1. CHAPTER 5: IMPERFECTIONS IN SOLIDS
ISSUES TO ADDRESS...
• 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?
How do point defects in ceramics differ from those
in metals?
In ceramics, how are impurities accommodated
in the lattice and how do they affect properties? 1

2. Imperfections in Solids
Introduction and Motivation
Why study this?
What I have shown you so far are “idealized” structures
You would get the impression that solids (particularly crystalline solids) have “perfect” structures
This is clearly not the case
All solids have imperfections, and these have profound influences on mechanical (e.g. alloys of Ag/Cu v pure silver), electrical (e.g. doping of silicon with boron) properties
“Crystalline defect” – a lattice irregularity having one or more of its dimensions on the order of an atomic distance
We will also organize this discussion around whether the defect involves a single atom (0 D), rows of atoms (1D), or interfacial (2D) defects
End of lecture 1

3. TYPES OF IMPERFECTIONS
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defects
Line defects
Area defects
• Dislocations
• Grain Boundaries 2

4. Imperfections in Solids
Point defects in metals
Start simple: what happens when you have a crystal structure and one of the atoms is missing  vacancy
Every crystal has vacancies
Why? From a thermodynamic viewpoint, crystalline solids have very low entropy (why?)
The introduction of vacancies increases the entropy of the crystal
Can estimate the number of vacancies in a crystal using a Boltzmann type description
End of lecture 1
Qv is the energy required for forming a vacancy
For a “typical” metal Nv/N slightly below the melting temperature is ~ 10-4

5. POINT DEFECTS • Vacancies: • Self-Interstitials:
-vacant atomic sites in a structure.
• Self-Interstitials:
-"extra" atoms positioned between atomic sites. 3

6. EQUIL. CONCENTRATION: POINT DEFECTS
• Equilibrium concentration varies with temperature! 4

7. MEASURING ACTIVATION ENERGY
• We can get Q from
an experiment.
• Measure this...
• Replot it... 5

8. ESTIMATING VACANCY CONC.
• Find the equil. # of vacancies in 1m3 of Cu at 1000C.
• Given:
• Answer: 6

9. OBSERVING EQUIL. VACANCY CONC.
• Low energy electron
microscope view of
a (110) surface of NiAl.
• 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.
Movie m3
Reprinted with permission from Nature (K.F. McCarty, J.A. Nobel, and N.C. Bartelt, "Vacancies in
Solids and the Stability of Surface Morphology",
Nature, Vol. 412, pp (2001). Image is
5.75 mm by 5.75 mm.) Copyright (2001) Macmillan Publishers, Ltd. 7

10. Imperfections in Solids
Point defects in ceramics
Point defects such as vacancies are also present in ceramics
Here it is a bit more involved, since ceramics have both cations and anions
You might imagine that since the anions are (much?) larger than the cations there are very few anion interstitial defects
“Defect structure” is often used to denote defects in ceramics – again need to deal with charge neutrality
End of lecture 1

11. Imperfections in Solids
Point defects in metals
A void left by an atom in the crystal structure is called a vacancy
An additional atom is called a self-interstitial
This is an atom that is located in one of the interstitial voids in the crystal structure (remember those) that are usually not occupied
These occur much less frequently than defects (why?)
End of lecture 1

12. Imperfections in Solids
Point defects in ceramics
Because of charge neutrality, defects in ceramics must occur in pairs
Frenkel defect -- cation-vacancy and cation-interstitial pair (cation moves from regular site to interstitial site)
Schottky defect – cation-vacancy and anion-vacancy pair (move one cation and one anion from the lattice to the external surface)
End of lecture 1

13. DEFECTS IN CERAMIC STRUCTURES
• Frenkel Defect
--a cation is out of place.
• Shottky Defect
--a paired set of cation and anion vacancies.
Adapted from Fig , Callister 5e. (Fig 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.) See Fig , Callister 6e.
• Equilibrium concentration of defects 8

