CRYSTAL IMPERFECTIONS
Dr. H. K. Khaira
Professor and HoD
MSME Deptt., MANIT, Bhopal
Chpt 5: Imperfections in Solids
ISSUES TO ADDRESS...
• What types of defects arise in solids? Describe them.
• Can the num...
TYPES of DEFECTS
TYPES of DEFECTS
•
•
•
•
•

Vacancy atoms
Interstitial atoms
Frankel defect
Impurity atoms
Dislocations

Point defects
Lin...
Length Scale of Imperfections
point, line, planar, and volumetric defects
Vacancies,
impurities
dislocations

Grain and tw...
Point Defects
• The defects which are confined to a point are
known as point defects
• Types of point defects
– Vacancy
– ...
Vacancy
• When an atom is missing from its regular
lattice site, it is known as VACANCY.
Vacancy
• Vacancies: vacant atomic sites in a structure.

distortion
of planes

Vacancy

11
Vacancy and Distortion of planes
Vacancy

Vacancy: a vacant lattice site
It is not possible to create a crystal free of vacancies.
About 1 out of 10,000 si...
Vacancy

Thermodynamics provides an expression for
Vacancy Concentration: CV =

 Q 
Nv
= exp  − v 
N
 k BT 

CV = Co...
Equilibrium Concentration of Vacancy
• Equilibrium concentration varies with temperature!
No. of defects
Cd=

Activation e...
Estimating Vacancy Concentration
• Find the equil. # of vacancies in 1m 3of Cu at 1000C.
• Given: ρ = 8.4 g/cm3
ACu = 63.5...
Equilibrium concentration of vacancies as a
function of temperature for aluminium (after Bradshaw and
Pearson, 1957).
Interstitialcy
Interstitialcy

distortion
of planes

selfinterstitial

• Self-Interstitials: "extra" atoms in between atomic sites.

19
Interstitialcy
• When an atom is present at an interstitial
position in its lattice, it is known as
interstitialcy.
• In t...
Self Interstitialcy and Distortion of
planes
Interstitialcy
Self-interstitial: atom crowded in ‘holes’

Self-interstitials are much less likely in metals, e.g.,,
as it...
Frenkel Defect
• It is a combination of vacancy and
interstitialcy defects.
• When an atom leaves its regular lattice site...
Impurity Atom
• When atom of another element is present as
an impurity in the lattice of an element, it is
known as impuri...
Impurity Atom
• Impurity atoms can occupy any of the
following position
– Interstitial position
– Substitutional position
Impurity Atom
• Types of Impurity Atom
– Interstitial Impurity Atom
• When impurity atom is present at an interstitial sit...
Impurity Atom
Interstitial Impurity in FCC
Interstitial impurity C in α-Fe. The C atom is small
enough to fit, after introducing some strain into the BCC
lattice.
VOIDS

BCC
Distorted TETRAHEDRAL

Distorted OCTAHEDRAL**

a√3/2

a
a

a√3/2

rvoid / ratom = 0.29
Note: Atoms are coloured...
Interstitial Impurity in FCC
Interstitial Impurity in FCC
Substitutional Impurity
Substitutional impurity and
distortion of planes
Point Defects
Point Defects
Line Defects
Or

Dislocations
Types of Dislocations

1. Edge Dislocation
2. Screw Dislocation
Edge Dislocation
• When a crystalographic plane ends abruptly
inside the grain, its edge defines a defect
known as screw d...
Edge Dislocation
Dislocation
Burgers Vector

Burgers circuit round a dislocation A fails to
close when repeated in a perfect lattice unless completed b...
Burgers Vector
Burgers Vector
• Burgers vector of an edge dislocation is
perpendicular to the dislocation line
The Edge Dislocations and Burger’s Vector
Looking along line direction of edge
Burger’s vector = extra step

• Edge looks ...
Stress States around
an Edge Dislocation
Screw Dislocation
• When the crystallographic planes spiral
around a line, the line defines a defect which
is known as Scr...
Screw Dislocation
Screw Dislocation
Screw Dislocation
Surface Defects
Types of Surface Defects
1. Stacking Fault
2. Grain Boundary
3. Twins
Stacking Faults
• It is the defect due to faulty stacking of planes.
• It occurs in FCC and HCP crystal structures
only
Stacking of planes in HCP

