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Ph.D. Admission 20XX Semester XWritten Examination

Materials Science & Engineering Department, IIT Kanpur

Date of Examination: XX, 20XX

Duration: 1 hour

Application# __________________

Maximum Points: 60 Please read these instructions carefully

Any unauthorised materials, such as books, paper, documents and electronic devices with communication and/or storage capabilities are not to be brought into the examination hall.

Handphones brought into the examination hall must be switched off at ALL times. Do NOT turn over the question paper placed on your desk until instructed to do so at the

time of commencement of the examination. You are not allowed to communicate by word of mouth or otherwise with another

candidate. Please raise your hand if you wish to communicate with an invigilator. Unless granted

permission by an invigilator, you are not allowed to leave your seat. Once you have entered the examination hall, you will not be allowed to leave the hall until

the end of examination. Do NOT continue to write after the examination has ended. You are to remain seated

quietly while your answer scripts are being collected and counted.

Type of Examination

Closed Book: No reference materials, in whatever format, are allowed. Calculators are allowed in the examination. However, memory should be cleared, prior

to examination. A candidate who is suspected of cheating in examination is liable to disciplinary action

including expulsion from the examination hall.

Paper Structure

The question paper consists of a total of 15 PAGES (including this page). This paper consists of FOUR SECTIONS, viz. A, B, C and D. All sections carry equal points. NO NEGATIVE MARKING SECTIONS A AND B are COMPULSORY while candidate has an option to CHOOSE

EITHER C OR D SECTION. Use the back side of the paper for the rough work.

Ph.D. Admission 20XX Semester X MSE Department IIT Kanpur XX, 20XX

For Examiner’s purpose only

Section Points

A (Aptitude and Mathematics)B (Fundamentals of Metallurgical and

Materials Engineering)C (Electronic Properties of Materials)

D (Mechanical Properties of Materials)

TOTAL

Fundamentals of Metallurgy and Materials include Thermodynamics, Kinetics, Physical Metallurgy and Process Metallurgy

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Ph.D. Admission 20XX Semester XX MSE Department IIT Kanpur Section A

SECTION A

(Aptitude and Mathematics)

1. Ben is rich but Jim is richer. Mike is poorer than Jim. Who is the richest? (2 marks)

(a) Mike(b) Jim(c) Ben(d) All are equally rich

2. A plane descends from 35000 ft at 9:20 am to 17500 ft at 9:34 am. The plane had a constant descend rate till 17,500 ft. If the plane descends at three times that rate from 17,500 ft to 2,500 ft, then what time will the plane reach 2,500 ft? (2 marks)(a) 9:38 am(b) 9:40 am(c) 9:45 am(d) 9:46 am

3. The evening before sunset Rekha and Hema were talking to each other face to face. If Hema's shadow was exactly to the right of Hema, which direction was Rekha facing?

(2 marks)(a) North(b) South(c) East(d) Data is inadequate

4. A speed of bus between stops is 54 km/hour. On including stoppages, the average speed is 45 km/hour. For how many minutes does the bus stop per hour? (2 marks)

(a) 9(b) 10(c) 12(d) 20

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5. What is the probability of selecting a black card or a 6 from a deck of 52 cards. (Hint: There are 26 black cards and 26 red cards in a deck. There are total of four ‘6’ in a deck of 52 cards, out of which two are red and two are black). (2 marks)

(a) 4/13(b) 5/13(c) 7/13(d) 15/26

6. If an inscribed rectangle, inside a circle of unit radius, has the maximum possible perimeter then the area of the rectangle is: (2 marks)

(a) 1(b) √2(c) √3(d) 2

7. Find the angle between the line parallel to the vector 2i-j and the plane given by the vector equation 3x+4z=5. (2 marks)

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8. Plot y= 1−x1−x2 with x varying from - to +. (2

marks)

9. Find the minima of the function y=x3−3 x2−9x+15. (2 marks)

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10. You find that a cup of coffee (initially at 90 ºC) is too hot to drink. For drinking coffee, a temperature of 60 ºC is comfortable. Hence, you leave it on a table for cooling. How long (in minutes) you will have to wait before you can drink the coffee? Assume that the cooling rate follows the Newton’s law of cooling, given by the following differential equation: (2 marks)

dTdt

=−0.05(T−25)

