M2 point defects

Point Defects

Presented By:

Anuradha Verma

Ph. D Scholar

Layout of Presentation

Imperfections and their types

Point Defects

Thermodynamics of Point Defects

Vacancy Concentration temperature dependence

Color Center

Why would we want to study defects?

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

Imperfections in Solids

Every lattice point

has exactly the same environment

Ideal structure of a solid

Deviations from ideal structure

Defects

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

0D (Point

defects)

Vacancy

Impurity

Frenkel defect

Schottky defect

Non-ionic crystals

Ionic crystals

Interstitial

Substitutional

Other ~

Vacancies: vacant atomic sites in a structure

Self-Interstitials: "extra" atoms positioned between atomic

sites

Vacancy

distortion

of planes

self-

interstitial distortion

of planes

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

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.

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

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

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