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7/28/2019 Ch-5 Compatibility Mode

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Chap: 05

IMPERFECTIONS IN SOLIDS

Chapter 4-


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ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...

What t es of defects arise in

IMPERFECTIONS IN SOLIDS

What are crystal imperfections?

Chapter 4-

solids? Can the number and type of defects be variedand controlled?

How do defects affect material properties?

1

Are defects undesirable?


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Why bother about imperfections?

Defects or disrupted regions may be as

small as 0.01%. Can be ignored if we are studying

structure insensitive properties.

Chapter 4-

Properties of crystalline materials dealt inengineering practice are structuresensitive.

Even ppm level imperfection can radicallychange the properties.


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The Big Picture

Mechanical properties are often related to thedefect structure, with macroscopic failurecommonly resulting from a coalescence ofdama e around existin flaws in a material

Chapter 4-

compact

We have to better understand material structurein order to predict mechanical performance of amaterial.


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The Bigger Picture

Presence of imperfections are not always

bad. Point imperfections in the form of controlled

impurities can improve the properties of the

Chapter 4-

ma er a s ras ca y. eg. Alloys where presence of impurities

improve the mechanical properties of thematerial.

Dopants in semiconductors drasticallyimproves the electrical properties.


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What are imperfections?

We can define imperfections or defects in acrystal as:

Chapter 4-

Discontinuity or absence of periodicityin certain region of the space lattice.


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Vacancy atoms

Interstitial atoms Substitutional atoms

Point defects(0-D)

TYPES OF IMPERFECTIONS

Chapter 4-

s oca ons Grain Boundaries

(1-D)

Area defects(2-D)

Foreign particle/ Volume defectsLarge Voids/pores/

Non-Cryst regions~10

3-D


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POINT IMPERFECTIONS

Imperfections of zero dimensions

May be created at the time of formation

Chapter 4-

o crys a sMay be created at a later time due tosome thermal disorder

They are thermodynamically stable


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Vacancies:-vacant atomic sites in a structure.

Vacancydistortionof planes

POINT DEFECTS

Chapter 4- 3

Impurity

Substitutional Interstitial


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Self-Interstitials:

-"extra" atoms positioned between atomic sites.

self-interstitialdistortion

of lanes

Chapter 4-

Low probability

because atoms aresubstantially largerthan the void


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Defects in Ceramics

Still have interstitials and vacancies

Chapter 4-


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Substitutional ions

Chapter 4-


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Frenkel Defect--a cation is out of place.

Schottky Defect--a paired set of cation and anion vacancies.

Shottky

Defect: Adapted from Fig. 13.20,

DEFECTS IN CERAMIC STRUCTURES

Schottky

Chapter 4- 7

Frenkel

Defect

Equilibrium concentration of defects /2~ D

Q kTe

Callister 5e. (Fig. 13.20 is from

W.G. Moffatt, G.W. Pearsall,and J. Wulff, The Structure andProperties of Materials, Vol. 1,Structure, John Wiley andSons, Inc., p. 78.) See Fig.12.21, Callister 6e.


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Impurities must also satisfy charge balance

Ex: NaCl Na+ Cl-

Substitutional cation impurityCa2+

Na+

cationvacancy

Imperfections in ionic crystals

Chapter 4- 8

Substitutional anion impurity

initial geometry Ca2+ impurity resulting geometry

Na+ Ca2+

initial geometry O2-

impurity

O2-

Cl-

anion vacancy

Cl-

resulting geometry


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Nonstoichiometry

Fe 2+ O 2- Fe 2+ O 2- O 2- Fe 2+

- - - -

Chapter 4-

Fe 3+ O 2- O 2- Fe 2+ O 2- Fe 2+

O 2- Fe 3+ O 2- Fe 2+ O 2- Fe 2+ O2-


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Consequences of presence of pointimperfections

Introduces distortion in crystals

Elastic strains created in the neighborhood of

Chapter 4-

the defect. large atom creates compressive stress-strain

smaller atom introduces tensile stress-strain

all these increases the energy of the system

to reach a stable state G/F has to be minimum


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Chapter 4-

The variation of Gibbs free energy with thenumber of point imperfections.


