky Defect –

The point imperfections in ionic crystal occurs when a –ve ion vacancy is associated with a +ve ion vacancy. It is thus localized vacancy pair of +ve & -ve ions. Due to these defects, the crystal is maintained electrically neutral. Here the following equation is applied –

$n=N e^{\frac {-E_{p}}{2KT}} \\$ Where $n =$ numbers of pairs $N=$ number of lattice side $K=$ Boltzmann constant $E_p =$ Energy required to create a pair $T=$ Temp in $^{\circ}k$  f)  Frankel Defect – For ionic crystal when a –ve ion vacancy is associated with an interstitial –ve ion or vice-versa it is called as Frankel Defect. Thus an ion shift to interstitial position in crystal lattice, then a vacancy is crated. This defect occurs in ionic crystal when, a) Anion is much larger than cation b) Anion has low co-ordinary number of Frankel creation is $N=(NN')^{\frac {1}{2}} \ e^{\frac {-E}{2KT}} $ where, $N=$ Numbers of lattice site $N'=$ Numbers of interstitial side $E=$ Energy required to remove an atom from lattice site to interstitial