Lectures 01-06, 2021-1.pdf

Thursday, Jan 26,
2023 (IUB)
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Lectures 01-06
Defects/Imperfections
Materials Simulation Group
(MSG)
By
Prof. Dr. Altaf Hussain
Institute of Physics (IoP),
The Islamia University of Bahawalpur

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Introduction
(MSG)
▪ Natural crystals always contain defects, often in abundance,
due to the uncontrolled conditions under which they are
formed.
▪ The presence of defects (which affects the
Color) can make these crystals valuable as
gems, as in ruby {(chromium replacing a
small fraction of Al in Al-oxide (Al2O3)}.
▪ The importance of defects depends upon:
(i) the material, (ii) type of defect, and (iii) properties which
are being considered.
▪ Properties, such as density & elastic constants, are
proportional to the concentration of defects.

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Continued . . .
(MSG)
▪ Other properties, e.g. the color of an insulating crystal or
the conductivity of a semiconductor crystal, may be much
more sensitive to the presence of small number of defects.
▪ The term defect carries with it the connotation of
undesirable qualities, but indeed the defects are responsible
for many of the important properties of materials and much
of materials science involves the study and engineering of
defects.
▪ A defect free, i.e. ideal Si crystal would be of little use in
modern electronics; the use of Si in electronic devices is
dependent upon small concentrations of chemical
impurities such as P & As which give it desired properties.

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Simple defects in a lattice
(MSG)

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Continued . . .
(MSG)

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Continued . . .
(MSG)

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Structure and Properties
(MSG)
▪ Structure insensitive properties ---> Properties such as
stiffness & electrical conductivity (excluding semiconductors)
are termed as structure insensitive and are not affected
by the presence of defects in crystals.
▪ Structure sensitive properties ---> Properties such as
mechanical strength, ductility, crystal growth, magnetic
hysteresis, dielectric strength, conduction in
semiconductors are greatly affected by the relatively
minor changes in crystal structure caused by defects or
imperfections.

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Defects classification
(MSG)
▪ Crystalline defects can be classified on the basis of their
geometry as follows:
(i) Point imperfections (0 D)
(ii) Line imperfections or DISLOCATIONS (1 D)
(iii) Surface & grain boundary imperfections (2 D)
(iv) Volume imperfections (3 D)
▪ Dimensions of a point defect are close to an interatomic space.
▪ Length of linear defects is several orders of magnitude greater than
the width.
▪ Surface defects have a small depth, while their width and length may
be several orders larger.
▪ Volume defects (pores & cracks) may have substantial dimensions in
all measurements, i.e. at least a few tens of Å.

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Dimensional ranges of defects
(MSG)

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(MSG)
Section-1
0D defects

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Point Imperfections
(MSG)
❑ Definition:
➢ In a crystalline solid, when the ideal
arrangement of solids is distorted around a
point/atom it is called a point defect.
➢ Point defects are accounted for when the
crystallization process occurs at a very
fast rate.
➢ These defects mainly happen due to
deviation in the arrangement of constituting
particles.

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Continued . . .
(MSG)
▪ Point imperfections (also called lattice errors) take place
due to:
(i) imperfect packing of atoms during crystallization &
(ii) due to vibrations of atoms at high temperatures.
▪ Point imperfections are completely local in effect, e.g. a
vacant lattice site.
▪ Point defects are always present in crystals and their
presence results in a decrease in the free energy.
▪ Types of point imperfections:
a)Vacancies
b)Self-Interstitials
c) Impurities: Substitutional & Interstitial atoms

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a) Vacancies
(MSG)
▪ The simplest point defect is a vacancy which refers to an
empty (unoccupied) site of a crystal lattice.
▪ Such defects may arise either from imperfect packing during
original crystallization or from thermal vibrations of the atoms
at higher temperatures.
▪ When the thermal energy due to vibration is increased, there is
always an increased probability that individual atoms will jump
out of their positions of lowest energy. Each temperature has a
corresponding equilibrium concentration of vacancies.

