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Transcript of material's properties under microscopic
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4-1
C H A P T E R 4
C R Y S T A L S T R U C T U R E S
4.1 ATOMIC ARRANGEMENTS
4.2 LATTICES AND UNIT CELLS
4.2.1 Unit Cel l s in Space
4.2.2 Atomic Packing in Crysta ls
4.3 METALLIC CRYSTAL STRUCTURES
4.3.1 Face-Centred Cubic (FCC)
Crysta l St ructure
4.3.2 Body-Centred Cubic (BCC) Crysta lSt ructure
4.3.3 Hexagonal Close-Packed (HCP)Structure
4.3.4 A l lot ropy/Polymorphism
4.4 CLOSE-PACKED CRYSTAL STRUCTURES
4.5 INTERSTITIAL POSITIONS AND SIZES
4. 6 CRYSTALLOGRAPHIC DIRECTIONS AND PLANES
4.7 CRYSTALLINE MATERIALS
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4.1 ATOMIC ARRANGEMENTS
• The properties of a material depend not only on atomic
bonding and forces, but also, equally important, on how
atoms pack together. There are 3 levels in which atoms
may be arranged:
• No order: there is no special positional
relationship or interaction between the
atoms; e.g. inert gases (Fig. 4.1-1a).
• Short-range order: the specific
arrangement of atoms extends only toan atom's nearest neighbours. Materials
exhibiting short-range order are
amorphous (glassy) (Fig. 4.1-1b).
• Long-range order: there is a special
arrangement of atoms that is repeated
throughout the entire material.
Crystalline materials exhibit both short-
range and long-range order. The
repetitive pattern formed by atoms in a
crystalline solid is known as a lattice (Fig.
4.1-1c).
(a) No order.
(b) Short-rangeorder.
(c) Long-rangeorder.
Fig. 4.1-1 The levelsof atomic
arrangement.
4-3
4.2 LATTICES AND UNIT CELLS
• A lattice is a collection of points (positions in space)
arranged in a periodic pattern so that surroundings of each
point in the lattice are identical. The points that make up
the lattice are called lattice points (Figs. 4.2-1, 4.2-2). An
everyday example in 2-dimensions is wall-paper.
Fig. 4.2-1 Lattices and unit cells in 2D.
Fig. 4.2-2 Lattices and unit cells in 3D.
• A unit cell is the smallest subdivision of a lattice that
contains all the characteristics of the entire lattice. A
complete crystal can be formed by translating its unit cell
along each of its edges.
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• The properties of a unit cell are therefore the same as those
of the whole crystal.
• Each unit cell is described by lattice parameters, which
are the lengths of the cell edges and the angles between
the axes. (Figs. 4.2-1, 4.2-2)
4.2.1 Unit Cells in Space
• By geometry, there are only 7 unique unit cell shapes that
may be stacked together in space. And there are only a
total of 14 possible ways in which atoms may be arranged
inside these unit cells. These 14 different unit cells are
known as Bravais lattices and they fall into one of 7 crystal
systems (Fig. 4.2-3).
• One or more atoms may be associated with each lattice
point. The "group of atoms" located at each lattice point is
the basis. The actual crystal structure itself is defined by a
combination of crystal lattice and crystal basis (Fig. 4.2-4).
Crystal lattice
+
+
crystalbasis
=
= crystal structure
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Fig. 4.2-3 14 Bravaislattices grouped into 7
crystal systems.
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4.2.2 Atomic Packing in Crystals
• When describing crystal structures, atoms are assumed to
be solid spheres that touch one another. This is known as
the hard sphere model. The centres of the solid spheres
coincide with the lattice points in unit cells (Fig. 4.2-5).
Fig. 4.2-5 Hardsphere model of
a unit cell.
• The coordination number is the number of nearest
neighbours (touching atoms) to any atom. For materials
with non-directional bonding (i.e. metals and ionic solids),
the lowest energy (most stable) configuration is obtained
when atoms pack as closely as possible, separated only by
their equilibrium bond lengths. In such crystals, the
number of nearest neighbours (i.e. coordination number)
would be as high as possible.
• The atomic packing factor (APF) is the fraction of space
occupied by atoms in a unit cell.
APF = Volume of atoms in unit cell
Volume of unit cell
=(Number of atoms in cell)(Volume of one atom)
Volume of unit cell
4-7
• The properties of an entire crystal, such as the theoretical
density, may be calculated from just one of its unit cells.
Density = Mass of unit cell
Volume of unit cell
=(Number of atoms in cell)(Mass of one atom)
Volume of unit cell
= (Number of atoms in cell)(Atomic mass)(Volume of unit cell)(Avogadro's number)
4.3 METALLIC CRYSTAL STRUCTURES
In pure metals, only one metal ion occupies each lattice
point. Many common metals may be defined by one of 3
crystal structures: face-centred cubic (FCC), body-centred
cubic (BCC) and hexagonal close-packed (HCP) crystal
structures (Table 4.3-1).
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4. 3. 1 Face-Centred Cubic (FCC) Crystal Structure
• Cubic geometry with one atom at each corner and one at
the centre of each face. (Fig. 4.3-1)
Fig. 4.3-1 FCC structure.
• Corner atoms touch face-centred atoms (along the facediagonal) but corner atoms do not touch one another.
Face-centred atoms also touch adjacent (but not opposite)
face-centred atoms in the midplanes of the cube.
• Unit cell length: a = 2R 2 (where R is the atomic radius)
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• Coordination number: consider a corner atom, which
touches 4 face-centred atoms on each of the 3 mutually
perpendicular planes passing through the corner atom
itself (Fig. 4.3-2), giving CN = 12.
Fig. 4.3-2 Finding thecoordination number in
FCC structures.
• Atomic packing factor: each atom at the centres of the
cube faces is shared by 2 cells; each corner atom is shared
by 8 cells (Fig. 4.3-3), such that:
• Atoms per cell = 4; !
APF = 0.74
Fig 4.3-3 Sharing of face and corner atoms in FCC structures.
• Examples of FCC metals: Al, Au, Ag, Cu, Ni, Pb, Pt.
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4. 3. 2 Body-Centred Cubic (BCC) Crystal Structure
• Cubic geometry with one atom at each corner and one at
the centre of the cube. (Fig. 4.3-4)
Fig. 4.3-4 BCC structure.
• Atoms touch along the body diagonal.
• a = 4R
3
• CN = 8.
• Atoms per cell = 2; APF = 0.68
• Examples of BCC metals: Cr, Fe, W, Mo, V.
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4.3. 3 Hexagonal Close-Packed (HCP) Structure
• Hexagonal faces at the top and bottom are linked by 6
rectangular side faces. There is one atom at each corner of
the top and bottom hexagons surrounding one atom at
the centre of each hexagon. 3 other atoms are located on
a plane midway between the hexagons (Fig. 4.3-5).
Fig. 4.3-5 HCP structure and its smaller primitive unit cell.
