[email protected] engr-45_lec-05_solidimperfections.ppt 1 bruce mayer, pe engineering-45:...

[email protected] • ENGR-45_Lec-05_SolidImperfections.ppt1

Bruce Mayer, PE Engineering-45: Materials of Engineering

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engineering 45

ImperfectioImperfectionsns

In SolidsIn Solids



Learning GoalsLearning Goals

Learn The Forms of Defects in Solids• Use metals as Prototypical Example

How the number and type of defects Can be varied and controlled

How defects affect material properties Determine if “Defects” or “Flaws” are

• Desirable

• UNdesirable



Classes of ImperfectionsClasses of Imperfections

POINT Defects• Atomic Vacancies• Interstitial Atoms• Substitutional Atoms

LINE Defects• (Plane Edge) Dislocations

Area Defects• Grain Boundaries

– Usually 3-D



Point DefectsPoint Defects Vacancy MISSING atom at Lattice Site

Self-Interstitial “Extra” Atom “Squeezed” into the Lattice Structure

Vacancydistortion of planes

self-interstitial

distortion of planes



Point Defect ConcentrationPoint Defect Concentration

Equilibrium Defect Concentration Varies With Temperature; e.g., for Vacancies:

k = • 1.38x10-23 J/at-K

• 8.62x10-5 eV/at-K

N Every Lattice Site is a Potential Vacancy

Boltzmann's constant

Nv

Nexp

Qv

kT

No. of defects

No. of potential defect sites.

Activation energy

Temperature



Measure Activation EnergyMeasure Activation Energy Recall The Defect

Density Eqn Take the ln of Eqn

kT

QD

D

eN

N

This form of a Negative Exponential is called an Arrhenius Relation• Svante Arrhenius:

1859-1927, Chem Nobel 1903

Tk

QNN D

D 1ln

This of the form

Tx

kQm

NNy

mxy

D

D

1

ln

where



Measure Activation Energy contMeasure Activation Energy cont Meausure ND/N vs T

Find the Activation Energy from the Slope

RePlot in Linear Form• y = mx + b

Nv

N

T

exponential dependence!

1/T

N

Nvln

-Qv /k

slope

By ENGR25 method of Function Discovery



Vacancy Concentration ExmplVacancy Concentration Exmpl In Defect Density

Rln QD Can Take Two forms• Qv Vacancies

• Qi Interstitials

Consider a Qv Case

• Copper at 1000 C

• Qv = 0.9 eV/at

• ACu = 63.5 g/mol

= 8400 kg/cu-m

Find the Vacancy Density• First Find N in units

of atoms per cu-m

3

3

23

//

Check units

0635.0

840010023.6

m

at

molkg

mkgmolatN

N

A

NN

Cu

A



Vacancy Concentration contVacancy Concentration cont Since Units Chk:

At 180C (Pizza Oven) The Vacancy Rate 98 pptr

328 /1097.7 msitesatN Now apply the Arrhenius Relation @1000 ºC

275 ppm Vacancy Rate

325

528

/1018.2

1273/1062.8

/9.0exp1097.7

exp

mvacN

KKateV

ateV

kT

QNN

v

vv



Observing Equil Vacancy ConcObserving Equil Vacancy Conc

Low energy electron microscope view of a (110) surface of NiAl.

Increasing T causes surface island of atoms to grow.

Why? The equil. vacancy conc. increases via atom motion from the

crystal to the surface, where they join the island.

575

μm

X 5

75

μm

Im

age

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



Point Impurities in SolidsPoint Impurities in Solids Two outcomes if impurity (B) added to host (A)

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

2. 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 (chem formula)• often different structure

• e.g.; BCC in FCC



W. Hume – Rothery RuleW. Hume – Rothery Rule

The Hume–Rothery rule Outlines the Conditions for substitutional solid soln• Δr (atomic radius) < 15%

• Proximity in periodic table – i.e., similar electronegativities

• Same crystal structure for pure metals

• Valency– All else being equal, a metal will have a greater

tendency to dissolve a metal of higher valency than one of lower valency



Imperfections in SolidsImperfections in Solids Application of Hume–Rothery rules

Solid Solutions

1. Would you predictmore Al or Ag to dissolve in Zn?

2. More Zn or Al in Cu?

Element Atomic Crystal Electro- ValenceRadius Structure nega-

(nm) tivity

Cu 0.1278 FCC 1.9 +2C 0.071H 0.046O 0.060Ag 0.1445 FCC 1.9 +1Al 0.1431 FCC 1.5 +3Co 0.1253 HCP 1.8 +2Cr 0.1249 BCC 1.6 +3Fe 0.1241 BCC 1.8 +2Ni 0.1246 FCC 1.8 +2Pd 0.1376 FCC 2.2 +2Zn 0.1332 HCP 1.6 +2



Apply Hume – Rothery RuleApply Hume – Rothery Rule

Would you predictmore Al or Ag to dissolve in Zn? • Δr → Al (close)

• Xtal → Toss Up

• ElectronNeg → Al

• Valence → Al

Element Atomic Crystal Electro- ValenceRadius Structure nega-

(nm) tivity

Cu 0.1278 FCC 1.9 +2C 0.071H 0.046O 0.060Ag 0.1445 FCC 1.9 +1Al 0.1431 FCC 1.5 +3Co 0.1253 HCP 1.8 +2Cr 0.1249 BCC 1.6 +3Fe 0.1241 BCC 1.8 +2Ni 0.1246 FCC 1.8 +2Pd 0.1376 FCC 2.2 +2Zn 0.1332 HCP 1.6 +2

