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1 MSE 280: Introduction to Engineering Materials Reading: Chapter 5 Imperfections in Solids ISSUES TO ADDRESS... What types of defects arise in solids? Can the number and type of defects be varied and controlled? MSE280 © 2007, 2008 Moonsub Shim, University of Illinois 1 How do defects affect materials’ properties? Are defects undesirable? Zero dimensional (point defects): vacancies, it titi l t b tit ti l t Defects by Dimension interstitial atoms, substitutional atoms. One dimensional (linear defects): Mistakes in stacking planes of atoms. A plane of atoms ends in a line. Dislocations. Two dimensional (planar or area defects) MSE280 © 2007, 2008 Moonsub Shim, University of Illinois 2 surfaces and grain boundaries. Three dimensional : Second phases.

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Page 1: 5.Imperfections in solids.pdf

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MSE 280: Introduction to Engineering Materials

Reading: Chapter 5Imperfections in Solids

ISSUES TO ADDRESS...

• What types of defects arise in solids?

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

MSE280© 2007, 2008 Moonsub Shim, University of Illinois1

• How do defects affect materials’ properties?

• Are defects undesirable?

• Zero dimensional (point defects): vacancies, i t titi l t b tit ti l t

Defects by Dimension

interstitial atoms, substitutional atoms. • One dimensional (linear defects): Mistakes in

stacking planes of atoms. A plane of atoms ends in a line. Dislocations.

• Two dimensional (planar or area defects)

MSE280© 2007, 2008 Moonsub Shim, University of Illinois2

(p )surfaces and grain boundaries.

• Three dimensional: Second phases.

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Why do we care about defects?Many properties may be altered by defects/impurities.

e.g.

1) M h i l ti M t l ll f i i t th1) Mechanical properties: Metal alloys for improving strength.

2) Electrical properties:

• Defects and impurities can reduce metal conductivity.

• Doping in semiconductors to control of conductivity.

3) Optical properties: W l th f li ht

MSE280© 2007, 2008 Moonsub Shim, University of Illinois3

Mn-doped ZnSe quantum dots.From Shim et al. MRS Bulletin Dec. 2001.

• Wavelengths of light being absorbed and/or emitted by materials can be altered with imperfections.

and many more examples….

Point Defects1. Vacancies: missing atoms from lattice sites.

Vacancydistortion of planes

Why should vacancies form?

Vacancies will also cause missing bonds (costs energy to create vacancies).

Consider the energy required to create a vacancy.

From Callister 6e resource CD.

MSE280© 2007, 2008 Moonsub Shim, University of Illinois4

Co s de t e e e gy equ ed to c eate a aca cyQv = Activation energy to create vacancy

Where does the energy to overcome Qv come from? Thermal Energy!

⎟⎠⎞

⎜⎝⎛−=

kTQNN v

v exp

No. of vacanciesTotal No. of lattice sites

k = Boltzmann constant

Nv depends on temperature!

Typically: 410~ −

NNv

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Point Defects2. Self-interstitial: an extra atom (of the same type as the lattice atoms) placed in between lattice sites.

self-interstitialdistortion

of planes

⎟⎞

⎜⎛ QNN s

For equilibrium number of self-interestials: treat similarly as vacancies.From Callister 6e resource CD.

MSE280© 2007, 2008 Moonsub Shim, University of Illinois5

⎟⎠⎞

⎜⎝⎛−=

kTQNN s

s exp

Self-interstitials are usually not as highly probable as vacancies. WHY?

Typically, interstitial sites are much smaller than lattice atoms.Self-interstitials would likely introduce significantly larger distortions!i.e. Qs >> Qv

Point defects: example problem

Calculate the equilibrium number of vacancies for a cubic ti t f t 1000 Ccentimeter of copper at 1000oC.

Qv = 0.9 eV/atomA = 63.5 g/mold = 8.4 g/cm3

k = 1.38 x 10-23 J/K = 8.62 x 10-5 eV/K

MSE280© 2007, 2008 Moonsub Shim, University of Illinois6

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Observing equilibrium vacancy concentration• Low energy electron

microscope view ofa (110) surface of NiAl.

• Increasing T causessurface island ofatoms to grow.

• Why? The equil. vacancyconc. increases via atommotion from the crystalt th f h

MSE280© 2007, 2008 Moonsub Shim, University of Illinois7

to the surface, where they join the island.

Island grows/shrinks to maintain equil. vancancy conc. in the bulk.

Reprinted with permission from Nature (K.F. McCarty, J.A. Nobel, and N.C. Bartelt, "Vacancies inSolids and the Stability of Surface Morphology",Nature, Vol. 412, pp. 622-625 (2001). Image is5.75 μm by 5.75 μm.) Copyright (2001) Macmillan Publishers, Ltd.

