Engineering 45
Imperfections
In Solids
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Learning Goals
 Learn The Forms of Defects in Solids
•
Use metals as Prototypical Example
 How the number and type of defects
Can be varied and controlled
 How defects affect material properties
 Determine if “Defects” or “Flaws” are
• Desirable
• UNdesirable
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Classes of Imperfections
 POINT Defects
• Atomic Vacancies
• Interstitial Atoms
• Substitutional Atoms
 LINE Defects
• (Plane Edge) Dislocations
 Area Defects
• Grain Boundaries
– Usually 3-D
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Point Defects
 Vacancy  MISSING atom at Lattice Site
Vacancy
distortion
of planes
selfinterstitial
distortion
of planes
 Self-Interstitial  “Extra” Atom “Squeezed”
into the Lattice Structure
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Point Defect Concentration
 Equilibrium Defect Concentration Varies With
Temperature; e.g., for Vacancies:
No. of defects
No. of potential
defect sites.
Activation energy
-Q
Nv
= exp 
 v
 kT
N



Temperature
Boltzmann's constant
 k=
• 1.38x10-23 J/at-K
• 8.62x10-5 eV/at-K
Engineering-45: Materials of Engineering
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 N  Every Lattice Site
is a Potential Vacancy
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Measure Activation Energy
 Recall The Defect
Density Eqn
ND
=e
N
QD
kT
 This form of a
Negative Exponential
is called an
Arrhenius Relation
• Svante Arrhenius:
1859-1927, Chem
Nobel 1903
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 Take the ln of Eqn
ln  N D
 QD 
N  = -
1 T 
 k 
 This of the form
y = mx where
y  ln  N D N 
m = -QD k 
x  1 T 
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Measure Activation Energy cont
 Meausure ND/N vs T  By ENGR25 method
of Function Discovery
Nv
ln
N
exponential
dependence!
Nv
N
slope
-Qv /k
T
 RePlot in Linear
Form
• y = mx + b
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 Find the Activation
Energy from the
Slope
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
1/T
Vacancy Concentration Exmpl
 In Defect Density
Rln QD Can Take
Two forms
• Qv  Vacancies
• Qi  Interstitials
 Consider a Qv Case
• Copper at 1000 C
• Qv = 0.9 eV/at
• ACu = 63.5 g/mol
•  = 8400 kg/cu-m
Engineering-45: Materials of Engineering
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 Find the Vacancy
Density
• First Find N in units
of atoms per cu-m


N A  6.023 10 23 8400 
N=
=
ACu
0.0635
N=
units Check

at / mol kg / m 3 
N
=
kg mol
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt

at
m3
Vacancy Concentration cont
 Since Units Chk:
N = 7.97 1028
at - sites / m3
 Now apply the Arrhenius Relation @1000 ºC
 Qv 
N v = N exp  
 kT 


- 0.9eV / at
= 7.97 10 exp 

-5
8
.
62

10
eV
/
at
K
1273
K


N v = 2.18 10 25 vac / m3
28
  275 ppm
Vacancy Rate
Engineering-45: Materials of Engineering
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

 At 180C (Pizza
Oven) The Vacancy
Rate  98 pptr
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Observing Equil Vacancy Conc
575μm X 575μm Image
 Low energy electron
microscope view of
a (110) surface of
NiAl.
 Increasing T causes
surface island of
atoms to grow.
 Why? The equil.
vacancy conc.
increases via atom
motion from the
Engineering-45: Materials of Engineering
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 crystal to the
surface, where they
join the island.
Island grows/shrinks to maintain
equil. vancancy conc. in the bulk.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Point Impurities in Solids

