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Transcript of crysta limperfactions
CRYSTAL IMPERFECTIONS
Dr. H. K. KhairaProfessor and HoD
MSME Deptt., MANIT, Bhopal
5
Chpt 5: Imperfections in Solids
ISSUES TO ADDRESS...
• What types of defects arise in solids? Describe them.
• Can the number and type of defects be varied and controlled?
• How do defects affect material properties?
• Are defects undesirable?
TYPES of DEFECTS
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• Vacancy atoms• Interstitial atoms• Frankel defect• Impurity atoms• Dislocations
Edges, Screws, Mixed
• Grain Boundaries• Stacking Faults• Anti-Phase and Twin Boundaries
Point defects
Line defects
Area/Planar defects
TYPES of DEFECTS
We need to describe them and understand their effects.
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Length Scale of Imperfections
Vacancies,impurities
dislocations Grain and twin boundaries
VoidsInclusionsprecipitates
point, line, planar, and volumetric defects
Point Defects
• The defects which are confined to a point are known as point defects
• Types of point defects– Vacancy– Interstitialcy– Frankel defect– Impurity atoms
Vacancy
• When an atom is missing from its regular lattice site, it is known as VACANCY.
11
Vacancy
• Vacancies:vacant atomic sites in a structure.
Vacancydistortion of planes
Vacancy and Distortion of planes
13
Vacancy
Vacancy: a vacant lattice site
It is not possible to create a crystal free of vacancies.About 1 out of 10,000 sites are vacant near melting.
14
Vacancy
Thermodynamics provides an expression for
Vacancy Concentration: CV = Nv
Nexp
Qv
kBT
CV = Concentration of vacanciesNv = Number of vacanciesN = Total number of atomic sitesQv = vacancy formation energykB = 1.38 x 10–23 J/atom-K = 8.62 x 10–5 eV/atom-K kB/mole = R = 1.987 cal/mol-K
Defects ALWAYS cost energy!
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Boltzmann's constant
(1.38 x 10-23 J/atom K)
(8.62 x 10-5 eV/atom K)
NDN
exp QDkT
No. of defects
No. of potential defect sites.
Activation energy
Temperature
Each lattice site is a potential vacancy site
• Equilibrium concentration varies with temperature!
Equilibrium Concentration of Vacancy
Cd=
16
Estimating Vacancy Concentration
• Find the equil. # of vacancies in 1m of Cu at 1000C.• Given:
3
ACu = 63.5g/mol = 8.4 g/cm3
QV = 0.9eV/atomNA = 6.02 x 1023 atoms/mole
8.62 x 10-5 eV/atom-K
0.9eV/atom
1273K
NDN
exp QDkT
For 1m3, N =NAACu
x x 1m3 = 8.0 x 1028 sites
= 2.7 · 10-4
• Solve:ND = 2.7 · 10-4 · 8.0 x 1028 sites = 2.2x 1025 vacancies
106 cm3 = 1 m3
* What happens when temperature is slowly reduced to 500 C, or is rapidly quenched to 500 C?
CV=
Equilibrium concentration of vacancies as afunction of temperature for aluminium (after Bradshaw and
Pearson, 1957).
Interstitialcy
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Interstitialcy
• Self-Interstitials:"extra" atoms in between atomic sites.
self-interstitialdistortion
of planes
Interstitialcy
• When an atom is present at an interstitial position in its lattice, it is known as interstitialcy.
• In this case an atom is present at a place where it should not have been.
Self Interstitialcy and Distortion of planes
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InterstitialcySelf-interstitial: atom crowded in ‘holes’
Self-interstitials are much less likely in metals, e.g.,,as it is hard to get big atom into small hole - there islarge distortions in lattice required that costs energy.
Frenkel Defect
• It is a combination of vacancy and interstitialcy defects.
• When an atom leaves its regular lattice site and goes to an interstitial site, it is known as Frenkel Defect.
Impurity Atom
• When atom of another element is present as an impurity in the lattice of an element, it is known as impurity atom.