• Corner atoms at the top and bottom hexagons are shared
between 6 cells; the central atom in each hexagon is
shared between 2 cells; the 3 atoms in the midplane
belong to only one cell.
• Lattice parameters: a = 2R; c = 4
6
a
• By considering the central atom in basal plane, CN =12.
• Atoms per cell = 6 (or 2 per primitive unit cell); APF = 0.74
• Examples of HCP metals: Co, Mg, Ti, Zn.
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4.3.4 Allotropy/Polymorphism
• Allotropy or polymorphism is the ability of an element or
compound to assume more than one crystal structure in
the solid state, depending on external conditions such as
temperature, pressure, magnetic and electric fields (Table 4.3-2)
• The change in crystal structure is usually accompanied by
changes in properties.
• Such property changes can be very useful; e.g. hardening/
softening of steel through controlled heating/cooling (Chps
9&10), piezoelectric transducers (Figs. 4.3-6 & 7).
• Or detrimental; e.g. distortion and cracking due to sudden
changes in volume, especially in brittle ceramics, but also
in metals (Fig. 4.3-8).
4-13
Fig. 4.3-6 PZT (lead zirconate titanate)ceramic changes its structure from
(a) cubic, to (b) tetragonal,in response to an electric field.
Fig. 4.3-7 Use of piezoelectric effectof PZT crystals in inkjet printer head.
Fig. 4.3-8 Tin changes from tetragonal to diamond structure below 13.2°C.The volume expansion accompanying this transformation from
soft, ductile white tin to hard, brittle grey tin causes it to disintegrate.
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4.4 CLOSE-PACKED CRYSTAL STRUCTURES
• Atoms in metals pack as closely as
possible, separated only by their
equilibrium bond lengths, r 0, as this
gives the lowest energy (most
stable) configuration (Fig 4.4-1).
• Close-packed planes or directions
refer to the planes or directions in a
crystal, where the atoms are in
direct contact, assuming a hard
sphere model of atomic packing.
• Plastic deformation in metals
occurs most readily on close-
packed planes along close-packed directions in those
planes (Sec. 6.1). The number and relative positions of these
planes and directions influence properties such as ductility.
• Packing same-sized atoms in FCC or HCP structures gives
the smallest volume (i.e. highest density). FCC and HCPare known as close-packed structures.
• FCC and HCP differ only in the arrangements of their
close-packed planes (Fig. 4.4-2, 4.4-3); this difference affects
plastic deformation and ductility (Sec. 6.1).
Fig. 4.4-1 Bonding energyis higher whenatoms are away from equilibriumseparation r 0.
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Fig. 4.4-2 Illustration of close-packed stacking sequence.
HCP FCC
Fig. 4.4-3 Close-packed stacking sequence and close-packed planes for HCP and FCC.
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4.5 INTERSTITIAL POSITIONS AND S IZES
• Lattices not completely filled with atoms. Interstices are
the ‘holes’ between lattice atoms.
• Interstitial sites are classified by geometry, based on the
shape of the polyhedron formed by existing lattice atoms
surrounding a particular site. (Fig. 4.5-1 & Table 4.5-1)
• The size of an interstitial site is defined by the radius ratio,
r
R, where r is the radius of the largest sphere that can
completely fill the site without straining the adjacent lattice
atoms, and R is the radius of the lattice atoms.
Tetrahedral interstitial Octahedral interstitial Cubic interstitialr
R = 0.225
r
R = 0.414
r
R = 0.732
Fig. 4.5-1 Interstitial sites and sizes in close-packed crystal structures.
• Atoms (alloy or impurity) occupying interstitial sites (Sec.
6.3.2) must be larger than the size of the holes; smaller
atoms are not allowed to “rattle” around loose in the sites.
4-17
Table 4.5-1 The size and number of interstitial sites in FCC, BCC and HCP.
Crystalstructure
Size of interstitial sites, r
R No. of sites per unit cell
Octahedral Tetrahedral Octahedral Tetrahedral
FCC 0.414 0.225 4 8
BCC 0.155 0.291 6 12
HCP 0.414 0.225 6 12
Fig. 4.5-2 Locations of the interstitial sites in FCC, BCC and HCP structures.
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4.6 CRYSTALLOGRAPHIC DIRECTIONS AND PLANES
• Some physical and mechanical material properties vary
with the direction or plane within a crystal in which they
are measured. Miller Indices provide a convenient
notation system for directions and planes in crystals.
• In cubic systems, 3 integers uniquely identify a direction
(Fig. 4.6-1) or plane (Fig. 4.6-2), when enclosed by a pair of
square brackets [hkl ], or parentheses (hlk ), respectively.
• In hexagonal crystals, a redundant axis is added to the
basal plane to reflect its symmetry, such that 4-integerMiller-Bravais indices of the form [uvtw ] and (uvtw ) are
often used instead (Fig. 4.6-3).
Fig. 4.6-1 Some common directions in a cubic unit cell.
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Fig. 4.6-2 Some planes in a cubic unit cell.
Fig. 4.6-3 4-integer Miller-Bravais indices for directions and planes.
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4.7 CRYSTALLINE MATERIALS
• In a single crystal, the same orientation and alignment of
unit cells is maintained throughout the entire crystal.
• Most materials are polycrystalline: their structures are
composed of many small crystals (grains) with identical
structures but different orientations (Fig. 4.7-1).
Fig. 4.7-1 The solidification of a polycrystalline material.
• Grain boundaries are the
interfaces where grains of
different orientations meet
(Fig. 4.7-2). Single crystals do
not contain grain boundaries.
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• The absence of grain boundaries in single crystals impart
unique properties but such crystals are extremely difficult
to grow, requiring carefully controlled conditions, which
are expensive. Single crystals are essential to some
applications; e.g. semiconductors and jet turbine blades,piezoelectric transducers.
• Besides the absence of grain boundaries, single crystals
exhibit directionality in properties, such as magnetism,
electrical conductivity and elastic modulus and creep
resistance, which depend on the crystallographic direction
of measurement. This directionality is called anisotropy.
• The random orientation of individual grains in apolycrystalline material means that measured properties
are independent of crystallographic direction. Such
materials are said to be isotropic.
• Grain boundaries are disordered regions of atomic
mismatch where atoms are displaced from their
equilibrium positions (Fig. 4.4-1) and there are improper
coordination numbers (Sec. 4.2.2) across the boundaries. Atoms at grain boundaries hence possess higher energy.
• This interfacial energy makes grain boundaries
preferential sites for chemical reactions and other chemical
changes.
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• Therefore, grain boundaries are attacked more aggressively
by chemical etchants. Under a microscope, the more
deeply etched grain boundaries scatter more light, and
appear darker (Figs. 4.7-3/4), thus revealing the microstructure.
This is the principle behind metallography.
Fig. 4.7-3 Observation of grains and grain boundaries in stainless steel sample.Note that different orientations of the grains result in differences in reflection.