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Continued . . .
(MSG)
▪ Each temperature has a corresponding equilibrium
concentration of vacancies.
▪ For instance, Cu can contain as many as 0.01% of
vacancies at temperature near the melting point (one
vacancy per 104 atoms).
▪ For most of the crystals the said (vacancy) thermal energy
is of the order of l eV per vacancy.
▪ The vacancies may be single or two or more of them may
condense into a di-vacancy or tri-vacancy.
▪ At higher temps., vacancies have a higher concentration &
can move from one site to another more frequently.
▪ Vacancies accelerate all processes associated with
displacements of atoms: diffusion, powder sintering, etc.

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Vacancies: equilibrium concentration
(MSG)

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Measuring activation energy
(MSG)

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Equilibrium concentration of vacancies
(MSG)

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Methods of producing point defects
(MSG)
▪ Growth and synthesis
Impurities may be added to the material during synthesis
▪ Thermal & thermochemical treatments & other
stimuli
➢ Heating to high temperature and quench
➢ Heating in reactive atmosphere
➢ Heating in vacuum --> e.g. in oxides it may lead to loss of
oxygen etc.
▪ Plastic Deformation
▪ Ion implantation and irradiation
➢ Electron irradiation (typically >1MeV)
→ Direct momentum transfer or during relaxation of
electronic excitations
➢ Ion beam implantation (As, B etc.)
➢ Neutron irradiation

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b) Self-Interstitials
(MSG)
▪ In a crystal if the APF is low, an extra atom may be lodged
within the crystal structure at interstitial position (or void).
▪ This happens only when the extra atom is substantially smaller
than the parent atoms, otherwise it will produce atomic
distortion.
▪ In close packed structures, e.g. FCC & HCP, the largest size of
an atom that can fit in the interstitial void or space has a radius
about 22.5% of the radii of parent atoms.
▪ Interstitialcies may also be single interstitial, di-interstitials, &
tri-interstitials. Moreover, the vacancy & interstitialcy are
inverse phenomena.

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c) Impurities: Substitutional & Interstitial atoms
(MSG)

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Frenkel Defect
(MSG)
▪ In ionic solids generally, the smaller ion (cation) moves
out of its place and occupies an intermolecular space.
▪ In this case, a vacancy defect is created on its original
position and the interstitial defect is experienced at its
new position.
▪ The density of a
substance remains
unchanged.
▪ It happens when there
is a huge difference in the size of anions and cations.
▪ Example: ZnS and AgCl.

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Shottky Defect
(MSG)
▪ This kind of vacancy defects is found in Ionic Solids.
▪ But in ionic compounds, we need to balance the
electrical neutrality (charge neutrality) of the
compound so an equal number of anions and cations
will be missing from the compound.
▪ It reduces the density
of the substance.
▪ In this, the size of
cations and anions
are of almost the
same.

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Point Defects in Ceramics
(MSG)
▪ Vacancies -- vacancies exist in ceramics for both cations
and anions
▪ Interstitials -- interstitials exist for cations
▪ Interstitials are not normally observed for anions because
anions are large relative to the interstitial sites.

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Continued . . .
(MSG)
▪ Frenkel Defect -- a cation vacancy-cation interstitial pair.
▪ Shottky Defect -- a paired set of cation and anion
vacancies.
▪ Equilibrium concentration of defects ∝ 𝒆 Τ
−𝑸𝑫 𝒌𝑻

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Stoichiometry
(MSG)
▪ The ratio of cations to anions is not altered by
the formation of either a Frenkel or a Shottky
defect.
▪ If no other defects are present, the material is
said to be stoichiometric.
▪ Stoichiometry may be defined as a state for
ionic compounds wherein there is the exact ratio
of cations to anions as predicted by the chemical
formula.
▪ For example, NaCl is stoichiometric if the ratio of
𝑁𝑎+ ions to 𝐶𝑙− ions is exactly 1:1.

