1. Chapter 5 Imperfections in Solids
Thanks to Jeff DePue, Greg Dykes, Alex Eaton

2. CHAPTER 5: IMPERFECTIONS IN SOLIDS
ISSUES TO ADDRESS...
• What are the solidification mechanisms?
• What types of defects arise in solids?
• Can the number and type of defects be varied
and controlled?
• How do defects affect material properties?
• Are defects undesirable?

3. 5.1 Introduction Every single solid has defects and imperfections.
Sometimes the imperfections are purposely created and used for a specific purpose.
Types of defects:
Point Defects (One or two atomic positions)
Linear Defects (One Dimensional)
Interfacial Defects (Boundaries)

4. 5.1 Imperfections in Solids
Solidification- result of casting of molten material
2 steps
Nuclei form
Nuclei grow to form crystals – grain structure
Start with a molten material – all liquid
nuclei
liquid
crystals growing
Adapted from Fig (b), Callister & Rethwisch 3e.
grain structure
Crystals grow until they meet each other

5. Polycrystalline Materials
Grain Boundaries
regions between crystals
transition from lattice of one region to that of the other
slightly disordered
low density in grain boundaries
high mobility
high diffusivity
high chemical reactivity
Adapted from Fig. 5.12, Callister & Rethwisch 3e.

6. Solidification
Grains can be - equiaxed (roughly same size in all directions)
- columnar (elongated grains)
~ 8 cm
heat
flow
Shell of equiaxed grains due to rapid cooling (greater T) near wall
Columnar in area with less undercooling
Adapted from Fig. 5.17, Callister & Rethwisch 3e.
Grain Refiner - added to make smaller, more uniform, equiaxed grains.

7. Imperfections in Solids
There is no such thing as a perfect crystal.
What are these imperfections?
Why are they important?
Many of the important properties of materials are due to the presence of imperfections.

8. Types of Imperfections
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defects
• Dislocations
Line defects
• Grain Boundaries
Area defects

9. I. Point defects

10. 5.2 Point Defects in Metals
• Vacancies:
-vacant atomic sites in a structure.
Vacancy
distortion
of planes
• Self-Interstitials:
-"extra" atoms positioned between atomic sites.
self-
interstitial
distortion
of planes

11. Equilibrium Concentration: Point Defects
• Equilibrium concentration varies with temperature!
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
-23
(1.38 x 10
J/atom-K) -5
(8.62 x 10
eV/atom-K)
Each lattice site
is a potential
vacancy site

12. Measuring Activation Energyç ÷ N v =
exp - Q k T æ è ö ø
• We can get Qv from
an experiment.
• Measure this... N v T
exponential
dependence!
defect concentration
• Replot it... 1/ T N v ln - Q /k
slope

13. Estimating Vacancy Concentration
• Find the equil. # of vacancies in 1 m3 of Cu at 1000C.
• Given: r
= 8.4 g / cm 3 A
= 63.5 g/mol Cu Q
= 0.9 eV/atom N
= 6.02 x 1023
atoms/mol v A
8.62 x 10-5
eV/atom-K
0.9 eV/atom
1273 K ç N v =
exp - Q k T æ è ö ø
= 2.7 x 10-4 ç
For 1 m3
, N = N A Cu r x
1 m3
= 8.0 x 1028 sites
• Answer: N v =
(2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacancies

14. 5.2 Point Defects in Metals
Vacancies:
Impossible to create a material without vacancies due to the laws of Thermodynamics.
The number of vacancies (Nv) calculated from
Nv = N exp(-Q/kT)
N = number of atomic sites;
Q = energy for vac. formation;
k = boltzmann’s constant
= 1.38×10-23 J/atom-K
= 8.62×10-5 eV/atom-K
T = absolute temperature (K)

15. 5.2 Point Defects in Metals
Self Interstitial:
When an atom is pushed into an interstitial site which is normally unoccupied.
Very small amount in metals because when it occurs, it highly distorts the metal.
Much lower concentrations than vacancies.

16. 5.3 Point Defects in Ceramics (i)
• Vacancies
-- vacancies exist in ceramics for both cations and anions
• Interstitials
-- interstitials exist for cations
-- interstitials are not normally observed for anions because anions are large relative to the interstitial sites
Cation
Interstitial
Vacancy
Anion
Adapted from Fig. 5.2, Callister & Rethwisch 3e. (Fig. 5.2 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.)