T = instantaneous temperature in ºCt = time in minutes

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Ph.D. Admission 20XX Semester XX MSE Department IIT Kanpur Section B

SECTION B

(Fundamentals of Metallurgical and Materials Engineering)1. At 1 atm pressure, aluminum melts at 660 °C with a latent heat of fusion of 10.7

kJ/mol. Evaluate the entropy of fusion for aluminum at 1 atm. (2 marks)

(a) 17.8 J/mol-K(b) 11.5 J/mol-K(c) -17.8 J/mol-K(d) -11.5 J/mol-K

2. In a binary Cu-Ni alloy containing 30 at% Ni, the intrinsic diffusion coefficients of Cu and Ni are 8 x 10-15 and 2 x 10-15 m2/s. What is the value of interdiffusion coefficient at this composition? (2 marks)

3. Which of the following is correct inequality in terms of strength of a steel obtained in the process? (2 marks)

(a) Recrystallization > Recovery > Cold Work(b) Cold Work > Recrystallization > Recovery(c) Cold Work > Recovery > Recrystallization (d) Recovery > Recrystallization > Cold Work

4. What is the equilibrium pearlite fraction of 0.6 wt%C steel just below the eutectoid temperature, at which the equilibrium concentration of ferrite is 0.08 wt%C. The eutectoid point is 727°C and 0.8 wt%C. (2 marks)

(a) 90.1% (b) 27.8%(c) 72.2% (d) can not be determined

5. X-ray diffraction peak of a plane (h k l) of a pure FCC metal appears at 2θ = 43°. What must be certainly true about the indices h, k and l? (2 marks)

(a) The sum of h, k and l must be an even number(b) The sum of h, k and l must be an odd number

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(c) h, k and l must be either all odd or all even(d) h, k and l must be alternately odd and even in that order

6. In a microstructure of Ti-Nb alloy taken by backscatter electron (BSE) imaging on an SEM, the phase separation into a Ti-rich and Nb-rich phases was clearly observed. Phase α was observed to be dark and phase β was observed to be brighter. Which of the following statement must be true about the two phases α and β? (Atomic numbers of Ti and Nb are 22 and 41 respectively). (2 marks)

(a) α phase is richer in Ti and β phase is richer in Nb(b) β phase is richer in Ti and α phase is richer in Nb(c) Both phases are same in composition(d) None of the above

7. Vacancy concentrations in a pure metal were observed to be 7.64 x 10-7 and 7.26 x 10-

4 at 400 and 900 °C respectively. If the vibrational entropy of vacancy formation is not zero, what should be the enthalpy of formation of vacancy in this metal? (2 marks)

(a) 788 kJ/mol(b) 104 kJ/mol(c) 504 kJ/mol(d) 90 kJ/mol

8. During the end blow period in LD steelmaking, the de-carburization rate is expressed

by the equation:dCdt

=−(c−c¿) . Here, c and c* are the instantaneous and equilibrium

concentration of carbon in steel respectively, in units of wt.%. Given that c* =0.04 wt.% and c (t=0 min) = 0.4 wt.%, the concentration of carbon in steel (in wt.%) at t=1 min is _____________ (answer up to three decimal places) (2 marks)

9. A zinc electrowinning cell is being operated at a current of 400 A, voltage of 3.5 V, and a cathodic current efficiency of 90%. The specific energy consumption (in kJ.kg-1 zinc) is ________ (answer up to two decimal places)

(2 marks)

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10. A phase diagram of Al-Zn binary system, which is age-hardenable, is shown below. Which of the following combination of atom% Zn, solutionizing temperature and ageing temperature i.e. (at% Zn, Tsol, TAge) will provide proper ageing response?

