Imperfections, Defects and Diffusion
Lattice Defects
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Week5
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Goals for the Unit
I. Recognize various imperfections in crystals (Chapter 4)
- Point imperfections
- Impurities
- Line, surface and bulk imperfections
II. Define various diffusion mechanisms (Chapter 5)
III. Identify factors controlling diffusion processes
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Defects in Materials
- Why study defects?
- Types of defects
- How are defects introduced
- Diffusion in materials
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Types of Defects
o Point defects (composition)
• Vacancies
(missing atoms)
• Interstitials
(extra atoms)
• Impurities (unwelcome segregation)
o Extensive chemical changes
- Solid solutions
- Not a defect in intentional alloying or doping
o Line defects (1-dimensional) (Deformation)
• dislocations - in metals
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Types of Defects, cont.
o Interfacial defects (2-dimensional) (Properties)
- surfaces - both interior (pore walls)
and exterior (surface of material)
- interfaces -(grain boundaries)
o Bulk-Volume defects (3-dimensional)
- cracks, foreign inclusions, other phases
(including pores).
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Point Defects in Metals
Self Interstitial
Interstitial
Impurity
Vacancy
Substitutional
Impurity
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Point defects
o Vacancy
An empty atomic site
o Interstitial
An atom somewhere other than an atomic site
- Self-interstitial
- Impurity interstitial
o Substitutional impurity
Some “foreign” species on an atomic site
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How are point defects introduced?
- Some types are thermally generated
- Direct result of thermal vibration of the atomic array
- The concentration of thermally-produced
defects increases exponentially with
increasing temperature
Hint: Equilibrium number of vacancies Nv, for a material
Nv = N exp [-Qv/kT]
N = total number of atomic sites
Qv = activation energy to form a vacancy, eV
k = Boltzmann’s constant (8.62 x 10-5 eV/atom-K)
T = Temperature (K)
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How are point defects introduced?
How are point defects introduced?
1. Added solutes (impurities or dopants)
ordered or disordered solid solution
How do they get uniformly distributed?
2. Stoichiometry changes
(cation/anion ratio changes)
e.g., ZrO2-δ , Fe1-δO (δ~ 0.05)
How is uniform composition accomplished?
(Stoichiometric: State in an ionic compound in which there is an exact ratio of
cations to anions as predicted by the chemical formula.)
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Point Defects in Ceramics
Schottky defect
(anion and cation
vacancies)
Frenkel defect
(cation vacancy +
cation interstitial)
Cation
Vacancy
Anion
Vacancy
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Point Defects in Ceramics
Interstitial
Cation Impurity
Substitutional
Cation Impurity
Anion impurity
Interstitial
(not shown)
Substitutional
Anion Impurity
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Solid Solution
All solids have some degree of impurities
dissolved in them
- Unintentional - called impurities
- Intentional - called dopants or alloying additives
Solute and solvent
- Solvent (present in greatest amount)
- Solute (present in minor concentration)
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Hume-Rothery Rules
• Complete mutual solid solubility will occur
between two metals if:
- Less than 15% difference in atomic radii
- Both have the same crystal structure in pure form
- Both have similar electronegativities
- Both have the same valence
• The more deviation, the less the solubility
• Can also be applied roughly in simple ceramics
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Solution of ~30 at% Cu dissolved in
solid Ni(substitutional solid solution)
Ni
Cu
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Disordered (normal) and ordered
solid solution
Expected gold or Copper
atom position
Ordered AuCu3
(Below 380oC)
Disorderd AuCu3
(Above 380oC)
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Gold atom
Copper atom
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Interstitial solid solution
C atom dissolve interstitially at
0.5 0 0.5 –type position
In BCC structure of α-Fe
For α-Fe, rinterstitial=0.0192 nm
rcarbon =0.077 nm
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Solution of NiO in MgO
(cations of same valence)
O2Ni2+
Mg2+
Random substitutional solid solution
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Week 5
Solution of Fe2O3 in FeO
(altervalent cation - vacancy charge compensation)
O2cation
Fe3+
vacancies
Fe2+
Vacancy
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Line Defects: Dislocation in Metals
Responsible for large mechanical deformation in crystalline solids
-Linear (one dimensional) defect around which
some of the atoms are misaligned
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Types of Dislocations
- Edge Dislocation:
A portion of an extra plane of atoms
- Screw Dislocation:
Helical atomic displacement around a line
extending through the crystal
- Mixed Dislocation:
Some edge, some screw nature
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Edge Dislocation
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Burgers vector
b
Perfect crystal
dislocated crystal
b-represents the magnitude of
the structural defect
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Screw Dislocation
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Mixed Dislocation
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Why are Dislocations Important?
The motion of dislocations is the principle
mechanism whereby metals deform
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Why? Energy, Energy, Energy!
o Lower
energy
than
breaking
all bonds
in a
plane at
once
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Shear occurs by dislocation movement producing
permanent (plastic) deformation by “slip”
Textbook ch6, pp 212-218
Direction of
Slip plane
dislocation movement
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Edge Dislocation Motion - 3D
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Slip occurs along densely packed
directions on densely packed planes
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(Plane)[Direction] pairs designate “slip
systems” (e.g., in FCC and HCP)
pp 215
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Dislocation movement and ductility
•
A large number of independent slip systems are required
for good ductility in polycrystalline materials so grains
can deform to accommodate their neighboring grains
Common in many metal structures (esp. bcc and fcc)
•
Dislocations are very complex in ceramic structures
This and complications of like charged ions encountering
each other during slip make dislocation movement almost
impossible in ceramics
Therefore ceramics are not ductile, they are brittle
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Impediments to easy dislocation movement
• Impurity atoms (“solute hardening”)
• Intersection with other dislocations
(entanglement) (“work hardening”)
• Grain boundaries (dislocations “pile up”)
• Small dispersed inclusions (“precipitation hardening”)
• All of these affect ductility and yield strength of a metals
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Grain boundaries and other dislocations impede the
movement of dislocations causing “hardening”
Dislocations
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2-D Defects
• Twin boundaries
• Grain boundaries
• Surfaces
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Twinning is common in some materials
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Small angle grain boundaries can be thought of
as arrays of dislocations
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Some details of surface structure
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Material Science Investigative Techniques “Microscopy”
• Optical microscope
surface microstructure (~ 1µm)
• Scanning electron microscope (SEM)
Surface microstructure, analytical chemistry (~50-100 nm)
• Transmission electron microscope
resolve the atomic structure from a very thin foil (30 Ao),
(~1 Ao)
• Atomic force microscope
3D surface topography, electrical, magnetic scanning (~1 nm)
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Reading Assignment
Shackelford 2001(5th Ed)
– Read Chapter 4, pp 115-136, 145-150
Read ahead Chapter 5, pp 158-181
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