This document discusses various types of crystal imperfections or defects. It describes point defects like vacancies, interstitials, and substitutions that involve missing or extra atoms at atomic sites. Line defects called dislocations are also covered, including edge dislocations formed by the insertion of an extra half plane of atoms, and screw dislocations where there is a spiral distortion of crystal planes. These defects influence material properties, for example increasing strength. Dislocations also enable plastic deformation through slip along crystal planes.

1. ME F213
Materials Science and
Engineering
CRYSTAL IMPERFECTIONS

2. Defects
• Defects are deviation from ideal crystal structure.
• Materials not considered defective from application
viewpoint.
• Defects have profound effect on the properties of
materials.
• Some defects are created intentionally.
• Defects can be desirable or undesirable.
– Dislocations are useful in increasing the strength of metals
and alloys.
– But a dislocation in silicon crystal is undesirable.

3. Defects ‐ Advantages
• Pure iron is soft but plain carbon steel exhibits high
strength.
• Crystal of pure alumina is transparent and colorless
but when chromium is added it creates ruby crystal.
• Addition of P or B atoms to Si impart special
electrical properties .

4. Defects ‐ Disadvantages
• Small concentration of elements on pure metal will
lower its electrical conductivity
• Grain boundaries creates resistance to current flow

5. Point Defect
• Localized disruptions – involving a region of several
atoms or ions.
• Causes:
– Due to imperfect packing of atoms during crystallisation.
– Due to vibrations of atoms at high temperatures.
– By quenching (quick cooling) from a higher temperature.
– By severe deformation of the crystal lattice ‐ hammering or
rolling.
– By external bombardment by atoms or high energy
particles, e.g. from the beam of cyclotron or neutrons in a
nuclear reactor.
• Although defect occurs at one or two sites still their
presence is felt over much larger distance.
• Point defects are always present in crystals and their
present results in a decrease in the free energy.

6. Point Defect

7. Radiation Damage
Seeger model of damage produced by
irradiation. P indicates the position where
the first “knock-on” terminates.
(Reprinted with permission from
A. Seeger, in Proc. Symp. Radiat.
Damage Solids React., Vol. 1,
(Vienna, IAEA, 1962) pp. 101, 105.)
Voids formed in nickel irradiated using 400
keV 14N2+ ions to a dose of 40 dpa at 500 ◦C;
notice the voids with polyhedral shape; dpa
= displacements per atom. (Courtesy of L. J.
Chen and A. J. Ardell.)

8. Vacancy
• Simplest point defect is a vacancy.
• Refers to an empty (unoccupied) site of a crystal lattice,
i.e. a missing atom or vacant atomic site
• When the thermal energy due to vibration is increased,
there is always an increased probability that individual
atoms will jump out of their positions of lowest energy.
• Each temperature has a corresponding equilibrium
concentration of vacancies.

9. Vacancy
• For instance, copper can contain 10E–13 atomic
percentage of vacancies at a temperature of 20–25°C and
as many as 0.01% at near the melting point (one vacancy
per 10E4 atoms).
• For most crystals the said thermal energy is of the order
of 1eV per vacancy.
• The vacancies may be single or two or more of them may
condense into a di‐vacancy or trivacancy.

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

11. Vacancy
• The atoms surrounding a vacancy tend to be closer
together, thereby distorting the lattice planes.
• At thermal equilibrium, vacancies exist in a certain
proportion in a crystal and thereby leading to an increase
in randomness of the structure.
• At higher temperatures, vacancies have a higher
concentration and can move from one site to another
more frequently.
• Vacancies are the most important kind of point defects;
they accelerate all processes associated with
displacements of atoms: diffusion, powder sintering, etc.

12. Arrhenius Behaviour
• Equilibrium concentration varies with temperature
No. of defects Activation energy
N
N k T
 Q v 
 

No. of potential
v  exp 
defect sites.
Boltzmann's constant
(1.38 x 10 ‐23 J/atom‐K)
Temperature
(8.62 x 10‐5 eV/atom‐K)
Each lattice site
is a potential
vacancy site

13. Measuring Activation Energy
• We can get Q from N  Q 
v
N k T
 
v = exp  v 
an experiment.
• Measure this... • Replot it...
slope
Nv
N
exponential
Nv
ln N
‐Qv /k
T
dependence!
1/T
defect concentration

14. Estimating Vacancy Concentration
• Find the equil. # of vacancies in 1 m3 of Cu at 1000C.
• Given:
 = 8.4 g /cm3
Qv = 0.9 eV/atom
ACu = 63.5 g/mol
NA = 6.02 x 1023 atoms/mol
N  Q 0.9 eV/atom
 
 exp  v  = 2.7 x 10‐4
NA
1273K
8.62 x 10‐5 eV/atom‐K
v
N k T
For 1 m3 , N =  x x 1 m3 = 8.0 x 1028 sites
ACu
• Answer:
Nv = (2.7 x 10‐4)(8.0 x 1028) sites = 2.2 x 1025 vacancies

15. Interstitials
• Interstitial atom is an atom transferred from a site into an
interstitial position or voids (normally unoccupied positions).
• In a closed packed structure of atoms in a crystal if the atomic
packing factor is low, an extra atom may be lodged within the
crystal structure.
• An extra atom can enter the interstitial space or void between
the regularly positioned atoms only when it is substantially
smaller than the parent atoms otherwise it will produce
atomic distortion.
• Still interstitial atoms are larger than interstitial sites they
occupy.