17. Point Defects in Ceramics (ii)
• Frenkel Defect
-- a cation vacancy-cation interstitial pair.
• Shottky Defect
-- a paired set of cation and anion vacancies.
Shottky
Defect:
Frenkel
Defect
Adapted from Fig. 5.3, Callister & Rethwisch 3e. (Fig. 5.3 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.)
• Equilibrium concentration of defects

18. 5.3 Point Defects in Ceramics
More types of defects than metals because there are more types of ions.
In order to keep electroneutrality, ions must be lost in equal amounts of charge. For example: One cation and one anion.
Two main types: Frenkel Defect, Shottky Defect
Most ceramics stay in a stoichiometric state, that is, they generally keep the same ratios as predicted by their empirical formula.
Exceptions occur in atoms like iron: Fe2+ and Fe3+

19. Frenkel Defect Neighboring cation vacancy and cation interstitial.
Nfr = N exp(-Qfr/2kT)

20. Shottky Defect Neighboring cation vacancy and anion vacancy.
Ns=N*exp(-Qs/2kT)

21. 5.4 Impurities in Metals
Two outcomes if impurity (B) added to host (A):
• Solid solution of B in A (i.e., random dist. of point defects) OR
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe)
• Solid solution of B in A plus particles of a new
phase (usually for a larger amount of B)
Second phase particle
-- different composition
-- often different structure.

22. Impurities in Metals
Conditions for substitutional solid solution (S.S.)
1. r (atomic radius) < 15%
2. Proximity in periodic table
i.e., similar electronegativities
3. Same crystal structure for pure metals
4. Valency
All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency

23. Imperfections in Metals (iii)
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
Table on p. 159, Callister & Rethwisch 3e.

24. Imperfections in Ceramics
• Electroneutrality (charge balance) must be maintained when impurities are present Na + Cl -
• Ex: NaCl
• Substitutional cation impurity
without impurity Ca 2+
impurity
with impurity Na +
cation
vacancy
• Substitutional anion impurity
without impurity O 2-
impurity Cl - an
ion vacancy
with impurity

25. 5.4 Impurities in Solids Impurities in Metals:
Alloy - metal in which impurities have been added to give it a certain characteristic.
Solid Solutions (See Next Slide)
Solvent - metal present in greatest amount
Solute - All other metals present
There is no such thing as a perfectly pure metal!

26. 5.4 Impurities in Solids Solid Solutions: Substitutional
replacement of ions
Interstitial
filling of voids
Dependent on:
Atomic size factor
Crystal Structure
Electronegativity
Valences
Impurities in Ceramics
Both types as well Can occur for the cations or for the anions
Usually both occur at same time (one cation + one anion).

27. 5.5 Point Defects in Polymers
Defects due in part to chain packing errors and impurities such as chain ends and side chains
Adapted from Fig. 5.7, Callister & Rethwisch 3e.
Adapted from Fig. 5.7, Callister & Rethwisch 3e.

28. 5.5 Point Defects in Polymers
Different from ceramics and metals
Chains can bond together forming loops.
Chains can tie two molecules together.
Impurities may include interstitials, side branches, or incorrect bending.
Vacancies can occur and alter the chain sequence.
Every chain end is considered a defect.

29. 5.6 Specification of Composition (or concentration)
weight percent
m1 = mass of component 1
nm1 = number of moles of component 1
atom percent
m = mass; n = moles (Compositions are easily converted
from one type to the other by manipulating m to n, or vice
versa, using the atomic weight, A)

30. II. Miscellaneous Imperfections

31. 5.7 Line Defects Dislocations: Schematic of Zinc (HCP): slip steps
• are line defects,
• slip between crystal planes result when dislocations move,
• produce permanent (plastic) deformation.
Schematic of Zinc (HCP):
• before deformation
• after tensile elongation
slip steps

32. Imperfections in Solids
Linear Defects (Dislocations)
Are one-dimensional defects around which atoms are misaligned
Edge dislocation:
extra half-plane of atoms inserted in a crystal structure
b perpendicular () to dislocation line
Screw dislocation:
spiral planar ramp resulting from shear deformation
b parallel () to dislocation line
Burger’s vector, b: measures the magnitude and direction of the lattice distortion

33. Imperfections in Solids
extra half-plane of atoms inserted in a crystal structure
Edge Dislocation
Fig. 5.8, Callister & Rethwisch 3e.

