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DEFECTS IN CRYSTALSDEFECTS IN CRYSTALS
Point defects
Line defects
Surface Imperfections
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PROPERTIES
Structure sensitive Structure Insensitive
E.g. Yield stress, Fracture toughness E.g. Density, elastic modulus
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0D
(Point defects)
CLASSIFICATION OF DEFECTS BASED ON DIMENSIONALITY
1D
(Line defects)
2D
(Surface / Interface)
3D
(Volume defects)
Vacancy
Impurity
Frenkel
defect
Schottky
defect
Dislocation Surface
Interphase
boundary
Grain
boundary
Twin
boundary
Twins
Precipitate
Faulted
region
Voids /
Cracks
Stacking
faults
Disclination
Dispiration
Thermal
vibration
Anti-phase
boundaries
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Translation
SYMMETRY ASSOCIATED DEFECTS
Rotation Screw
Atomic
LevelDislocation Disclination Dispiration
Mirror
SYMMETRY ASSOCIATED DEFECTS
Rotation Inversion
Twins Multi-atom
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Random
DEFECTS
Structural
Random
DEFECTS
Ordered
Based onorigin
Based on
position
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THE ENTITY IN QUESTION
GEOMETRICAL PHYSICAL
E.g. atoms, clusters etc. E.g. spin, magnetic moment
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0D0D
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0D
(Point defects)
Vacancy
Impurity
Frenkel defect
Schottky defect
Non-ionic
crystals
Ionic
crystals
Imperfect point-like regions in the crystal about the size of 1-2 atomicdiameters
Interstitial
Substitutional
Other ~
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G = H T S
Let nbe the number of vacancies,N the number of sites in the lattice
Assume that concentration of vacancies is small i.e. n/N
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T (C) n/N
500 1 x 1010
1000 1 x 105
1500 5 x 104
2000 3 x 103
Hf = 1 eV/vacancy= 0.16 x 1018 J/vacancy
G
(G
ib
b
s
fre
e
e
n
e
rg
y
)
n ( n u m b e r o f v a c a n c i e s )
Gm i n
E q u i l i b r i u mc o n c e n t r a t i o n
G (perfect crystal)
Certain equilibrium number of vacancies are preferred at T > 0K
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1D1D
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2D2D
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2D DEFECTS
Variables defining a planar defect (leading to symmetry breaking)
Translation [R(r)] + Rotation [Axis (n), Angle ()]
+ Chemistry (concept of colour symmetry)
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Translation Boundary
Phase Boundary
2D defects Grain Boundary
= 0
Chemistry same
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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
Descriptors
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Atom Structure
Crystal
Electro-magnetic
Microstructure Component
Thermo-mechanical
Treatments
Phases Defects+
Casting Metal Forming Welding
Powder Processing
Machining
Vacancies Dislocations Twins
Stacking Faults Grain Boundaries Voids Cracks
+
Residual
Stress
Processing determines shape and microstructure of a component
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