1. CHAPTER 4: IMPERFECTIONS IN SOLIDS
ISSUES TO ADDRESS...
• What are the solidification mechanisms?
• What types of defects arise in solids?
• How do defects affect material properties?
• Are defects undesirable?

2. Solidifcation 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
Adapted from Fig.4.14 (b), Callister 7e.
grain structure
crystals growing
liquid
Crystals grow until they meet each other

3. Grain Structure
Grains can be - equiaxed (roughly same size in all directions)
- columnar (elongated grains)
High Purity, polycrystalline Lead ingot
Adapted from Fig. 4.12, Callister 7e.
Columnar in area with less undercooling
Shell of equiaxed grains due to rapid cooling (greater T) near wall
heat
flow
~ 8 cm
Grain Refiner - added to make smaller, more uniform, equiaxed grains.

4. 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.

5. Crystal = Lattice + Unit Cell
An ideal crystal can be described in terms a three-dimensionally periodic arrangement of points called lattice and an atom or group of atoms associated with each lattice point called unit cell:
Crystal = Lattice + Unit Cell
However, there can be deviations from this ideality.
These deviations are known as crystal defects.

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

7. Vacancy: A point defect

8. Vacancy scanning probe micrograph
(generated using a scanning-tunneling
microscope) that shows a (111)-type
surface plane* for silicon. The arrow
points to the location of a silicon
atom that was removed using a tungsten
nanotip probe. This site from
which an atom is missing is the surface
analogue of a vacancy defect—
that is, a vacant lattice site within
the bulk material. Approximately
20,000,000. (Micrograph courtesy
of D. Huang, Stanford University.)

9. Crystalline Imperfections
“Crystalline defect” is a lattice irregularity having one or more of its dimensions on the order of an atomic diameter.
Classification of crystalline imperfections is frequently made according to geometry or dimensionality of the defect.

10. Defects Dimensionality Examples
Point 0 Vacancy
Line 1 Dislocation
Surface 2 Free surface,
Grain boundary

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

12. Defects in Ionic Solids
Frenkel defect
Cation vacancy + cation interstitial
Schottky defect
Cation vacancy + anion vacancy

13. 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
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.

14. Substitutional Solid Solutions
Conditions for substitutional solid solution (S.S.)
W. Hume – Rothery rules
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

15. Hume-Rothery Rules 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
More Al !
More Al !
Table on p. 106, Callister 7e.

16. Specification of Impurities/Solutes
Specification of composition
weight percent
m1 = mass of component 1
nm1 = number of moles of component 1
atom percent

17. Line Defects
Dislocations

18. Missing half plane A Defect

19. An extra half plane…
…or a missing half plane

20. What kind of defect is this?
A line defect?
Or a planar defect?

21. Extra half plane
No extra plane!

22. Missing plane
No missing plane!!!

23. An extra half plane…
Edge Dislocation
…or a missing half plane

24. If a plane ends abruptly inside a crystal we have a defect.
The whole of abruptly ending plane is not a defect
Only the edge of the plane can be considered as a defect
This is a line defect called an EDGE DISLOCATION

25. Callister FIGURE The atom positions around an edge dislocation; extra half-plane of atoms shown in perspective. (Adapted from A. G. Guy, Essentials of Materials Science, McGraw-Hill Book Company, New York, 1976, p. 153.)

26. Slip Dislocations: Schematic of Zinc (HCP): slip steps
• are line defects,
• slip between crystal planes result when dislocations move,
• produce permanent (plastic) deformation.
• after tensile elongation
slip steps
Schematic of Zinc (HCP):
• before deformation
Adapted from Fig. 7.8, Callister 7e.

27. 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.
Atomic view of edge
dislocation motion from
left to right as a crystal
is sheared.
(Courtesy P.M. Anderson)

28. Glide of an Edge Dislocation 

29. Glide of an Edge Dislocation

30. Glide of an Edge Dislocation

31. Glide of an Edge Dislocation

32. Glide of an Edge Dislocation

33. Glide of an Edge Dislocation
A surface step of b is created if a dislocation sweeps over the entire slip plane
Surface step, not a dislocation

34. f03_07_pg177
Dislocation Motion
f03_07_pg177.jpg

35. f06_04_pg92 f06_04_pg92.jpg Figure 4.6 A transmission electron
micrograph of a titanium alloy in which the
dark lines are dislocations.
(Courtesy of M. R. Plichta, Michigan
Technological University.)

36. Johannes Martinus BURGERS
Burgers Vector
Johannes Martinus BURGERS
Burger’s vector
Burgers vector

37. The magnitude and direction of the lattice distortion associated with a dislocation is expressed in terms of a Burgers vector, denoted by a b.
For metallic materials, the Burgers vector for a dislocation will point in a close-packed crystallographic direction and will be of magnitude equal to the interatomic spacing.