Two outcomes if impurity (B) added to host (A)
1. Solid solution of B in A (i.e., random dist. of point
defects)
OR
Substitutional alloy
(e.g., Cu in Ni)
Interstitial alloy
(e.g., C in Fe)
2. Solid solution of B in A plus particles of a NEW
PHASE (usually for a larger amount of B)
Second phase particle
• different composition (chem
formula)
• often different structure
Engineering-45: Materials of Engineering
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• e.g.; BCC in FCC
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
W. Hume – Rothery Rule
 The Hume–Rothery rule Outlines the
Conditions for substitutional solid soln
• Δr (atomic radius) < 15%
• Proximity in periodic table
– i.e., similar electronegativities
• Same crystal structure for pure metals
• Valency
– All else being equal, a metal will have a greater
tendency to dissolve a metal of higher valency
than one of lower valency
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Imperfections in Solids
 Application of Hume–Rothery rules 
Solid Solutions
Element
Atomic Crystal
ElectroRadius Structure
(nm)
1. Would you predict
more Al or Ag
to dissolve in Zn?
2. More Zn or Al
in Cu?
Engineering-45: Materials of Engineering
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Cu
C
H
O
Ag
Al
Co
Cr
Fe
Ni
Pd
Zn
0.1278
0.071
0.046
0.060
0.1445
0.1431
0.1253
0.1249
0.1241
0.1246
0.1376
0.1332
Valence
negativity
FCC
1.9
+2
FCC
FCC
HCP
BCC
BCC
FCC
FCC
HCP
1.9
1.5
1.8
1.6
1.8
1.8
2.2
1.6
+1
+3
+2
+3
+2
+2
+2
+2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Apply Hume – Rothery Rule
 Would you predict
more Al or Ag
to dissolve in Zn?
• Δr → Al (close)
• Xtal → Toss Up
• ElectronNeg → Al
• Valence → Al
 More Zn or Al
in Cu?
• Δr → Zn (by far)
• Xtal → Al
Engineering-45: Materials of Engineering
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Element
Cu
C
H
O
Ag
Al
Co
Cr
Fe
Ni
Pd
Zn
Atomic Crystal
Radius Structure
(nm)
0.1278
0.071
0.046
0.060
0.1445
0.1431
0.1253
0.1249
0.1241
0.1246
0.1376
0.1332
Electronegativity
Valence
FCC
1.9
+2
FCC
FCC
HCP
BCC
BCC
FCC
FCC
HCP
1.9
1.5
1.8
1.6
1.8
1.8
2.2
1.6
+1
+3
+2
+3
+2
+2
+2
+2
• ElectronNeg → Zn
• Valence →BruceAlMayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Composition/Concentration
 Composition  Amount of impurity/solute (B)
and host/solvent (A) in the SYSTEM.
 Two Forms
• Weight-%
mB
CB =
 100
m A m B
• Where
– mJ = mass of
constituent “J”
• Atom/Mol %
n mB
C =
100
n mA  n mB
'
B
• Where
– nmJ = mols of
constituent “J”
 Convert Between Forms Using AJ
kg
UNITS
nmJ = mJ AJ 
= mol
kg / mol
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Linear Defects → Dislocations
 Edge dislocation:
extra half-plane of
atoms
• linear defect
• moves in response
to shear stress and
results in bulk atomic
movement (Ch 7,8)
– cause of slip between
crystal planes when
they move
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Movement of Edge Dislocations
 Dislocations Move Thru the Crystal in
Response to Shear Force
• Results in Net atomic Movement or DEFORMATION
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Motion of Edge Dislocation
 Dislocation motion
requires the
successive bumping
of a half plane of
atoms (from left to
right here).
 Bonds across the
slipping planes are
broken and remade
in succession
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Carpet Movement Analogy
 Moving a Large Carpet All At Once Requires
MUCH Force (e.g.; a ForkLift Truck)
• Using a DISLOCATION Greatly Facilitates the Move
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Carpet Dislocation
 Continue to Slide Dislocation with little effort
to the End of the Crystal
• Note Net Movement at Far End
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Dislocations
 First PREDICTED as defects in crystals since
theoretical strength calculations (due to multibond
breaking) were far too high as compared to experiments
 later invention of the Transmission Electron Microscope