A plane
B plane
A plane
Stacking Fault
Stacking Faults: Messed up stacking
FCC

HCP

or C

slip

or C

• All defects cost energy (J/m2 or erg/cm2).
• Stress, dis...
Grain Boundary
• It is the boundary between two grains having
different orientations.
Grain Boundaries

Grain
Boundaries
Relative Energies of Grain Boundaries
Which GB is lower in energy, low-angle GB or high-angle GB?
Hint: compare number of ...
Grain Boundary
Grain Boundry
Twins
• When two parts of a crystal become mirror
image of each other, the defect is known as
twins.
Twins
Twin Boundry
Twin Boundaries: an atomic mirror plane

original atomic positions
before twinning

• There has to be another opposite twi...
THANKS
crysta limperfactions
crysta limperfactions
crysta limperfactions
crysta limperfactions
crysta limperfactions
crysta limperfactions
crysta limperfactions
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crysta limperfactions

  1. 1. CRYSTAL IMPERFECTIONS Dr. H. K. Khaira Professor and HoD MSME Deptt., MANIT, Bhopal
  2. 2. 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
  3. 3. TYPES of DEFECTS
  4. 4. 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
  5. 5. Length Scale of Imperfections point, line, planar, and volumetric defects Vacancies, impurities dislocations Grain and twin boundaries Voids Inclusions precipitates 8
  6. 6. 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
  7. 7. Vacancy • When an atom is missing from its regular lattice site, it is known as VACANCY.
  8. 8. Vacancy • Vacancies: vacant atomic sites in a structure. distortion of planes Vacancy 11
  9. 9. Vacancy and Distortion of planes
  10. 10. 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
  11. 11. 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
  12. 12. 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
  13. 13. 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
  14. 14. Equilibrium concentration of vacancies as a function of temperature for aluminium (after Bradshaw and Pearson, 1957).
  15. 15. Interstitialcy
  16. 16. Interstitialcy distortion of planes selfinterstitial • Self-Interstitials: "extra" atoms in between atomic sites. 19
  17. 17. 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.
  18. 18. Self Interstitialcy and Distortion of planes
  19. 19. 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
  20. 20. 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.
  21. 21. Impurity Atom • When atom of another element is present as an impurity in the lattice of an element, it is known as impurity atom.
  22. 22. Impurity Atom • Impurity atoms can occupy any of the following position – Interstitial position – Substitutional position
  23. 23. 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.
  24. 24. Impurity Atom
  25. 25. Interstitial Impurity in FCC
  26. 26. Interstitial impurity C in α-Fe. The C atom is small enough to fit, after introducing some strain into the BCC lattice.
  27. 27. 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
  28. 28. Interstitial Impurity in FCC
  29. 29. Interstitial Impurity in FCC
  30. 30. Substitutional Impurity
  31. 31. Substitutional impurity and distortion of planes
  32. 32. Point Defects
  33. 33. Point Defects
  34. 34. Line Defects Or Dislocations
  35. 35. Types of Dislocations 1. Edge Dislocation 2. Screw Dislocation
  36. 36. Edge Dislocation • When a crystalographic plane ends abruptly inside the grain, its edge defines a defect known as screw dislocation
  37. 37. Edge Dislocation
  38. 38. Dislocation
  39. 39. 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.
  40. 40. Burgers Vector
  41. 41. Burgers Vector • Burgers vector of an edge dislocation is perpendicular to the dislocation line
  42. 42. 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
  43. 43. Stress States around an Edge Dislocation
  44. 44. Screw Dislocation • When the crystallographic planes spiral around a line, the line defines a defect which is known as Screw Dislocation
  45. 45. Screw Dislocation
  46. 46. Screw Dislocation
  47. 47. Screw Dislocation
  48. 48. Surface Defects
  49. 49. Types of Surface Defects 1. Stacking Fault 2. Grain Boundary 3. Twins
  50. 50. Stacking Faults • It is the defect due to faulty stacking of planes. • It occurs in FCC and HCP crystal structures only
  51. 51. Stacking of planes in HCP A plane B plane A plane
  52. 52. Stacking Fault
  53. 53. 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
  54. 54. Grain Boundary • It is the boundary between two grains having different orientations.
  55. 55. Grain Boundaries Grain Boundaries
  56. 56. 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
  57. 57. Grain Boundary
  58. 58. Grain Boundry
  59. 59. Twins • When two parts of a crystal become mirror image of each other, the defect is known as twins.
  60. 60. Twins
  61. 61. Twin Boundry
  62. 62. 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
  63. 63. THANKS
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