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CHAPTER 3

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 high concentration region to low concentration region

� Why study diffusion?

Materials of all types are often heat treated or mixed to improve their properties.During heating or mixing atomic diffusion always exist.

� To control the diffusion speed and mechanism, one should 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 the bonds: Vibrational energy increasing with temperature

increasing elapsed time

a) Vacancy diffusion: Host or substitutional impurity atoms replace with vacancies

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Diffusion Mechanism Simulation

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b) Interstitial diffusion: Host or substitutional impurity atoms place between 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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1330.07.2007 Polystyrene Beads On A Slide

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

3230.07.2007 Polystyrene Beads On A Slide

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 Equilibrium Concentration 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