From Callister 6e resource CD.

Impurities in solids1. In the limit of small number of impurities: consider as point defects.

2. When there is a large amount: consider as solution.gMany familiar materials are highly impure (e.g. metal alloys).

Solid solutionsHomogeneous distribution of impurities (similar to liquid solutions) with the crystal structure of the host material maintained.

MSE280© 2007, 2008 Moonsub Shim, University of Illinois8

Solvent: element or compound that is most abundant (host atoms).

Solute: element or compound present in minor concentration (impurity).

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Point defects in alloysTwo outcomes if impurity (B) added to host (A):

• Solid solution of B in A (i.e., random dist. of point defects)

• Solid solution of B in A plus particles of a new

OR

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

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

MSE280© 2007, 2008 Moonsub Shim, University of Illinois9

So d so ut o o p us pa t c es o a ephase (usually for a larger amount of B)

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

From Callister 6e resource CD.

Solubility for solid solutionsA. Solubility of substitutional solution will depend on:

1. Atomic size factor: typically, atomic radii difference < 15%.Too large or too small impurity atoms will cause too much

lattice distortions!

2. Crystal structure: For appreciable solubility, host and impurity atoms should have the same crystal structure.

3 Electronegativity:Too large electronegativity difference will

MSE280© 2007, 2008 Moonsub Shim, University of Illinois10

3. Electronegativity:Too large electronegativity difference will lead to intermetallic compounds rather than solutions.

4. Valence: Same valence is preferred for high solubility.

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ExampleIs solid-solution favorable, or not?

• Si-Ge AlloysRule 1: rSi = 0.117 nm and rGe= 0.122 nm.

√ΔR%= 4% favorable √

Rule 2: Si and Ge have the diamond crystal structure. favorable √

Rule 3: ESi = 1.90 and EGe= 2.01. Thus, ΔE%= 5.8% favorable √

Rule 4: Valency of Si and Ge are both 4. favorable √

MSE280© 2007, 2008 Moonsub Shim, University of Illinois11

Expect Si and Ge to form S.S. over wide composition range.

In fact, solid solution forms over entire composition at high temperature.

ExampleIs solid-solution favorable, or not?

• Cu-Ag AlloysRule 1: rCu = 0.128 nm and rAg= 0.144 nm.

√g

ΔR%= 9.4% favorable √

Rule 2: Ag and Cu have the FCC crystal structure. favorable √

Rule 3: ECu = 1.90 and ENi= 1.80. Thus, ΔE%= -5.2% favorable √

Rule 4: Valency of Cu is +2 and Ag is +1. NOT favorable

MSE280© 2007, 2008 Moonsub Shim, University of Illinois12

Expect Ag and Cu to have limited solubility.

In fact, the Cu-Ag phase diagram (T vs. c) shows that a solubility of only 18% Ag can be achieved at high T in the Cu-rich alloys.

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Alloying a surface• Low energy electron

microscope view ofa (111) surface of Cu.( )

• Sn islands move alongthe surface and "alloy"the Cu with Sn atoms,to make "bronze".

• The islands continuallymove into "unalloyed" From A.K. Schmid, N.C. Bartelt, and R.Q. Hwang,

MSE280© 2007, 2008 Moonsub Shim, University of Illinois13

regions and leave tinybronze particles intheir wake.

• Eventually, the islandsdisappear.

"Alloying at Surfaces by the Migration of Reactive Two-Dimensional Islands", Science, Vol. 290, No. 5496, pp. 1561-64 (2000). Field of view is 1.5 μm and the temperature is 290K.

From Callister 6e resource CD.

Solubility for solid solutionsB. Interstitial solutions:

Large difference in atomic radii is usually required.g y qMost metals have close packing with relatively large APF.(e.g. APFFCC = APFHCP = 0.74. that means 74% of the space is filled!)

Only small atoms will fit into these small interstitial sites without requiring high energies.