More Zn or Al in Cu?• Δr → Zn (by far)

• Xtal → Al

• ElectronNeg → Zn

• Valence → Al



Composition/ConcentrationComposition/Concentration Composition Amount of impurity/solute (B)

and host/solvent (A) in the SYSTEM. Two Forms

Convert Between Forms Using AJ

• Weight-%

• Where– mJ = mass of

constituent “J”

100'

mBmA

mBB nn

nC

• Atom/Mol %

• Where– nmJ = mols of

constituent “J”

molmolkg

kgAmn UNITSJJmJ

/

100

BA

BB mm

mC



Linear Defects → DislocationsLinear Defects → Dislocations Edge dislocation:

extra half-plane of atoms• linear defect

• moves in response to shear stress and results in bulk atomic movement (Ch 7,8)– cause of slip between

crystal planes when they move



Movement of Edge DislocationsMovement of Edge Dislocations Dislocations Move Thru the Crystal in

Response to Shear Force• Results in Net atomic Movement or DEFORMATION



Motion of Edge DislocationMotion of Edge Dislocation

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

Bonds across the slipping planes are broken and remade in succession



Carpet Movement AnalogyCarpet Movement Analogy Moving a Large Carpet All At Once Requires

MUCH Force (e.g.; a ForkLift Truck)• Using a DISLOCATION Greatly Facilitates the Move

Dislocation



Carpet DislocationCarpet Dislocation Continue to Slide Dislocation with little effort

to the End of the Crystal• Note Net Movement at Far End

Dislocation



DislocationsDislocations First PREDICTED as defects in crystals since

theoretical strength calculations (due to multibond breaking) were far too high as compared to experiments

later invention of the Transmission Electron Microscope (TEM) PROVED their Existence

deformed steel (40,000X)

Ti alloy (51,500X)



Interfacial DefectsInterfacial Defects

2D, Sheet-like Defects are Termed as Interfacial

Some Macro-Scale Examples• Solid Surfaces (Edges)

– Bonds of Surface Atoms are NOT SatisfiedSource of “Surface Energy” in Units of J/sq-m

• Stacking Faults – When atom-Plane Stacking Pattern is Not as Expected

• Phase Boundaries – InterFace Between Different Xtal Structures



Interface Def. → Grain BoundariesInterface Def. → Grain Boundaries

Grain Boundaries• are Boundaries BETWEEN crystals

• Produced by the solidification process, for example

• Have a Change In Crystal Orientation across them

• IMPEDE dislocation motion

• Generally Weaker that the Native Xtal– Typically Reduce Material Strength

thru Grain-Boundary Tearing

Crack Along GB



Area Defects: Grain BoundariesArea Defects: Grain Boundaries Schematic

Representation• Note GB Angles

grain boundaries

Metal Ingot: GB’s Follow Solidification Path

heat flow

~ 8cm



Optical MicroscopyOptical Microscopy Since Most Solid Materials

are Opaque, MicroScope Uses REFLECTED Light• These METALLOGRAHPIC

MScopes do NOT have a CONDENSOR Lens



Optical MicroScopy contOptical MicroScopy cont The Resolution, Z The Magnification, M

NAZ

61.0

• Where Light Wavelength

550 nm For “White” Light (Green Ctr)

– NA Numerical Aperture for the OBJECTIVE Lens 0.9 for a Very

High Quality Lens

Typical Values• Z 375 nm

– Objects Smaller than This Cannot be observed

– Objects Closer Together than This Cannot Be Separated

• Mtrue 200

mmtrue

NAM

12.0



Optical MicroScopy cont.2Optical MicroScopy cont.2

Sample Preparation• grind and polish surface until flat and shiny

• sometimes use chemical etch

• use light microscope

• different orientations → different contrast

• take photos, do analysis– e.g. Grain Sizing



Optical MicroScopy cont.3Optical MicroScopy cont.3 Grain Boundaries

• are imperfections, with high surface energy

• are more susceptible to etching; may be revealed as – dark lines due to the change of

direction in a polycrystal

ASTM E-112 Grain Size Number, n 12 nN• Where

– N grain/inch2

microscope

grain boundary

surface groove

polished surface

Fe-Cr alloy



Electron MicroscopyElectron Microscopy For much greater resolution, use a BEAM OF

ELECTRONS rather that light radiation Transmission Electron Microscopy (TEM):

• VERY high magnifications

• contrast from different diffraction conditions

• very thin samples needed for transmission

Scanning Electron Microscopy (SEM):• surface scanned, TV-like

• depth of field possible



Atomic Force MicroScopy Atomic Force MicroScopy AFM is Also called Scanning

Probe Microscopy (SPM)• tiny probe with a tinier tip

rasters across the surface

• topographical map on atomic scale

Polymer



SEM Photo Scaling

MEMS Hinge ► Find Rectangle Length

3.02 in-photo

2.91 in-photo

Lactual



SEM Photo Scaling

Use “ChainLink” Cancellation of Units (c.f. ENGR10)

Thus the Rectangular Connecting Bracket is about 48µm in Length

actualphoto

actualphoto µm 2.48inch .023

µm 05

1

inch 91.2actualL

3.02 in-photo

2.91 in-photo

Lactual



Olympus DUV Metallurgical MscopeOlympus DUV Metallurgical Mscope

DeepUltravioletMicroscope U-UVF248

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