14. Imperfections in Solids
Stoichiometry
Stoichiometric materials are those where the exact cation:anion ratio is predicted from the chemical formula (i.e. NaCl); deviation from this leads to nonstoichiometric materials
How would you get this?
Ions with multiple oxidation states (e.g. Fe+2, Fe+3)
Impurities
These types of issues can lead to
defects
End of lecture 1
Fe1-xO
x < 1
Non-stoichiometry
Deficiency of Fe

15. Imperfections in Solids
Impurities in solids (metals)
It is very hard to make ultra-high purity metals
Often turns out you don’t want to!
Mixtures of metals (or alloys) often have better properties than the pure compounds – e.g. alloying silver with copper
Some definitions:
Solid solution – single “solid phase” containing two (or more) metals
Formed upon addition of impurity
For binary metal solid solutions – solvent/solute nomenclature used
End of lecture 1

16. POINT DEFECTS IN ALLOYS
Two outcomes if impurity (B) added to host (A):
• Solid solution of B in A (i.e., random dist. of point defects) OR
Substitutional alloy
(e.g., Cu in Ni)
Interstitial alloy
(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. 9

17. Imperfections in Solids
Solid solutions
In the case of a solid solution, upon addition of the impurity to the host material, the crystal structure is maintained
Analogy to liquids
Add two miscible liquids together (water & methanol)
The composition is homogeneous throughout
Same idea with solid solutions – impurity atoms are randomly and uniformly dispersed within the solid
End of lecture 1

18. ALLOYING A SURFACE • Low energy electron microscope view of
a (111) surface of Cu.
• Sn islands move along
the surface and "alloy"
the Cu with Sn atoms,
to make "bronze".
• The islands continually
move into "unalloyed"
regions and leave tiny
bronze particles in
their wake.
• Eventually, the islands
disappear.
Movie m4
Reprinted with permission from: A.K. Schmid, N.C. Bartelt, and R.Q. Hwang, "Alloying at Surfaces by the Migration of Reactive Two-Dimensional Islands", Science, Vol. 290, No. 5496, pp (2000). Field of view is 1.5 mm and the temperature is 290K. 10

19. Imperfections in Solids
Substitutional solid solutions
Regarding substitutional defects, there are several features that determine how well the impurity dissolves in the host material
Atomic size factor – close in size, the better; if the difference is more than about +/-15%, form new solid phases
Crystal structure – crystal structures for both species should be the same (i.e. hard to dissolve an FCC metal in a BCC metal)
Electronegativity – closer the better; if the difference between the two is large, they will likely form an intermetallic compound instead of a substitutional solid solution
Valence – Metal will have a tendency to dissolve a metal of higher valency versus lower valency
Example: Cu and Ni are “model” substitutional solid solution system
Size similar, both FCC, similar electronegativities, Ni+2, Cu+1
End of lecture 1

20. Imperfections in Solids
Interstitial solid solutions
Impurity atoms fill voids or interstices among the host lattice
Given the high packing factors in metal structure (bcc, fcc, hcp), the size of these positions is small
So, dinterstitial atom < dhost atom
Also very few of these defects (why?)
Example – Carbon forms an interstitial solid with iron (what is this?) – however can only add 2% carbon
End of lecture 1

21. Imperfections in Solids
Impurities in Ceramics
Can also have impurities in ceramics (again, issue of anions v cations, electroneutrality)
End of lecture 1

22. IMPURITIES • Impurities must also satisfy charge balance • Ex: NaCl
• Substitutional cation impurity
• Substitutional anion impurity 11

23. Imperfections in Solids
Sections 5.5, 5.6 – Read
5.5 – can have point defects in polymers
5.6 – composition units conversion, you should know all of this already from 204(?)
End of lecture 1

24. COMPOSITION Definition: Amount of impurity (B) and host (A)
in the system.
Two descriptions:
• Weight %
• Atom %
• Conversion between wt % and at% in an A-B alloy:
• Basis for conversion: 12

