Ppt solid state physics

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

2. Chapter 4 - 2
• 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
Solidifcation
• Crystals grow until they meet each other
crystals growing
Adapted from Fig.4.14 (b), Callister 7e.
grain structure
liquid
nuclei

3. Chapter 4 - 3
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.

4. Chapter 4 - 4
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.

5. Chapter 4 - 5
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defects
Types of Imperfections
• Dislocations Line defects
• Grain Boundaries Area defects

6. Chapter 4 - 6
Vacancy: A point defect

7. Chapter 4 - 7
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.)

8. Chapter 4 -
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.
8

9. Chapter 4 - 9
Defects Dimensionality Examples
Point 0 Vacancy
Line 1 Dislocation
Surface 2 Free surface,
Grain boundary

10. Chapter 4 - 10
• Vacancies:
-vacant atomic sites in a structure.
• Self-Interstitials:
-"extra" atoms positioned between atomic sites.
Point Defects
Vacancy
distortion
of planes
self-
interstitial
distortion
of planes

11. Chapter 4 - 11
Frenkel
defect
Schottky
defect
Defects in Ionic Solids
Cation vacancy
+
cation interstitial
Cation vacancy
+
anion vacancy

12. Chapter 4 - 12
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)
OR
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe)
Second phase particle
--different composition
--often different structure.
Impurities in Solids

13. Chapter 4 - 13
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

14. Chapter 4 - 14
Line Defects
Dislocations

15. Chapter 4 - 15
Missing half plane A Defect

16. Chapter 4 - 16
An extra half plane…
…or a missing half plane

17. Chapter 4 - 17
What kind of
defect is this?
A line defect?
Or a planar
defect?

18. Chapter 4 - 18
Extra half plane No extra plane!

19. Chapter 4 - 19
Missing plane No missing plane!!!

20. Chapter 4 - 20
An extra half plane…
…or a missing half plane
Edge
Dislocation

21. Chapter 4 - 21
This is a line defect called an
EDGE DISLOCATION

22. Chapter 4 - 22
• are line defects,
• slip between crystal planes result when dislocations move,
• produce permanent (plastic) deformation.
Dislocations:
Slip
• after tensile elongation
slip steps
Schematic of Zinc (HCP):
• before deformation
Adapted from Fig. 7.8, Callister 7e.

23. Chapter 4 - 23
• 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)
Motion of Edge Dislocation

24. Chapter 4 - 24
Surface
Defects

25. Chapter 4 - 25
Surface Defects
External Internal
Free surface Grain boundary
Stacking fault
Twin boundary
Interphase
boundary
Same
phase
Different
phases
Domain Wall

26. Chapter 4 - 26
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

27. Chapter 4 - 27
Is a lattice finite or infinite?
Is a crystal finite or infinite?
Free surface:
a 2D defect

28. Chapter 4 - 28
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.

29. Chapter 4 - 29
Grain 1
Grain 2
Grain
Boundary
Internal surface: grain boundary
A grain boundary is a boundary between two
regions of identical crystal structure but
different orientation

30. Chapter 4 - 30
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.

31. Chapter 4 - 31
• 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.)
Summary
• Strength can be increased by making dislocation
motion difficult.
• Heating (annealing) can reduce dislocation density
and increase grain size. This decreases the strength.