Fig. 4.7-4 Observed microstructure in 2-D and the underlying 3-D structure.
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C H A P T E R 5
CRYSTAL DEFECTS
AND DIFFUSION
5.1 CRYSTAL DEFECTS
5.1.1 Thermal V ibrat ion of Atoms
5.1.2 Vacanc ies
5.2 DIFFUSION
5.2.1 Vacancy Di f fus ion
5.2.2 Inters t i t ia l D i f fus ion
5.2.3 Concentrat ion and F lux
5.3 FACTORS AFFECTING RATE OF DIFFUSION
5.3.1 Temperature
5.3.2 Di f fus ion Mechanism
5.3.3 Atomic Bonding
5.3.4 Crysta l St ructure
5.3 .5 Crystal Defects (Short Circuit Diffusion)
5-2
5.1 CRYSTAL DEFECTS
• In a perfect crystal, atoms would exist only on lattice sites
and every lattice site would be occupied by an atom.
• A crystal defect or imperfection is an irregularity in the
crystal lattice, a departure from the perfect crystal. Defects
affect material properties, but not necessarily adversely.
• Point defects are zero dimensional imperfections that
involve only a few atoms at most. These include: vacancies
(Sec. 5.1.2) and impurities (Sec. 6.3.2).
• Linear defects are one-dimensional imperfections wherelocal faults in the atomic arrangement lie along a straight
line, curve or loop through the crystal. Linear defects are
collectively known as dislocations (Sec. 6.2).
• Planar defects are two-dimensional imperfections that
serve as boundaries between regions having different
crystal structures and/or crystallographic orientations.
Grain boundaries (Sec. 4.7) are one class of planar defects.
• Volume defects are macroscopic (large-scale) defects that
represent inhomogeneities in a solid. Among these are:
inclusions (unwanted foreign particles), precipitates (Sec.
6.3.3), cracks (Chp. 7) and voids.
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5.1.1 Thermal Vibration of Atoms
• At temperatures above absolute zero (0 Kelvin), atoms
possess kinetic energy and vibrate about their equilibrium
lattice positions (see also Sec. 3.7).
• At any given temperature, the average kinetic energy of a
material is fixed; however, the kinetic energy of an
individual atom at any time is not constant but randomly
distributed over a wide range (Fig. 5.1-1).
Fig. 5.1-1 Distribution ofkinetic energy of atomschanging with temperature.N(E) represents the number
of atoms that possess Eamount of kinetic energy.
• Sometimes an atom in a solid may possess high enough
kinetic energy to enable it to break its bonds with its
neighbours and jump away from its original lattice position
to another site.
• The amount of energy required for breaking atomic bonds
and making a jump is known as the activation energy, Q
(Fig. 5.1-2).
5-4
Fig. 5.1-2 Illustrationshowing how an atom must
overcome an activationenergy, Q, to move fromone stable position to a
similar adjacent position.
• The number of atoms that possess enough kinetic energy
to overcome the activation energy barrier (i.e. E ! Q) and
make successful jumps may be found from the kinetic
energy distribution of atoms.
• The rate at which atoms make successful jumps must be
proportional to number of such atoms (with enough E ).
• This rate is described by the Arrhenius equation:
Rate = C exp
" QRT
#
$ %
&
' ( where C = material constant
Q = activation energy
R = gas constantT = absolute temperature
• The Arrhenius equation implies that a low activation
energy and/or a high temperature will result in faster rates.
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5.1.2 Vacancies
• A vacancy is a vacant lattice site from which an atom is
missing (Fig. 5.1-3). Vacancies are defects that occur naturally
as a result of atomic vibrations; they may also beintroduced during processing, or arise from radiation
damage.
• There is an equilibrium number of vacancies, N v, at any
temperature, T :
N v = N exp
" QRT
#
$
%
&
'
( where
N = total no. of lattice sites
Qv = energy required to form avacancy (J/mol)
R = gas constant (J/mol.K)
T = absolute temperature (K)
Fig. 5.1-3 A vacancy.
• A crystal will always contain vacancies at any temperature
above absolute zero (0 K). The equilibrium number of
vacancies, N v, increases with temperature.
• Vacancies are the basis of an important mechanism for the
movement of atoms (diffusion) within metals and
ceramics.
5-6
5.2 D IFFUSION
• Diffusion is the spontaneous movement of atoms within a
material as a result of atomic vibrations. The manufacture
of many materials (e.g. surface hardening, microchips) andmost changes in microstructure (and therefore, properties)
are accomplished through diffusion.
• Self-diffusion is the constant, random, movement of
atoms of the same type within pure materials.
• It occurs in the absence of a concentration gradient; there
is no net flow of atoms.
• The effects on material properties are insignificant.
• Interdiffusion is the movement of atoms from one
material into another unlike material.
• It occurs in the presence of a concentration gradient; there
is a net flow of atoms from high to low concentration.
• Interdiffusion affects material properties.
• This type of diffusion is also known as impurity
diffusion
or heterogeneous
diffusion.
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5.2.1 Vacancy Diffusion
• In vacancy diffusion, the diffusing atom moves from its
normal lattice position to an adjacent vacancy . (Fig. 5.2-1)
Fig. 5.2-1 Schematic representation of vacancy diffusion.
• Vacancy diffusion is the mechanism for self-diffusion, as
well as interdiffusion, when the diffusing atoms and host
atoms are of comparable size.
• Since vacancies must first be
available for atoms to move
into (Fig. 5.2-2), the rate of
diffusion is limited by the
number of vacancies.
Fig. 5.2-2 A mechanical analogy ofvacancy diffusion using a puzzle in a
frame, showing how a vacancy must firstexist before an atom can move into it.
5-8
5.2.2 Interstitial Diffusion
• In interstitial diffusion, the diffusing atom moves from
one interstitial site to an adjacent empty interstitial site. (Fig.
5.2-3)
• The interstitial diffusion mechanism is limited to small
solute atoms such as H, C, N, O, which are small enough
to squeeze into the interstitial sites between lattice atoms.
Fig. 5.2-3 Schematic representation of interstitial diffusion.
• No vacancies are required for interstitial diffusion to occur.
• At lower temperatures, interstitial diffusion is generally faster than vacancy diffusion, since interstitial sites are far
more abundant than vacancies. Furthermore, interstitial
atoms are smaller and more mobile.
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5.2.3 Concentration and Flux
• When there is a difference in concentration (i.e.
composition), random atomic jumps will result in a net
flow of atoms from high to low concentration, until thediffusing atoms are uniformly distributed and the
concentration gradient is zero (Fig. 5.2-4).
Concentration profile Concentration profileof copper of nickel
Fig. 5.2-4 Interdiffusion of copper atoms into nickel and vice versa.
5-10
• The plot of concentration, C, against distance (along x, y
or z axis), is called the concentration
profile. The slope,
" C
" x , at a particular point on the concentration profile is the
concentration
gradient. These can change with time.