16. Interstitials
• Self‐Interstitials:
‐"extra" atoms positioned between atomic sites.
self‐
interstitial
distortion
of planes

17. Interstitials
• In close packed structures, e.g. FCC and HCP, the largest
size of an atom that can fit in the interstitial void or space
have a radius about 22.5% of the radii of parent atoms.
• Interstitials may also be single interstitial, di‐interstitials,
and tri‐interstitials.
• Examples:
Hydrogen are often present as impurities
– Carbon (small concentrations) are intentionally added to iron to
produce steel
• Dislocations will face resistance to move because of
these type of defects – increases strength.
• Number of interstitial atoms remains constant with
temperature.

18. Interstitials 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 solid soln. Interstitial solid soln.
(e.g., Cu in Ni) (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.

19. Substitutional Defect
• Whenever a foreign atom replaces the parent atom of
the lattice and thus occupies the position of parent
atom the defect caused is called substitutional defect.
• Occupies the normal lattice site
• Atom which replaces the parent atom may be of same
size or slightly smaller or greater than that of parent
atom.
• Number of defects is relatively independent of
temperature.
• Will increase the strength of metallic materials.

20. Solid solution of nickel in copper shown along a (100)
plane. This is a substitutional solid solution with nickel
atoms substituting for copper atoms on fcc atom
sites.

21. Random, substitution solid solution can
occur in Ionic Crystalline materials as well.
Here of NiO in MgO. The O2− arrangement is
unaffected. The substitution occurs among
Ni2+ and Mg2+ ions.

22. Imperfections in Solids
Conditions for substitutional solid solution
• 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 equality
• All else being equal, a metal will have a greater tendency to
dissolve a metal of higher valency than one of lower valency
(it provides more electrons to the “cloud”)

23. Imperfections in Solids
Element Atomic
Radius
(nm)
Crystal
Structure
Electro‐
nega‐
tivity
Valence
Cu 0.1278 FCC 1.9 +2
C 0.071
H 0.046
O 0.060
Ag 0.1445 FCC 1.9 +1
Al 0.1431 FCC 1.5 +3
Co 0.1253 HCP 1.8 +2
Cr 0.1249 BCC 1.6 +3
Fe 0.1241 BCC 1.8 +2
Ni 0.1246 FCC 1.8 +2
Pd 0.1376 FCC 2.2 +2
Zn 0.1332 HCP 1.6 +2
Application of Hume–Rothery rules – Solid Solutions
1. Would you
predict more Al or
Ag
to dissolve in Zn?
More Al because size is closer and val. Is
higher – but not too much because of
structural differences – FCC in HCP
2. More Zn or
Al in Cu?
Surely Zn since size is closer thus causing
lower distortion (4% vs 12%)
Table on p. 106, Callister 7e.

24. Defects in Ceramic Structures
• Frenkel Defect
‐‐a cation is out of place.
• Shottky Defect
‐‐a paired set of cation and anion vacancies.
from W.G. Moffatt, G.W. Pearsall,
and J. Wulff, The Structure and
Shottky
Defect:
Properties of Materials, Vol. 1,
Structure, John Wiley and Sons,
Inc., p. 78.
Frenkel
Defect
• Equilibrium concentration of defects ~ eQD / kT

25. Frenkel Defect
•
vacancy occupies an interstitial site (responsible
Whenever a missing atom, which is responsible for
for
interstitial defect) the defect caused is known as Frenkel
defect.
• Frenkel defect is a combination of vacancy and interstitial
defects.
• These defects are less in number because energy is
required to force an ion into new position.
• This type of imperfection is more common in ionic
crystals, because the positive ions, being smaller in size,
get lodged easily in the interstitial positions.

26. Schottky Defect
• Unique to ionic materials and commonly found in
ceramic materials.
• These imperfections are similar to vacancies.
• Caused whenever a pair of positive and negative ions is
missing from a crystal.
• This type of imperfection maintains a charge neutrality.
• For example one Mg2+ and one O2− missing in MgO
constitute a defect.

27. Rules for ionic solids
• Charge balance must be maintained so the crystalline
material is electrically neutral.
• Mass balance must be maintained.
• Number of crystallographic sites must be conserved.

