Metallurgy MMS Module 1 and 2
Metallurgy MMS Module 1 and 2
Metallurgy MMS Module 1 and 2
Module 1
Prince Mattom
Mechanical Engg. Dept
Crystal Structure
Solid materials can be classified according to the regularity with which
atoms are arranged.
Only 14 possible types of space lattices (Bravis lattices) and they fall
in 7 crystal systems
Total = 6 atoms
Coordination Number
In BCC coordination no is 8
In FCC coordination no is 12
In HCP coordination no is 12
Atomic Radius (r)
It is defined as half the distance between the nearest neighbours in the crystal
structure. It is expressed in terms of cube edge a.
the cube edge length a and the atomic radius R
a) Simple cubic lattice
One atom is there at each of the corners of a cube.
r = a/2
(4 r)2 = a2 + a2
16 r2 = 2 a2
r = 2 a
4
c) HCP lattice
Atomic Packing Factor (APF)
The APF is defined as the fraction of solid sphere volume in a unit cell, or
Class assignment
POINT COORDINATES
The position of any point located within a unit cell may be
specified in terms of its coordinates as fractional multiples of
the unit cell edge lengths.
Any two planes parallel to each other are equivalent and have identical
indices.
1. If the plane passes through the selected origin, either another parallel
plane must be constructed within the unit cell by an appropriate
translation, or a new origin must be established at the corner of another
unit cell.
by fracture
by yielding
Stress strain behaviour
Here some atoms are said to have slipped past the other
atoms on a certain plane in a certain direction.
For face-centered cubic, there are 12 slip systems: four unique {111} planes and,
within each plane, three independent <110> directions.
(a) A {111} <110> slip system shown within an FCC unit cell. (b) The (111) plane from
(a) and three <110> slip directions (as indicated by arrows) within that plane comprise
possible slip systems.
Slip Systems for Face-Centered Cubic, Body-centered Cubic, and
Hexagonal Close-Packed Metals
Even though an applied stress may
be pure tensile (or compressive),
shear components exist at all but
parallel or perpendicular alignments
to the stress direction. These are
termed resolved shear stresses
Inclination of the normal to slip plane
with the applied force be .
r = cos cos
open circles represent atoms that did not move, and dashed and solid circles represent
original and final positions, respectively, of atoms within the twinned region.
Mechanical twinning occurs in metals that have BCC and
HCP crystal structures
at low temperatures,
and at high rates of loading (shock loading), conditions
under which the slip process is restricted
(few operable slip systems)
Mechanical twinning occurs in metals that have BCC and HCP crystal structures, at
low temperatures, and at high rates of loading (shock loading), conditions under
which the slip process is restricted; that is, there are few operable slip systems.
The amount of bulk plastic deformation from twinning is
normally small relative to that resulting from slip.
Volume defects
I. Point defects localised imperfections
a) Vacancy
formed when atoms are missing from a lattice leaving a hole
The number of
vacancies increases
exponentially with
temperature
may be created by
local disturbances during the crystal growth
thermal vibrations causing individual atoms to jump
atomic arrangements in an existing crystal
plastic deformation, rapid cooling
bombardment with energetic particles
b) Substitutional
Alloying elements can dissolve in 2 ways
replace or substitute host atoms in the lattice
(1) vacancy;
(2) self-interstitial;
(3) interstitial impurity;
(4,5) substitutional impurities
Cations are generally the smaller ions, it is possible for them to get
displaced into the void spaces. (generally anions do not get displaced)
it is only during the passage of the extra half plane that the
lattice structure is disrupted.
Note that for an edge, the dislocation line moves in the direction of the
applied shear stress or parallel to the direction of the applied shear stress
Glide of
an Edge
Dislocation
Glide of crss
an Edge
Dislocation
crss is
critical
resolved
shear
stress on
the slip
plane in
the
direction
crss of b.
Glide of crss
an Edge
Dislocation
crss is
critical
resolved
shear
stress on
the slip
plane in
the
direction
crss of b.
Glide of crss
an Edge
Dislocation
crss is
critical
resolved
shear
stress on
the slip
plane in
the
direction
crss of b.
Glide of crss
an Edge
Dislocation
crss is
critical
resolved
shear
stress on
the slip
plane in
the
direction
crss of b.