• Diffusion problems in solids often involve finding out how
fast diffusion occurs. This rate of mass transfer is measured
by the diffusion
flux, J , defined as the mass (or
equivalently, the number of atoms) passing through a unit
cross-sectional area of the solid per unit time (Fig. 5.2-5).
• The flux at any position along a diffusion path is related to
the instantaneous concentration gradient at that point:
J = -D
" C
" x
where D is the diffusion coefficient or diffusivity (m2/s)
Fig. 5.2-5 Illustration of diffusion flux. The units of J are kg/m2.s or atoms/m2.s
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5.3 FACTORS AFFECTING RATE OF DIFFUSION
• The flux of atoms is proportional to the concentration
gradient, with the constant of proportionality being the
diffusion coefficient, D. The magnitude of D is indicative ofthe rate at which atoms diffuse.
• D is directly related to the frequency at which atoms jump
from site to site within a solid. Jumps can only occur when
atoms possess high enough kinetic energy to overcome
the activation energy barrier. D is thus described by the
Arrhenius equation:
D = Doexp
" QRT
#
$
%
&
'
(
where Do = material constant (m2/s)
Q = activation energy (J/mol)
R = gas constant (J/mol.K)
T = absolute temperature (K)
5.3.1 Temperature
With higher temperatures, the number of atoms withkinetic energy high enough to overcome the activation
energy barrier increases, so the jump frequency of the
atoms rises. Therefore, the higher T is, the larger D
becomes, and the faster the rate of diffusion (Fig.5.3-1).
5-12
Fig. 5.3-1 Arrhenius plot of logarithm of diffusion coefficientD as a function ofthe reciprocal of absolute temperature of some metals and ceramics.
A rise in T (i.e. lower 1
T
) increases D.
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5.3. 2 Diffusion Mechanism
• The activation energy, Q, depends on the diffusion
mechanism (vacancy or interstitial). When Q is high, few
atoms possess the kinetic energy required to overcome Q
and make a jump, so D is low and diffusion is slow.
• In vacancy diffusion, a vacancy must first be created before
an atom can jump from an adjacent lattice site. Q then
consists of the energy required for vacancy formation plus
the energy required for an atom to jump.
• In interstitial diffusion, interstitial spaces are always
available, so Q is simply the energy an atom requires tojump into an adjacent interstitial site.
• In general, Qvacancy > Qinterstitial. (Fig. 5.3-2 & Table 5.3-1)
Fig. 5.3-2
Qvacancy > Qinterstitial.
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5.3.3 Atomic Bonding
The activation energy, Q, also depends on the atomic
bond strength. Q is high for materials with strong atomic
bonds (reflected in the high melting points)(Table 5.3-2),
because an atom in such a material requires high kinetic
energy in order to break its bonds with its neighbours and
make a jump.
Table 5.3-2 Typical Activation Energies for Self-Diffusion, Q
5-16
5.3.4 Crystal Structure
The influence of atomic packing within the crystal structure
is reflected in Q and Do. It is more difficult for atoms to
squeeze through regions that are densely packed; in
general, Q is higher and/or Do is smaller in close-packed
structures (e.g. FCC), resulting in lower D and slower
diffusion. (Fig. 5.3-3 & Table 5.3-3)
Fig. 5.3-3 Arrhenius plots
showing approximate rangesof D for vacancy diffusion in
BCC and FCC alloys. T M is themelting point of the alloy.
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5.3.5 Crystal Defects (Short Circuit Diffusion)
• Crystal defects such as dislocations (Sec. 6.2), grain boundaries
(Sec. 4.7) and surfaces provide open, disordered regions
through which atoms can move easily. Q for diffusion alongsuch short circuits is much lower than through the bulk of
the crystal (Fig. 5.3-4), so D is higher and diffusion faster.
• Since the cross-sectional areas of these easy diffusion paths
are usually small, volume diffusion is still dominant under
most temperatures. Only at low temperatures does short
circuit diffusion become significant.
Fig. 5.3-4 Arrhenius plots showing D for diffusion along various different paths. 5-18
• In nanocrystalline materials , which have a large proportion
of grain boundaries, grain boundary diffusion can
dominate. Similarly, in fine powders with large surface area,
surface diffusion can dominate; e.g. sintering of powders in
powder metallurgy or manufacture of ceramics (Fig. 5.3-5).
Fig. 5.3-5 Surface diffusion is significant in the sintering of powders.
• Short circuit diffusion in microelectronic devices is a
reliability issue due to the comparable dimensions of the
electronic circuits and crystal defects.
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6-1
C H A P T E R 6
D I S L O C A T I O N S ,D E F O R M A T I O N A N D
S T R E N G T H E N I N G I NM E T A L S
6.1 PLASTIC DEFORMATION BY SLIP
6.2 DISLOCATIONS AND SLIP
6.3 STRENGTHENING MECHANISMS
6.3.1 Dis locat ion Stress F ie lds andStra in Energies
6.3 .2 Stra in Hardening
6.3.3 Gra in S ize Strengthening
6.3.4 Sol id Solut ion Strengthening
6.3.5 Dispers ion Hardening
6.3.6 Combined StrengtheningMechanisms
6.4 ANNEALING
6.4.1 Recovery
6.4 .2 Recrysta l l i zat ion
6.4.3 Gra in Growth
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6-2
6.1 PLASTIC DEFORMATION BY SL IP
• Plastic deformation in a crystal mostly involves the sliding
of one plane of atoms over another under the action of a
shear stress (Fig. 6.1-1); this process is known as slip.
Fig. 6.1-1 Plastic deformation by slip in an ideal crystal occurs when one plane
of atoms slides over another, producing a step of one atomic spacing.
• The plane and direction in which slip occurs are the slip
plane and slip direction. The slip direction always lies
within the slip plane. The combination of a slip plane and a
slip direction forms a slip system.
• Slip does not take place in any arbitrary plane or direction.
The preferred slip planes and directions are those in which
the atoms are most densely packed. This is because slip
occurs in steps of one atomic spacing, so moving atoms
from one stable site to the next would involve the least
energy when the atoms are closest together (Figs. 6.1-2 & 3).
6-3
" max
#ba
Fig. 6.1-2 The maximum shear stress, ! max, required to move one plane of atomsover another by one atomic spacing is a function of the interatomic distances,
such that smaller stresses are necessary for closely-spaced atoms.
Fig. 6.1-3 Slip requires less energy on (a) a close-packed plane in a close-packed direction than on (b) a less closely-packed plane and direction.
• Since most engineering alloys are polycrystalline, the
change in orientation from grain to grain means that each
grain is strained differently by an applied stress (Fig. 6.1-4).
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6-4
Fig. 6.1-4 Resolving a uniaxial tensile stress ! into shear stress " =F sin#
A/cos# = $ sin# cos#
• Slip will begin on a slip system when the resolved shear
stress acting on the slip plane in the slip direction reaches a
critical value. If two or more slip systems have the required
shear stress acting on them, they all slip together (Fig. 6.1-5).
