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CHAPTER 6
DIFFUSION and
IMPERFECTIONS IN SOLIDS
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OUTLINE1. TYPES OF DIFFUSIONS
1.1. Interdiffusion1.2. Selfdiffusion1.3.Diffusion mechanisms1.4.Examples
2. TYPES OF IMPERFECTIONS2.1.Point Defects2.2.Line Defects2.3.Area Defects
3. METHODS TO SEE DEFECTS3.1.Optical microscope3.2.Scanning electron microscope (SEM)3.3.Transmission electron microscope3.4.Atomic force microscope
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1.Diffusion� What is diffusion?
It is the material transport by atomic motion from highconcentration region to low concentration region
� Why study diffusion?
Materials of all types are often heat treated or mixed toimprove their properties.During heating or mixing atomicdiffusion always exist.
� To control the diffusion speed and mechanism, oneshould know the mechanisms and types of diffusion.
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1.1.Interdiffusion(Impurity diffusion)� In a SOLID Alloy Atoms will Move From HIGH
Concentration to LOW Concentration REGĐONS
� Initial Condition � After Time+Temp
100%
Concentration Profiles0
Cu Ni100%
Concentration Profiles0
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Alloying a surface
� Low energy electron microscope view of a (111) surface of Cu.
� Sn islands move along the surface and "alloy" the Cu with Sn atoms, to make "bronze".
� The islands continually move into "unalloyed" regions and leave tinybronze particles in their wake.
� Eventually, the islandsdisappear.
Click to animate
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1.2.Self-Diffusion� Diffusion in pure elemental solids( also liquids and gases)
All Atoms exchanging their positions are the same type.
� Label Atoms � After Time+Temp
A
B
C
DA
B
C
D
� How to Label an ATOM?� Use a STABLE ISOTOPE as a tag
� e.g.; Label 28Si (92.5% Abundance) with one or both of�
29Si → 4.67% Abundance
�30Si → 3.10% Abundance
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1.3. Diffusion Mechanisms� For an atom to change position:
1.There must be an empty site
2.The atom must have sufficient energy to break thebonds: Vibrational energy increasing with temperature
increasing elapsed time
a) Vacancy diffusion: Host or substitutional impurity atoms replacewith vacancies
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Diffusion Mechanism Simulation
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b) Interstitial diffusion: Host or substitutional impurity atoms placebetween the other atoms.
•Applies to interstitial impurities:H,C,N,O small enough to fit into the interstitial positions•More rapid than vacancy diffusion.
Simulation showsthe jumping of a smaller atom (gray) from one interstitial site to another in a BCC structure. The interstitial sites considered here are at midpoints along the unit cell edges.
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Interstitial Alloy
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Diffusion in Processing: Case1� Example: CASE Hardening
� Diffuse carbon atoms into the host iron atoms at the surface.
� Example of interstitial diffusion is a case Hardened gear.
� Result: The "Case" is� hard to deform: C atoms "lock"
planes from shearing.
� hard to crack: C atoms put the surface in compression
ShearResistant
CrackResistant
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• Doping Silicon with Phosphorus for n-type
semiconductors:
• Process:
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1. Deposit P rich
layers on surface.
2. Heat it.
3. Result: Doped
semiconductor
regions.
silicon
silicon
magnified image of a computer chip
0.5mm
light regions: Si atoms
light regions: Al atoms
Diffusion in Processing:Case2
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What Do You See?
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Why study imperfections in solids?
� types of defects arise in solids.
� defects affect material properties.
� the number and type of defects can be varied and controlled.
� defects are sometimes desirable.� silicon transistors are based on controlled “doping”
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2. Types of Imperfectıons• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
• Dislocations
• Grain Boundaries
2.1.Point defects
2.2.Line defects
2.3.Area defects
}
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2.1 Point Defects• Vacancies:
-vacant atomic sites in a structure. (An empty atomic site)
Vacancydistortion
of planes
• Interstitials:
-"extra" atoms positioned between atomic sites. An atom somewhere other
than an atomic site 1)Self-interstitial 2)Impurity interstitial
self-interstitialdistortion
of planes
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Point Defects:Mixing On The Molecular Scale
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How are point defects introduced?