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Continued . . .
(MSG)

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Nonstoichiometry
(MSG)
▪ A ceramic compound is nonstoichiometric if there is any
deviation from this exact ratio.
▪ Nonstoichiometry may occur for some ceramic materials in
which two valence (or ionic) states exist for one of the
ion types.
▪ Iron oxide (FeO) is one such material, for the iron can be
present in both 𝑭𝒆𝟐+
and 𝑭𝒆𝟑+
states; the number of each of
these ion types depends on temperature and the ambient
oxygen pressure.
▪ The formation of an 𝐹𝑒3+
ion disrupts the
electroneutrality of the crystal by introducing an excess
+1 charge, which must be offset by some type of defect.
▪ This may be accomplished by the formation of one 𝑭𝒆𝟐+
vacancy for every two 𝐹𝑒3+ ions that are formed.

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Iron Oxide: FeO
(MSG)
▪ The crystal is no longer stoichiometric because there is one
more O ion than Fe ion; however, the crystal remains electrically
neutral.
▪ This phenomenon is fairly common in iron oxide, and, in fact, its
chemical formula is often written as 𝐅𝐞𝟏−𝒙𝐎 (where x is some
small and variable fraction substantially less than unity) to
indicate a condition of nonstoichiometry with a deficiency of Fe.

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Impurities in Solids
(MSG)
▪ A pure metal consisting of only one type of atom just
isn’t possible; impurity or foreign atoms will always be
present, and some will exist as crystalline point defects.
▪ In fact, even with relatively sophisticated techniques, it is
difficult to refine metals to a purity in excess of
99.9999%.
▪ At this level, on the order of 1022 to 1023 impurity atoms
will be present in one cubic meter of material.
▪ Most familiar metals are not highly pure; rather, they are
alloys, in which impurity atoms have been added
intentionally to impart specific characteristics to the
material.
▪ Ordinarily, alloying is used in metals to improve
mechanical strength and corrosion resistance.

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Continued . . .
(MSG)
▪ E.g., sterling silver is a 92.5% silver & 7.5% copper alloy.
▪ In normal ambient environments, pure silver is highly corrosion
resistant, but also very soft.
▪ Alloying with copper significantly enhances the mechanical
strength without depreciating the corrosion resistance
appreciably.
▪ The addition of impurity atoms to a metal will result in the
formation of a solid solution and/or a new second phase,
depending on the kinds of impurity, their concentrations, and the
temperature of the alloy.
▪ With regard to alloys, solvent represents the element or
compound that is present in the greatest amount; on occasion,
solvent atoms are also called host atoms.
▪ Solute is used to denote an element or compound present in a
minor concentration.

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(MSG)
Section-2
1D defects

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Line Imperfections
(MSG)
▪ Line imperfections also called
dislocations are 1D
imperfections in the
geometrical sense of the
atomic arrangement.
▪ Types: Line imperfections are
of three types
(i) edge, (ii) screw dislocation
& (iii) mixed.
▪ These defects are the most striking imperfections and are
responsible for the useful property of ductility in metals,
ceramics and crystalline polymers.

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a) Edge Dislocation
(MSG)
Dislocation Line:
▪ The dislocation centers
around the line (Dislocation
Line) that is defined along the
end of the extra half-plane of
atoms.
▪ Dislocation line for the edge
dislocation shown in Figure is
perpendicular to the plane of
the page.
Dislocation:
▪ A dislocation is a linear or one-dimensional defect around
which some of the atoms are misaligned.

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Burger Vector Concept
(MSG)

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Slip mechanism
(MSG)
➢ Deformation of ductile materials occurs when a line defect
(dislocation) moves (slip) through the material.
➢ slip between crystal planes result when dislocations move;
➢ produce permanent (plastic) deformation.
Schematic view of slip mechanism.

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Plastic deformation via dislocation
(edge) movement
(MSG)

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b) Screw Dislocation
(MSG)
▪ Screw dislocation
may be thought of
as being formed by
a shear stress that is
applied to produce
the distortion.
▪ In Figure: the upper
front region of the
crystal is shifted one
atomic distance to
the right relative to
the bottom portion.