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We can get Q froman experiment.

ND

N

= expQD

kT

Measure this... Replot it...

MEASURING ACTIVATION ENERGY

Chapter 4- 5

1/T

NDln 1

-QD/kN

T

exponentialdependence!

defect concentration


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

3

ACu = 63.5g/mol = 8.4 g/cm3

QV = 0.9eV/atom NA = 6.02 x 1023 atoms/mole

0.9eV/atom

ESTIMATING VACANCY CONC.

Chapter 4- 6

8.62 x 10-5 eV/atom-K

1273K

N = exp kT

For 1m

3

, N =

NA

ACu x x 1m3 = 8.0 x 1028 sites

= 2.7 10-4

Answer:

ND = 2.7 10-4 8.0 x 1028 sites = 2.2x 1025 vacancies


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Impurities in Solids

Completely pure metal (or othersubstance) Impossible!!

for 99.9999% - purity still 10still 10still 10still 1022222222 to 10to 10to 10to 1023232323 impurities per mimpurities per mimpurities per mimpurities per m3333

Chapter 4-

AlloyAlloyAlloyAlloy deliberately add impurity todeliberately add impurity todeliberately add impurity todeliberately add impurity toengineer properties.engineer properties.engineer properties.engineer properties. Copper (7.5%) inCopper (7.5%) inCopper (7.5%) inCopper (7.5%) in

silversilversilversilver


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Terminology - Alloys

Solvent component in highestconcentration also called host

Chapter 4-

Solute component present in minor

concentration


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Two outcomes if impurity (B) added to host (A): Solid solution ofB in A (i.e., random dist. of point defects)

OR

POINT DEFECTS IN ALLOYS

Chapter 4- 8

Solid solution ofB in A plus particles of a newphase (usually for a larger amount of B)

Substitutional alloy(e.g., Cu in Ni)

Interstitial alloy(e.g., C in Fe)

Second phase particle--differentcomposition--often different structure.


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Factors that Govern Solid Solution

Atomic size - < 15% difference

Hume-Rothary empirical rules

Chapter 4-

Crystal structure same Electro-negativity - ??

Valences more likely to dissolve another

metal of higher valence

Ag-Au, Cu-Ni, Ge-Si are ideal examples


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Copper and Nickel

Element Cu Ni

Radii 0.128 nm 0.125

Unit cell FCC FCC

Chapter 4-

. .

Oxidation

(Valence)

+1 (+2) +2

Expect to form solid solution?

Ni 3d8 4s2 (28)

Cu - 3d

10

4s

1

(29)

Substitutional solid solution


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Copper-ZincUnit cell Zn (HCP) Cu (FCC)

35% of Zn dissolves in Cu where as1% of Cu dissolves in Zn.

Chapter 4-

e ex ra on ng e ec ron o n s moreeasily accommodated than a deficiency ofbonding electron.

In brass 50 Cu-50 Zn the crystal structure isBCC


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Carbon in Iron

Element C Fe

Radii 0.071 nm 0.124nm

Unit cell Hex BCC/FCC

Electro negativity 2.5 1.6

Chapter 4-

Valence +4 +2 (+3)

Solid solution ?

Interstitial or substitional?

