Structural Defects

1
Lecture 3.0

• Structural Defects
• Mechanical Properties of Solids

2
Defects in Crystal Structure

• Vacancy, Interstitial, Impurity
• Schottky Defect
• Frenkel Defect
• Dislocations edge dislocation, line, screw
• Grain Boundary

3
Substitutional Impurities Interstitial Impurities
4
Self Interstitial Vacancy
Xv exp(-?Hv/kBT)
5
Vacancy Equilibrium
Xv exp(-?Hv/kBT)
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Defect Equilibrium
Sc kBln gc(E) Sb kBln Wb
Entropy Ss kBln Ws
dFc dE-TdSc-TdSs, the change in free
energy dFc 6 nearest neighbour bond energies
(since break on average 1/2 the bonds in the
surface) Wb(Nn)!/(N!n!) (Nn1)/(n1)
(Nn)/n (If one vacancy added) dSbkBln((Nn)/n)
  For large crystals dSsltltdSb   \ \n N exp
dFc/kBT
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Ionic Crystals
Shottky Defect Frenkel Defect
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Edge Dislocation
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Grain Boundaries
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Mechanical Properties of Solids

• Elastic deformation
• reversible
• Youngs Modulus
• Shear Modulus
• Bulk Modulus
• Plastic Deformation
• irreversible
• change in shape of grains
• Rupture/Fracture

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Modulii
Shear
Youngs
Bulk
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Mechanical Properties

• Stress, ?xx Fxx/A
• Shear Stress, ?xy Fxy/A
• Compression
• Yield Stress
• ?yield Y/10
• ?yieldG/6 (theory-all atoms to move together)

• Strain, ??x/xo
• Shear Strain, ??y/xo
• Volume Strain ?V/Vo
• Brittle Fracture
• stress leads to crack
• stress concentration at crack tip 2?(l/r)
• Vcrack Vsound

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Effect of Structure on Mechanical Properties

• Elasticity
• Plastic Deformation
• Fracture

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Elastic Deformation

• Youngs Modulus
• Y(or E) (F/A)/(?l/lo)
• Shear Modulus
• G?/? Y/(2(1?))
• Bulk Modulus
• K-P/(?V/Vo)
• KY/(3(1-2?))

• Pulling on a wire decreases its diameter
• ?l/lo -??l/Ro
• Poissons Ratio, ??0.5 (liquid case0.5)

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Microscopic Elastic Deformation

• Interatomic Forces
• FT Tensile Force
• FCCompressive Force
• Note F-d(Energy)/dr

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Plastic Deformation
?
?

• Single Crystal
• by slip on slip planes

Shear Stress
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Deformation of Whiskers
Without Defects Rupture
With Defects generated by high stress
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Dislocation Motion due to Shear
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Slip Systems in Metals
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Plastic Deformation
Ao

• Poly Crystals
• by grain boundaries
• by slip on slip planes
• Engineering Stress, Ao
• True Stress, Ai

Ai
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Movement at Edge Dislocation
Slip Plane is the plane on which the dislocation
glides Slip plane is defined by BV and I
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Plastic Deformation -Polycrystalline sample

• Many slip planes
• large amount of slip (elongation)
• Strain hardening
• Increased difficulty of dislocation motion due to
  dislocation density
• Shear Stress to Maintain plastic flow, ? ?oGb??
• dislocation density, ?

Strain Hardening
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Strain Hardening/Work Hardening

• Dislocation Movement forms dislocation loops
• New dislocations created by dislocation movement

• Critical shear stress that will activate a
  dislocation source
• ?c2Gb/l
• GShear Modulus
• bBurgers Vector
• llength of dislocation segment

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Depends on Grain Size
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Burgers Vector-Dislocations are characterised
by their Burger's vectors.  These represent the
'failure closure' in a Burger's circuit in
imperfect (top) and perfect (bottom) crystal.
BV Perpendicular to Dislocation
BV parallel to Dislocation
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Solution Hardening (Alloying)

• Solid Solutions
• Solute atoms segregate to dislocations reduces
  dislocation mobility
• higher ? required to move dislocation
• Solute Properties
• larger cation sizelarge lattice strain
• large effective elastic modulus, Y
• Multi-phase alloys - Volume fraction rule

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Precipitation Hardening

• Fine dispersion of heterogeneity
• impede dislocation motion
• ?c2Gb/?
• ? is the distance between particles
• Particle Properties
• very small and well dispersed
• Hard particles/ soft metal matrix
• Methods to Produce
• Oxidation of a metal
• Add Fibers - Fiber Composites

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Cracking vs Plastic Deformation

• Brittle
• Poor dislocation motion
• stress needed to initiate a crack is low
• Ionic Solids
• disrupt charges
• Covalent Solids
• disrupt bonds
• Amorphous solids
• no dislocations

• Ductile
• good dislocation motion
• stress needed to initiate slip is low
• Metals
• electrons free to move
• Depends on T and P
• ductile at high T (and P)