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Screw Dislocation Line
(MSG)
▪ The atomic distortion associated with a screw dislocation
is also linear and along a dislocation line (Line AB in
Figure).
▪ The screw dislocation
derives its name from the
spiral or helical path or ramp
that is traced around the
dislocation line by the
atomic planes of atoms.
▪ Sometimes the symbol
is used to designate a screw
dislocation.

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Continued . . .
(MSG)
▪ A screw dislocation does not exhibit climb motion.
➢ The following effects of screw dislocation are of great
importance.
(i) The force required to form & move a screw dislocation is
somewhat greater than that required to initiate an edge dislocation.
(ii) Without breaking the continuity of the lattice, the plastic
deformation is possible under low stress.
(iii) Screw dislocation causes distortion of the crystal lattice for a
considerable distance from the center of the line and takes the form
of spiral distortion of the planes.
➢ We must remember that the dislocations of both types, i.e.,
combinations of edge & screw, are closely associated with the
crystallization as well as deformation.

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Burgers vector
(MSG)
▪ Burgers vector for a screw dislocation is parallel to the
line of the dislocation.

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Dislocation density
(MSG)
▪ The total length of all dislocation lines in a unit volume
is called the dislocation density.
▪ It may be equal to 104 – 105 cm–2 in semiconductor
crystals and 106 – 108 cm–2 in annealed metals.
▪ Attempts to raise the dislocation density above 1012
cm–2 end quickly in cracking & failure of the metal.
▪ Dislocations participate in phase transformations &
recrystallization.

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Cottrell atmospheres
(MSG)
▪ The rate of diffusion along dislocation lines is several
orders of magnitude greater than that through a crystal
lattice without defects.
▪ Dislocations serve as places for concentration of
impurity atoms, especially of interstitial impurities and
decrease lattice distortions.
▪ Impurity atoms can concentrate around dislocations &
form the Cottrell atmospheres which impede
dislocation movement & strengthen the metal.

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Dislocations & materials strength
(MSG)
▪ Dislocations show pronounced effect on the strength of
crystals.
▪ The experimentally measured yield strength of metals turns
out to be the only one-thousandth of its theoretical value,
the loss being mainly attributed to the effect of mobile
dislocations.
▪ By increasing substantially the dislocation density &
decreasing the dislocation mobility, the strength of a metal
can be raised several times compared with its strength in
the annealed state.
▪ Faultless pieces of metals exhibit a strength approaching the
theoretical value.

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Geometrical characteristics
(MSG)
(i) The vector sum of the Burgers vectors of dislocations
meeting at a point called the node must be zero
(analogous to Kirchhoff’s law for electrical currents meeting at a junction) &
(ii) A dislocation line cannot end abruptly within the
crystal.
(iii) It either ends at a node or at the surface.

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Distortional energy of dislocations
(MSG)
➢ The elastic strain energy E per unit length of a dislocation
of Burgers vector b can be expressed approximately by
𝑬 ≃
𝝁𝒃𝟐
𝟐
Here 𝝁 is the shear modulus of the crystals. For BCC iron
(a = 2.87 Å), E is of the order 2.5 × 10–9 J-m–1.
➢ From above relation, it is obvious that the elastic strain
energy of a dislocation is proportional to the square of the
Burgers vector, dislocations tend to have as small a Burgers
vector as possible.

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Full & partial dislocations
(MSG)
▪ In real crystals, the dislocations can be classified as
full & partial dislocations.
▪ For a partial dislocation, the Burgers vector is a
fraction of a lattice translation, whereas
▪ for a full dislocation, the Burgers vector is an
integral multiple of a lattice translation.

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Mixed Dislocations
(MSG)
▪ Most dislocations found in
crystalline materials are
probably neither pure edge
nor pure screw, but exhibit
components of both types.
▪ These are termed mixed
dislocations.
▪ All three dislocation types are
represented schematically 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 & Mechanical properties
(MSG)
▪ The strength of a material with no dislocations is 20-100
times greater than the strength of a material with a high
dislocation density.
▪ So, materials with no dislocations may be very strong, but
they cannot be deformed.
▪ The dislocations weaken a material, but make plastic
deformation possible.

