Chapter 4 - 1
ISSUES TO ADDRESS IN THIS CHAPTER
• Linear defects
• Interfacial/planar defects
• Volume defects
CHAPTER 4 (+12): IMPERFECTIONS IN
SOLIDS
• Point defects
There is no such a thing as a perfect crystal!
Are defects good for properties?
Why do we study materials imperfections?
Chapter 4 - 2
Callister study guide
• 4.4: No need to study composition conversions
• 4.5 – 4.7: Study all parts
• 4.8: Not covered
CHAPTER 4: IMPERFECTIONS IN SOLIDS
• 4.1 – 4.3: Study all parts
• 4.9 – 4.10: Covered in week 13
• 4.11: Not covered
• 12.15: Study all part
Chapter 4 - 3
Types of Imperfections
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defectsZero-dimensional
defects
• DislocationsLinear defectsOne-dimensional
defects
• Grain Boundaries
• Twin Boundaries
• Stacking Faults
Interfacial/planar
defects
Two-dimensional
defects
Three-dimensional
defects
Volume defects • Impurity inclusions
• Pores
• Cracks
Defects are places where the periodic array of atoms stop.
We will learn in Chapter 7 that:
Dislocations are the most important
defects for mechanical properties
including yield strength, tensile
strength, and ductility.
Other defects affect the mechanical
properties through their interactions
with dislocations that affect
dislocation behaviours.
Chapter 4 - 4
• Vacancies:
-vacant atomic sites in a structure.
• Self-Interstitials:
-"extra" atoms positioned between atomic sites.
Point Defects
Vacancy
distortion
of planes
self-
interstitial
distortion
of planes
Lattice distortion
increases system energy
Chapter 4 - 5
Boltzmann's constant
(1.38 x 10 -23 J/atom-K)
(8.62 x 10-5 eV/atom-K)
 Nv N= exp
-Qv
kT






No. of defects
No. of total
Atomic sites
Activation energy
Temperature
(Kelvins= ºC + 273)
• Equilibrium concentration varies with temperature!
Equilibrium Concentration of Point Defects
__Nv
N
~ 10-4 at T just below melting
High temperature and low
activation energy → high
density of point defects.
Q for vacancies < Q for self-
interstitials → more vacancies
than self-interstitial atoms.
Chapter 4 - 6
• 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 crystal
to the surface, where
they join the island.
Observing Equilibrium Vacancy Concentration
Island grows/shrinks to maintain
equil. vancancy conc. in the bulk.
Chapter 4 - 7
Two outcomes if impurity (B) added to host (A):
• Solid solution of B in A (i.e., random dist. of point defects)
• Solid solution of B in A plus particles of a new
phase (usually for a larger amount of B)
OR
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe)
Second phase particle
--different composition
--often different structure.
Point Defects in Alloys
Solvent
Solute
Chapter 4 - 8
xx
x
x x
x x
x
x
xx
x
x
Interstitial positions in FCC structure
Tetrahedral Octahedral
xx
x
x x
x x
x
x
xx
x
x
In an FCC unit cell (the messages below are very important for crystal structures of ceramics):
4 atoms – 8 (corners) x 1/8 + 6 (face centers) x ½
8 tetrahedral interstitial positions – each corner forms a tetrahedrons with 3 face-centers.
4 octahedral interstitial positions – 1 (center) + 12 (edge centers) x 1/4
Chapter 4 - 9
Concentration
• Specification of composition
– weight percent 100x
21
1
1
mm
m
C
+
=
m1 = mass of component 1
100x
21
1'
1
mm
m
nn
n
C
+
=
nm1 = number of moles of component 1
– atom percent
For industry as industry does not
count the numbers of atoms.
Mainly for research
wt.%
at.%
Chapter 4 - 10
• Frenkel Defect
--a cation is out of place.
• Schottky Defect
--a paired set of cation and anion vacancies.
