IMPERFECTIONS IN SOLIDS’’ - Home - Materials Science...
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‘’IMPERFECTIONS IN SOLIDS’’
IE-114 Materials Science and General Chemistry
Lecture-4
1) Imperfect crystal
2) Types of Imperfections (Point, Linear, Area)
3) Microscopic Examination of defects and
the structure of materials
Outline
Perfectly ordered
crystalline structure
Imperfection
Such an idealized solid generally does not exist
All solids contain large number of various
defects or imperfections
Defects may exist:
1) In impure metals or alloys (Substitutional or interstitial foreign
atoms)
2) During solidification (e.g. Grain boundaries, dislocations, vacancies) 3) During deformation (e.g. Dislocations)
The properties (mechanical, optical, electrical, etc.) of the materials are profoundly influenced by the presence of imperfections (defects)
The influence is not always adverse, often specific characteristics are enhanced.
EXAMPLE 1: Mechanical property
Materials are stronger when they have defects
Pure iron & Fe-C alloy
Pure iron : soft and ductile
Fe-C alloy (steel) : strong and tough
EXAMPLE 2: Electrical conductivity
Electrical conductivity decreases when materials have defects
Electrical conductivity of pure copper is higher than that of impure copper Impure Copper: Copper containing impurity (unwanted) elements
Why study Imperfections in Solids?
O-Dimensional (point) defects
(associated with one or two atomic positions)
Vacancies
Impurities
a) Interstitial atoms
b) Substitutional atoms
1-Dimensional (line) defects
Dislocations (edge, screw and mixed dislocations)
2-Dimensional (area) defects
Stacking Faults
External Surfaces
Grain Boundaries (High angle and small angle grain boundaries)
3-Dimensional (volume) defects
Cracks, pores, foreign inclusions
Types of Imperfections:
Vacancies
Self interstitials
Impurities (seen in solid-solution alloys)
vacant atomic sites in a structure.
Vacancydistortion of planes
O-Dimensional (point) defects
A lattice vacancy is equivalent to missing atom or ions (in case of ionic crystal).
Formed during solidification or as a result of atomic vibration (atomic vibration increases by temperature)
1) Vacancy
Equilibrium concentrations of
vacancies
* As T increases the number of vacancies increases exponentially.
For most of the metals just below melting point, the fraction of vacancies (N/Nv) is
on the order of 10-4. This means one lattice site out of 10.000 is empty.
Example:
Find the equilibrium # of vacancies in 1m3 of Cu at 1000oC.
• Given:
Solution:
"extra" atoms positioned between atomic sites.
self-interstitialdistortion
of planes
Atoms of same type accomodate into interstitial sites,
which are not occupied under ordinary circumstances.
Self interstitial defects produce large lattice distortion.
Because self-interstitial atoms usually larger than the void
space (interstitial sites).
2) Self-Interstitials:
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.
The addition of impurity atoms to a metal will result in the formation of SOLID SOLUTION or a new second phase (, ,
)
Solvent: Represents the element or compound that is
present in the greatest amount (host atoms)
Solute : An element or compound present in a minor
concentration (e.g. Impurity atoms)
3) Impurities in solids
A foreign atom (the solute), whether it be an impurity atom or deliberate
alloying addition, can occupy one of two distinct positions in a crystal,
(1) Substitutional alloy
(e.g., Cu in Ni)
(2)Interstitial alloy
(e.g., C in Fe)
Solid Solutions
Solute atoms substitute for solvent atoms in a
crystalline lattice Solute atoms( C, H, O, N) fit into spaces
between solvent atoms in a crystalline lattice.
Some important features for
substitutional solid solution
1) Atomic size difference should be less than 15%. Otherwise the solute
atoms will create substantial lattice distortions and a new phase will form.
2) Crystal structure should be the same.
3) Electronegativities should be similar to prevent the ionic bonding.
4) Valances:Other factors being equal, a metal has a higher tendency to dissolve another metal of higher valency.
EXAMPLE: Cu-Ni solid solution. The type is substitutional. WHY?
Because: a) Radii for Cu and Ni are 0.128 and 0.125 nm respectively.
b) They both have FCC structure.
c) Their electronegativities are 1.9 and 1.8 for Cu and Ni respectively.
d) The most common valence is +1 for Cu and +2 for Ni.
Impurity atoms fill the voids or interstices among the host atoms.
Interstitial atoms introduce lattice strains since most of the interstitial atoms have atomic radii higher than interstitial site’s radius
For metals with a high APF, the interstitial positions are small in size and therefore the diameter of the impurity atoms should be smaller than that of the host atoms.
The concentration of impurity atoms is low (<10 %).
