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 number and type of defects be varied
• How do defects affect material properties?
• Are defects undesirable?
TYPES of DEFECTS
Edges, Screws, Mixed
• Grain Boundaries
• Stacking Faults
• Anti-Phase and Twin Boundaries
We need to describe them and understand their effects.
Length Scale of Imperfections
point, line, planar, and volumetric defects
Grain and twin
• The defects which are confined to a point are
known as point defects
• Types of point defects
– Frankel defect
– Impurity atoms
• When an atom is missing from its regular
lattice site, it is known as VACANCY.
• Vacancies: vacant atomic sites in a structure.
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.
Thermodynamics provides an expression for
Vacancy Concentration: CV =
= exp − v
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!
Equilibrium Concentration of Vacancy
• Equilibrium concentration varies with temperature!
No. of defects
No. of potential
(1.38 x 10-23 J/atom K)
(8.62 x 10 -5 eV/atom K)
Each lattice site
is a potential
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
= 2.7 · 10-4
For 1m3, N =
8.62 x 10-5 eV/atom-K
x 1m3 = 8.0 x 1028 sites
• 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
Equilibrium concentration of vacancies as a
function of temperature for aluminium (after Bradshaw and
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.
• It is a combination of vacancy and
• When an atom leaves its regular lattice site
and goes to an interstitial site, it is known as
• When atom of another element is present as
an impurity in the lattice of an element, it is
known as impurity atom.
• Impurity atoms can occupy any of the
– Interstitial position
– Substitutional position
• 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
• 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 like extra plane of atoms.
• Burger’s vector is perpendicular to line.
• Positive Edge (upper half plane)
at an Edge
• Is there a Negative Edge?
• Where is it?
• What happens when edge gets to
surface of crystal?
• What are the stresses near edge?
Stacking Faults: Messed up stacking
• 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?
• It is the boundary between two grains having
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.
• The grains affect properties
• electrical, …
• Recall they affect diffraction so you
know they’re there.
• What should happen to grains
as temperature increases?
surfaces (interfaces) cost energy.
Twin Boundaries: an atomic mirror plane
original atomic positions
• 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?