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(MSG)
Section-3
2D defects

▪ Crystalline materials are broadly divided into two
classes:
1. Single Crystals
2. Polycrystalline Materials
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CRYSTALLINE MATERIALS
(MSG)

▪ For a crystalline solid, when the periodic and repeated arrangement of atoms is
perfect or extends throughout the entirety of the specimen without interruption,
the result is a single crystal.
▪ All unit cells interlock in the same way and have the same orientation.
▪ Single crystals exist in nature, but they may also be produced artificially.
▪ They are ordinarily difficult to grow, because the environment must be carefully
controlled.
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SINGLE CRYSTALS
(MSG)
▪ If the extremities of a single crystal are permitted to grow
without any external constraint, the crystal will assume a
regular geometric shape having flat faces, as with some of
the gem stones; the shape is indicative of the crystal
structure.
▪ A photograph of a garnet single crystal is shown in Figure.
▪ Within the past few years, single crystals have become
extremely important in many of our modern technologies,
in particular electronic microcircuits, which employ single
crystals of silicon and other semiconductors.

▪ Most crystalline solids are composed of a collection of many small crystals or
grains;
▪ such materials are termed polycrystalline.
▪ Various stages in the solidification of a polycrystalline specimen are represented
schematically in Figure below.
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Polycrystalline Materials
(MSG)

1. Initially, small crystals or nuclei form at various positions. These have random
crystallographic orientations, as indicated by the square grids.
2. The small grains grow by the successive addition from the surrounding liquid of atoms to
the structure of each.
3. The extremities of adjacent grains impinge on one another as the solidification process
approaches completion.
▪ As indicated in Figure above, the crystallographic orientation varies from grain to grain.
▪ Also, there exists some atomic mismatch within the region where two grains meet; this
area is called a grain boundary.
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CONTINUED . . .
(MSG)

▪ The physical properties of single crystals of some substances depend on
the crystallographic direction in which measurements are taken.
▪ For example, the elastic modulus, the electrical conductivity, and the
index of refraction may have different values in the [100] and [111]
directions.
▪ This directionality of properties is termed anisotropy, and it is associated
with the variance of atomic or ionic spacing with crystallographic
direction.
▪ Substances in which measured properties are independent of the
direction of measurement are isotropic.
▪ The extent and magnitude of anisotropic effects in crystalline materials
are functions of the symmetry of the crystal structure;
▪ the degree of anisotropy increases with decreasing structural
symmetry—
▪ triclinic structures normally are highly anisotropic.
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ANISOTROPY
(MSG)

▪ For many polycrystalline materials, the crystallographic orientations
of the individual grains are totally random.
▪ Under these circumstances, even though each grain may be
anisotropic, a specimen composed of the grain aggregate behaves
isotropically.
▪ Also, the magnitude of a measured property represents some
average of the directional values.
▪ Sometimes the grains in polycrystalline materials have a preferential
crystallographic orientation, in which case the material is said to
have a “texture”.
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CONTINUED . . .
(MSG)
▪ The modulus of elasticity values
at [100], [110], and [111]
orientations for several materials
are presented in Table as:

▪ The magnetic properties of some iron alloys used in transformer
cores are anisotropic—that is, grains (or single crystals) magnetize in
a <100>-type direction easier than any other crystallographic
direction.
▪ Energy losses in transformer cores are minimized by utilizing
polycrystalline sheets of these alloys into which have been
introduced a “magnetic texture”: most of the grains in each sheet
have a <100>-type crystallographic direction that is aligned (or
almost aligned) in the same direction, which direction is oriented
parallel to the direction of the applied magnetic field.
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CONTINUED . . .
(MSG)

❖ Interfacial defects are boundaries that have two
dimensions (2D) and normally separate regions of the
materials that have different crystal structures and/or
crystallographic orientations.
➢ These imperfections include
1. External surfaces,
2. Grain boundaries,
3. Twin boundaries,
4. Stacking faults, and
5. Phase boundaries.
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INTERFACIAL DEFECTS
(MSG)