MSE280© 2007, 2008 Moonsub Shim, University of Illinois14

e.g. C in Fe:RC = 0.071 nmRFe = 0.124 nmEven with this large difference max. conc. is only ~2% C in Fe

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Effects of Composition in Solid Solutions

Electrical:Cu + 3.32 at%Ni

Cu + 2.16 at%Ni

+ 1.12 at%Ni

3

4

5

6

vity

, ρ

hm

-m)

Mechanical: Strengthening(a major purpose of making ll )

T (°C)-200 -100 0

deformed Cu + 1

1

2

3R

esis

tiv(1

0-8

Oh

0

Cu + 1.12 at%Ni

“Pure” Cu

alloys)

Composition can change Phases/Structure which in turn determine properties!

and many more effects…

MSE280© 2007, 2008 Moonsub Shim, University of Illinois15

Composition SpecificationDefinition: Amount of impurity (B) and host (A)

in the system.T d i ti• Weight %Two descriptions:

• Atom %

CB = mass of Btotal mass

x 100 C' B = # atoms of Btotal # atoms

x 100

• Conversion between wt % and at% in an A-B alloy:

CB =C' BAB

x 100 C'CB/AB

MSE280© 2007, 2008 Moonsub Shim, University of Illinois16

CB = C' AAA + C' BAB

x 100 C' B = CA/AA + CB/AB

• Basis for conversion:

mass of B = moles of B x AB

atomic weight of B

mass of A = moles of A x AA

atomic weight of A

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Example problem: conversion

• Determine the composition in at% of an ll ith 80 t% Al d 20 t% Calloy with 80wt% Al and 20wt% Cu

AAl = 26.98g/molACu = 63.55g/mol

MSE280© 2007, 2008 Moonsub Shim, University of Illinois17

Average alloy density

BA

BAavg VV

mmvolumetotalmasstotal

++

==__ρ

BA

WithA

AA

mVρ

= andB

BB

mVρ

=

BBAA

BAavg mm

mmρρ

ρ// +

+=

MSE280© 2007, 2008 Moonsub Shim, University of Illinois18

BBAAavg CC ρρ

ρ//

100+

=BBBAAA

BBAAavg ACAC

ACACρρ

ρ// ''

''

++

=

In terms of wt% and at%:

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Imperfections in ionic solids

Vacancy

Recall point defects in solids….

ydistortion of planes

self-interstitialdistortion

of planes

MSE280© 2007, 2008 Moonsub Shim, University of Illinois19

Imperfections in ionic solidsPoint defects also possible in ionic solids. But… ?

MSE280© 2007, 2008 Moonsub Shim, University of Illinois20

Charge neutrality needs to be met!

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Imperfections in ionic solids

MSE280© 2007, 2008 Moonsub Shim, University of Illinois21

Can we have a Frenkel defect of anions?

Example problem

1. When a Ca2+ is substituted for a Na+ ion in a NaCl crystal, what point defects are possible and how many of these defects exist for every Ca2+ ion?

2. What point defects are possible for MgO as 2

MSE280© 2007, 2008 Moonsub Shim, University of Illinois22

impurity in Al2O3 and how many Mg2+ ion must added to form each of these defects?

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Linear Defects: edge dislocationDislocations: Linear defects around which atoms are misaligned

1. Edge dislocation: Linear defect that centers around a line that is gdefined along the end of an extra plane of atoms

MSE280© 2007, 2008 Moonsub Shim, University of Illinois23

Denoted by or

Points to the extra plane of atoms

MSE280© 2007, 2008 Moonsub Shim, University of Illinois24

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Edge dislocation

Atomic view of edgedislocation motion fromleft to right as a crystalis sheared.(Courtesy P.M. Anderson)

From Callister 6e resource CD.

MSE280© 2007, 2008 Moonsub Shim, University of Illinois25

Note that the edge dislocations cause slip between crystal planes when they move leading to plastic (permanent) deformation.

Linear Defects: Screw dislocation2. Screw dislocation: shifted by one atomic distance

MSE280© 2007, 2008 Moonsub Shim, University of Illinois26

Fig. 4.4 Callister

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Mixed edge/screw dislocation

Top view

MSE280© 2007, 2008 Moonsub Shim, University of Illinois27

Burgers Vector

Perfect latticeBack at the same atom

With an edge dislocationN d t b k t i

MSE280© 2007, 2008 Moonsub Shim, University of Illinois28

Burgers vector: the magnitude and direction of the lattice distortion associated with dislocations

Back at the same atom Need to go back an atomic spacing to end at the same atom.

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Example: Burgers vector

• Find the Burgers vector for a BCC crystal.Note: Burgers vectors for BCC and FCC can

be expressed as

][2

hkla

MSE280© 2007, 2008 Moonsub Shim, University of Illinois29

Lattice parameterMiller index

Calculate the magnitude of Burgers vector for α-Fe (BCC) given that RFe = 0.1241 nm. Compare to the atomic spacing of 2 RFe.

Observing dislocations

MSE280© 2007, 2008 Moonsub Shim, University of Illinois30

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Planar DefectsPrimary defect types:

Twins

Grain Boundaries• Lattices (and so bonds) do not match up

Surfaces & Interfaces• Places where reactions occur and materials mix

MSE280© 2007, 2008 Moonsub Shim, University of Illinois31

• Planes shear to change material shape

Stacking Faults• Errors in stacking (eg: ABCABCABACBACBABCABC)

External surface• surface atoms are in higher energy states than internal atoms.

