just keep some basic in mind, its give u enough information about this topic.

1. CRYSTAL IMPERFECTIONS
Dr. H. K. Khaira
Professor and HoD
MSME Deptt., MANIT, Bhopal

5. Chpt 5: Imperfections in Solids
ISSUES TO ADDRESS...
• What types of defects arise in solids? Describe them.
• Can the number and type of defects be varied
and controlled?
• How do defects affect material properties?
• Are defects undesirable?
5

6. TYPES of DEFECTS

7. TYPES of DEFECTS
•
•
•
•
•
Vacancy atoms
Interstitial atoms
Frankel defect
Impurity atoms
Dislocations
Point defects
Line defects
Edges, Screws, Mixed
• Grain Boundaries
Area/Planar defects
• Stacking Faults
• Anti-Phase and Twin Boundaries
We need to describe them and understand their effects.
7

8. Length Scale of Imperfections
point, line, planar, and volumetric defects
Vacancies,
impurities
dislocations
Grain and twin
boundaries
Voids
Inclusions
precipitates
8

9. Point Defects
• The defects which are confined to a point are
known as point defects
• Types of point defects
– Vacancy
– Interstitialcy
– Frankel defect
– Impurity atoms

10. Vacancy
• When an atom is missing from its regular
lattice site, it is known as VACANCY.

11. Vacancy
• Vacancies: vacant atomic sites in a structure.
distortion
of planes
Vacancy
11

12. Vacancy and Distortion of planes

13. Vacancy
Vacancy: a vacant lattice site
It is not possible to create a crystal free of vacancies.
About 1 out of 10,000 sites are vacant near melting.
13

14. Vacancy
Thermodynamics provides an expression for
Vacancy Concentration: CV =
 Q 
Nv
= exp  − v 
N
 k BT 
CV = Concentration of vacancies
Nv = Number of vacancies
N = Total number of atomic sites
Qv = vacancy formation energy
kB = 1.38 x 10–23 J/atom-K = 8.62 x 10–5 eV/atom-K
kB/mole = R = 1.987 cal/mol-K
Defects ALWAYS cost energy!
14

15. Equilibrium Concentration of Vacancy
• Equilibrium concentration varies with temperature!
No. of defects
Cd=
Activation energy
 −Q 
ND =
D
exp


 kT 
N
No. of potential
Temperature
defect sites.
Boltzmann's constant
(1.38 x 10-23 J/atom K)
(8.62 x 10 -5 eV/atom K)
Each lattice site
is a potential
vacancy site
15

16. Estimating Vacancy Concentration
• Find the equil. # of vacancies in 1m 3of Cu at 1000C.
• Given: ρ = 8.4 g/cm3
ACu = 63.5g/mol
QV = 0.9eV/atom NA = 6.02 x 1023 atoms/mole
0.9eV/atom
 −Q 
ND
D
= exp

 = 2.7 · 10-4
CV=
 kT 
N
For 1m3, N =
1273K
8.62 x 10-5 eV/atom-K
NA
x 1m3 = 8.0 x 1028 sites
ρ x
ACu
• Solve: ND = 2.7 · 10 -4 · 8.0 x 10 28 sites = 2.2x 1025 vacancies
* What happens when temperature is slowly
reduced to 500 C, or is rapidly quenched to 500 C?
106 cm3 = 1 m3
16

17. Equilibrium concentration of vacancies as a
function of temperature for aluminium (after Bradshaw and
Pearson, 1957).

18. Interstitialcy

19. Interstitialcy
distortion
of planes
selfinterstitial
• Self-Interstitials: "extra" atoms in between atomic sites.
19

20. Interstitialcy
• When an atom is present at an interstitial
position in its lattice, it is known as
interstitialcy.
• In this case an atom is present at a place
where it should not have been.

21. Self Interstitialcy and Distortion of
planes

22. Interstitialcy
Self-interstitial: atom crowded in ‘holes’
Self-interstitials are much less likely in metals, e.g.,,
as it is hard to get big atom into small hole - there is
large distortions in lattice required that costs energy.
22

23. Frenkel Defect
• It is a combination of vacancy and
interstitialcy defects.
• When an atom leaves its regular lattice site
and goes to an interstitial site, it is known as
Frenkel Defect.

25. Impurity Atom
• When atom of another element is present as
an impurity in the lattice of an element, it is
known as impurity atom.