(TEM) PROVED their Existence
deformed
steel
(40,000X)
Engineering-45: Materials of Engineering
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Ti alloy
(51,500X)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Interfacial Defects
 2D, Sheet-like Defects are Termed
as Interfacial
 Some Macro-Scale Examples
• Solid Surfaces (Edges)
– Bonds of Surface Atoms are NOT Satisfied
 Source of “Surface Energy” in Units of J/sq-m
• Stacking Faults – When atom-Plane
Stacking Pattern is Not as Expected
• Phase Boundaries – InterFace Between
Different Xtal Structures
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Interface Def. → Grain Boundaries
 Grain Boundaries
• are Boundaries BETWEEN crystals
• Produced by the solidification
process, for example
• Have a Change In Crystal
Orientation across them
• IMPEDE dislocation motion
Crack Along GB
• Generally Weaker that the Native Xtal
– Typically Reduce Material Strength
thru Grain-Boundary Tearing
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Area Defects: Grain Boundaries
 Schematic
Representation
• Note GB Angles
 Metal Ingot: GB’s
Follow Solidification
Path
~ 8cm
grain
boundaries
heat
flow
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Optical Microscopy
 Since Most Solid Materials
are Opaque, MicroScope
Uses REFLECTED Light
• These METALLOGRAHPIC
MScopes do NOT have a
CONDENSOR Lens
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Optical MicroScopy cont
 The Resolution, Z
0.61
Z=
NA
• Where
–   Light Wavelength
 550 nm For “White”
Light (Green Ctr)
– NA  Numerical
Aperture for the
OBJECTIVE Lens
 0.9 for a Very
High Quality Lens
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 The Magnification, M
M true =
0.12 NA
mm
 Typical Values
• Z 375 nm
– Objects Smaller than
This Cannot be observed
– Objects Closer Together
than This Cannot Be
Separated
• Mtrue  200
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Optical MicroScopy cont.2
 Sample Preparation
• grind and polish surface until flat and shiny
• sometimes use chemical etch
• use light microscope
• different orientations
→ different contrast
• take photos,
do analysis
– e.g. Grain Sizing
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Optical MicroScopy cont.3
 Grain Boundaries
microscope
• are imperfections, with
high surface energy
• are more susceptible to etching;
may be revealed as
polished surface
surface groove
grain boundary
– dark lines due to the change of
direction in a polycrystal
 ASTM E-112 Grain Size
Number, n
n -1
• Where
N =2
– N  grain/inch2
Engineering-45: Materials of Engineering
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Fe-Cr alloy
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Electron Microscopy
 For much greater resolution, use a BEAM OF
ELECTRONS rather that light radiation
 Transmission Electron Microscopy (TEM):
• VERY high magnifications
• contrast from different
diffraction conditions
• very thin samples
needed for transmission
 Scanning Electron Microscopy (SEM):
• surface scanned, TV-like
• depth of field possible
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Atomic Force MicroScopy
 AFM is Also called Scanning
Probe Microscopy (SPM)
• tiny probe with a tinier tip
rasters across the surface
• topographical map on atomic scale
Polymer
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
SEM Photo Scaling
 MEMS Hinge ► Find Rectangle Length
Lactual
2.91 in-photo
3.02 in-photo
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Lactual
SEM Photo Scaling
2.91 in-photo
 Use “ChainLink”
Cancellation of Units
(c.f. ENGR10)
Lactual =
2.91 inch photo
1
3.02 in-photo
50 µm actual

= 48.2 µm actual
3.02 inch photo
 Thus the Rectangular Connecting
Bracket is about 48µm in Length
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt
Olympus DUV Metallurgical Mscope
Deep
Ultraviolet
Microscope
U-UVF248
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-05_SolidImperfections.ppt