25. Imperfections in Solids
Dislocations/linear defects
A dislocation is a linear (one-dimensional) defect around which atoms are misaligned
Simplest type of dislocation – the presence of an extra portion of a plane of atoms, which terminates inside the crystal
This is called an edge dislocation
This is an extra plane of atoms
Note lattice distortion around plane
Atoms above dislocation line are squeezed together, those below are pushed apart
End of lecture 1
Magnitude and direction of
lattice distortion is expressed
in terms of the Burgers vector

26. Imperfections in Solids
Edge dislocation
Few other points
Where the plane ends is often called the “edge dislocation line” denoted by the ┴ symbol
The symbol points up if the extra plane is in the “top” of the crystal; points down if it is the “bottom” of the crystal
Also note the Burgers vector b
This is perpendicular to the edge dislocation
End of lecture 1

27. LINE DEFECTS Dislocations: Schematic of a Zinc (HCP): slip steps
• are line defects,
• cause slip between crystal plane when they move,
• produce permanent (plastic) deformation.
Schematic of a Zinc (HCP):
• before deformation
• after tensile elongation
slip steps 13

28. Imperfections in Solids
Screw dislocation
Can think of this as being due to a shear stress applied to the crystal
The upper front region of the crystal is shifted one atomic distance to the right
This also can be thought of as a linear dislocation along the line AB in the bottom Figure
End of lecture 1

29. Imperfections in Solids
Screw dislocation
Atomic positions above the “slip plane” are open circles, those below are solid circles
Here the Burgers vector b is parallel to the screw dislocation
In reality, most defects have components of both types … these are referred to as mixed dislocations
End of lecture 1

30. INCREMENTAL SLIP • Dislocations slip planes incrementally...
• The dislocation line (the moving red dot)...
...separates slipped material on the left
from unslipped material on the right.
Simulation of dislocation
motion from left to right
as a crystal is sheared.
Click on image to animate
(Courtesy P.M. Anderson) 14

31. BOND BREAKING AND REMAKING
• 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)
Click on image to animate 15

32. Imperfections in Solids
Interfacial defects
We have now talked about zero-dimensional (i.e. point) and one-dimensional (linear) defects. Can also have two-dimensional defects
These are boundaries that normally separate regions of the material with different crystal structures and/or crystallographic orientation (remember about grains?)
The most common – external surfaces, grain boundaries, stacking faults, twin boundaries, and phase boundaries
End of lecture 1

33. Imperfections in Solids
Interfacial defects
External surfaces
Why defects? Surface atoms are not bonded to the same number of atoms as the “bulk” atoms
They are therefore in a higher energy state
Nature (thermodynamics) says minimize your free energy (here dominated by surface free energy effects)
In liquids – typically get spherical droplets (why?)
Solids can’t do this
However, it is common to see structural rearrangement at surfaces to minimize energy
End of lecture 1

34. Imperfections in Solids
Interfacial defects
Grain boundaries
Boundaries between domains (or grains) of a polycrystalline material that possesses different crystallographic orientations
Within the boundary there is mismatch of the atomic arrangements as compared to the crystallographic domains
Orientation mismatch can be minor (small- or low-angle grain boundaries) or major (large- or high-angle grain boundaries)
End of lecture 1

35. AREA DEFECTS: GRAIN BOUNDARIES
• are boundaries between crystals.
• are produced by the solidification process, for example.
• have a change in crystal orientation across them.
• impede dislocation motion.
Metal Ingot
Schematic
~ 8cm
Adapted from Fig. 4.10, Callister 6e. (Fig is from Metals Handbook, Vol. 9, 9th edition, Metallography and Microstructures, Am. Society for Metals, Metals Park, OH, 1985.)
Adapted from Fig. 4.7, Callister 6e. 16

36. Imperfections in Solids
Interfacial defects
Grain boundaries
Tilt boundary – series of edge dislocations leading to a small-angle grain boundary
Key point here – the edge dislocations are aligned with respect to one another
End of lecture 1

