Engineering 45
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Engineering 45. Imperfections In Solids. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer 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

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Engineering 45

ImperfectionsIn Solids

Bruce Mayer, PE

Licensed Electrical & Mechanical

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

  • POINT Defects

    • Atomic Vacancies

    • Interstitial Atoms

    • Substitutional Atoms

  • LINE Defects

    • (Plane Edge) Dislocations

  • Area Defects

    • Grain Boundaries

      • Usually 3-D

Point Defects

  • Vacancy  MISSING atom at Lattice Site



of planes




of planes

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

Point Defect Concentration

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

Activation energy

No. of defects














No. of potential






defect sites.


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

  • 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

  • By ENGR25 method of Function Discovery

  • Meausure ND/N vs T












  • RePlot in Linear Form

    • y = mx + b

  • Find the Activation Energy from the Slope

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

  • Since Units Chk:

  • Now apply the Arrhenius Relation @1000 ºC

  •  275 ppm Vacancy Rate

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

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


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.

Substitutional 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)


  • 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

  • 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

ElementAtomicCrystalElectro-ValenceRadius Structure nega- (nm) tivity


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?

ElementAtomicCrystalElectro-ValenceRadius Structure nega- (nm) tivity


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  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

  • 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

  • Dislocations Move Thru the Crystal in Response to Shear Force

    • Results in Net atomic Movement or DEFORMATION

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

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

    • Using a DISLOCATION Greatly Facilitates the Move


Carpet Dislocation

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

    • Note Net Movement at Far End





Ti alloy



  • 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

  • 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

Crack Along GB

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

Schematic Representation

Note GB Angles

~ 8cm

Area Defects: Grain Boundaries

  • Metal Ingot: GB’s Follow Solidification Path

Optical Microscopy

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

  • These METALLOGRAHPIC MScopes do NOT have a CONDENSOR Lens

Optical MicroScopy cont

  • 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

  • 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

  • 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


polished surface

surface groove

grain boundary

  • Where

    • N  grain/inch2

Fe-Cr alloy

Electron 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

  • 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

  • MEMS Hinge ► Find Rectangle Length


2.91 in-photo

3.02 in-photo

SEM Photo Scaling

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

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

Olympus DUV Metallurgical Mscope

DeepUltravioletMicroscope U-UVF248

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