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Engineering 45. Imperfections In Solids. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. Learning 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

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Bruce mayer pe licensed electrical mechanical engineer bmayer chabotcollege

Engineering 45

ImperfectionsIn Solids

Bruce Mayer, PE

Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu


Learning goals
Learning 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 imperfections
Classes of Imperfections

  • POINT Defects

    • Atomic Vacancies

    • Interstitial Atoms

    • Substitutional Atoms

  • LINE Defects

    • (Plane Edge) Dislocations

  • Area Defects

    • Grain Boundaries

      • Usually 3-D


Point defects
Point Defects

  • Vacancy  MISSING atom at Lattice Site

Vacancy

distortion

of planes

self-

interstitial

distortion

of planes

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


Point defect concentration
Point Defect Concentration

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

Activation energy

No. of defects

æ

ö

-

N

Q

ç

÷

v

v

=

ç

÷

exp

No. of potential

è

ø

N

k

T

defect sites.

Temperature

Boltzmann's constant

  • k =

    • 1.38x10-23 J/at-K

    • 8.62x10-5 eV/at-K

  • N  Every Lattice Site is a Potential Vacancy


Measure activation energy
Measure Activation Energy

  • Recall The Defect Density Eqn

  • Take the ln of Eqn

  • This of the form

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

    • Svante Arrhenius: 1859-1927, Chem Nobel 1903


Measure activation energy cont

N

N

v

v

N

N

Measure Activation Energy cont

  • By ENGR25 method of Function Discovery

  • Meausure ND/N vs T

slope

ln

-

Q

/k

v

exponential

dependence!

T

1/

T

  • RePlot in Linear Form

    • y = mx + b

  • Find the Activation Energy from the Slope


Vacancy concentration exmpl
Vacancy 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


Vacancy concentration cont
Vacancy Concentration cont

  • Since Units Chk:

  • Now apply the Arrhenius Relation @1000 ºC

  •  275 ppm Vacancy Rate

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


Observing equil vacancy conc

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

I

sland grows/shrinks to maintain

equil. vancancy conc. in the bulk.

Observing Equil Vacancy Conc

575μm X 575μm Image

  • 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.


Point impurities in solids

Substitutional NiAl. alloy

(e.g., Cu in Ni)

Interstitial alloy

(e.g., C in Fe)

Point Impurities in Solids

  • Two outcomes if impurity (B) added to host (A)

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

OR

  • Solid solution of B in A plus particles of a NEW PHASE (usually for a larger amount of B)

  • Second phase particle

  • different composition (chem formula)

  • often different structure

    • e.g.; BCC in FCC


W hume rothery rule
W. Hume – Rothery Rule NiAl.

  • 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 solids

Element Atomic Crystal Electro- Valence NiAl. Radius Structure nega- (nm) tivity

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

Imperfections 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?


Apply hume rothery rule

Element Atomic Crystal Electro- Valence NiAl. Radius Structure nega- (nm) tivity

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

Apply Hume – Rothery Rule

  • Would you predictmore Al or Ag to dissolve in Zn?

    • Δr → Al (close)

    • Xtal → Toss Up

    • ElectronNeg → Al

    • Valence → Al

  • More Zn or Al in Cu?

    • Δr → Zn (by far)

    • Xtal → Al

  • ElectronNeg → Zn

  • Valence → Al


Composition concentration
Composition/Concentration NiAl.

  • Composition  Amount of impurity/solute (B) and host/solvent (A) in the SYSTEM.

  • Two Forms

  • Weight-%

  • Atom/Mol %

  • Where

    • mJ = mass of constituent “J”

  • Where

    • nmJ = mols of constituent “J”

  • Convert Between Forms Using AJ


Linear defects dislocations
Linear Defects → Dislocations NiAl.

  • 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 dislocations
Movement of Edge Dislocations NiAl.

  • Dislocations Move Thru the Crystal in Response to Shear Force

    • Results in Net atomic Movement or DEFORMATION


Motion 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

Motion of Edge Dislocation


Carpet movement analogy
Carpet Movement Analogy half plane of atoms (from left to right here).

  • Moving a Large Carpet All At Once Requires MUCH Force (e.g.; a ForkLift Truck)

    • Using a DISLOCATION Greatly Facilitates the Move

Dislocation


Carpet dislocation
Carpet Dislocation half plane of atoms (from left to right here).

  • Continue to Slide Dislocation with little effort to the End of the Crystal

    • Note Net Movement at Far End

Dislocation


Dislocations

deformed half plane of atoms (from left to right here).

steel

(40,000X)

Ti alloy

(51,500X)

Dislocations

  • 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


Interfacial defects
Interfacial Defects half plane of atoms (from left to right here).

  • 2D, Sheet-like Defects are Termed as Interfacial

  • Some Macro-Scale Examples

    • Solid Surfaces (Edges)

      • Bonds of Surface Atoms are NOT Satisfied

        • Source 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 boundaries

Crack Along GB half plane of atoms (from left to right here).

Interface 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


Area defects grain boundaries

Schematic Representation half plane of atoms (from left to right here).

Note GB Angles

~ 8cm

Area Defects: Grain Boundaries

  • Metal Ingot: GB’s Follow Solidification Path


Optical microscopy
Optical Microscopy half plane of atoms (from left to right here).

  • Since Most Solid Materials are Opaque, MicroScope Uses REFLECTED Light

  • These METALLOGRAHPIC MScopes do NOT have a CONDENSOR Lens


Optical microscopy cont
Optical MicroScopy cont half plane of atoms (from left to right here).

  • The Resolution, Z

  • The Magnification, M

  • 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


Optical microscopy cont 2
Optical MicroScopy cont.2 half plane of atoms (from left to right here).

  • 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 3
Optical MicroScopy cont.3 half plane of atoms (from left to right here).

  • 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

microscope

polished surface

surface groove

grain boundary

  • Where

    • N  grain/inch2

Fe-Cr alloy


Electron microscopy
Electron Microscopy half plane of atoms (from left to right here).

  • 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

Polymer half plane of atoms (from left to right here).

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


Sem photo scaling
SEM Photo Scaling half plane of atoms (from left to right here).

  • MEMS Hinge ► Find Rectangle Length

Lactual

2.91 in-photo

3.02 in-photo


Sem photo scaling1
SEM Photo Scaling half plane of atoms (from left to right here).

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

  • Thus the Rectangular Connecting Bracket is about 48µm in Length


Olympus duv metallurgical mscope
Olympus DUV Metallurgical half plane of atoms (from left to right here).Mscope

DeepUltravioletMicroscope U-UVF248