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

2. 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

3. Classes of Imperfections
POINT Defects
Atomic Vacancies
Interstitial Atoms
Substitutional Atoms
LINE Defects
(Plane Edge) Dislocations
Area Defects
Grain Boundaries
Usually 3-D
HRTEM image of SrTiO3 Grain Boundary
* ULTRAMICROSCOPY, vol 86 (2001) pp

4. Point Defects Vacancy  MISSING atom at Lattice Site
distortion
of planes
self-
interstitial
distortion
of planes
Self-Interstitial  “Extra” Atom “Squeezed” into the Lattice Structure

5. Point Defect Concentration
Equilibrium Defect Concentration Varies With Temperature; e.g., for Vacancies:
No. of defects
Activation energy æ - ö N Q v ç v ÷ =
exp ç ÷
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

6. 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: , Chem Nobel 1903

7. Measure Activation Energy cont
Meausure ND/N vs T
By ENGR25 method of Function Discovery N v
slope N v ln - Q /k v
exponential
dependence! T 1/ T
RePlot in Linear Form
y = mx + b
Find the Activation Energy from the Slope

8. 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 

9. Vacancy Concentration cont
Since Units Chk:
Now apply the Arrhenius ºC
 275 ppm Vacancy Rate
At 180C (Pizza Oven) The Vacancy Rate  98 pptr

10. Observing Equil Vacancy Conc
Low energy electron microscope view of a (110) surface of NiAl.
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. I
sland grows/shrinks to maintain
equil. vancancy conc. in the bulk.

11. 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)
Substitutional alloy
(e.g., Cu in Ni)
Interstitial alloy
(e.g., C in Fe) 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

12. 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

13. Imperfections in Solids
Application of Hume–Rothery rules  Solid Solutions
1. Would you predict more Al or Ag to dissolve in Zn?
2. More Zn or Al in Cu?
Element Atomic Crystal Electro- Valence Radius Structure nega- (nm) tivity
Cu FCC C H O Ag FCC Al FCC Co HCP Cr BCC Fe BCC Ni FCC Pd FCC Zn HCP

14. Apply Hume – Rothery Rule
Would you predict more Al or Ag to dissolve in Zn?
Δr → Al (close)
Xtal → Toss Up
ElectronNeg → Al
Valence → Al
Element Atomic Crystal Electro- Valence Radius Structure nega- (nm) tivity
Cu FCC C H O Ag FCC Al FCC Co HCP Cr BCC Fe BCC Ni FCC Pd FCC Zn HCP
More Zn or Al in Cu?
Δr → Zn (by far)
Xtal → Al
ElectronNeg → Zn
Valence → Al

15. Composition/Concentration
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

16. 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

17. Movement of Edge Dislocations
Dislocations Move Thru the Crystal in Response to Shear Force
Results in Net atomic Movement or DEFORMATION

18. 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

19. 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
Dislocation

20. Carpet Dislocation
Continue to Slide Dislocation with little effort to the End of the Crystal
Note Net Movement at Far End
Dislocation

21. 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
deformed
steel
(40,000X)
Ti alloy
(51,500X)
* move through crystal lattice  permanent deformation
* CREATED during deformation
* can act as obstacles, if too many → Work Harding

22. 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

23. Interface Def. → 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

24. Area Defects: Grain Boundaries
Schematic Representation
Note GB Angles
Metal Ingot: GB’s Follow Solidification Path
~ 8cm

25. Optical Microscopy
Since Most Solid Materials are Opaque, MicroScope Uses REFLECTED Light
These METALLOGRAHPIC MScopes do NOT have a CONDENSOR Lens

26. 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

27. 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

28. 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
microscope
polished surface
surface groove
grain boundary
Where
N  grain/inch2
Fe-Cr alloy

29. 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

30. 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

31. SEM Photo Scaling MEMS Hinge ► Find Rectangle Length Lactual
2.91 in-photo
This is an SEM photograph of a MEMS microscopic hinge. The hinge is connected to the edge of a mirror, which can be seen in the right part of the micrograph. The flexible springs in the hinge allow the mirror to tilt and pivot. The mirror is connected to two vertical lifters (outside the field of view of this photograph). This hinge, combined with the lifting action of the two vertical lifters, allow the mirror to be pointed in a variety of directions. The mirror is used in optical switching systems.
3.02 in-photo

32. SEM Photo Scaling Use “ChainLink” Cancellation of Units (c.f. ENGR10)
Thus the Rectangular Connecting Bracket is about 48µm in Length

33. Olympus DUV Metallurgical Mscope
Deep Ultraviolet Microscope U-UVF248