Glide of crss
an Edge
Dislocation
A surface
step of b
is created
if a Surface
dislocation
step, not a
sweeps
over the dislocation
entire slip
plane
crss
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
Burgers vector
b Slip plane
slip no slip
1 2 3 4 5 6 7 8 9
Edge Dislocation
432 atoms
55 x 38 x 15 cm3
Dislocation Line:
A dislocation line is the boundary between
slip and no slip regions of a crystal
Burgers vector:
The magnitude and the direction of the
slip is represented by a vector b called
the Burgers vector,
Line vector
A unit vector t tangent to the dislocation
line is called a tangent vector or the line
vector.
S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
F 1
9
2
8
3
7 A closed
6 Burgers 4
5 Circuit in an 5
4 ideal crystal 6
7
3
8
2
1 9
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
F b
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
9 S 1
2
8
3
7
Map the same 4
6
5
Burgers circuit on a 5
4 real crystal 6
7
3
8
2
1 9
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
RHFS convention
b is a lattice translation
Surface defect
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Elastic strain field associated with an
edge dislocation
N+1 planes
Compression
Above the slip plane
Tension
Below the slip plane
N planes
A dislocation line cannot end
abruptly inside a crystal
T
F
Screw dislocation
formed by applying a shear stress (upward and downward ) that is
applied to a perfect crystal to produce the distortion that have been
separated by a cutting plane
The upper front region of the crystal is shifted one atomic distance
to the right relative to the bottom portion.
b
b || t
3
2
1
Screw Dislocation (another view)
Positive Negative
Left-handed Right-handed
spiral ramp spiral ramp
Screw
Dislocation b parallel to t b antiparallel to t
most dislocations are of the mixed type
Movement of dislocations or displacement distance of atoms
around the dislocation : Slip or Burgers vector
This transition zone that is not aligned with either of the grains
is known as grain boundary
There is a grain boundary energy similar to the surface energy.
Cross slip can occur only with screw dislocation because a screw
dislocation only can shift to different intersecting slip planes.
(edge dislocations can move along parallel slip planes only)
An edge dislocation can move out of its slip plane to another parallel
slip plane just above or below it.
But, the screw dislocation can slip on any plane which contains
the dislocation line and Burgers vector.
Jogs and Kinks
As these dislocations are in the same crystal, the slip planes are
represented together in fig (c).
When the dislocation AB moves down, it intersects with the
other dislocation CD upon crossing the slip plane WXYZ.
The jog JJ also is having the features of edge dislocation and slips
along with the dislocation CD.
When Burgers vectors of intersecting dislocations are parallel to
each other, jogs are formed on both the dislocations.
These jogs will lie on the original slip planes itself and they will
have features of screw dislocation.
The two slip planes are normal to each other, but the Burgers
vectors are parallel.
These kinks are unstable, because they can line up and annihilate
during further slip.
Forest of Dislocations
Nucleation
Homogeneous
Hetrogeneous
Nucleation involves the appearance of very small
particles, or nuclei of the solid phase (often consisting
of only a few hundred atoms), which are capable of
growing.
Such stable solid regions within the liquid are called Nuclei.
Subsequent to the formation of nuclei, release of heat of fusion
takes place and the temperature will be raised to the freezing
point again.
A cluster of radius less than the critical radius will shrink and
redissolve.
where Hf is the latent heat of fusion (i.e., the heat given up during
solidification)
Thus, both the critical radius r* and the activation free energy
G* decrease as temperature T decreases.
Schematic free energy-versus-embryo/nucleus radius curves for
two different temperatures.
This means that with a lowering of temperature at temperatures
below the equilibrium solidification temperature (Tm), nucleation
occurs more readily. Furthermore, the number of stable nuclei n*
(having radii greater than r*) is a function of temperature as
critical nucleus size mainly determined by GV
N=2 (n-1)
At this stage some of small grains, having favorable growth axis, start
to grow in the direction opposite to the direction of heat flow.
For many materials, the yield strength varies with grain size
according to Hall - Petch equation. (not valid for both very large
and extremely fine grain materials)
Note that the grain diameter increases from right to left and is not linear.
Diffusion
For an atom to move from its lattice site, two conditions are
to be satisfied :
(a) there must be an empty neighbouring site
(b) the atom must have sufficient energy to break bonds with
surrounding atoms
Vacancy Diffusion
Interstitial Diffusion
Interstitialcy Diffusion
Direct Interchange Diffusion
Vacancy Diffusion
J dC/dx or
=
Ficks second law. The time rate of change of concentration is
proportional to the second derivative of concentration. This
relationship is employed in nonsteady-state diffusion situations.