Fig. 6.1-5 Slip lines on the surface of polycrystalline copper that has beendeformed. Slip lines are actually a series of fine steps on the surface.
Note that the slip lines change direction at grain boundaries.Note also intersecting sets of lines within the same grain,indicating the operation of more than one slip system.
6-5
• In a polycrystalline solid, the deformation in each grain
must be compatible with its neighbours to maintain
mechanical integrity and coherency along the grain
boundaries. This requires the grains of various orientations
to slip on 5 independent systems simultaneously.
• Metals with FCC and BCC structures are ductile because
they possess a relatively large number of slip systems (12 in
FCC; up to 48 in BCC) (Table 6.1-1).
• The slip systems in FCC and BCC are also well-distributed
in space, such that at least one slip system would be
favourably oriented for slip at low applied stresses.
Table 6.1-1 Primary slip systems in the common metal structures. BCC and HCP containsecondary slip systems, which are not shown.
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6-6
• Furthermore, slip systems in FCC and BCC intersect, so if
one system be constrained, slip can continue on a different
intersecting slip system; this is known as cross-slip.
• However, unlike the FCC structure, the BCC structure does
not contain close-packed planes, so slipping atoms must
move greater distances from one equilibrium lattice
position to another. Higher shear stresses are thus
necessary for slip in BCC than in FCC metals (Fig. 6.1-2 & Table
6.1-2), which translates into higher strengths for BCC metals.
[Note: critical shear stress is the shear stress required to move a dislocation in its slip system.
• Although the HCP structure contains both close-packed
planes and directions, its geometry gives rise to fewer slip
systems. Furthermore, the slip systems, being parallel, do
not intersect, so cross-slip is not possible (Fig. 6.1-6). Most
polycrystalline HCP metals are relatively brittle.
6-7
Fig. 6.1-6 Comparison of the slip systems in(a) an FCC structure, and (b) an HCP s tructure.
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6-8 6-9
6.2 D ISLOCATIONS AND SLIP
• In a perfect crystal, slip would involve a whole plane of
atoms sliding over another in a single movement, which
would require the simultaneous stretching, breaking, and
remaking of all atomic bonds in the slip plane. The
theoretical shear strengths of metals have been roughly
estimated to be in the order of 1010 N/m2 (10 GPa).
• However, the actual measured yield strengths of bulk
metals are at least 1,000–10,000 times lower than this
value (Table 6.2-1). This is because slip in real metal crystals
occurs via the movement of dislocations , during which only
a small fraction of atomic bonds are broken at any one
time, with minimal disruption to the crystal lattice.
Table 6.2-1 Comparison of theoretical and experimental yield strengths of some metals.
• Dislocations are linear or one-dimensional crystal defects
where local faults in the atomic arrangement lie along a
straight line, curve or loop through the crystal.
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6-10
• Dislocations can be introduced into a crystal in a number
of ways: during solidification, during plastic deformation,
or as a result of thermal stresses arising from rapid cooling.
All bulk crystalline materials (metals and ceramics) contain
dislocations.
• There are two fundamental types of dislocations: edge and
screw. An edge dislocation may be thought of as an extra
half-plane of atoms inserted into the crystal (Fig. 6.2-1). The
bottom edge of half-plane that ends within crystal is the
edge dislocation line . [Note: the extra half-plane of atoms itself is not the
dislocation.]
Fig. 6.2-1 An edge dislocation, showing the extra half planes of atoms.Note the regions of compression and tension around the dislocation line.
6-11
• A screw dislocation may be thought of as making a cut
half-way through the crystal, and then skewing the two
halves by one atomic spacing (Fig.6.2-2).
Fig. 6.2-2 A screw dislocation, showing the spiral screw-likearrangement of atoms above and below the plane of the cut.
• Most dislocations, however, are mixed dislocations, whichcontain both edge and screw dislocation components with
a transition region in between (Fig. 6.2-3).
Fig. 6.2-3 A mixed dislocation. Fig. 6.2-4 Transmission electronmicrograph of a titanium alloy
in which dark lines are dislocations.
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• When a shear stress is applied to the edge dislocation
shown in Fig. 6.2-5, the extra half-plane of atoms, plane A,
will be forced to the right; this in turn pushes the top
halves of planes B, C, D, etc., to the right.
• If the shear stress is high enough, plane A eventually
becomes closer to the bottom half of plane B than the top
half of plane B itself. It is then more favourable
energetically for the atomic bonds across the two halves of
plane B to be severed and for plane A to bond with the
bottom half of plane B.
• The extra half-plane moves by discrete steps through thecrystal and ultimately emerges from the surface, forming a
slip step that is one atomic distance wide (~10-10m).
Macroscopic plastic deformation is the cumulative effect of
the motion of large numbers of dislocations.
Fig. 6.2-5 The step-by-step movement of an edge dislocationunder a low shear stress produces a unit step of slip.
6-13
• Before and after the movement of a dislocation through a
region of the crystal, the atomic arrangement is perfect
and ordered; it is only during the passage of the dislocation
that the lattice structure is disrupted. Only a relatively small
shear stress is required to operate in the immediate vicinity
of the dislocation in order to produce a step-by-step shear.
Fig. 6.2-6 Heimlichthe caterpillar illustrating
(a) the difficulty ofmoving without (b) a
dislocation mechanism.
• Although the edge, screw and mixed dislocation move in
different directions, the result is the same shear (Fig. 6.2-7).
Partially sheared Totally sheared
Fig. 6.2-7 Shear produced by motion of (a) edge, (b) screw and (c) mixed dislocations.The dark arrows indicate the direction in which the dislocations move.
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• While bulk ceramics and other crystalline compounds
contain dislocations, the shear stress required for
dislocation motion is at least 2-4 times that in metals. Not
only are covalent and ionic bonds stronger, but ions in the
more complex ceramic structures must also move greater
distances between equilibrium lattice positions.
• In addition, ceramics in which the bonding is
predominantly ionic contain very few slip systems. If slip
were to occur in some directions, ions of the same charge
would be brought close together (see also Sec. 3.8.4), generating
strong electrostatic repulsion that would resist slip (Fig. 6.2-8).
Fig. 6.2-8 (a) Before slip; (b) like charges repel in this slip direction; (c) slip possible.
• For ceramics with highly covalent bonding, the directional
nature of the bonds makes the displacement of atoms
from their lattice sites extremely difficult.
• The shear stress that must be applied to activate slip in
bulk ceramics is higher than that required to cause fracture
(Chp. 7). Ceramics are therefore hard and brittle, and do not
generally undergo plastic deformation by slip, except at
high temperatures (~ 0.5-0.7 T M [Note: T M is the melting temperature] ).
6-15
6.3 STRENGTHENING MECHANISMS IN METALS
• Because plastic deformation in metals corresponds to the
movement of large numbers of dislocations, the capacity
of a metal for plastic deformation depends on the ability ofdislocations to move.