38. In general, there can be any angle between the Burgers vector b (magnitude and the direction of slip) and the line vector t (unit vector tangent to the dislocation line)
b  t  Edge dislocation
b  t  Screw dislocation
b  t , b  t  Mixed dislocation

39. Edge & Screw Dislocations

40. Screw Dislocation Line
b || t b 1 2 3

41. A closed Burgers Circuit in an ideal crystal1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 F 9 1 8 2 7
A closed Burgers Circuit in an ideal crystal 3 6 4 5 5 4 6 3 7 2 8 1 9 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

42. Map the same Burgers circuit on a real crystal1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 F 9 S 1 8 2
Map the same Burgers circuit on a real crystal 7 3  6 4 5 5 4 6 3 7 2 8 1 9 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

43. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 F 9 S 1 8 2 7 3  6 4 5 5 4 6 3 7 2 8 1 9 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

44. Hence the name SCREW DISLOCATION
If b || t
Then parallel planes  to the dislocation line lose their distinct identity and become one continuous spiral ramp
Hence the name SCREW DISLOCATION

45. Screw Dislocation

46. Edge, Screw, and Mixed Dislocations
Adapted from Fig. 4.5, Callister 7e.

47. b is the shortest lattice translation
Energy of a dislocation line is proportional to b2.
Thus dislocations with short b are preferred.
b is a lattice translation
b is the shortest lattice translation

48. A dislocation line cannot end abruptly inside a crystal
It can end on
Free surfaces
Grain boundaries
On other dislocations at a point called a node
On itself forming a loop

49. Dislocations & Plastic Deformation
Cubic & hexagonal metals - plastic deformation by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations).
So we saw that above the yield stress plastic deformation occurs. But how? In a perfect single crystal for this to occur every bond connecting tow planes would have to break at once! Large energy requirement
Now rather than entire plane of bonds needing to be broken at once, only the bonds along dislocation line are broken at once.
If dislocations don't move, deformation doesn't occur!
Adapted from Fig. 7.1, Callister 7e.

50. Dislocations & Crystal Structures
• Structure: close-packed
planes & directions
are preferred.
view onto two
close-packed
planes.
close-packed directions
close-packed plane (bottom)
close-packed plane (top)
• Comparison among crystal structures:
FCC: many close-packed planes/directions;
HCP: only one plane, 3 directions;
BCC: none
Sec A
• Specimens that
were tensile
tested.
Mg (HCP)
tensile direction
Al (FCC)

51. Deformation Mechanisms
Slip System
Slip plane - plane allowing easiest slippage
Wide interplanar spacings - highest planar densities
Slip direction - direction of movement - Highest linear densities
FCC Slip occurs on {111} planes (close-packed) in <110> directions (close-packed)
=> total of 12 slip systems in FCC
in BCC & HCP other slip systems occur
Adapted from Fig. 7.6, Callister 7e.

52. Dislocation Motion
Dislocation moves along slip plane in slip direction perpendicular to dislocation line
Slip direction same direction as Burgers vector
Edge dislocation
Adapted from Fig. 7.2, Callister 7e.
Screw dislocation

53. Dislocations & Materials Classes
• Metals: Disl. mvt easier.
-non-directional bonding
-close-packed directions
for slip.
electron cloud
ion cores +
• Covalent Ceramics
(Si, diamond): Movement difficult.
-directional (angular) bonding
• Ionic Ceramics (NaCl):
Movement difficult.
-need to avoid ++ and - -
neighbors. + -

54. Positive
Negative
Extra half plane above the slip plane
Extra half plane below the slip plane
Edge Dislocation
Left-handed spiral ramp
Right-handed spiral ramp
Screw Dislocation
b parallel to t
b parallel to t

55. f05_07_pg179
f05_07_pg179.jpg

56. Surface Defects

57. Surface Defects External Internal Free surface Grain boundary
Twin boundary
Same phase
Stacking fault
Domain Wall
Interphase boundary
Different phases

58. Surface energy is anisotropic
Surface energy depends on the orientation, i.e., the Miller indices of the free surface
nA, nB are different for different surfaces

59. Is a lattice finite or infinite?
Is a crystal finite or infinite?
Free surface: a 2D defect

60. Surface Defects High-resolution transmission electron
micrograph that shows single crystals of (Ce0.5Zr0.5)O2;
this material is used in catalytic converters for
automobiles. Surface defects represented schematically
in Figure 4.10 are noted on the crystals.

61. Internal surface: grain boundary
A grain boundary is a boundary between two regions of identical crystal structure but different orientation

62. Grain Boundaries and Dislocations
The atoms are bonded less regularly along a grain boundary (e.g., bond angles
are longer), and consequently, there is an interfacial or grain boundary energy similar
to the surface energy.
The magnitude of this energy is a function
of the degree of misorientation, being larger for high-angle boundaries.
Impurity atoms often preferentially segregate along these boundaries because of their higher energy state.
The total interfacial energy is lower in large or coarse-grained materials than in fine-grained ones, since there is less total boundary area in the former.