37. Imperfections in Solids
Interfacial defects
Grain boundaries
Turns out that atoms along the grain boundary have less regular bonding as compared to that of the “bulk”
This is analogous to surface atoms
As a result they have a higher energy
Tend to be more reactive
Often impurity atoms will segregate into/along the grain boundaries
Grow at elevated temperatures to reduce the total boundary energy
End of lecture 1

38. Imperfections in Solids
Interfacial defects
Twin boundaries
Special type of grain boundary – across the grain boundary there is a mirror symmetry
The region between the boundary is called a twin
These are formed due to applied shear forces (mechanical twins) or during high temperature heat treatments (annealing twins)
These twins occur on a definite crystallographic plane and in a specific direction
End of lecture 1

39. Imperfections in Solids
Interfacial defects
Stacking faults
Exactly what it sounds like … the layers in a structure are stacked incorrectly
For example, in the FCC structure an interruption of the ABCABC.. stacking sequence of close-packed planes
Phase boundaries – domains between solids that phase separated (multiphase materials)
End of lecture 1

40. Imperfections in Solids
Bulk/volume defects
These are “3-D” defects
Pores – holes in the material
Cracks
“Foreign inclusions” – a large impurity domain?
Usually result from processing/fabrication
All effect material properties
Atomic vibrations – read
Microscopic examination – read
Key point – microscopy allows you to generate real space images of solids
Resolution of the image (i.e. size of the objects/features you can see) depends on the wavelength of the radiation used
End of lecture 1

41. Cu atomic shells for (Cu0. 25Ni0
Cu atomic shells for (Cu0.25Ni0.75)343 at various temperatures during the heating process
(MD simulations, S-P Huang and PB Balbuena, J. Phys. Chem. B, 2002) 0K
300 K
200 K
400 K
700 K
1300 K

42. Cu0.25Ni0.75 nanocluster (343 atoms) deposited on graphite (not shown)
700 K
800 K
900 K
1200 K
(S-P Huang, D. S. Mainardi and P. B. Balbuena, Surf. Sci., 2003)

43. OPTICAL MICROSCOPY (1) • Useful up to 2000X magnification.
• Polishing removes surface features (e.g., scratches)
• Etching changes reflectance, depending on crystal
orientation.
close-packed planes
Adapted from Fig. 4.11(b) and (c), Callister 6e. (Fig. 4.11(c) is courtesy
of J.E. Burke, General Electric Co.
micrograph of
Brass (Cu and Zn)
0.75mm 17

44. OPTICAL MICROSCOPY (2) Grain boundaries... • are imperfections,
• are more susceptible
to etching,
• may be revealed as
dark lines,
• change direction in a
polycrystal.
Adapted from Fig. 4.12(a) and (b), Callister 6e.
(Fig. 4.12(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].) 18

45. Electron Microscopy
Instead of light radiation, uses beams of electrons
A high-velocity electron becomes wave-like (QM), and its wavelength is inversely proportional to its velocity. If accelerated (high V), wavelengths could be of ~0.003 nm (3pm). => high magnification and high resolution

46. Electron microscopy
Transmission electron microscope (TEM): an electron beam goes through an specimen (usually prepared as a thin foil) => transmission of a high % of the incident beam.
Transmitted beam is projected for visualization. Magnifications of 1,000,000X or more. (useful for dislocations)

47. Electron microscopy
Scanning electron microscope (SEM): the surface of a specimen is scanned with an electron beam, and the reflected beam of electrons is collected on a cathode ray tube (similar to a TV screen). The surface must be electrically conductive. Magnifications from 10 to 50,000X.

48. SCANNING TUNNELING MICROSCOPY
• 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”.
Uses a tiny probe with a very sharp tip brought in very close proximity of the specimen. The probe
movements are monitored, and a 3-D image of the surface is generated. 19

49. SUMMARY • Point, Line, and Area defects arise 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.) 20

50. ANNOUNCEMENTS Reading: Chapter 5 HW # 4: Due Monday, February 19th21