C - 2s2 2p2

Fe 3d6 4s2

Octahedral void in fcc Fe

has radius 0.53Tetrahedral void in bcc Fehas radius 0.365


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Specification of Composition

of Alloy of 1 and 2

Weight % C1 = [m1/m1 + m2] x 100

Atom % nm1 = m1/

/A1C1/= [nm1/nm1 + nm2] x 100

C2/= [nm2/nm1 + nm2] x 100

Chapter 4-

C1/= [C1A2/C1A2 + C2A1] x 100

C2/= [C2A1/C1A2 + C2A1] x 100

C1 = [C1/A1/C1/A1 + C2/A2] x 100 C1 + C2 = 100C2 = [C2

/A2/C1/A1 + C2

/A2] x 100 C1/+ C2

/= 100


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Wt. % to mass of 1 component / unit volume of

materialC1

//= [C1/(C1/1) + (C2/2)] x 1000

C2//= [C2/(C1/1) + (C2/2)] x 1000

ave = [100 / (C1/1) + (C2/2)]

Chapter 4-

ave =

(C1/A1 + C2

/A2) / [(C1/A1/1) + (C2

/A2)/2]

A ave = [100 / (C1/ A1) + (C2/ A2)]

A ave = (C1/A1 + C2

/A2) / 100


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Derivation of composition conversion equationDerivation of composition conversion equationDerivation of composition conversion equationDerivation of composition conversion equation

C1/= [C1A2/(C1A2 + C2A1)] x 100

Total alloy mass :M/= m1/+ m2

/(in units of grams)

C1

/= (nm1/nm

1+ nm

2) x 100

= [(m1//A1) (m1

//A1) + (m2//A2)] x 100

m1/= C1M

//100A1 ( since C1 = (m1//m1

/+ m2/) x 100)

Chapter 4-

C1/

= [(C1M/

/100A1)(C1M/

/100A1+ C2M/

/100A2)] x 100

C1/= (C1A2/C1A2 + C2A1) x 100

Problem: Determine the composition in atom percent of analloy that consists of 97 wt% Al and 3 wt% Cu


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AlAlAlAl----Cu alloy compositionCu alloy compositionCu alloy compositionCu alloy composition

CAl/= {(CAlACu)/(CAlACu + CCuAAl} x 100

= {(97 x 63.55 g/mol)/

(97x63.55 g/mol + 3x26.98 g/mol)} x 100= 98.7 at%

Chapter 4-

CCu/= {(CCuAAl)/(CAlACu + CCuAAl} x 100

= {(3)(26.98 g/mol)/(3)(26.98 g/mol) +

(97)(63.55 g/mol)} x 100= 1.30 at%


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are linear defects,

geometrically one dimensional defect may arise due to incomplete crystal plane or due to

plastic deformation

Dislocations:

LINEAR DEFECTS

Chapter 4- 11

crystal undergoes shear part of the crystal is displaced in the direction of

the shear due to the shear stress cause slip between crystal plane when they move,

produce permanent (plastic) deformation. Boundary between slipped and unslipped region isthe line of dislocation


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Schematic of a Zinc (HCP):

before deformation after tensile elongation

Chapter 4-


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a

Slipvector

T

Edge dislocations

Chapter 4-

a. Elastic strain

around the

dislocation.b. A possible

arrangement of

Atoms

b


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Edge Dislocation: MovementEdge Dislocation: MovementEdge Dislocation: MovementEdge Dislocation: Movement

b

Chapter 4-


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Chapter 4-

Slip plane

Dislocationline


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To determine the Burgers vector of a dislocation in a two-

dimensional primitive square lattice, proceed as follows:Trace around the end of the dislocation plane to form a

closed loop. Record the number of lattice vectors traveled

along each side of the loop (shown here by the numbers

in the boxes):

Chapter 4-


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Chapter 4-

Screw dislocation: The dislocation line is parallel to thethe slip vector.

b


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Screw DislocationScrew DislocationScrew DislocationScrew Dislocation

Chapter 4-


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Motion of Screw Dislocation

Chapter 4-

Apply shear


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Chapter 4-

Mi d Di l ti


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Mixed Dislocation

Chapter 4-


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Dislocations of the same sign repel andthose of opposite sign cancel each other

Dislocations can interact with point

imperfections Dislocations usually appear during growth

Chapter 4-

o crys a s or as a resu o pr or mec an cadeformation of the crystal.