❑ One of the most obvious boundaries is the external surface, along
which the crystal structure terminates.
➢ Surface atoms are not bonded to the
maximum number of nearest neighbors,
and are therefore in a higher energy state
than the atoms at interior positions.
❑ The bonds of these surface atoms that are
not satisfied give rise to a surface energy,
expressed in units of energy per unit area (J/m2 or erg/cm2).
❖ To reduce this energy, materials tend to minimize, if at all possible, the
total surface area.
❖ For example, liquids assume a shape having a minimum area—the
droplets become spherical.
❖ Of course, this is not possible with solids, which are mechanically rigid.
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EXTERNAL SURFACES
(MSG)

▪ Another interfacial defect, the grain boundary separates two
small grains or crystals having different crystallographic
orientations in polycrystalline materials.
▪ A grain boundary is represented
schematically from an atomic
perspective in Figure.
▪ Within the boundary region,
which is probably just several
atom distances wide, there is
some atomic mismatch in a
transition from the crystalline
orientation of one grain to that
of an adjacent one.
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GRAIN BOUNDARIES
(MSG)

▪ Various degrees of crystallographic misalignment between adjacent
grains are possible (Figure on previous slide).
▪ When this orientation mismatch is slight, on the
order of a few degrees, then the term small-
(or low- ) angle grain boundary is used.
▪ These boundaries can be described in terms of
dislocation arrays.
▪ One simple small angle grain boundary
is formed when edge dislocations are aligned
in the manner of Figure.
▪ This type is called a tilt boundary;
the angle of misorientation, is also indicated in
the figure.
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CONTINUED . . .
(MSG)

▪ When the angle of misorientation is parallel to the boundary, a twist
boundary results, which can be described by an array of screw
dislocations.
▪ The atoms are bonded less regularly along a grain boundary (e.g., bond
angles are longer), and consequently, there is an interfacial or grain
boundary energy similar to the surface energy described above.
▪ The magnitude of this energy is a function of the degree of
misorientation, being larger for high-angle boundaries.
▪ Grain boundaries are more chemically reactive than the grains
themselves as a consequence of this boundary energy.
▪ Furthermore, impurity atoms often preferentially segregate along these
boundaries because of their higher energy state.
▪ The total interfacial energy is lower in large or coarse-grained materials than
in fine-grained ones, since there is less total boundary area in the former.
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CONTINUED . . .
(MSG)

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CONTINUED . . .
(MSG)
▪ In spite of this disordered arrangement of atoms and lack of regular
bonding along grain boundaries, a polycrystalline material is still very
strong; cohesive forces within and across the boundary are present.
▪ Furthermore, the density of a polycrystalline specimen is virtually
identical to that of a single crystal of the same material.
▪ The lattices of adjacent grains are oriented at random and differently
(Figure) and a boundary between any two grains is essentially a
transition layer of thickness of 1–5 nm.

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(MSG)
▪ When the orientation difference b/w neighboring grains is more than
10°–15°, boundaries are called high angle grain boundaries.
▪ If the angle of mis-orientation b/w adjacent sub-grains are not large (not
more than 5°), the boundaries are termed as ‘low angle’.
CONTINUED . . .

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TILT BOUNDARY
(MSG)
▪ This is a type of low-angle boundary as
the orientation difference b/w two
neighboring crystals is less than 10°.
▪ This type of boundary is associated with
relatively little energy & is composed of
edge dislocations lying one above the
other.
▪ The angle or tilt, 𝜽 =
𝒃
𝑫
, where
▪ b is the magnitude of Burgers vector
and
▪ D is the average vertical distance b/w
dislocations.

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PHASE BOUNDARY
(MSG)
▪ Phase boundaries exist in multiphase materials, wherein a
different phase exists on each side of the boundary.
▪ Furthermore, each of the constituent phases has its own
distinctive physical and/or chemical characteristics.
▪ Phase boundaries play an important role in determining the
mechanical characteristics of some multiphase metal alloys.
▪ A phase may be defined as a homogeneous portion of a
system that has uniform physical and chemical
characteristics.
▪ Every pure material is considered to be a phase; so also is
every solid, liquid, and gaseous solution.
▪ For example, the sugar–water syrup solution is one phase,
and solid sugar is another.