63. Grain Size Number Grain boundaries... Fe-Cr alloy N = 2 n -1
• are imperfections,
• are more susceptible
to etching,
• may be revealed as
dark lines,
• change in crystal
orientation across
boundary.
Fe-Cr alloy
(b)
grain boundary
surface groove
polished surface
(a)
Adapted from Fig. 4.14(a) and (b), Callister 7e.
(Fig. 4.14(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].)
ASTM grain
size number N
= 2 n -1
number of grains/in2
at 100x
magnification

64. Planar Defects in Solids
One case is a twin boundary (plane)
Essentially a reflection of atom positions across the twin plane.
Stacking faults
For FCC metals an error in ABCABC packing sequence
Ex: ABCABABC
Annealing twins found in FCC metals while mechanical twins found in BCC and HCP metals.
Adapted from Fig. 4.9, Callister 7e.

65. Strategies for Strengthening: Reduce Grain Size
• Grain boundaries are
barriers to slip.
• Barrier "strength"
increases with
Increasing angle of
misorientation.
• Smaller grain size:
more barriers to slip.
Adapted from Fig. 7.14, Callister 7e.
(Fig is from A Textbook of Materials Technology, by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.)

66. Strategies for Strengthening: Solid Solutions
• Impurity atoms distort the lattice & generate stress.
• Stress can produce a barrier to dislocation motion.
• Smaller substitutional
impurity
Impurity generates local stress at A and B that opposes dislocation motion to the right. A B
• Larger substitutional
impurity
Impurity generates local stress at C and D that opposes dislocation motion to the right. C D

67. Strengthening by Alloying
small impurities tend to concentrate at dislocations
reduce mobility of dislocation  increase strength
Adapted from Fig. 7.17, Callister 7e.

68. Strengthening by alloying
large impurities concentrate at dislocations on low density side
Adapted from Fig. 7.18, Callister 7e.

69. 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 - see the individual grains
Crystallites (grains) can be quite small (mm or less) – necessary to observe with a microscope.
Photograph of xyz positioning microstage,
realized in single crystal silicon.
Quartz Single Crystal

70. Optical Microscopy • Useful up to 2000X magnification.
• Polishing removes surface features (e.g., scratches)
• Etching changes reflectance, depending on crystallographic orientation.
0.75mm
crystallographic planes
Adapted from Fig. 4.13(b) and (c), Callister 7e. (Fig. 4.13(c) is courtesy
of J.E. Burke, General Electric Co.
Micrograph of
brass (a Cu-Zn alloy)

71. Polarized Light
metallographic scopes often use polarized light to increase contrast
Also used for transparent samples such as polymers

72. Concept Check
Does the grain size number (n of Equation 4.16) increase or decrease with decreasing grain size? Why?
Answer: Taking logarithms of Equation 4.16 and then rearranging such that the grain size number n is the dependent variable leads to the expression!
n = 1 + log N / log 2
In other words, the value of n increases with decreasing grain size.

73. Electron 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 (10-12m ~0.003 nm)
(Magnification - 1,000,000X)
Atomic resolution possible
Electron beam focused by magnetic lenses.
Optical microscopy good to ca. wavelength of light. Focusing means to bend the photon's path without changing its energy too much, and that is not easy to do with gamma-rays or x-rays. This means that images we have from the gamma-ray region are not as sharp (that is, they have poorer angular resolution) than images taken in the visible or most other wavelengths
Higher frequencies
X-rays – good idea but difficult to focus
Electrons - wavelength proportional to velocity with high voltage (high acceleration) get wavelengths ca. 3pm (0.003nm) (x1,000,000)

74. Scanning Probe Microscopy
Neither light nor electrons are used to form an image!
The microscope generates a topographical map, on an atomic scale, that is a representation of the surface features and characteristics of the specimen.
Examination on the nanometer scale is possible, magnifications as high as109x are possible;
Three-dimensional magnified images are generated that provide topographical information about features of interest.
Some SPMs may be operated in a variety of environments (e.g., vacuum, air,liquid); thus, a particular specimen may be examined in its most suitable environment.

75. Scanning Tunneling Microscopy (STM)

76. Scanning Electron Microscopy
Pollen
Seed
Space Shuttle Tile
Lead-Tin Solder
Ceramic with pores
Fracture Surface

77. Scanning Electron Microscopy
Dislocations in Ti
Alloy at 51,450X
Zirconia/Alumina Interface
Ant’s Head

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

79. Scanning Tunneling Microscopy (STM)
(110) Surface of Ni
2 point defects on (111)
plane of Cu lattice

81. 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.)
• Strength can be increased by making dislocation
motion difficult.
• Heating (annealing) can reduce dislocation density
and increase grain size. This decreases the strength.