Mumbai University_Mechanical Enginnering_SEM III_ Material technology_Module 1.2 Lattice Imperfections: Definition, classification and significance of Imperfections Point defects: vacancy, interstitial and impurity atom defects, Their formation and effects, Dislocation - Edge and screw dislocations Burger’s vector, Motion of dislocations and their significance, Surface defects - Grain boundary, sub-angle grain boundary and stacking faults, their significance, Generation of dislocation, Frank Reed source, conditions of multiplication and significance

1. Module 1

2.  Crystal Imperfections are the defects in the regular
geometrical arrangement of the atoms in a Crystalline
solid.
 A Perfect Crystal is an idealization; there is no such thing
in nature.
 The defects may be the results of the crystal deformation or
rapid cooling from high temperature or high energy
radiation striking the solid.
 The defects influence the mechanical, electrical, and
optical behavior of the crystal.

3.  Technically important properties such as
mechanical strength, ductility, crystal growth,
magnetic hysteresis, dielectric strength, conduction
in Semiconductors etc. are greatly affected by
relatively minor changes in crystal Structure caused
by DEFECTS/ IMPERFECTIONS.

4.  The imperfections may be classified widely as:
1. Point Defects-
2. Line Defects
3. Surface Defects
4. Volume Defects

6. 0D
(Point defects)
CLASSIFICATION OF DEFECTS BASED ON DIMENSIONALITY
1D
(Line defects)
2D
(Surface / Interface)
3D
(Volume defects)
Vacancy
Impurity
Frenkel
defect
Schottky
defect
Dislocation
External
surfaces defects
Interphase
boundary
Grain
boundary
Twin
boundary
Twins
Precipitate
Faulted
region
Voids /
Cracks
Stacking
faults
Disclination
Thermal
vibration
Internal
surfaces defects

7.  These are the lattice errors at isolated points , takes place due to the
imperfect packing of atoms during crystallization or due to the vibrations of
atoms at high temperatures.
 Number of defects at equilibrium concentration , at a certain temperature is
given by
Where
a. n —number of imperfections
b. N—number of atomic sites per mole
c. Ed—free energy required to form defects
d. kb—Boltzmann’s constant (kb= 8.62*10-5 eV/K)
e. T —Absolute temperature

8.  Vacancies
 Impurity
 Interstitial Atoms
 Impurity Atoms
 Frenkel Imperfection
 Schottky Imperfection
0D
(Point defects)
Vacancy
Impurity
Frenkel defect
Schottky defect
Interstitial
Substitutional

9.  Refers to missing atom from vacant atomic site
 Atoms which are around the vacancy are
displaced
 Tensile stress field produced in the vicinity
 Arise either from imperfect packing during
original crystallisation or from thermal
vibrations at high temperatures
 They are common, especially at high
temperatures when atoms are frequently and
randomly change their positions leaving behind
empty lattice sites
Tensile Stress
Fields ?

10. Impurity
Interstitial
Substitutional

11.  Foreign atom sitting in the void of a crystal
 Interstitial impurity atoms are much smaller
than the atoms in the bulk matrix.
 Interstitial impurity atoms fit into the open
space between the bulk atoms of the lattice
structure
 An example of interstitial impurity atoms is
the carbon atoms that are added to iron to
make steel. Carbon atoms, with a radius of
0.071 nm, fit nicely in the open spaces
between the larger (0.124 nm) iron atoms.
Compressive
Stress
Fields
Relative
size

12.  A substitutional impurity atom is an atom of a
different type than the bulk atoms, which has
replaced one of the bulk atoms in the lattice
 Simply, Foreign atom replacing the parent
atom in the crystal
 Substitutional impurity atoms are usually close
in size (within approximately 15%) to the bulk
atom
 An example of substitutional impurity atoms is
the zinc atoms in brass. In brass, zinc atoms
with a radius of 0.133 nm have replaced some
of the copper atoms, which have a radius of
0.128 nm
Tensile Stress
Fields
Compressive
stress fields

13.  It arises when an ion is missing from its normal position
and occupies an interstitial site between the lattice points.
 when an ion displaced from a regular position to an
interstitial position creating a vacancy
 the pair of vacancy-interstitial is called Frenkel defect
 Cations are usually smaller and thus displaced easily than
anions.
 Closed packed structures have fewer interstitials and
displaced ions than vacancies because additional energy is
required to force the atoms into the interstitial positions.

14.  A pair of one cation and one anion
can be missing from an ionic crystal
 The pair of vacant sites, thus
formed, is called Schottky defect.