Why?

Surface atom has missing bonds

Internal atom is fully

MSE280© 2007, 2008 Moonsub Shim, University of Illinois32

Internal atom is fully surrounded by neighboring atoms (i.e. no missing bonds).

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Grain Boundaries- 2D defects that separate small grains (crystals having different crystallographic orientations within a polycrystalline materials)

single crystal: periodic arrangement of atoms is perfect and extends the entire crystal.

• polycrystalline: composed of many small crystals (grains).

Same facesPerfect alignment.No grain boundary is formed

MSE280© 2007, 2008 Moonsub Shim, University of Illinois33

No grain boundary is formed.

different faces Mismatch leads to grain boundary

Depending on which planes are brought together, the angle of alignment will

MSE280© 2007, 2008 Moonsub Shim, University of Illinois34

alignment will vary.

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Small angle grain boundary such as this tilt boundary can be considered as an array of edge dislocations.y g

Array of screw dislocations lead to a

MSE280© 2007, 2008 Moonsub Shim, University of Illinois35

twist boundary. 0o

misalignment or parallel misalignment.

Twin Boundaries- Special misorientation where atoms on one side of the boundary is the mirror image of the atoms on the other side.

MSE280© 2007, 2008 Moonsub Shim, University of Illinois36

Mechanical twins: produced by shear force (in BCC and HCP).Annealing twins: produced by heat treatment (in FCC).

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Effects of grain boundariesChanges mechanical properties• Boundaries are good places for fracture to occur

f• Boundaries interrupt the movement of dislocations

Changes in electrical properties• Good places to scatter electrons or inhibit their movement

Sites for atom diffusion• Diffusing atoms move more easily in the boundaries

MSE280© 2007, 2008 Moonsub Shim, University of Illinois37

g y• Some atoms like to sit in the boundaries (weakens them) • Materials can “creep” which means even metals at high

temperatures can flow like liquids by diffusion, often through grain boundaries.

Oops... A World-war II liberty ship which

Materials Embrittlement

A World-war II liberty ship which broke in half due to poor welds. The major problem was sulfur impurities in the iron of the weld which caused weak grain boundaries.

MSE280© 2007, 2008 Moonsub Shim, University of Illinois38

http://www.twi.co.uk/j32k/protected/band_13/oilgas_caseup31.html

From UIUC MatSE 101 website.

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Observing grain boundaries: Optical microscopy

• Useful up to 2000X magnification.• Polishing removes surface features (e.g., scratches)

Et hi h fl t d di t l• Etching changes reflectance, depending on crystalorientation.

microscope

close-packed planesAdapted from Fig. 4.11(b) and (c), Callister 6e. (Fig. 4.11(c) is courtesy

f J E B k G l El t i C

MSE280© 2007, 2008 Moonsub Shim, University of Illinois39

micrograph ofBrass (Cu and Zn)

of J.E. Burke, General Electric Co.

0.75mm

From Callister 6e resource CD.

Stacking faultsAny time the stacking sequence of atoms makes a

difference an error in stacking of atoms can change the properties of the materialproperties of the material

Example: stacking faults can convert FCC to HCP structures B

AC

BAC

BA

C

MSE280© 2007, 2008 Moonsub Shim, University of Illinois40

to HCP structures. Materials of these two structures often contain such faults and many have altered properties as a result.

Stacking faults look almost exactly like twins in the electron microscope.

AB

CA

BA

BA

B

From UIUC MatSE 101 website.

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Imperfections in polymers• Some are similar to metals and ceramics: e.g. interstitials and

vacancies.• Chain ends can be considered as imperfections since they are

different than the repeating units (e g initiator attached at end)different than the repeating units (e.g. initiator attached at end).• Amorphous regions between crystalline regions.• Copolymers:

MSE280© 2007, 2008 Moonsub Shim, University of Illinois41

http://mrsec.uchicago.edu/Nuggets/Stripes/defects.html

Defect diffusion in block-copolymers

Concepts to remember• Point defects: vacancies, self-interstitials, impurities.

S lid l ti i t titi l b tit ti l l bilit d• Solid solutions: interstitial, substitutional, solubility, and alloy composition and densities.

• Dislocations: edge, screw, dislocation motion, and Burgers vector.

• Grain boundaries and related: tilt and twist boundaries,f i f i ki f l d i l

MSE280© 2007, 2008 Moonsub Shim, University of Illinois42

surfaces, interfaces, twins, stacking faults, and optical microscopy.

• Imperfections have very important consequences on the properties of materials.