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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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