metallurgy iit bombay

1. Numerical questions by individual members
Aakash Patel
1. Explain Burger Vector and its relation edge and screw dislocation. Give burger vector for
fcc,bcc and hcp.
Ans. The magnitude and direction of the lattice distortion associated with a dislocation is
expressed in terms of a Burgers vector, denoted by a b. Burger vector gives direction of motion
of dislocation in material.
Burger vector is perpendicular to edge dislocation and parallel with screw dislocation.
B(FCC)=a/2<110>
B(BCC)=a/2<111>
B(HCP)=a/3<11-20>
Deepak Dilipkumar
2. Calculate the approximate fraction of Schottky defects per cation/anion site, per unit volume
in common salt, at room temperature.
(Enthalpy of defect formation = 2.3 eV)
The formula for number of Schottky defects per unit volume is
n= N exp(-H/2kT)
H= 2.3 eV
k= Boltzmann constant = 1.38 * 10^-23
T= Room temperature = 300K
N= number of cation and anion sites per unit cell
Required fraction = n/N = exp(- 2.3*1.6*10^-19/2*1.38*10^-23*300) = 0.011744
VaibhavOjha
3. Consider a planar arrangement of atoms, such that there are rows of atoms stacked together
in an alternating fashion. For such an arrangement, what can be the maximum size of an
interstitial impurity that wont distort the lattice?
Ans–radius if atom = R and radius of interstitial atom = r.
We have, (r+R)*(cos(30deg)) = R
Which implies, r=R*((2-sqrt(3))/sqrt(3))

2. GirishChandani
A single crystal of zinc is oriented for a tensile test such that its slip plane normal makes an
angle of with the tensile axis. Three possible slip directions make angles of and with the same
tensile axis.
(a) Which of these three slip directions is most favored?
(b) If plastic deformation begins at a tensile stress of 2.5 MPa (355 psi), determine the critical
resolved shear stress for zinc.
Ans
We are asked to compute the critical resolved shear stress for Zn. As stipulated in the problem,
φ = °, hile possi le alues for λ are 0°, °, a d °.
(a) Slip ill o ur alo g that dire tio for hi h os φ os λ is a a i u , or, i this ase, for
the largest os λ. The osi es for the possi le λ alues are gi e elo .
cos(30°) = 0.87
cos(48°) = 0.67
cos(78°) = 0.21
Thus, the slip direction is at an angle of 30° with the tensile axis.
(b) From Equation (7.3), the critical resolved shear stress is just
τ rss=σ os φ os λ a
= (2.5 MPa)cos(65°)cos(30°)[]= 0.90 MPa (130 psi)
Alan John
Q) Why is that the x-axis of the Fe-C phase diagram goes only upto 6.7%? Also show the
derivation of how 6.7% is obtained?
Ans) In a steel alloy you cannot add carbon to the iron as much as you want. Because the
carbon present in the alloy is not in its elemental form but as a compound Fe3C. As you keep on
adding more carbon you will reach a limit where the entire mixture is formed of Fe3C.
The maximum % of Carbon content= %of carbon when the mixture has maximum Fe3C content.
Maximum Fe3C content= 100% of the mixture.
Molwt of Fe=56
So % of Carbon when the entire mixture is Fe3c= (Molwt of Carbon)/(molwt of Fe3C)*100
=( 12*1)/(56*3+12*1)*100
=6.7%

3. One Group Question
1. Name the four types of Volume defects. Arrange them in order of their sizes, and
classify them based on their effect (positive,negative) on material properties.
Precipitates<Dispersants< (Inclusions,Voids)
Precipitates and dispersants enhance the required mechanical properties of the
material. Inclusions and voids however, are detrimental to mechanical, and often,
electrical properties. They promote failure at small loads.
2. Briefly describe different strengthening mechanisms.
 Grain size reduction - Grain size or average grain diameter can influence the
mechanical properties of a material.Different orientation between two grains
hinders dislocation motionAtomic disorder within a grain boundary region results in
discontinuity of slip planes from one grain into the other.
 Solid solution strengthening - Alloys are stronger than pure metals because impurity
atoms that go into solid solution ordinarily impose lattice strains on the surrounding
host atoms. Lattice strain field interactions between dislocations and these impurity
atoms restrict dislocation movement. In this situation, a greater stress is required for
plastic deformation.
 Strain hardening - Phenomenon whereby a ductile metal becomes harder and
stronger as it is plastically deformeddislocation density increases with deformation
or cold work. On the average, dislocation–dislocation strain interactions are
repulsive. The net result is that the motion of a dislocation is hindered by the
presence of other dislocations.
 Precipitation hardening - also called age hardening, is a heat treatment technique
used to increase the yield strength of malleable materials. First an alloy of required
composition is made and heated to particular temperature where it exists in some
phase. It is in its natural phase. If this is cooled suddenly then there would be phase
change but there is no time for atoms to separate. This would result in a super
saturated solid-solution. Then the precipitate starts forming and strengthens the
material. In course of time the atoms slowly diffuses and the material weakens. This
is called "agi g“

4. 3. Explain recovery, recrystallization and grain growth.
 Recovery - increase in atomic diffusion occurs that relieves some of the internal
strain energy, atoms recover a normal position in the lattice structure at elevated
temperature, reduction in the dislocation density and a movement of dislocation to
lower-energy positions, no appreciable reduction in the strength and hardness of
the material but corrosion resistance often improves.
 Recrystallization - new, strain-free grains nucleate and grow inside the old distorted
grains and at the grain boundaries, mechanical properties return to their original
states, size the new grains is also partially dependent on the amount of strain
hardening
 Growth - the larger grains lose fewer atoms and grow at the expense of the smaller
grains, larger grains will reduce the strength and toughness of the material.
4. Differentiate between frankel and schottky defect.
Frankel defect - a pair of anion and cation is missing, density decreases and the lattice
remains electrically neutral.
Schottky defect - a cation is displaced from its position, density remains the same and
lattice is electrically neutral.
5. Explain the relationship between dislocation line and burgers vector for screw, edge and
mixed dislocations, also giving the dislocation energy formula.
For a screw dislocation, the dislocation line is perpendicular to the burgers vector, and
energy is given byGb^2/2
For an edge dislocation, the dislocation line is parallel to the burgers vector, amd energy
is given by Gb^2/2*(1-v)
For mixed dislocation, the burgers vector is inclined to the dislocation line at varying
angles.
6. What are the four types of point defects?
1. Self interstitial- An atom of the same element is present in an interstitial site of the
lattice
2. Vacancy- An atom is missing from its expected position in the crystal
3. Substitutional Impurity- An atom of another element replaces an atom of the lattice
at a point
4. Interstitial Impurity- An atom of another element is present in an interstitial site of
the lattice

5. 7. What is twinning? Mention the two types of twinning, and give a brief description of
each. Twinning is the phenomenon wherein atoms on one side of a particular plane are
present in mirror image positions with respect to atoms on the other side.
The two types are:
1. stress. It is common in BCC and HCP crystals
2. Annealing Twinning: This type of twinning occurs on application of stress after
heating to a high temperature. It is common in FCC crystals.