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.

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Vacancy

• Vacancies:vacant atomic sites in a structure.

Vacancydistortion of planes

Vacancy and Distortion of planes

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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.

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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=

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Estimating Vacancy Concentration

• Find the equil. # of vacancies in 1m of Cu at 1000C.• Given:

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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

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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

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• 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

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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

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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