• Since the hardness and strength of a metallic alloy are
related to the stress at which plastic deformation can be
made to occur (and thus, the stress at which dislocations
are able to move), there are two possible methods of
hardening or strengthening a metal:
! Eliminating all crystal defects, including dislocations –
this has only been achieved in “whiskers” (very thin
single crystals only a few µm in diameter), in which
strengths approaching theoretical values are possible.
! Creating so many crystal defects that they restrict or
hinder the passage of dislocations – this is the method
used to strengthen bulk metals, but yield strengths are
still much lower than theoretical levels.
• In the second approach, strengthening is achieved through
interactions of the stress fields of moving dislocations with
those created by other crystal defects.
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6-16
6. 3. 1 Dislocation Stress Fields and Strain Energies
• Atoms surrounding a dislocation are displaced from their
equilibrium lattice positions. Such elastic strain produces
an elastic stress field around the dislocation.
• In an edge dislocation, the presence of the extra half plane
of atoms above the dislocation line means that atoms in its
vicinity are squeezed together, resulting in compressive
stresses. Conversely, the atoms below the dislocation line
experience tensile stresses due to an increase in
interatomic separation in this region (Fig. 6.3-1).
Fig. 6.3-1 (a) Regions of compression and tension located around an edge dislocation.(b) Detailed stress state of an edge dislocation showing
compressive, tensile and shear stresses.
• In a screw dislocation, the lattice spirals around the centre
of the dislocation. The stress field is one of pure shear and
is symmetrical about the dislocation line (Fig. 6.3-2).
6-17
Fig. 6.3-2 Shear stress and strain associated with a screw dislocation.
• The distortion of atomic bonds around any dislocation
increases potential energy because of non-equilibrium
interatomic separations (see also Sec. 3.7). This energy is known
as strain energy, since it is associated with the strain or
distortion of the crystal lattice.
• When a dislocation is in close proximity to another, the
stress fields surrounding each dislocation will interact. For
example, if the compressive and tensile stress fields of two
edge dislocations lie on the same sides of the slip plane (Fig.
6.3-3a), the overall strain energy will be raised if the two
fields overlap; this gives rise to mutual repulsion as the
dislocations approach each other.
• Conversely, if the compressive and tensile stress fields were
on opposite sides (Fig. 6.3-3b), the dislocations would
annihilate each other when they meet, with a lowering of
the overall strain energy; the dislocations would thus be
attracted to each other.
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Fig. 6.3-3 (a) The interaction of two edge dislocations of the same sign causesrepulsion, (b) while that of different signs cause s attraction and annihilation.
C and T denote compressive and tensile regions, respectively.
• Two dislocations can attract and annihilate each other only
if they meet exactly on the same slip plane, and the
components of their stress fields match exactly and are of
opposite signs (Fig. 6.3-3b); i.e. tension cancels compression,
but tension/compression does not interact with shear.
• Since most dislocations are randomly curved mixed
dislocations, there is a only a very low probability that all
the conditions for dislocation annihilation will be fulfilled
simultaneously. Thus, dislocation interactions with one
another tend to be mutually repulsive.
6-19
• These repulsive interactions obstruct the motion of those
interacting segments of different dislocations, while non-
interacting segments continue to move, creating many
dislocation tangles (Figs. 6.3-4&5) during plastic deformation.
• Dislocations are therefore obstacles to the movement of
other dislocations.
Fig. 6.3-4 An edge dislocation (wavy black line) moving through a “forest” of otherdislocations (red verticle lines). Intersecting segments that are mutually obstructive
tangle with one another, distorting and lengthening the original dislocation.
Fig. 6.3-5 Tangling dislocations marked with a ‘b’.
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6.3.2 Strain Hardening
• Strain hardening, or work hardening is the phenomenon
whereby a ductile metal becomes harder and stronger as it
is plastically deformed. It is also known as cold working
because the temperature at which deformation takes place
is “cold” relative to the melting temperature of the metal.
• During plastic deformation, dislocations move under the
action of a shear stress and encounter other dislocations.
Since their interactions are generally repulsive (Sec. 6.3.1), a
higher applied stress is necessary to overcome this mutual
repulsion such that dislocation movement can continue;
i.e. the metal has become stronger/harder.
• Furthermore, many new dislocations are continuously
created during plastic deformation (Fig. 6.3-6), significantly
increasing the dislocation density. The average distance
between dislocations decreases, and the mutual resistance
to motion becomes more pronounced, requiring an
increasingly higher applied stress for continued plastic
deformation; thus, the metal strengthens until fracture.
• Crystals that have intersecting slip systems, e.g. FCC and
BCC, often strain-harden rapidly because slip tends to
occur in more than one slip system, causing dislocations
on different systems to intersect, impeding mutual motion.
6-21
Fig. 6.3-6 The sequence of events for the multiplication of a dislocation from a Frank-
Read source. A segment of dislocation pinned at two points bows out into a loop.Continued stress will cause the loop to expand and the residual segment to bow out
again into another loop. This process repeats over and over, sending out a set ofconcentric loops away from the source, creating many new dislocations. This is
analogous to the ripples generated when a pebble is dropped into a quiet pond.
• The yield strength and tensile strength of a metal increases
with increasing cold work, but ductility decreases (Figs. 6.3-7 &
6.3-8). Physical properties such as thermal and electrical
conductivity are also reduced due to the scattering of
electrons and phonons by dislocations.
• Strain hardening in metals explains why the true stress-
strain curve obtained during a tensile test shows a rising
stress from the start of yielding to fracture (Sec. 2.2.5).
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Fig. 6.3-7 Stress-strain diagram showing the effects of strain hardening.(a)
Initially, yielding beings at A; (b) upon unloading and re-loading, yielding now occurs at the higher stress B.
Fig. 6.3-8 The effects of cold work on the mechanical properties of copper.
• Metals may be shaped and strengthened at the same time
by cold working (Fig. 6.3-9).
6-23
Fig. 6.3-9 Common metalworking processes: (a) rolling, (b) forging(open and closed die), (c) extrusion (direct and indirect), (d) wire drawing, (e) stamping.
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6.3.3 Grain Size Strengthening
• In a polycrystal, each grain is has a different orientation to
its neighbours. Since slip occurs only on specific planes,
dislocations cannot move from one grain into another in a
straight line (Fig. 6.3-10). Furthermore, the atomic disorder at
grain boundaries interrupts the continuity of the slip
planes, and acts as a barrier to dislocation motion.
Fig. 6.3-10 Slip planes arediscontinuous and changedirections across the grain
boundary. Dislocationscannot move through the
grain boundary.
• A dislocation can move only within the grain in which it
was created. Dislocations pile up at the grain boundary,
causing strain energy to increase locally, creating a back
stress that repels other dislocations approaching the pile-
up (Fig. 6.3-11). A higher applied stress is needed to overcome
this repulsion for continued dislocation movement.
Fig. 6.3-11 Dislocation pile-upat a grain boundary.