(For example, in Fe-C alloys in which carbon is an interstitial atom, max. Carbon solubility is 2%)
Some important features for
interstitial solid solutions
Summary of point defects
Specification of Composition
Weight percent
100x %BA
A
mm
mAcomponentofwt
mA = mass of component A
Atomic percent
nA = number of moles of component A= mA/ MWA
Consider an alloy system containing components A and B;
100x %BA
A
nn
nAcomponentofat
MWA = molecular weight of A, gr/mol
Composition Conversions
Assume that you have an A-B alloy;
at. % A + at. % B =100 % wt. % A + wt. % B =100 % or
at.% A = (wt.%A / MWA) / [(wt.%A / MWA) + (wt.%B / MWB)]
at.% B = (wt.%B / MWB) / [(wt.%A / MWA) + (wt.%B / MWB)]
Where MW is molecular weight of each component, gr/mol
wt.% A = (at.%A x MWA) / [(wt.%A x MWA) + (wt.%B x MWB)]
wt.% B = (at.%B x MWB) / [(wt.%A x MWA) + (wt.%B x MWB)]
Convertion from wt% to at%
Convertion from at% to wt%
• cause slip between crystal plane when they move,
• produce permanent (plastic) deformation.
Dislocation: It is a group of point defects forming a linear one
dimensional defect in the structure of the material.
Edge Dislocation
Screw Dislocation
Mixed Type of Dislocation
Types of Dislocations
Dislocations (edge, screw and mixed dislocations)
Dislocations are introduced;
during solidification of crystalline solids
by the permanent deformation of crystalline solids
1-Dimensional (line) defects
1)Edge dislocation:
Edge dislocation is shown by symbol ‘’ ’’
Extra plane of atoms causes localized lattice distortion.
The magnitude and direction of lattice distortion is expressed in terms
of a Burgers vector, b, which is perpendicular to edge dislocation line.
(Perpendicular to the plane of
page)
Atoms squeezed together
Atoms pulled
apart
is created in a crystal by insertion of an extra half plane of atoms
Edge Dislocation Motion
Dislocation line is linear.
Burgers vector is parallel to dislocation line.
2) Screw Dislocation: can be formed in a perfect crystal by applying upward and
downward shear stresses to regions of a perfect crystal
Dislocation line
Edge dislocation
Screw dislocation
3) Mixed dislocations: very common
Mixed dislocation has both edge and screw character
Nature of dislocation is defined by relative orientations of dislocation
line and Burgers vector
Dislocation line and Burger’s vector (b)
Relation
Edge Screw Mixed
Relative
orientation
Perpendicular Parallel Neither parallel
nor
perpendicular
Direction and magnitude of Burger’s vector;
Direction : In the close packed crystallographic direction
Magnitude: One interatomic distance
2-Dimensional (area) defects
Interfacial (area) defects are boundaries that have two dimensions and
separate regions of different crystal structures or crystallographic
orientations.
External Area Defects Internal Area Defects
Grain Boundaries
Twin Boundaries
Stacking Fault
Phase boundaries
External Surface
1)External surface: is the boundary of material at which the
structure terminates.
e.g. Solid-gas, solid-liquid
Surface atoms are not bonded (surface have higher energy state than the atoms at
the inner parts of the structure). This energy is called surface energy (J/m2 or
erg/cm2). To minimize this energy, materials minimizes the surface area.
2) Grain boundary:
Grain boundary may be defined as the interface between crystals that
differ in crystallographic orientation, composition or dimension of the crystal
lattice (in some cases in two or all of these).
A) High Angle Grain Boundary
B) Small Angle Grain boundary
Tilt boundary
Twist boundary
grain boundaries
t=t1 t=t2
t=t3 t=t3
Structure of the
material seen under
microscope
Completely solid. Material
contains many
grains(polycrystalline material)
Liquid and small
crystals
Liquid and relatively larger
crystals
2.1. High-angle grain boundary
Formed during solidification
Fracture surface of a steel
a.1. Tilt boundary
Orientation mismatch is slight, on the order of
a few degrees. Tilt boundary is formed when
dislocations are aligned, Angle represents
angle of misorientation.
a.2. Twist boundary
Results from arrays of screw dislocations
2.1. Small-angle grain boundary
3)Twin Boundary: is a special type of grain boundary across which
there is a mirror lattice symmetry.
observed due to atomic displacements produced as a result of shear force
application and during annealing heat treatments following deformation.
Annealing twin is commonly observed in materials with FCC structures.
Mechanical twins are observed in BCC and HCP metals.
Twinning plane
Energies of Boundaries
External Surface
High Angle Grain Boundary
Low Angle grain Boundary
Energy is related to number of unbonded atoms through the interface
Increasing energy
Chemical reactivity increases as the energy of the boundary increases
Observation of Crystal Defects
Macroscopic Examination
Microscopic Examination (optical and electron microscopes (SEM,
TEM))
Sample Preparation Steps for Microscopic Examination
Surfaces of metals are prepared before examination
1) Cutting
2) Grinding (with emery papers)
3) Polishing (water+Al2O3 solution or diamond paste)
4) Etching (acid solutions)
More reaction is observed in defects having higher energies
• Useful up to 2000X magnification.
Optical Microscopy
Examination of Grain Boundaries by optical microscope
are more susceptible to etching
may be revealed as dark lines
Polished Surface Grain Boundary Phases
Electron Microscopy
Beam of electrons of shorter
wave-length (0.003nm) (when
accelerated across large voltage
drop)
High resolutions and
magnification (up to 50,000x
SEM); (TEM up to 1,000,000x)
Dislocation are observed using
TEM(transmission electron
microscope)