Chapter 4
Imperfections in solids
HW2: 3, 4, 6, 8, 9, 15, 16, 21 Due Wensday 13/10/2010
Why study imperfections in solids?
 Properties of materials are affected by the
presence of imperfections
 Crystalline defect: a lattice irregularity having
one or more of its dimensions in the order of an
atomic diameter
 Classification of imperfections is made
according to geometry or dimensionality of the
defect.
 3 basic types of imperfections:
1. Point defects (PD).
2. Line defects (dislocations).
3. Surface defects, SD.
Point Defects (PD)
 Localized disruptions in otherwise perfect atomic
or ionic arrangement in a crystal structure.
 These imperfections may be introduced by
movement of atoms or ions when they gain
energy:
1
1. by heating,
2. during processing,
3. by introduction of impurities,
4. doping
 Impurities: elements or compounds that is
present from raw materials or processing.
 Dopants: elements or compound that is
deliberately added, in known concentrations, at
specific location in the microstructure, with an
intended beneficial effect on properties or
processing.
Vacancies and self-interstitials
 Produced when an atom or an ion is missing
from its normal site in the crystal structure
(Figure 1).
 Are introduced into metals & alloys during
solidification at high temperatures.
2
Figure 1: Point Defects: (a) Vacancy (b) Interstitial (c) small
substititional atom (d) large substititional atom (e) Frenkel
defect (f) Schottky defect
 Concentration of vacancies increases
exponentially with T:
Qv
N v  N exp(
)
kT
Nv = total no. of vacancies per cm3
N = no. of atoms per cm3
Qv = energy required for the formation of a
vacancy
3
k = Gas constant = 1.38×10-23J/atom.K =
8.62×10-5 eV/atom.K
T = absolute temp in K
N A
N 
A
 For most metals, the fraction Nv/N just below the
melting point is on the order of 10-4
 A self-interstitial: an atom from the crystal that
is crowded into an interstital site, a small void
space that under ordinary circumestances is not
occupied
 Example 4.1
Impurities in solids
 The addition of impurity atoms to a metal will
result in the formation of a solid solution and/or
a new 2nd phase depending on:
1. Kinds of impurity
2. Their concentrations
3. Temperature
 Solvent (host): element or compound that is
present in the greatest amount
 Solute: element or compound present in a minor
concentration
4
Solid solutions
 A solid solution forms as the solute atoms are
added to the host material, the crystal structure is
maintained and no new structures are formed.
 A solid solution is also compositionally
homegenous, the impurity atoms are randomly
and uniformly dispersed within the solid.
Substitutional Defects
 Introduced when one atom or ion is replaced by a
different type of atom or ion (Figure 1).
 Can be introduced either as an impurity or as a
deliberate addition.
 No. of defects is relatively independent of T.
 Examples: dopants such as P or B into Si.
 If we add Cu to Ni, Cu atoms will occupy
crystallographic sites where Ni atoms would
normally be present.
 Rules for Substitutional solid solution:
1. Atomic size factor: difference in atomic radii
between the two atom types is less than 15%.
Otherwise, the solute atoms will create
substantial lattice distorsions and a new phase
will form.
2. Same Crystal structure for both solvent and
solute
5
3. Electronegativity: the more electropositive one
element and the more electronegative the other,
the greater is the likelihood that they will form an
intermetallic compound instead of a substituional
solid solution
4. Valences: a metal will have more of a tendency
to disolve another metal of higher valence than
one of a lower valence
Interstitial Defects
 Formed when an extra atom or ion is inserted
into the crystal structure at a normally
unoccupied position (Figure 1).
 C atoms occupy interstitial sites in Fe crystal
structure, introducing a stress in the localized
region of the crystal in their vicinity. If there are
DLs in the crystals trying to move around these
types of defects, they face a resistance to their
motion, making it difficult to create permanent
deformation in metals & alloys. This is one
important way of increasing strength of metallic
materials.
 No. of interstitial atoms or ions in structure
remain nearly constant with T.
Specification of composition
Weight % basis
6
m1
C1 
100
m1  m 2
Atom % basis
m1'
nm1 
A1
nm1
1
C1 
100
nm1  nm 2
 Composition Conversions: Eq. 4.6 and 4.7
 Concentration in terms of mass of one
component per unit volume of material: Eq 4.9
 Average density and average atomic weight:
Eq4.10 and 4.11
 Example 4.2
 Example 4.3
7
Dislocations (DLs)
 DLs are line imperfections in an otherwise perfect crystal.
 3 types of DLs: screw, edge, & mixed.
 DLs are useful in increasing strength of metals & alloys.
Edge DL (EDL)
 Slicing partway through a perfect crystal, spreading the
crystal apart, & partly filling the cut with an extra plane of
atoms. The bottom edge of this inserted plane represents the
EDL.
 BV is perpendicular to the EDL.
Screw DLs (SDL)
 F4.4: Cut partway through a perfect crystal and then skew
the crystal one atom spacing.