Unlike point imperfections they are not

thermodynamically stable They can be removed by proper posttreatment


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Dislocation motion requires the successive bumpingof a half plane of atoms (from left to right here).

Bonds across the slipping planes are broken and

remade in succession.

BOND BREAKING AND REMAKING

Chapter 4- 13

Atomic view of edgedislocation motion from

left to right as a crystalis sheared.

For metallic materials, b will point in

A close-packed crystallograhic

direction and will be of magnitudeE ual to interatomic s acin .


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Motion of edge dislocation

Chapter 4-


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AREA DEFECTS

2 D imperfections

Regions of distortions that lie on the surfaceor grain boundaries having a layer ofthickness of a few

Chapter 4-

ur ace a oms are on e o ess neares

neighbours as compared to coordinationnumbers.

Hence they are at higher energy state

compared to atoms in the interior. The broken bonds of these atoms give riseto surface energy.


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Grain boundaries: are boundaries between crystals. are produced by the solidification process, for example. have a change in crystal orientation across them. impede dislocation motion.

AREA DEFECTS: GRAIN BOUNDARIES

Chapter 4-

grain

boundaries

heatflow

Angle of misalignment


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Area Defects

Tilt Boundary array of edge defectsTwin Boundary

Chapter 4-

Twist Boundary array of screw defects(atleast 2 sets of parallel screwdislocation)


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Twin BoundariesTwin BoundariesTwin BoundariesTwin Boundaries

Chapter 4-

A twin boundary is a special type of grain boundary acrosswhich there is a specific mirror lattice symmetry. Atoms on

one side of the boundary are located in mirror-imagepositions of the atoms on the other side. The region ofmaterial between these boundaries is termed a twin.


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Twin BoundaryTwin BoundaryTwin BoundaryTwin Boundary

Twinned

Chapter 4-

Twin boundaries

region

Oth I t f i l d f t


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Other Interfacial defects

Stacking faultsABCABCABABCABC

Stacking fault is a thin region of hcp in fcclattice.

Chapter 4-

Twin stacking fault

Bulk defects like pores, cracks etc occur

during process Atomic vibrations Not all atoms vibratewith same energy, distribution of energies

present.


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Useful up to 2000X magnification. Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal

orientation. microscope

OPTICAL MICROSCOPY (1)

Chapter 4- 16

micrograph ofBrass (Cu and Zn)

Adapted from Fig. 4.11(b) and (c),Callister 6e. (Fig. 4.11(c) is courtesyof J.E. Burke, General Electric Co.

0.75mm

O ICAL IC OSCO Y ( )


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microscope

surface roove

polished surface

Grain boundaries... are imperfections, are more susceptible

to etching, may be revealed as

dark lines,

OPTICAL MICROSCOPY (2)

Chapter 4-

Fe-Cr alloy

grain boundary

17

c ange rec on n a

polycrystal.Adapted from Fig. 4.12(a)and (b), Callister 6e.(Fig. 4.12(b) is courtesyof L.C. Smith and C.Brady, the NationalBureau of Standards,Washington, DC [now theNational Institute ofStandards andTechnology, Gaithersburg,MD].)

ASTM grainsize number

N = 2n-1

no. grains/in2at 100xmagnification

SUMMARY


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Point, Line, and Area defects arise in solids.

The number and type of defects can be varied

and controlled (e.g., T controls vacancy conc.)

Defects affect material properties (e.g., grain

SUMMARY

Chapter 4- 18

oun ar es con ro crys a s p .

Defects may be desirable or undesirable(e.g., dislocations may be good or bad, dependingon whether plastic deformation is desirable or not.)


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Top view of screw dislocationTop view of screw dislocationTop view of screw dislocationTop view of screw dislocation

Atoms above theslip plane

Chapter 4-

A B

CD

b

Mi d di l tii d di l ii d di l iMi d di l ti


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Mixed dislocationMixed dislocationMixed dislocationMixed dislocation

Edge dislocation

Chapter 4-

Screw dislocation

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