16.  Line imperfections (one-dimensional defects) are also called Dislocations
 They are abrupt changes in the regular ordering of atoms along a line
(dislocation line) in the solid.
 They occur in high densities and strongly influence the mechanical
properties of material.
 The theory was originally developed by Vito Volterra in 1905.
 Dislocations can be best understood by referring to two limiting cases -
Edge dislocation and Screw dislocation
 They are characterized by the Burgers vector (b), whose direction and
magnitude can be determined by constructing a loop around the disrupted
region

17.  Burgers vector, named after Dutch physicist Jan
Burgers.
 Denoted as “b”
 Represents the magnitude and direction of the lattice
distortion resulting from a dislocation in a crystal
lattice.
 The burgers vector is perpendicular to the dislocation
line in Edge Dislocations and it is parallel to the
dislocation line in Screw Dislocations.

19.  The edge defect can be easily visualized as an
extra half-plane of atoms in a lattice.
 Thus regions of compression and tension are
associated with an edge dislocation.
 The dislocation is called a line defect because
the locus of defective points produced in the
lattice by the dislocation lie along a line.
 This line runs along the top of the extra half-
plane.
 The inter-atomic bonds are significantly
distorted only in the immediate vicinity of the
dislocation line.

22.  The screw dislocation is slightly
more difficult to visualize.
 The motion of a screw
dislocation is also a result of
shear stress, but the defect line
movement is perpendicular to
direction of the stress and the
atom displacement, rather than
parallel.
 Dislocation line parallel to the
Burger’s vector

25.  Observations show that new dislocations are created to permit plastic deformation
 The observed shear displacements require about 1000 active dislocations on a single slip plane
 A source of these dislocations that can emit dislocation loops on a single slip plane is needed
 Frank and Reed proposed a dislocation source that is illustrated below for an isotropic material
 The critical shear stress will be that
stress that activates a Frank-Reed
source and permits dislocation
multiplication to occur.
 The straight segment (a) bows into a
loop due to the external forces. This
closes on itself, creating a free loop (g)
and a new segment that can repeat the
process

27.  These are two dimensional imperfections
 Lies in the metal with polycrystalline structures
 Defined as boundaries that have two dimensional
imperfections in crystalline solids, and have
different crystal structures on either side of them
 External surfaces imperfections
 Internal surface imperfections

28.  Imperfections represented by a boundary
 The environment of an atom at a surface differs from that of an atom in the
bulk(inside)
 The number of neighbouring atoms (coordination) at surface is less
 The external surface of a material is an imperfection itself because the bonds
do not extend beyond it since surface atoms are not entirely surrounded by
other atoms on other side
 Thus the unsaturated bonds of surface atoms give rise to a surface energy
 They posses higher energy than that of internal atoms.

29.  Grain boundaries
 Tilt boundaries
 Twin boundaries
 Stacking faults

30.  The separate crystals/ grains of different orientation are formed in a polycrystalline material
during crystallisation
 Crystalline solids are, usually made of number of grains separated by grain boundaries
 Grain boundaries are several atoms distances wide, and there is mismatch of
orientation of grains on either side of the boundary
 When this misalignment is slight, on the order of few degrees (< 10°), it is called low angle
grain boundary
 If the low grain boundary is formed by edge dislocations, it is called tilt boundary,
 Twist boundary if formed of screw dislocations
 If the orientation of difference between neighbouring grains is more than 15˚ then the
boundaries are known as high angle grain boundaries

32.  Twin boundaries occur in pairs such that
the orientation change introduced by
one boundary is restored by the other.
 The region between the pair of
boundaries is called the twinned region.
 Twins which forms during the process
of recrystallization are called annealing
twins,
 Whereas deformation twins form during
plastic deformation

33.  This is a low angle boundary
as the orientation difference
is between 2 neighbouring
crystals is less than 10˚
 Also called as low angle
boundary
 This is composed of edge
dislocation lying one above
the other

34.  They are faults in stacking sequence of atom planes
 When there is disturbance in the stacking sequence,
formation of stacking faults takes place
 Stacking sequence in an FCC crystal is
ABC ABC ABC
 The sequence for HCP crystals is AB AB AB
 Stacking faults in FCC crystals :
ABC AC ABC
ABC ACB CABC

36.  As name suggests they are 3 Dimensional Imperfections
 These may arise when there is only a small electrostatic dissimilarities b/w the
stacking sequences of close packed planes in metals. For example cracks.
 These include pores, cracks, foreign inclusions and other phases.
 When clusters of atoms are missing, a large vacancies or voids are created which are
also the volume imperfections.
 These defects are normally introduced during processing and fabrication steps.
 All these defects are capable of acting as stress raisers, and thus deleterious to parent
metal’s mechanical behaviour.
 However, in some cases foreign particles are added purposefully to strengthen the
parent material