6-25
• The more grain boundaries there are (i.e. the smaller the
grain size), the more obstacles there are to dislocation
motion, and the higher the stress needed to cause plastic
deformation; i.e. the metal becomes stronger/harder.
• The relationship between yield strength and grain size is
expressed by the Hall-Petch equation:
! y = ! 0 +k y
d where ! y = yield strength
d = average grain diameter
! 0, k y = material constants
• Generally, polycrystals are stronger than single crystals (Fig.
6.3-12); fine-grained metals are stronger than coarse-grained
(Fig. 6.3-13). Effective strengthening can be realized only when
the grain size is of the order of 5 µm or less.
.
Fig. 6.3-12 Stress-strain curves for singlecrystal and polycrystalline copper.
Fig. 6.3-13 Hall-Petch plot for brass, showingthe effects of grain size on yield strength.
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• Grain size strengthening is one of the major reasons for the
interest in nanocrystalline materials , in which grain sizes are
less than 100 nm. However, as grain size is reduced below
~ 20 nm and becomes comparable to the width of grain
boundaries, a reverse Hall-Petch effect is observed, where
decreasing grain size causes softening (Fig. 6.3-14).
Fig. 6.3-14 Hardness of a metal as a function of grain size.
• Grain size may be refined by cooling quickly from the
molten state, inoculation of the melt (i.e. adding numerous
impurity particles to the liquid to encourage solidification
on the particles), or by extensive plastic deformation followed by rapid annealing (Sec. 6.4). Other special
techniques are required to obtain grain sizes in the
nanometre range.
6-27
6.3.4 Solid Solution Strengthening
• All materials contain small amounts of foreign atoms
(element or compound). These impurities may arise
unintentionally from raw materials and processing, or may
be added intentionally to obtain specific properties.
• Impurities added intentionally are also known as alloying
elements in metals, additives in polymers and ceramics,
and dopants in semiconductors.
• Within a crystal, impurities (solute) may occupy interstitial
sites or substitute for atoms of the host material (solvent),
depending on the relative sizes of solute and solventatoms. The incorporation of solute atoms without altering
the crystal structure of the host results in a solid solution.
• Solute atoms distort the surrounding lattice and increase
the strain energy of the crystal (Fig. 6.3-15).
Fig. 6.3-15 Compressive strain imposed on host atoms by(a)
an interstitial solute atom, and (b) a large substitutional atom.(c) Tensile strain imposed by a small substitutional atom.
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• The solute stress field could interact with that of an
approa-ching dislocation such that repulsion arises (Fig. 6.3-
16), similar to repulsion between dislocations of like signs
(Sec 6.3-1). A higher applied stress is needed to overcome this
repulsion.
Fig. 6.3-16 Repulsion betweencompressive stress fields of solute anddislocation.
• On the other hand, if an interstitial or large substitutional
solute atom with a compressive stress field were to be
located in the tensile region around a dislocation, lattice
strain is reduced (Fig. 6.3-17). A similar reduction in strain is
seen for a small substitutional atom with tensile strain field
located in the compressive region of a dislocation (Fig. 6.3-18).
• Once such a configuration of low strain are established
between a solute atom and dislocation, further movement
of the dislocation (i.e. away from the solute) would again
raise strain energy (Fig. 6.3-19). This increase in energy is met
by applying a higher stress; i.e. the metal strengthens.
6-29
Fig. 6.3-17 (a) Compressive strains imposed by a large substitutional solute atom.
(b)
Possible locations of large solute atoms relative to an edge dislocation,leading to a reduction in overall lattice strain.
Fig. 6.3-18 (a) Tensile strains imposed by a small substitutional solute atom.(b) Possible locations of small solute atoms relative to an edge dislocation, leading to a
reduction in overall lattice strain.
Fig. 6.3-19 Interaction with a suitable solute lowers dislocation strain energy.Continued plastic deformation requires the movement of dislocation away from the
solute, which returns the dislocation and solute to their states before interaction. A higher stress is needed to restore the original strain energies of dislocation and solute.
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• Higher stresses are thus required for dislocation movement
in the presence of solute atoms, which act as obstacles.
The more solute added (without exceeding the solubility
limit), the greater the strengthening (Fig. 6.3-20). Metals are
seldom used pure, but are usually alloyed for strength.
• The degree of solid solution strengthening depends on the
relative sizes of the solute and solvent atoms. The larger
the size difference, the greater the distortion of the
surrounding lattice, and the stronger the strengthening
effect (Fig. 6.3-20). Too large a size difference, however, would
lower solute solubility in the host lattice (Sec. 9.3.1).
• The strengthening effect further depends whether the
solute is substitutional or interstitial, and the crystal
structure of the solvent. The stress field of a substitutional
solute atom in close-packed FCC or HCP crystals is
spherically symmetric, without any shear component, and
as such, does not interact with the shear stress fields of
screw dislocations. Conversely, interstitial solute atoms in
non-close-packed crystals such as BCC cause a non-
symmetric tetragonal distortion, generating a stress field
that can interact with both edge and screw (and thus,
mixed) dislocations.
6-31
• Only the very small non-metallic atoms, such as H, B, C, N
and O, tend to dissolve interstitially in metals (Sec. 9.3.1).
Fig. 6.3-20 The effects of several substitutional alloying elementson the yield strength of copper.
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6.3.5 Dispersion Hardening
• Small, hard particles of a second phase dispersed in a
softer, ductile matrix are effective obstacles to dislocation
motion, and lead to significant strengthening. Such
particles may be introduced intentionally, or arise naturally
from precipitation reactions in an alloy, the latter
producing a precipitation or age hardening effect.
• The interaction between dislocation and dispersed particle
depends on the nature of the particle-matrix boundary. For
particles that are intentionally incorporated, and for many
precipitates, the particle-matrix interface is non-coherent
and disordered (Fig. 6.3-21a); i.e. there is no atomic matching
between the crystal lattice of the particle and matrix. Such
particles do not distort the surrounding lattice.
Fig. 6.3-21 (a) A particle that has no relationship with the crystal structure of thesurrounding matrix forms a non-coherent interface with the matrix.
(b) When there is a definite relationship between the crystal structures of the precipatateand matrix, a coherent or semi-coherent interface exists.
6-33
• At a non-coherent interface between particle and matrix
(Fig. 6.3-21a), there is a discontinuity of slip planes, much like
that at grain boundaries (Sec. 6.3.3). A dislocation would be
unable to move through such a particle.
• The dislocation may be forced to keep on moving by
extruding or bowing between the particles (Fig. 6.3-22). Since
a curve between two points is longer than a straight line,
the bowed dislocation introduces greater lattice distortion
and higher strain energy than the original, straight
dislocation. A larger shear stress must now be applied to
cause such bowing and continued plastic deformation.
Fig. 6.3-22 A view looking down on a slip plane showing the bowing of a dislocationpast particles having a non-coherent interface with the matrix.
[Note that the circles represent particles, not single atoms.]