� Some types are thermally generated
Direct result of thermal vibration of the atomic array.The concentration of thermally-produced defects increases exponentially with increasing temperature
� Doping:Added solutes (impurities or dopants)
ordered or disordered solid solution
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Temperature Effect On Vacancies
Click to animate
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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
phase (usually for a larger amount of B)
OR
Substitutional alloy
(e.g., Cu in Ni)
Interstitial alloy
(e.g., C in Fe)
Second phase particle
--different composition
--often different structure.
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Point Defects In Ceramic Structures
• Frenkel Defect--a cation(+ve, metallic ion) is out of place.
• Shottky Defect--a paired set of cation and anion(-ve, nonmetallic ion) vacancies.
Shottky
Defect:
Frenkel
Defect
• Equilibrium concentration of defects
Adapted from Fig. 13.20, Callister 5e.
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1.2 Line Defects
� Dislocations: � are line defects,
� cause slip between crystal plane when they move,
� produce permanent (plastic) deformation.
� Schematic of a Zinc bar (HCP):� Before deformation After Deformation
slip steps
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INCREMENTAL SLIP� Dislocations slip planes incrementally...
� The dislocation line (the moving red dot)...
...separates slipped material on the left from unslipped material on the right.
Simulation of dislocation
motion from left to right
as a crystal is sheared.
(Courtesy (Courtesy (Courtesy (Courtesy
P.M. Anderson)P.M. Anderson)P.M. Anderson)P.M. Anderson)
Click to animate
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Dislocation:Incremental Slip
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Carpet Dislocation Anology� Continue to Slide Dislocation with little effort to the End of the Crystal� Note Net Movement at Far End
Dislocation
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Edge dislocations� An edge dislocation occurs when there is an extra crystal plane
http://pilot.mse.nthu.edu.tw/tem/gallery/Tem-11.JPG h
ttp://www.mse.nthu.edu.tw/jimages/Beuty/
copper sulphidecactus!
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Bond Breaking And Remaking
� Dislocation motion requires the successive jumpingof a half plane of atoms (from left to right here).
� Bonds across the slipping planes are broken andremade in succession.
Click to animate Click to animate
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Screw dislocation
� In screw dislocations, the atom planes look like they have been ‘sheared’
350Å
GaNhttp://www.iap.tuwien.ac.at/www/surface/STM_Gallery/screw_disl_schem.gif
http://nano.phys.uwm.edu/li/new_pa4.jpg
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Area Defects: Grain BoundariesGrain boundaries:• are boundaries between crystals.
• are produced by the solidification process, for example.
• have a change in crystal orientation across them.
grain boundaries
heat flow
Schematic
Adapted from Callister 6e.
~ 8cmMetal Ingot
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Area Defects
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Finally What Do You See?
intersitial
vacancy
grain boundary
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3.Methods To See Defects
� Optical microscope� surface microstructure (~ 1µm)
� Scanning electron microscope (SEM)� Surface microstructure, analytical chemistry (~50-100 nm)
� Transmission electron microscope� Resolve the atomic structure from a very thin foil (30 Ao), (~1 Ao)
� Atomic force microscope� 3D surface topography, electrical, magnetic scanning (~1 nm)
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Optical Microscopy� Useful up to 2000X magnification.
� Polishing removes surface features (e.g., scratches)
� Etching changes reflectance, depending on crystal orientation.
microscope
close-packed planes
micrograph of
Brass (Cu and Zn)
Adapted from Fig. 4.11(b) and (c), Callister 6e.
(Fig. 4.11(c) is courtesy
of J.E. Burke, General Electric Co.
