Transcript 2009 Al-Abdallat Properties of Eng. Material

Chapter 4
Imperfections in Solids
Properties of Eng. Material
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Imperfections in Solids
Why Study Imperfections in Solids?
 The properties are profoundly influenced by
the presence of imperfections.

Pure metals + Impurities

Sterling Silver (92.5% Silver, 7.5% Copper)
is much harder and stronger than pure silver
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Alloys
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Introduction
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Perfect order in solids does not exist.
All solids contain large number of various
defects (imperfections).
Many material properties are profoundly
sensitive to deviations from crystalline
perfection.
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Introduction (Cont.)

Crystalline defect: A lattice irregularity

Defects are classified according to geometry or
dimensionality of the defect: (1) Point defect
(associated with one or two atomic position), (2)
Linear (one dimensional), (3) Interfacial defects or
boundaries (Two dimensional), (4) Bulk or volume
(three dimensional).
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TYPES OF IMPERFECTIONS
• Vacancy atoms
• Interstitial atoms
• impurities
Point defects
• Dislocations
Line defects
• Grain Boundaries
Area defects
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(1) Point Defects
1. Vacancy
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vacant lattice sites in a structure.
All crystalline solids contain vacancy,
presence of vacancies increases the entropy
(randomness) of the crystal (preferable).
Impossible to create a material without
vacancies.
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Vacancies and Self-Interstitials
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Distortion of Atomic Planes Due to Point
Defects
Vacancy
distortion
of planes
selfinterstitial
distortion
of planes
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Equilibrium Number of Vacancies
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Equilibrium number of vacancies Nv:
Qv
N v  N exp( 
)
KT
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Where: N is the number of atomic sites, Qv is
the activation energy for vacancy formation,
K is Boltzmann’s constant, and T is absolute
temperature.
For most metals, Nv/N is of the order of 10-4
(just below the melting temperature).
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Cont…..
Find the equil. # of vacancies in 1m of
Cu at 1000C. Given:
Qv
N

N
exp(

)
-5
v
K= 8.62x 10 ev/atom.K
KT
Avog. Number: 6.023X1023 atoms/mol
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Estimating Vacancy Concentration
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Find the equil. # of vacancies in 1m of Cu at 1000C.
• Given:
0.9eV/atom
Q 
ND
 exp 
 D 
= 2.7 · 10-4
 kT 
N
• Answer:
For 1m 3, N =
Properties of Eng. Material
1273K
8.62 x 10-5 eV/atom-K
NA
x 1m3 = 8.0 x 1028 sites
 x
ACu
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2. Self-interstitial
•
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"extra" atoms positioned between atomic
sites.
It introduces relatively large distortions in
the surrounding lattice because the atom is
substantially larger than the interstitial
position in which it is situated.
THUS: Its formation is not highly probable,
it exists in small concentrations (lower than
vacancies).
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3. Impurities

Pure metal is not possible. Impurity
(foreign) atoms will always be present.
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Impurities (Cont.)
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Addition of impurity atoms to a metal results
in formation of solid solution AND/OR new
second phase (Depending on: Kind of
impurity, Impurity concentration,
Temperature of the alloy).
Solvent: Element or compound that is
present in the greatest amount (host atoms).
Solute: Element or compound present in
minor concentrations.
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Impurities (Cont.)
Solid solution: It forms when solute atoms
are added to host material.
Features of solid solutions:
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Crystal structure is maintained.
No new structure is formed.
Homogenous composition (impurity atoms are
randomly and uniformly dispersed within the
solid).
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Impurities (Cont.)

Types of impurity point defects:
(1) Substitutional (Impurity atoms substitute or
replace for the host atoms).
(2) Interstitial

Features of solute and solvent atoms that
determine degree to which solute dissolves in
solvent: Atomic factor size, Crystal
structure, Electronegativity, Valences.
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Substitutional & Interstitial
Impurity Atoms
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Two outcomes if impurity (B) added to
host (A):
• 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)
• 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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Impurities in Solids (Contd.)
SPECIFICATION OF COMPOSITION

Two most common ways to specify the composition or
concentration are Weight or mass percent: weight of a
particular element relative to the total alloy weight.
Weight %: C1 = {m1 / (m1+ m2)} x 100
where m1 and m2 represent the weight or mass of elements.

Atom percent: number of moles of an element in relation
to the total moles of the elements in the alloy.
Atom %: C1' = {nm1 / (nm1 + nm2)} x 100
where No. of moles (nm) = {(mass in grams) / Atomic weight )
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SPECIFICATION OF COMPOSITION
(Contd.)
COMPOSITION
CONVERSIONS
Weight% to
Atom%
C1
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SPECIFICATION OF COMPOSITION
(Contd.)
Weight% to Kg/m3
(mass of one component
per unit volume of
material)
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SPECIFICATION OF COMPOSITION
(Contd.)
Density and
Atomic Weight of
Binary Alloy
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(2) Dislocations-Linear Defects
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Dislocation: Linear (1-D) around which
some of the atoms are misaligned.
Types
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Edge
Screw
Mixed
Most dislocations are of mixed type.
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MISCELLANEOUS IMPERFECTIONS
Dislocations __ Linear Defects
Dislocation is a linear or
one dimensional defect
around which some of the
atoms are misaligned.
Edge dislocation: An extra
portion of a plane of
atoms, or half plane, the
edge of which terminates
within the crystal.
Dislocation line: For the
edge dislocation in Figure,
it is perpendicular to the
plane of the paper.
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Screw Dislocation: May be
thought of as being formed by a
shear stress that is applied to
produce the distortion as shown
The upper front region of the
crystal is shifted one atomic
distance to the right relation to
the bottom portion.
Atomic distortion is also linear
and along a dislocation line,
Line AB.
Derived name from the spiral
or helical path or ramp traced
around the dislocation line.
Symbol in Figure
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Most dislocations found
in crystalline materials
are probably neither pure
edge nor pure screw, but
mixed.
All three dislocations are
represented in Figure
The lattice distortion that
is produced away from
the two faces is mixed,
having varying degrees of
screw and edge character.
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Dislocations (Cont.)
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Dislocations can be observed using electron
microscope.
All crystalline materials contain dislocations
introduced during: Solidification, plastic
deformation, and as a consequence of
thermal stresses resulting from rapid
cooling.
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TEM Of
dislocations
(dark lines) in
titanium alloy
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Lattice Distortion Around
Dislocations
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Some localized lattice distortion within the
region around the dislocation line. Some
atoms are squeezed together (compression)
and others are pulled apart (tension).
Magnitude of distortion decreases with
distance away from the dislocation line. At
positions far removed, crystal lattice is
virtually perfect.
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Dislocations (Cont.)
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Burgers vector: Determines magnitude and
direction of lattice distortion associated with the
dislocation.
For metallic materials, Burgers vector points in a
closed-packed crystallographic direction and is of
magnitude equal to interatomic spacing.
Nature of dislocation (edge, screw, or mixed)
defined by: Relative orientations of dislocation line
and Burgers vector (perpendicular for edge, parallel
for screw).
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