DEFECTS IN CRYSTALS

1
DEFECTS IN CRYSTALS

• Point defects
• Line defects
• Surface Imperfections

2
PROPERTIES
Structure sensitive
Structure Insensitive
E.g. Density, elastic modulus
E.g. Yield stress, Fracture toughness
3
CLASSIFICATION OF DEFECTS BASED ON DIMENSIONALITY
3D(Volume defects)
1D(Line defects)
2D(Surface / Interface)
0D(Point defects)
Twins
Surface
Vacancy
Dislocation
Interphaseboundary
Precipitate
Disclination
Impurity
Faultedregion
Frenkeldefect
Dispiration
Grainboundary
Voids / Cracks
Twinboundary
Schottkydefect
Stackingfaults
Thermalvibration
Anti-phaseboundaries
4
SYMMETRY ASSOCIATED DEFECTS
Screw
Translation
Rotation
AtomicLevel
Dislocation
Disclination
Dispiration
SYMMETRY ASSOCIATED DEFECTS
Inversion
Mirror
Rotation
Twins
Multi-atom
5
Based on origin
DEFECTS
Random
Structural
Based on position
DEFECTS
Random
Ordered
6
THE ENTITY IN QUESTION
GEOMETRICAL
PHYSICAL
E.g. spin, magnetic moment
E.g. atoms, clusters etc.
7
0D
8
Vacancy
Interstitial
Non-ioniccrystals
Impurity
Substitutional
0D(Point defects)
Frenkel defect
Ioniccrystals
Other
Schottky defect

• Imperfect point-like regions in the crystal
  about the size of 1-2 atomic diameters

9

• Let n be the number of vacancies, N the number
  of sites in the lattice
• Assume that concentration of vacancies is small
  i.e. n/N ltlt 1
• ? the interaction between vacancies can be
  ignored
• ? ?Hformation (n vacancies) n . ?Hformation (1
  vacancy)
• Let ?Hf be the enthalpy of formation of 1 mole
  of vacancies

?G ?H ? T ?S
10
T (ºC) n/N
500 1 x 10?10
1000 1 x 10?5
1500 5 x 10?4
2000 3 x 10?3
?Hf 1 eV/vacancy 0.16 x 10?18 J/vacancy ?Hf 1 eV/vacancy 0.16 x 10?18 J/vacancy

• Certain equilibrium number of vacancies are
  preferred at T gt 0K

11
1D
12
2D
13
2D DEFECTS

• Variables defining a planar defect (leading to
  symmetry breaking)
• ? Translation R(r) Rotation Axis (n), Angle
  (?) Chemistry (concept of colour symmetry)

14
Translation Boundary
? 0
2D defects
Grain Boundary
Chemistry same
Phase Boundary
15
Descriptors
Dimension Density Average spacing (S) Examples
0 ?0 ?v N/V /m3 Sv (?v)-3 m Vacancy, interstitials
1 ?0 ?d L/V /m2 Sd (?d)-2 m Dislocation, disclination
2 ?2 ?b A/V /m Sb (?b)-1 m Grain boundary, twin boundary
3 ?3 ?p Vp/V /m0 S? (f?)1/3 m Precipitate, dispersoid, void
Key v-vacancy, d-dislocation, b-boundary,
p-particle/void, (f?)1/3- volume fraction
16

• Casting
• Metal Forming
• Welding
• Powder Processing
• Machining

Thermo-mechanical Treatments
Crystal
Atom
Structure
Microstructure
Component
Electro- magnetic
Phases
Defects

• Vacancies
• Dislocations
• Twins
• Stacking Faults
• Grain Boundaries
• Voids
• Cracks

Residual Stress

Processing determines shape and microstructure of
a component
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)