This document discusses various types of imperfections, or defects, that can occur in crystalline solids. It describes point defects like vacancies, which are missing atoms, and interstitials, which are atoms that occupy spaces between normal lattice sites. Larger defects include Schottky defects, which involve both cation and anion vacancies, and Frenkel defects, where an atom moves from its normal site to an interstitial site. Equations are provided for calculating the concentrations of Schottky and Frenkel defects based on thermodynamic principles. Applications of point defects mentioned include their ability to influence electrical, magnetic, and optical properties of materials.

1. Government Vidharbha institute of Science
and Humanities , Amravati
Department of Physics and electronics
Seminar Presentation on
Imperfections In Solids
Presented By
Samiksha R. Deole
M.Sc. II year (Sem-III)

2. Contents
 Imperfection in crystal
 Classification of defects in crystalline solids
 Point defects
 Vacancy defects
 Interstitial defects
 Schottky defect
 Frenkel defect
 Applications

3. Imperfection In Crystal
 An important feature of crystal is the
regular atomic arrangement but no crystal
is perfectly regular.
 Any deviation from this perfect atomic
periodicity is an imperfection which also
called as lattice defect.
 Lattice defect – a state in which the
atomic arrangement in smaller region of a
crystal has departed from regular crystal

5. POINT DEFECT
 Point defect are the irregularity or deviations
from ideal arrangement around a point or an
atom in a crystalline substance.

6. Vacancy Defect
 The defects due to the missing atoms at their
lattice sites are called vacancies

7. Interstitial defect
 When some constituent particals (atoms or
molecules) occupy an interstitial site, the
crystal is said to have interstitial defect

8. SCHOTTKY DEFECT
 Schottky defect in ionic crystals arises when
equal no of cation and anions are missing
from their normal sites , resulting in equal
number of cation and anion vacancies.

9. Consequences Of Schottky Defect
 In Schottky Defect the volume of the crystal
increases without any change in the mass
and therefore, the density of the crystal
decreases.
 The crystal begins to conduct electricity to a
small extent by ionic mechanism
 The presence of too many voids lowers
energy and the stability of the crystal.

10. Concentration of Schottky Defect
N: Total No of Ions
n: cation vacancies
Thermodynamic probability is given by
WA = N! / n! (N-n)! WC = N! / n! (N-n)!
Total Thermodynamic probability is
W = WA.WC = (N! / n!(N-n)!)2
Change in Entropy is given by,
ΔS= K ln W
ΔS= K ln (N! / n! (N-n)!)2
ΔS= 2K [ln N! - ln n! – ln(N-n)!]

11. By using stirlings Approximation formula
2K [ N ln N – n ln n- (N-n) ln (N-n) ]
Net Change in free energy
ΔG = n Δ H – TΔ S
Putting the value ΔS
ΔG = n Δ H – 2KT[N ln N – n ln n –(N-n) ln(N-n)]
We know that change in free energy is zero
d(ΔG) / ∂n = 0
ln (N-n) / n = ΔH / 2KT
As n << N , (N-n) = N
n/N = e(- ΔH / 2KT )
n= N exp (-ΔH / 2KT)

12. FRENKEL DEFECT
 A Frenkel defect is a type of point defect in a
crystal lattice. The defect forms when an
atom or smaller ion leaves its place in the
lattice, creating a vacancy, and becomes an
interstitials by lodging in a nearby location.

13. Concentration Of Frenkel
Defects
N : Total No of Ions
Ni : be the interstitial species
N : No of Frenkel Defects
Thermodynamic probability is given by
W = N! / (N-n)! n! . Ni ! / (Ni - n)! n!
Change in entropy
ΔS = K ln [ N! / (N-n)! n! . Ni ! / (Ni-n)! n!]
= k[ln N! + ln Ni ! – ln(N-n) ! –ln(Ni-n)-2 ln n!]

14. By solving the above equation , we get change in
free energy is
ΔG = n ΔH – T ΔS
Δ H –TK [ ln (N-n) + 1 + ln(Ni-n) + 1 -2ln n-2] = 0
Δ H –TK ln [ (N-n) (Ni-n) / n2 ] = 0
As n<< N , Ni
N-n = N
Ni – n = Ni
We get,
ஃ n = (N-Ni)1/2 exp (- Δ H / 2KT )

15. Application of point defects
 Point defects can influence the electrical
and magnetic properties of material
 Point defects can influence the optical
properties of materials.
 Colour Centres
Generations of colour centres
i. By the introduction of chemical impurities.
ii. By the introduction of excess of metal.