34. Imperfections in Solids
Screw Dislocation: b || dislocation line
Screw Dislocation
Dislocation
line b
Burgers vector b
(b)
(a)
Adapted from Fig. 5.9, Callister & Rethwisch 3e.

35. Edge, Screw, and Mixed Dislocations
Adapted from Fig. 5.10, Callister & Rethwisch 3e.

36. Imperfections in Solids
Dislocations are visible in electron micrographs; TEM Titanium alloy, dark lines are dislocations 51,450x
Fig. 5.11, Callister & Rethwisch 3e.

37. 5.7 Dislocations – Linear Defects
A dislocation is a linear (one dimensional) defect around which other atoms are misaligned
Edge Dislocation – where an extra plane or half plane of atoms stops
Screw Dislocation – where a shear stress causes a region of a crystal to shift
Mixed Dislocation – a combination of edge and screw dislocations
Burges Vector – the magnitude and direction of lattice distortion associated with a dislocation

38. 5.8 Interfacial defects 2D Boundaries
Separate xtal structures & xtalographic orientations
Examples:
external surfaces
Lower nearest neighbors
Atoms in higher energy states
Tend to minimize the total surface area
grain boundaries
Low angle example: tilt boundary
High angle
twin boundaries
stacking faults
phase boundaries (in multiphased materials)

40. Twin boundary (plane) Stacking faults
Essentially a reflection of atom positions across the twin plane.
Stacking faults
For FCC metals an error in ABCABC packing sequence
Ex: ABCABABC
Adapted from Fig. 5.14, Callister & Rethwisch 3e.

41. Catalysts and Surface Defects
A catalyst increases the rate of a chemical reaction without being “consumed”
Active sites on catalysts are normally surface defects
Fig. 5.15, Callister & Rethwisch 3e.
Single crystals of (Ce0.5Zr0.5)O2 used in an automotive catalytic converter
Fig. 5.16, Callister & Rethwisch 3e.

42. 5.8 Interfacial Defects
Interfacial defects are two dimensional boundaries with different crystal structures and/or orientations
External Surfaces – where the crystal terminates
Grain Boundaries – crystals often form groups of atoms known as grains, which when combined with other grains in a large crystal, often have misalignments that form boundaries
Phase Boundaries – where a crystal forms more than one phase (i.e. solid and liquid)
Twin Boundaries – A special grain boundary where one grain forms a mirror lattice symmetry with another
Other miscellaneous interfacial defects include stacking faults and ferromagnetic domain walls.

43. 5.8 Interfacial Defects Grain Boundary

44. 5.9 Bulk or Volume Defects
Much larger defects than the previous ones, usually introduced during processing and fabrication steps
Examples include:
Pores
Cracks
Foreign Inclusions
Other Phases

45. Every atom vibrates even at zero Kelvin (OK?)
5.10 Atomic Vibrations
(Introduce during the creation of the universe)
Every atom vibrates even at zero Kelvin (OK?)
Frequencies in the order of 10 THz

46. 5.10 Atomic Vibrations
At any given time, each atom in a crystal is vibrating about its lattice position within the crystal
The amplitudes and frequencies of the vibrations vary between atoms and can be considered imperfections or defects
The vibrations change with temperature and influence many properties of the crystal such as melting point

47. III.Microscopic Examination

48. Microscopic Examination
Crystallites (grains) and grain boundaries. Vary considerably in size. Can be quite large.
ex: Large single crystal of quartz or diamond or Si
ex: Aluminum light post or garbage can - see the individual grains
Crystallites (grains) can be quite small (mm or less) – necessary to observe with a microscope.