8
 Following a crystallographic plane one rev around axis on
which crystal was skewed, starting at a point x & traveling
equal atom spacing in each direction, we finish one atom
spacing below our starting point (y).
 The vector required to complete the loop & return us to our
starting point is the Burgers vector (BV) b.
 The axis, around which we trace this path, is the screw DL.
 BV is parallel to the SDL.
Mixed DLs
9
 When a shear force acting in direction of BV is applied to a
crystal containing a DL, the DL can move by breaking the
bonds between the atoms in one plane. The cut plane is
shifted slightly to establish bonds with the original partial
plane of atoms. This shift causes DL to move one atom
spacing to the side (F4.8a).
 If this process continues, DL moves through the crystal until
a step is produced on the exterior of the crystal; the crystal
has then been deformed.
 The speed with which DLs move in materials is close to or
greater than the speed of sound.
10
Surface defects (SD)
 SDs are the boundaries, or planes, that separate a material
into regions, each region having the same crystal structure
but different orientations.
 Grains and grain boundaries.
 By reducing the grain size, we increase the no. of grains, and
hence increase the amount of grain boundary area. Any DL
moves only a short distance before encountering a GB and
being stopped, and strength of metallic material is increased.
 Small angle grain boundaries (SAGB): an array of DLs that
produces a small mis-orientation between the adjoining
crystals (F4.19). Because the energy of surface is less than
that of a regular GB, the SAGB are not effective in blocking
slip.
11
 SAGB formed by EDL are called tilt boundaries, and those
caused by SDL are called twist boundaries.
 Stacking Faults: which occur in FCC metals, represent an
error in the stacking sequence of CPP. Normally a stacking
sequence of ABCABCABC is produced in a perfect FCC
crystal. Suppose the following sequence is produced:
o ABC ABABC ABC
 This small region, which has HCP stacking sequence instead
of FCC stacking sequence, represents a stacking fault.
Stacking faults interfere with the slip process.
 Twin Boundaries (TB): is a plane across which there is a
special mirror image mis-orientation of the crystal structure
(F4.20). Twins can be produced when a shear force, acting
along the twin boundary, causes the atoms to shift out of
position.
 Twinning occurs during deformation or HT of certain metals.
TB interferes with the slip process and increase the strength
12
of metal. The movement of TB can also cause a metal to
deform. The effectiveness of surface defects in interfering
with slip process can be judged from surface energies.
Microscopic Examination
 Grain size and shape are only two features of what is termed
the microstructure.
 Applications of microstructural examination:
1. Understand the relation between properties and structure
13
2. Predict properties of materials once these relationships have been
established.
3. Design alloys with new property combinations
4. Monitor and control results of heat treatment
5. Study the mode of mechanical fracture
Microscopic techniques
1. Optical microscopy
2. Electron microscope
o Transmission Electron microscope
o Scanning Electron microscope
3. Scanning probe microscopy
Optical microscopy
 Used in a reflecting mode
 Contrasts in the image produced result from differences in
reflectivity of the various regions of the microstructure
 Specimen surface must be ground and polished to a smooth
and mirrorlike finish
 Microstructure is revealed using chemical etching
 Chemical reactivity of the grains of some single phase
materials depends on crystalographic orientation
 In a polycrystalline specimen, etching char vary from grain to
grain
 F4-11
 Small grooves form along grain boundaries as a result of
etching. Since atoms along GB regions are more chemically
active, they dissolve at a greater rate than those within the
grains.
 GBs reflect light at an angle different from that of the grains
themselves (F4-12)
 2000X
Electron microscopy
 An image is formed using beams of electrons
14
 A high velocity electron will become wave like with a wave
length that is inversely proportional to its velocity
 The electron beam is focused and the image formed with
magnetic lenses
Transmission Electron microscope (TEM)
 Image seen with TEM is formed by an electron beam that
passes through specimen
 Transmitted beam is projected onto a fluorscent screen or a
photographic film
 1000,000X
Scanning Electron microscope (SEM)
 Surface of specimen to be examined is scanned with a beam
of electrons and the reflected beam of electrons is collected
then displayed at the same scanning rate on a cathode ray
tube.
 The surface may or may not be polished and etched but it
must be electrically conductive
 Very thin metallic surface coating must be applied to nonconductive materials
 Up to 50,000X
Scanning probe microscopy (SPM)
 Neither light nor electrons is used to form image
 Microscope generate a topographical map on an atomic scale
 109X
 3-D magnified images
 Variety of enviroments
 SPM employ a tiny probe with a very sharp tip that it brought
into close proximty of specimen surface
 Probe is raster scanned across the plane of the surface
15
 During
scanning,
probe
experiences
deflections
perpendicular to this plane in response to electronic or other
interactions between the probe and the specimen surface
 The in surface plane and out of plane motions of the probe
are controlled by piezoelectric ceramic components.
Grain Size determination
 Intercept method
 ASTM method
Standard comparison charts
Each is assigned a number ranging from 1 to 10 (grain
size number) at 100X
N =2n-1
n =grain size number
N = average number of grains per square inch at 100X
16