5.imperfections in solids.pdf
TRANSCRIPT
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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
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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.
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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.
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⎟⎠⎞
⎜⎝⎛−=
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
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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
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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.
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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)
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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
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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 √
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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
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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,
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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.
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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…
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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
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Average alloy density
BA
BAavg VV
mmvolumetotalmasstotal
++
==__ρ
BA
WithA
AA
mVρ
= andB
BB
mVρ
=
BBAA
BAavg mm
mmρρ
ρ// +
+=
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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
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Imperfections in ionic solidsPoint defects also possible in ionic solids. But… ?
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Charge neutrality needs to be met!
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Imperfections in ionic solids
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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
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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
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Denoted by or
Points to the extra plane of atoms
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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.
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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
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Fig. 4.4 Callister
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Mixed edge/screw dislocation
Top view
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Burgers Vector
Perfect latticeBack at the same atom
With an edge dislocationN d t b k t i
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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
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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
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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
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• 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
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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
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No grain boundary is formed.
different faces Mismatch leads to grain boundary
Depending on which planes are brought together, the angle of alignment will
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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
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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.
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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
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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.
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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
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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
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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:
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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
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surfaces, interfaces, twins, stacking faults, and optical microscopy.
• Imperfections have very important consequences on the properties of materials.