point defects, calculation

1. Point Defects
Presented By:
Anuradha Verma
Ph. D Scholar

2. Layout of Presentation
Imperfections and their types
Point Defects
Thermodynamics of Point Defects
Vacancy Concentration temperature
dependence
Color Center

3. Why would we want
to study defects?

4. Electrical
(all defects, especially point
defects)
Mechanical e.g., strength,
toughness, hardness, etc) (all
defects, especially
dislocations)
Optical
(all defects,
especially point
defects)
Magnetic
(all defects)
Kinetic e.g., diffusion
(all defects,
especially point
defects)
Affect properties of material

5. Imperfections in Solids
Every lattice point
has exactly the same
environment
Ideal structure
of a solid
Deviations from
ideal structure Defects

6. 0D-
Point
Defects
• Vacancies
• Interstitials
1D-Line
Defects
• Dislocations
2D-
Planar or
Area
Defects
3D-
Volume
Defects
Types
of
Imperfections
•Inclusion
•Voids
•Grain boundary
•Stacking fault

8. 0D
(Point
defects)
Vacancy
Impurity
Frenkel defect
Schottky defect
Non-ionic
crystals
Ionic
crystals
Interstitial
Substitutional
Other ~

9. Vacancies: vacant atomic sites in a structure
Self-Interstitials: "extra" atoms positioned between atomic
sites
Vacancy
distortion
of planes
self-
interstitial
distortion
of planes

11. Schottky defect and Frenkel defect
Schottky Defect:
 Forms when oppositely
charged ions leave their lattice
sites, creating vacancies.
 These vacancies are formed
in stoichiometric units, to maintain
an overall neutral charge in the ionic
solid.
 Density of the solid crystal is less
than normal
 Occurs only when there is small
difference in size between cations
and anions.
Frenkel Defect:
 Smaller ion (usually the cation) is
displaced from its lattice position to
an interstitial site.
 Creates a vacancy defect at its
original site and an interstitial
defect at its new location.
 Does not change the density of the
solid.
 Shown in ionic solids with large size
difference between the anion and
cation.
Missing Anion
Missing Cation

12. Antisite Defects
 Occur in an ordered alloy or compound when atoms of
different type exchange positions.
 Assume-
Type A atoms- at corners of cubic lattice
Type B atoms- center of cube.
If one cube has an A atom at its center, the atom
is on a site usually occupied by a B atom, and is thus
an antisite defect.
This is neither a vacancy nor an interstitial, nor an
impurity.

13. Thermodynamics of intrinsic defects
 Formation of a vacancy- missing bonds and distortion of the lattice
 Potential energy (Enthalpy) of the system increases
 Work required for the formation of a point defect →
Enthalpy of formation (Hf) [kJ/mol or eV/defect]
 n defects are distributed over N lattice sites
W possible arrangements
 Now and
Therefore,
For minimum
For n << N
0


n
G





 


n
nN
kT
H f
ln 




 

kT
H
N
n f
exp

14. Vacancy Concentration Dependence on
Temperature
The equilibrium number of vacancies for a given quantity of material
depends on and increases with temperature as follows:
 Nv
N
= exp
Q V
kT






Equilibrium no. of vacancies
Total no. of atomic sites
Energy required to form vacancy
k = gas or Boltzmann’s constant
T = absolute temperature
in Kelvin
N v
N
T
exponential
dependence!
defect concentration

15. Color Centers
 Imperfections in crystals
 Causes color (by absorption of light)
Examples:
 Diamond with C vacancies- Green color.
 Replacement of Al3+ for Si4+ in quartz-
smoky quartz color.
 Ruby (Al2O3) with < 1% - Pink or red
color.
F center: Excess alkali atoms are added to
an alkali halide crystal, a corresponding
number of negative vacancies are
created.
M center: An M center consists of two
adjacent F centers.
R center: An R center consists of three
adjacent F centers