0.75mm
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Scannıng Electron Mıcroscopy(SEM)
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Scanning Tuneling Microscopy(Atomic Force Microscope)
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• Atoms can be arranged and imaged!
Carbon monoxide
molecules arranged on a
platinum (111) surface.
Photos produced from the
work of C.P. Lutz,
Zeppenfeld, and D.M.
Eigler.IBM 1995.
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SCANNING TUNNELING MICROSCOPY(2)
• Atoms can be arranged and imaged!
Photos produced from the
work of C.P. Lutz,
Zeppenfeld, and D.M.
Eigler. IBM1995.
Iron atoms arranged on
a copper (111) surface.
These Kanji characters
represent the word
“atom”.
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SCANNING TUNNELING MICROSCOPY
Click to animate
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SUMMARY
� Point, Line, and Area defects arise in solids� The number and type of defects can be variedand controlled (e.g., T controls vacancy conc.)
� Defects affect material properties (e.g., grainboundaries control crystal slip).
� Defects may be desirable or undesirable (e.g., dislocations may be good or bad, depending on whether plastic deformation is desirable or not.)
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PROBLEM 1.
� Using the table given find:
� a) substitutional solid solution havingcomplete solubility in copper.
� b) substitutional solid solution of incomplete solubility in copper.
� c) An interstitial solid solution in copper.
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SOLUTION 1.
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PROBLEM 2.
� The concentration of silicon in an iron-silicon alloy is 0.25% by mass. What is the concentration in kilograms of silicon per meter cube of alloy.
� ρSi =2.33 gcm-3 ρFe =7.87 gcm
-3
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3/01956.0)675.12107.0/(25.0
3675.1287.7/75.99
3107.033.2/25.0
87.7/
33.2/
)/(
cmgc
cmV
cmV
Vmd
Vmd
VVmc
Si
Fe
Si
FeFeFe
SiSiSi
FeSiSiSi
=+=
==
==
==
==
+=
Convert the concentration into kgm-3
Solution of Problem 2:
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PROBLEM 3.
� Molybdenum forms a substitutional solid solution with tungsten. Compute the number of molybdenum atoms per cubic centimeter for a molybdenum-tungsten alloy that contains 16.4 wt% Mo and 83.6 wt% W.
� ρMo =10.22 gcm-3 ρW =19.30 gcm-3
� Molar mass of Mo=95.94 gmol-1
� # of Mo in 1 cm3 = ?
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Solution of Problem 3:
10173.0#
0288.094.95/762.2
3/762.2)332.4605.1/(4.16
3332.430.19/6.83
3605.122.10/4.16
30.19/
22.10/
)/(
xatomsMoof
moln
cmgc
cmV
cmV
Vmd
Vmd
VVmc
Mo
W
Mo
WWW
MoMoMo
WMoMoMo
=
==
=+=
==
==
==
==
+=
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PROBLEM 4.
� Germanium forms a substitutional solid solution with silicon. Compute the weight percent of Germanium that must be added to silicon to yield an alloy that contains 2.43 x 1021 Ge atoms per cubic centimeter.
� # of Ge in 1 cm3 = 2.43 x 1021 Ge atoms
� ρGe =5.32 gcm-3 ρSi =2.33 gcm-3
� Molar mass of Ge=72.59 gmol-1
� Molar mass of Si=28.09 gmol-1
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Solution of Problem 4:
Answer: Ge % by mass= 11.7
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• Equilibrium concentration varies with temperature!
Advanced topic:Calculating EquilibriumConcentration of Point Defects
Boltzmann's constant
(1.38 x 10-23 J/atom K)
(8.62 x 10-5 eV/atomK)
NDNNNN
= exp−QD
kT
No. of defects
No. of potentialNo. of potentialNo. of potentialNo. of potentialdefect sites.defect sites.defect sites.defect sites.
Activation energy
Temperature
Each lattice siteis a potentialvacancy site