49. 5.11 Microscopic Examination
The grains of many crystals have diameters in the order of microns (10-6 meters)
Microstructure – Structural features subject to observation under a microscope
Microscopy – Use of a microscope in studying crystal structure
Photomicrograph – A picture taken by a microscope

50. 5.11 Microscopic Examination
Electron Microscope
Optical Microscope
Scanning Probe Microscope

51. 5.12 Microscopic Techniques Optical Microscopy
0.75mm
5.12 Microscopic Techniques Optical Microscopy
• Useful up to 2000X magnification.
• Polishing removes surface features (e.g., scratches)
• Etching changes reflectance, depending on crystal orientation.
crystallographic planes
Micrograph of brass (a Cu-Zn alloy)
Adapted from Fig. 5.18(b) and (c), Callister & Rethwisch 3e. (Fig. 5.18(c) is courtesy
of J.E. Burke, General Electric Co.)

52. Optical Microscopy Uses a series of lenses
polished surface
Uses a series of lenses
Three basic lenses (4x, 10x, and a third ranging from 20x - 100x)
surface groove
(a)
grain boundary
Adapted from Fig. 5.19(a) and (b), Callister & Rethwisch 3e.
(Fig. 5.19(b) is courtesy
of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)
Grain boundaries
• are imperfections,
• are more susceptible
to etching,
• may be revealed as
dark lines,
• change in crystal
orientation across
boundary.
Fe-Cr alloy
(b)

53. Optical Microscopy Polarized light
metallographic scopes often use polarized light to increase contrast
Also used for transparent samples such as polymers
Cast iron with spherulitic graphite, polished, C-DIC; Dr. H.-L. Steyer, Kesselsdorf, Germany

54. Microscopy Optical resolution ca. 10-7 m = 0.1 m = 100 nm
For higher resolution need higher frequency
X-Rays? Difficult to focus.
Electrons
wavelengths ca. 3 pm (0.003 nm)
(Magnification - 1,000,000X)
Atomic resolution possible
Electron beam focused by magnetic lenses.

55. M i c r o s c o p y f r o m C a r l Z e i s s

56. Scanning Tunneling Microscopy (STM)
• Atoms can be arranged and imaged!
Carbon monoxide molecules arranged on a platinum (111) surface.
Iron atoms arranged on a copper (111) surface. These Kanji characters represent the word “atom”.
Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright 1995.

57. Microscopic Techniques: Electron Microscopy
Uses focused beam of electrons to magnify target
Magnification up to 2,000,000x
4 main types
TEM, SEM, REM, STEM
A TEM image of the polio virus. The polio virus is 30 nm in size

58. Transmission Electron Microscopy (TEM)
Original form of electron microscope
Utilizes an electron gun with a tungsten filament
Image projected unto a phosphor viewing screen

59. Microscopic Techniques Scanning Electron Microscopy (SEM)
Scans rectangular area by using a focused beam of electrons
Electrons give off differing energies based on structure of target
Microscope reads these energies and produces a visual representation

60. Microscopic Techniques Reflection Electron Microscopy (REM)
REM study of Co electro-deposition on Pt(111) surfaces
Like TEM, uses a beam of electrons to develop a picture of the target
Reads the reflected beam of electrons to form visual representation

61. Microscopic Techniques Scanning Transmission Electron Microscope (STEM)
A type of Transmission Electron Microscope
Electrons focus on a small area of specimen
Electrons pass through the sample, and a visual is formed

62. 5.13 Grain size determination
N = ASTM grain size number
N = 2n-1
n = number of grains/in2 at 100× magnification
American Society for Testing and Materials

63. Section 5.13 Grain Size Determination

64. Grain Size Determination
Photomicrographic techniques used for determination
Two techniques used:
Intercept comparison
Standard comparison

65. Grain Size Determination Intercept Method
Draw straight lines through photograph of grain structure
Count number of grains that pass through each line
Line length divided by number of intersected grains

66. Grain Size Method Standard Method
Developed by American Society for Testing and Materials (ASTM)
Photograph specimen at 100x
Compare grain size to a set of charts with grain size scale 1-10
Grain size (n) is determined by number of grains per square inch (N) at 100x
N = 2n-1

67. Summary • Point, Line, and Area defects exist in solids.
• The number and type of defects can be varied
and controlled (e.g., T controls vacancy conc.)
• Defects affect material properties (e.g., grain
boundaries 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.)