• Equilibrium concentration of defects
kT/QDe~ -
Point Defects in Ceramic Structures
Schottky
Defect:
Frenkel
Defect
2
12
Charge neutrality requirement for point defects
Chapter 4 - 11
• Impurities must also satisfy charge balance = Electroneutrality
• Ex: NaCl
• Substitutional cation impurity
Impurities (Point Defects in Ceramics)
Na+ Cl-
initial geometry Ca2+ impurity resulting geometry
Ca2+
Na+
Na+
Ca2+
cation
vacancy
• Substitutional anion impurity
initial geometry O2- impurity
O2-
Cl-
anion vacancy
Cl-
resulting geometry
12
Chapter 4 - 12
• are line defects,
• slip between crystal planes result when dislocations move,
• produce permanent (plastic) deformation.
Dislocations:
Schematic of a Plastic Deformation Process:
• before deformation • after tensile elongation
slip steps
Line Defects
Chapter 4 - 13
Imperfections in Solids
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
Burger’s vector, b: measure of lattice distortion
Chapter 4 - 14
Imperfections in Solids
Edge Dislocation
Burgers circuit – clockwise,
counterclockwise?
b I line_
Chapter 4 - 15
Imperfections in Solids
Screw Dislocation
Burgers vector b
Dislocation
line
b
(a)
(b)
Screw Dislocation b // line
Chapter 4 - 16
Edge, Screw, and Mixed Dislocations
Edge
Screw
Mixed
A dislocation line has only one Burgers vector but its type can vary from one portion to another
depending on the curvature of the local dislocation line and the orientation relationship between
the dislocation line and its Burgers vector.
Chapter 4 - 17
Dislocations seen in TEM
Dislocations are visible in electron micrographs
8 steps
down
8 steps
right
8 steps
up
8 steps
left
Edge-on
Edge-on
Inclined
Inclined
Chapter 4 - 18
Dislocations & Crystal Structures
• Structure: close-packed
planes & directions
are preferred.
view onto two
close-packed
planes.
close-packed plane (bottom) close-packed plane (top)
close-packed directions
• Comparison among crystal structures:
FCC: many close-packed planes/directions;
HCP: only one plane, 3 directions;
BCC: none
• Specimens that
were tensile
tested.
Mg (HCP)
Al (FCC)
tensile direction
Chapter 4 - 19
Close-packed planes/directions
A
B
C
A
A
A
B
B
B
C
C
Chapter 4 - 20
Dislocations in Ceramics
Ex: GaN
Copied from APL 72 (1998)2680 12
In ceramic with a
Perovskite structure
Copied from Nature Comm. 13 (2022) 335
The structure of a
dislocation core in
ceramics is much
more complicated
than that in metals.
Chapter 4 - 21
Planar Defects in Solids
• One case is a twin boundary (plane)
– Essentially a reflection of atom positions across the twin
plane.
• Stacking faults
– For FCC metals an error in ABCABC packing sequence
– Ex: ABCABABC
Chapter 4 - 22
TEM images of twins and a stacking fault in
FCC
Twins Stacking Fault
Twin: ABCABCABCBACBACBA
Twin plane
SF: ABCABCBCABC or ABCABACABCABC
“A” is removed “A” is inserted
Chapter 4 - 23
Twins and Stacking Faults
FCCWhat is the relationship between twins and SFs?
What if SFs appear periodically?
ABCABCABCABCABCABCABC
Chapter 4 - 24
Other interfacial defects
• External surfaces
• Grain boundaries
• Anti-phase domain
boundaries
• Phase boundaries
• …
Chapter 4 - 25
Volume defects (impurity precipitates)
Chapter 4 - 26
Volume defects (impurity precipitates)
1.5mm
Chapter 4 - 27
• Point, Line, plane and Volume 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.)
Summary
Chapter 4 - 28
Point defects including vacancy, interstitial atoms and
substitutional atoms; solid solution, solute and solvent;
(equilibrium) concentration of point defects (4.3, 4.5) and its
relationships with temperature and activation energy; edge,
screw, and mixed dislocations; Burgers vectors; relationship
between dislocations and crystal structures; twins and
stacking faults and their relationship; volume defects.
Concepts and equations to be remembered