• After a dislocation has bowed past, dislocation loops are
left around the particles (Fig. 6.3-22). The stress fields of these
loops would interact with subsequent dislocations, and
add resistance to their motion, leading to further
strengthening.
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• Fine particles that are precipitated from an alloy often have
planes of atoms in their crystal structures that are related
to, or even continuous with, planes in the matrix lattice;
such precipitate-matrix interfaces are said to be coherent
(Fig. 6.3-21b).
• Since a coherent precipitate does not usually share the
same lattice parameters as the matrix, this results in lattice
strain. The stress field thus generated would interact with
passing dislocations in a manner analogous to that of solid
solution strengthening (Sec. 6.3.4).
• Because the stress field generated by a coherent precipitate
is relatively wide, interactions with dislocations would
occur wherever the stress fields impinge upon one
another. The precipitate does not need to be on the slip
plane of a dislocation to have a strengthening effect.
• When a coherent precipitate lies directly in the path of a
dislocation, the coherency at the interface would allow the
slip plane of the dislocation to pass from the matrix into
the precipitate and shear the precipitate (Fig. 6.3-23).
However, the creation of new matrix-precipitate surface
area after shearing raises interfacial energy. For such
shearing to occur, a higher stress must be applied to fund
the increase in energy, thus strengthening the alloy.
6-35
Fig. 6.3-23 The formation of new precipitate-matrix interfaces when adislocation cuts through a coherent precipitate.
• The degree of strengthening depends on the number and
distribution of dispersed particles and precipitates: these
should be as numerous as possible and uniformly
distributed, so that they are closely spaced.
• Dispersion hardening is the principle behind metal matrix
composites (MMCs), in which an alloy is strengthening by a
dispersion of fine, hard particles, usually of a ceramic
material. Ceramics retain their shape, distribution and
superior hardness when heated, and are more effective at
strengthening an alloy at high temperatures than
precipitates, which tend to agglomerate (and hence,
reduce in number) and re-dissolve into the matrix.
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6.3.6 Combined Strengthening Mechanisms
Two or more strengthening mechanisms may operate
simultaneously to improve strength and hardness in metals
(Tables 6.3-1&2 & Fig. 6.3-24).
Table 6.3-1 The effectiveness of the various strengthening mechanisms on copper.
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Fig. 6.3-24 Strengthening mechanisms in copper alloys and the variation in properties.
Table 6.3-2 Metal alloys with typical applications, and the strengthening mechanisms used.
Alloy Typical uses Solutionhardening
Precipitationhardening
Workhardening
Pure Al Kitchen foil !!!
Pure Cu Wire !!!
Cast Al, Mg Automotive parts !!! !
Bronze (Cu-Sn), Brass (Cu-Zn) Marine components !!! ! !!
Non-heat-treatable wrought Al Ships, cans, structures !!! !!!
Heat-treatable wrought Al Aircraft, structure s ! !!! !
Low-carbon steels Car bodies, structures,ships, cans
!!! !!!
Low alloy steels Automotive parts, tools ! !!! !
Stainless steels Pressure vessels !!! ! !!!
Cast Ni alloys Jet engine turbines !!! !!!
Symbols: !!!= Routinely used. != Sometimes used.
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6.4 ANNEALING
• There is a limit to which metals may be plastically
deformed, beyond which fracture occurs.
• During forming operations, it is sometimes necessary torestore the ductility of work-hardened metals to their state
prior to deformation, in order to carry out further plastic
deformation.
• Work hardening also lowers the thermal and electrical
conductivity of metals, which might require restoring; e.g.
copper electrical wires.
• The effects of work hardening can be removed by heating
the metal to a sufficiently high temperature in a process
called annealing. Annealing replaces the highly distorted
work-hardened grains with new, equiaxed grains
containing few dislocations.
• The driving force for annealing is the reduction of strain
energy associated with the high density of dislocations in a
severely work-hardened metal.
• In annealing, there are three temperature ranges (from low
to high) in which different phenomena occur: recovery,
recrystallization and grain growth.
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6.4.1 Recovery
• When heated sufficiently, dislocations in a strain hardened
metal rearrange themselves into configurations with lower
strain energy, forming the cell boundaries of a subgrain
structure within the old grains (Fig. 6.4-1c), in a process called
polygonization.
• Dislocation density is lowered slightly through mutual
annihilation, but because the reduction is not significant,
hardness, strength and ductility are almost unchanged (Fig.
6.4-2). However, thermal and electrical conductivity are
restored close to their pre-cold-worked states.
6.4.2 Recrystall ization
• After recovery is complete, the strain energy of the crystal
is still relatively high due to the large number of
dislocations remaining. If the temperature were raised
further, recrystallization will follow.
• New, small, dislocation-free grains nucleate at the high-
energy cell boundaries of the polygonized subgrain
structure (Fig. 6.4-1d), eliminating most of the dislocations as
they grow and replace the strain hardened grains (Fig. 6.4-1e).
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Fig. 6.4-1 Microstructural changes in cold working and annealing:(a) original state with few dislocations; (b) high density of dislocations after
cold working; (c) recovery; (d) recrystallization; (e) fully recrystallizedstructure of new relatively strain-free grains with few dislocations.
• Since recrystallized grains are relatively free of dislocations,
the hardness, strength and ductility of the metal are
restored to their pre-cold-worked values; i.e. hardness and
strength decrease while ductility increases (Fig. 6.4-2).
• The low strength and high ductility of a recrystallized
metal are exploited in hot working, in which plasticdeformation of a metallic alloy is carried out at
temperatures above its recrystallization temparature
(usually above 0.6 T M ). The continually recrystallizing metal
allows extensive deformation without strain hardening.
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• The main disadvantage of hot working is the poor surface
finish as a result of oxidation of the metal surface at high
temperatures. Dimensional accuracy is also an issue due to
the elastic recovery (springback) and thermal contraction
that occur when the component is cooled subsequently.
Fig. 6.4-2 The effects of annealing temperatureon mechanical properties and grain size.
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6.4.3 Grain Growth
• If heating were to continue after complete recrystallization
has occurred, the new grains will grow in size. [Note that grain
growth occurs in all polycrystalline materials at sufficiently high temperatures; it is not related
to cold-working. Only in cold-worked metals do recovery and recrystallization take place
before grain growth.]
• The driving force for grain growth is the reduction of the
interfacial energy associated with the atomic disorder at
grain boundaries (Sec. 4.7). Grain growth results in fewer
grains, thereby decreasing the total area of grain
boundaries and lowering the interfacial energy.
• Grain growth involves the diffusion of atoms across thegrain boundary from one grain to another, such that some
grains grow at the expense of others (Fig. 6.4-3).
Fig. 6.4-3 Grain growth occurs as atoms diffuse across the brain boundary from one grain to another.
• Grain growth reduces the strength and hardness of
metallic alloys (Sec. 6.3.2), because the number of grain
boundaries, which are barriers to dislocation motion, are
now fewer.