26. Impurity Atom
• Impurity atoms can occupy any of the
following position
– Interstitial position
– Substitutional position

27. Impurity Atom
• Types of Impurity Atom
– Interstitial Impurity Atom
• When impurity atom is present at an interstitial site, it
is known as interstitial impurity atom.
– Small atoms C, N, B and H can occupy interstitial sites
– Substitutional Impurity Atom
• When impurity atom substitutes a parent atom at its
regular lattice site, it is known as substitutional
impurity atom.

28. Impurity Atom

29. Interstitial Impurity in FCC

30. Interstitial impurity C in α-Fe. The C atom is small
enough to fit, after introducing some strain into the BCC
lattice.

31. VOIDS
BCC
Distorted TETRAHEDRAL
Distorted OCTAHEDRAL**
a√3/2
a
a
a√3/2
rvoid / ratom = 0.29
Note: Atoms are coloured differently but are the same
rVoid / ratom = 0.155

32. Interstitial Impurity in FCC

33. Interstitial Impurity in FCC

34. Substitutional Impurity

35. Substitutional impurity and
distortion of planes

36. Point Defects

37. Point Defects

38. Line Defects
Or
Dislocations

39. Types of Dislocations
1. Edge Dislocation
2. Screw Dislocation

40. Edge Dislocation
• When a crystalographic plane ends abruptly
inside the grain, its edge defines a defect
known as screw dislocation

42. Edge Dislocation

43. Dislocation

44. Burgers Vector
Burgers circuit round a dislocation A fails to
close when repeated in a perfect lattice unless completed by
a closure vector FS equal to the Burgers vector b.

45. Burgers Vector

46. Burgers Vector
• Burgers vector of an edge dislocation is
perpendicular to the dislocation line

47. The Edge Dislocations and Burger’s Vector
Looking along line direction of edge
Burger’s vector = extra step
• Edge looks like extra plane of atoms.
• Burger’s vector is perpendicular to line.
• Positive Edge (upper half plane)
Stress fields
at an Edge
dislocation
• Is there a Negative Edge?
• Where is it?
• What happens when edge gets to
surface of crystal?
• What are the stresses near edge?
47

48. Stress States around
an Edge Dislocation

49. Screw Dislocation
• When the crystallographic planes spiral
around a line, the line defines a defect which
is known as Screw Dislocation

50. Screw Dislocation

51. Screw Dislocation

53. Screw Dislocation

54. Surface Defects

55. Types of Surface Defects
1. Stacking Fault
2. Grain Boundary
3. Twins

56. Stacking Faults
• It is the defect due to faulty stacking of planes.
• It occurs in FCC and HCP crystal structures
only

57. Stacking of planes in HCP
A plane
B plane
A plane

59. Stacking Fault

60. Stacking Faults: Messed up stacking
FCC
HCP
or C
slip
or C
• All defects cost energy (J/m2 or erg/cm2).
• Stress, dislocation motion can create Stacking Faults.
• What is stacking of FCC and HCP in terms of A,B, and C positions in (111) planes?
…ABCABCABC…
hcp
...ABCACABABCABC...
…….fcc
fcc ………..
60

61. Grain Boundary
• It is the boundary between two grains having
different orientations.

62. Grain Boundaries
Grain
Boundaries

63. Relative Energies of Grain Boundaries
Which GB is lower in energy, low-angle GB or high-angle GB?
Hint: compare number of reduced preferred bonds.
Why?
high-angle
• The grains affect properties
• mechanical,
• electrical, …
Grain I
• Recall they affect diffraction so you
know they’re there.
• What should happen to grains
as temperature increases?
Grain 2
Hint:
surfaces (interfaces) cost energy.
Grain 3
low-angle
63

64. Grain Boundary

65. Grain Boundry

67. Twins
• When two parts of a crystal become mirror
image of each other, the defect is known as
twins.

68. Twins

69. Twin Boundry

70. Twin Boundaries: an atomic mirror plane
original atomic positions
before twinning
• There has to be another opposite twin nearby to get back to perfect crystal,
because all defects cost energy (J/m2 or erg/cm2) and to much defect costly.
• Stress twins can be created (e.g., Tin) in which case the atoms must move
at the speed of sound.
What happens when something moves at speed of sound?
70

71. THANKS