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CONTINUED . . .
(MSG)
▪ Each has different physical properties (one is a liquid, the
other is a solid).
▪ Furthermore, each is different chemically (i.e., has a
different chemical composition); one is virtually pure sugar,
the other is a solution of H2O and C12H22O11.
▪ If more than one phase is present in a given system, each
will have its own distinct properties, and a boundary
separating the phases will exist across which there will be a
discontinuous and abrupt change in physical and/or
chemical characteristics.
▪ When two phases are present in a system, it is not
necessary that there be a difference in both physical and
chemical properties; a disparity in one or the other set of
properties is sufficient.

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67
CONTINUED . . .
(MSG)
▪ When water and ice are present in a container, two
separate phases exist; they are physically dissimilar (one is
a solid, the other is a liquid) but identical in chemical
makeup.
▪ Also, when a substance can exist in two or more
polymorphic forms (e.g., having both FCC and BCC
structures), each of these structures is a separate phase
because their respective physical characteristics differ.
▪ Sometimes, a single-phase system is termed
homogeneous.
▪ Systems composed of two or more phases are termed
mixtures or heterogeneous systems.

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TWIN BOUNDARY
(MSG)
▪ A special type of grain boundary across which there is a specific mirror lattice
symmetry; i.e., atoms on one side of the boundary are located in mirror-image
positions of the atoms on the other side (Figure below) is called Twin Boundary.
▪ The region of material between these boundaries is appropriately termed a twin.
▪ Twins result from atomic displacements that are produced from applied
mechanical shear forces (mechanical twins), and also during annealing heat
treatments following deformation (annealing twins).

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2023 (IUB)
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CONTINUED . . .
(MSG)
▪ Twinning occurs on a definite crystallographic plane and in a specific
direction, both of which depend on the crystal structure.
▪ Annealing twins are typically found in metals that have the FCC crystal
structure, while mechanical twins are observed in BCC and HCP metals.
▪ The mechanical twins play role in the deformation process.

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2023 (IUB)
70
STACKING FAULTS
(MSG)
▪ A Stacking Fault (SF) is a an error in
the staking sequence of planes in
the crystal.
▪ Common examples are intrinsic &
extrinsic SF on {111} in FCC metals.
▪ In the first case, the lattice
“collapse” along [111] by d111= a/√3,
leaving two overlapping layers AB,
AB of HCP stacking. Produced by
quenching.
▪ In the second case, is produced by
adding a new layer: two non
overlapping layers of HCP stacking.
Produced by irradiation.

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71
(MSG)
Section-4
3D defects

▪ Volume imperfections, e.g. cracks may arise when there is only
small electrostatic dissimilarity b/w the stacking sequences of
close packed planes in metals.
▪ Moreover, when clusters of atoms are missing, a large vacancy or
void is got which is also a volume imperfection.
▪ Foreign particle inclusions, large voids or noncrystalline regions
which have the dimensions of the order of 0.20 nm are also
termed volume imperfections.
➢ Pores (esp. ceramics) - can greatly affect optical, thermal, mechanical
properties
➢ Cracks - can greatly affect mechanical properties
➢ Foreign inclusions - can greatly affect electrical, mechanical, optical
properties
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2023 (IUB)
72
Volume imperfections
(MSG)

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2023 (IUB)
73
Problems for Students
(MSG)
Problem Book Page
No.
Example Problem
12.4
Materials Sci & Eng by WD
Callister (2007)
436
Example Problem
12.5
Callister (2007)
438
Example Problem
4.1
Callister (2007)
82
Example Problem
20-24
Material Science by SL K & Amit K
(2004)
109-
110

Thursday, Jan 26,
2023 (IUB)
74
Materials Simulation Group (MSG)

Lectures 01-06, 2021-1.pdf

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