Impurity Atom
• Impurity atoms can occupy any of the following position– Interstitial position– Substitutional position
Impurity Atom
• Types of Impurity Atom– Interstitial Impurity Atom
• When impurity atom is present at an interstitial site, it is known as interstitial impurity atom.
– Small atoms C, N, B and H can occupy interstitial sites
– Substitutional Impurity Atom• When impurity atom substitutes a parent atom at its
regular lattice site, it is known as substitutional impurity atom.
Impurity Atom
Interstitial Impurity in FCC
Interstitial impurity C in α-Fe. The C atom is smallenough to fit, after introducing some strain into the BCC
lattice.
VOIDS
Distorted TETRAHEDRAL Distorted OCTAHEDRAL**
BCC
a
a3/2
a a3/2
rvoid / ratom = 0.29 rVoid / ratom = 0.155
Note: Atoms are coloured differently but are the same
Interstitial Impurity in FCC
Interstitial Impurity in FCC
Substitutional Impurity
Substitutional impurity and distortion of planes
Point Defects
Point Defects
Line Defects
Or
Dislocations
Types of Dislocations
1. Edge Dislocation2. Screw Dislocation
Edge Dislocation
• When a crystalographic plane ends abruptly inside the grain, its edge defines a defect known as screw dislocation
Edge Dislocation
Dislocation
Burgers VectorBurgers circuit round a dislocation A fails to
close when repeated in a perfect lattice unless completed bya closure vector FS equal to the Burgers vector b.
Burgers Vector
Burgers Vector
• Burgers vector of an edge dislocation is perpendicular to the dislocation line
47
The Edge Dislocations and Burger’s Vector
Looking along line direction of edge
Stress fieldsat an Edgedislocation
Burger’s vector = extra step
• Edge looks like extra plane of atoms.• Burger’s vector is perpendicular to line.• Positive Edge (upper half plane)
• Is there a Negative Edge?• Where is it?• What happens when edge gets to surface of crystal?
• What are the stresses near edge?
Stress States aroundan Edge Dislocation
Screw Dislocation
• When the crystallographic planes spiral around a line, the line defines a defect which is known as Screw Dislocation
Screw Dislocation
Screw Dislocation
Screw Dislocation
Surface Defects
Types of Surface Defects
1. Stacking Fault2. Grain Boundary3. Twins
Stacking Faults
• It is the defect due to faulty stacking of planes.• It occurs in FCC and HCP crystal structures
only
Stacking of planes in HCP
A plane
B plane
A plane
Stacking Fault
60
• All defects cost energy (J/m2 or erg/cm2).• Stress, dislocation motion can create Stacking Faults.• What is stacking of FCC and HCP in terms of A,B, and C positions in (111) planes?
FCC HCP
…ABCABCABC…
Stacking Faults: Messed up stacking
slip
...ABCACABABCABC...hcp
…….fcc fcc ………..
or C
or C
Grain Boundary
• It is the boundary between two grains having different orientations.
Grain Boundaries
GrainBoundaries
63
Relative Energies of Grain Boundaries
Which GB is lower in energy, low-angle GB or high-angle GB? Why?Hint: compare number of reduced preferred bonds.
low-angle
high-angle
Grain I
Grain 2
Grain 3
• The grains affect properties• mechanical,• electrical, …
• Recall they affect diffraction so you know they’re there.
• What should happen to grainsas temperature increases?
Hint: surfaces (interfaces) cost energy.
Grain Boundary
Grain Boundry
Twins
• When two parts of a crystal become mirror image of each other, the defect is known as twins.
Twins
Twin Boundry
70
Twin Boundaries: an atomic mirror plane
• There has to be another opposite twin nearby to get back to perfect crystal,because all defects cost energy (J/m2 or erg/cm2) and to much defect costly.
• Stress twins can be created (e.g., Tin) in which case the atoms must move at the speed of sound.
What happens when something moves at speed of sound?
original atomic positionsbefore twinning
THANKS