28. Frenkel Defect

29. Phonon
• When the temperature is raised, thermal
vibrations takes place.
• This results in the defect of a symmetry and
deviation in shape of atoms.
• This defect has much effect on the magnetic
and electric properties.

30. Properties change
• All kinds of point defects distort the crystal lattice and
have a certain influence on the physical properties.
• In commercially pure metals, point defects, increase
the electric resistance and have almost no effect on the
mechanical properties.
• Only at high concentrations of defects in irradiated
metals, the ductility and other properties are reduced
noticeably.

31. Dislocation
• Line imperfections are called dislocations.
• Introduced typically during solidification of material or when
the material is deformed plastically.
• Most important kinds of linear defects:
– Edge dislocation
– screw dislocation
– Mixed dislocation
• These defects are the most striking imperfections and are
responsible for the useful property in metals, ceramics and
crystalline polymers.

32. Line Defects
Are called Dislocations:
And:
• Slip between crystal planes result when dislocations move,
• This motion produces permanent (plastic) deformation.
Schematic of Zinc (HCP):
• before deformation • after tensile elongation
slip steps which are
the physical evidence
of large numbers of
dislocations slipping
along the close
packed plane {0001}
Adapted from Fig. 7.8, Callister 7e.

33. Edge and Screw Dislocations
(a) Perfect crystal.
(b) Edge dislocation.
(c) Screw dislocation.

34. Edge Dislocation
• Dislocation is formed by adding an extra partial plane of
atoms to the crystal.
• Illustrated by slicing part away through a perfect crystal,
spreading the crystal apart and partially filling the cut
with extra plane of atoms.
• Bottom edge of inserted plane represent dislocation line.
• Edge dislocation in its cross‐section is essentially the
edge of an ‘extra’ half‐plane in the crystal lattice.
• The lattice around dislocation is elastically distorted.

36. Edge Dislocation
• When an extra half plane is inserted from the top, the
displacement of atoms happens and the defects so
produced is represented by (inverted tee) and if the
extra half plane is inserted from the bottom, the defects
so produced is represented by T (Tee).
• The crystal above and below the line XY appears perfect.
Before After

38. Line Defects
(a) Rug with a fold.
Caterpillar with a hump.

39. Burgers vector
• Near the dislocation, the distortion is due to the presence of
zones of compression and tension in the crystal lattice.
• The lattice above the line of dislocation is in a state of
compression, whereas below this line, it is in tension.
• The dislocation line is a region of higher energy than the rest
of the crystal.
• The criterion of distortion is what is called the Burgers vector.
Burger’s vector, b:
• a measure of
lattice distortion
and
• measured as a
distance along the
close packed
directions in lattice

40. Burgers vector
• It can be determined if a closed contour is drawn
around a zone in an ideal crystal by passing from one
site to another and then the procedure is repeated a
zone in a real crystal containing a dislocation.
• The contour described in real crystal turns out to be
unclosed.
• The vector required for the closing the contour is the
Burgers vector.
• The Burger vector of an edge dislocation is equal to
the interatomic space and perpendicular to the
dislocation line.

41. Screw Dislocation
• Here the atoms are displaced in two separate planes
perpendicular to each other.
• Illustrated by cutting part away through a perfect crystal
and skewing the crystal by one atom spacing.
• The arrangement of atoms in screw dislocations appear
like that of a screw or a helical surface.
• The axis or line around which the path is traced is called
screw dislocation line.

42. Screw dislocation. The spiral stacking of crystal planes leads to the
Burgers vector being parallel to the dislocation line.

43. Before After

45. Screw Dislocation
Burgers vector b
Dislocation
line
b
(b)
(a)
Adapted from Fig. 4.4, Callister 7e.

46. Screw Dislocation
• Effects of screw dislocation
(i) The force required to form and move a screw dislocation is
somewhat greater than that required to initiate an edge
dislocation.
(ii) Without breaking the continuity of the lattice, the plastic
deformation is possible under low stress.
(iii) Screw dislocation causes distortion of the crystal lattice for a
considerable distance from the centre of the line and takes the
form of spiral distortion of the planes.

47. Linear Defects (Dislocations)
– Are one‐dimensional defects around which atoms are misaligned
• Edge dislocation:
– extra half‐plane of atoms inserted in a crystal structure
– b (the berger’s vector) is  (perpendicular) to dislocation line
• Screw dislocation:
– spiral planar ramp resulting from shear deformation
– b is  (parallel) to dislocation line

48. Mixed Dislocation
• Dislocations of both types, i.e., combinations of edge and screw, are
closely associated with the crystallization as well as deformation.
This dislocation has both edge and screw character with a single
Burgers vector consistent with the pure edge and pure screw
regions.

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

50. Thanks