m2 point defects
DESCRIPTION
point defects, calculationTRANSCRIPT
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Point Defects
Presented By:
Anuradha Verma
Ph. D Scholar
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Layout of Presentation
Imperfections and their types
Point Defects
Thermodynamics of Point Defects
Vacancy Concentration temperature dependence
Color Center
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Why would we want to study defects?
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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
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Imperfections in Solids
Every lattice point
has exactly the same environment
Ideal structure of a solid
Deviations from ideal structure
Defects
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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
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0D (Point
defects)
Vacancy
Impurity
Frenkel defect
Schottky defect
Non-ionic crystals
Ionic crystals
Interstitial
Substitutional
Other ~
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Vacancies: vacant atomic sites in a structure
Self-Interstitials: "extra" atoms positioned between atomic
sites
Vacancy
distortion
of planes
self-
interstitial distortion
of planes
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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
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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.
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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
0n
G
n
nN
kT
H fln
kT
H
N
n fexp
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Vacancy Concentration Dependence on Temperature
The equilibrium number of vacancies for a given quantity of material
depends on and increases with temperature as follows:
N v
N = exp
Q V
k T
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
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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
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