CHAPTER 4 IMPERFECTIONS IN SOLIDS

1
CHAPTER 4IMPERFECTIONS IN SOLIDS
ISSUES TO ADDRESS...
What types of defects arise in solids?
Can the number and type of defects be varied
and controlled?
How do defects affect material properties?
Are defects undesirable?
What are the solidification mechanisms?
2
Introduction

• Ideally Perfect Order
• Really various defects or imperfections
• Atomic Vibration
• Every Atom is vibrating around its lattice
  position ? Defects
• Levels of Defects
• Point
• Linear
• Interfacial
• Bulk pores, cracks and foreign inclusions
  (bubble, sand ..etc).
• Require Examination of Structure ? Techniques
• Application
• Solid Solutions Solvent (host atoms) and Solute
  ? Alloy
• Why?
• 1) to improve mechanical properties
• 2) Most metals are alloys (impurities always
  exist).

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Imperfections in Solids

• There is no such thing as a perfect crystal !
• Thermodynamically impossible
• defects lower the energy of a crystal make
  it more stable
• always have vacancies and impurities, to some
  extent
• Many of the important properties are due to the
  presence of imperfections.
• Defect does not necessarily imply a bad thing
• addition of C to Fe to make steel
• addition of Cu to Ni to make thermocouple
  wires
• addition of Cr to Fe for corrosion resistance
• introduction of grain boundaries to strengthen
  materials
• Defect can be either desirable or undesirable.

4
Solidification Mechanism

• Solidification- result of casting of molten
  material
• Mechanism - 2 steps
• Nuclei form
• Nuclei grow to form crystals grain structure
• Start with a molten material all liquid

• Crystals grow until they meet each other

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Polycrystalline Materials

• Grain Boundaries
• regions between crystals
• transition from lattice of one region to that of
  the other
• slightly disordered
• low density in grain boundaries
• high mobility
• high diffusivity
• high chemical reactivity

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Solidification

• Grains can be - equiaxed (roughly same size in
  all directions)
• - columnar (elongated grains)

heat
flow
Shell of equiaxed grains due to rapid cooling
(greater ?T) near wall
Columnar in area with less undercooling
Grain Refiner - added to make smaller, more
uniform, equiaxed grains.
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Types of Imperfections
Vacancy atoms Substitutional atoms
Interstitial atoms
Point defects
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Point Defects
Vacancies
-vacant atomic sites in a structure.
Vacancy
distortion
of planes
Self-Interstitials
-"extra" atoms positioned between atomic sites.
self-
interstitial
distortion
of planes
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Equilibrium ConcentrationPoint Defects - Vacancy
Equilibrium concentration of vacancies varies
with temperature!
Activation energy
No. of defects
æ
ö
-
N
Q
ç

v
v

ç

exp
No. of potential
è
ø
N
k
T
defect sites.
Temperature
Boltzmann's constant

-23
(1.38 x 10
J/atom-K)
-5
(8.62
x
10
eV/atom-K)
Each lattice site
is a potential
vacancy site
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Measuring Activation Energy
We can get Qv from an experiment.
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Estimating Vacancy Concentration
Find the equil. of vacancies in 1 m3 of Cu
at 1000?C.
Given
3
r
8.4 g
/
cm
A
63.5 g/mol
Cu
N
6.02 x 1023
atoms/mol
Q
0.9 eV/atom
A
v

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Point Defects in Alloys
Two outcomes if impurity (B) added to host (A)
Solid solution of B in A (i.e., random dist.
of point defects)
OR
Substitutional solid soln. (e.g., Cu in Ni)
Interstitial solid soln. (e.g., C in Fe)
When similar smaller
Partial Solubility Solid solution of B in A plus
particles of a new phase (usually for a larger
amount of B)
Second phase particle - different composition -
often different structure.
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Interstitial Solid Solution

• Impurity atoms fill voids among the host atoms
• Always APF lt 1 ? there are always voids
• For metals strong (metallic bonding) ? highly
  packed
• ? small voids ? Small portion can be dissolved
• Condition
• Atomic radius must be very small compared to host
  atom
• Example carbon in steel
• Exercise
• Calculate the maximum size of an interstitial
  atom for dissolving in BBC iron ?

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Conditions for Substitutional Solid Solution SSS

• For Material A and B they can form
  substitutional solid solution if they satisfy W.
  Hume Rothery rule i.e.
• IF
• ?r (atomic radius) lt or - 15
• Same crystal structure for pure metals
• Similar electronegativities - i.e., Proximity in
  periodic table
• the difference in electronegativity must be
  0.4 eV
• (i.e. large differences ? compound formation
  (intermetallics))
• 4. Valency
• All else being equal,
• a solute with a higher valency is more likely to
  be soluble than one of lower valency
• If only part of the conditions are satisfied
• ? SSS with partial solubility
• If any portion of A dissolves in any portion of B
  
• ? SSS with complete solubility

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Examples Substitutional Solid Solution
Application of HumeRothery rules Solid
Solutions

• Examples
• Check Cu in Ni
• All O.K. ?
• SSS with complete solubility
• 2) Check Cu in Ag
• All O.K.
• SSS with complete solubility
• 3) Check Ni in Co
• Crystal structure is different
• SSS with partial solubility

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Composition of Solutions

• Specification of composition
• weight percent

m1 mass of component 1
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Linear Defects

• Linear Defects (Dislocations)
• Are one-dimensional defects around which, atoms
  are misaligned
• Edge dislocation
• extra half-plane of atoms inserted in a crystal
  structure
• b ? to dislocation line
• Screw dislocation
• spiral planar ramp resulting from shear
  deformation
• b ?? to dislocation line

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Dislocations

• Edge Dislocation

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Dislocations
Screw Dislocation

• Screw Dislocation

b
Dislocation line
(b)
Burgers vector b
(a)
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Edge, Screw, and Mixed Dislocations
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Planar Defects in Solids

• External Surfaces
• Grain Boundaries
• Twin boundary (plane) Essentially a reflection
  of atom positions across the twin plane.
• 4. Stacking faults
• - For FCC metals an error in ABCABC packing
  sequence
• - Ex ABCABABC

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Microscopic Examination

• Crystallites (grains)
• - Have grain boundaries.
• - Vary considerably in size.
• - Crystallites can be quite large
• ex Large single crystal of quartz or diamond or
  Si
• ex Aluminum light post or garbage can - see the
  individual grains
• - Crystallites (grains) can be quite small
• (mm or less) necessary to observe with a
  microscope.
• Preparation of specimen
• - Cutting
• - grinding polishing ? mirror like surface
• - etching (immersing in chemical solution)
• reaction with atoms at grain boundaries high
  chemical reactivity
• They dissolve into the solution forming grooves
  among the grain boundaries

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Optical Microscopy
Useful up to 2000X magnification. Polishing
removes surface features (e.g., scratches)
Etching changes reflectance, depending on crystal
orientation.
crystallographic planes
Micrograph of brass (a Cu-Zn alloy)
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Optical Microscopy
Grain boundaries...
are imperfections, are more susceptible to
etching, may be revealed as dark lines,
change in crystal orientation across boundary.
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Summary
Point, Line, and Area defects exist in solids.
The number and type of defects can be varied
and controlled (e.g., T controls vacancy
conc.)
Defects affect material properties (e.g.,
grain boundaries control crystal slip).
Defects may be desirable or undesirable
(e.g., dislocations may be good or bad,
depending on whether plastic deformation is
desirable or not.)