(2 marks)

(a) (30%, 600 °C, 100 °C)(b) (30%, 200 °C, 600 °C)(c) (10%, 400 °C, 100 °C)(d) (10%, 100 °C, 500 °C)

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Al-Zn Phase Diagram

Ph.D. Admission 20XX Semester XX MSE Department IIT Kanpur Section C

SECTION C

(Electronic Properties of Materials)

1. Mass of electron: 9.1x10-31 kg2. 1 eV=1.6x10-19 J3. kBT=25 meV at room temperature4. Avogadro number: 6.023x1023

5. Density of Copper: 8.96 gm/cm3

6. Atomic weight of Copper: 63.54 gm/mol7. Fermi energy of Copper: 7 eV8. Charge of an electron: 1.6x10-19 C9. Planck's constant: 6x10-34 J.s10. Speed of light: 3x108 m/s11. Boltzmann constant: 1.38 x 10-23 J/K

1. In case of copper, assume electron relaxation time at room temperature to be 2x10-14 s. Calculate the number of free electrons per m3 and resistivity of copper in the unit of ohm m. (2 marks)

2. In case of copper, calculate the probability of occupancy of energy level E by an electron at room temperature for E=6.95 eV. (2 marks)

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3. Draw M vs. H curve for (a) diamagnetic, (b) paramagnetic and (c) ferromagnetic material (3 marks)

4. Match the physical phenomenon and governing law or parameter: (3 marks)

(i) Wiedemann-Franz law (a) Anti-ferromagnetism

(ii) Debye temperature (b) Thermoelectricity

(iii) Peltier effect (c) Thermal/electrical conductivity of metal

(iv) Neel temperature (d) Lattice specific heat

(i) -- (ii)-- (iii)-- (iv)--

5. In a neutral region of a forward -biased PN junction diode, the electron and hole current is due to: (2 marks)(a) Only drift

(b) Only diffusional

(c) Both drift and diffusion

6. For direct bandgap semiconductor (bandgap=3.5 eV), the smallest wavelength for which it remains transparent is equal to ________________ nm. (2 marks)

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7. Calculate the saturation magnetization for bcc iron of lattice parameter 2.866 Å.(2

marks)

8. In a metal 1 cm x 1 cm x 1 cm, the lowest energy free-electron has a wavelength of (2

marks)(a) 0.5 cm

(b) 1 cm

(c) 1.5 cm

(d) 2 cm

Answer:________________________________

9. The color of a metal is determined by the wavelength distribution of the radiation that is: (1 marks)(a) transmitted

(b)refracted

(c) reflected

(d) diffracted

Answer:_______________________________

10. Ionic polarization: (1

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marks)(a) decreases with temperature

(b) increases with temperature

(c) may increase or decrease with temperature

(d) is independent of temperature

Answer:______________________________

SECTION D

(Mechanical Properties of Materials)

I. Multiple Option Questions (Only one choice is correct): (4 X 1 marks)

1. The stress-strain plot for a material is given. Which of the following statement is true:

(a) Stress strain behavior is given by = Kεn

(b) Plastic strain is zero(c) Elastic strain is zero(d) There is no strain hardening in the material

2. Hydrostatic stress produces(a) Only elastic volume changes and not plastic deformation(b) Only plastic deformation and not elastic volume changes(c) Only permanent deformation and not volume changes(d) Elastic volume changes as well as plastic deformation

Based on the Mohr circle given below, answer Q3 and Q4

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ε


3. Maximum shear stress that exists on the element is given by(a) σ1(b) σ1-σ3(c) σ1-σ2(d) ½( σ1-σ3)

4. In a 2-D pure shear state, which of the following will be true:(a) σ2= σ1(b) σ3= - σ1(c) σ3=0(d) σ1=0

II. Multiple Option Questions (More than one choice is correct): (3 X 2 marks)

1) Which of these are characteristics of edge dislocations(a) Dislocation line and burger vector are perpendicular(b) Direction of motion of dislocation is parallel to burger vector(c) Direction of motion of dislocation is perpendicular to burger vector(d) It is a point defect

2) Which of these show precipitation hardening (strengthening)(a) Pure aluminum(b) Al-Zn alloys(c) Pure magnesium(d) Al-Cu alloys

3. Which of the following are true regarding uni-axial tensile testing of a polycrystalline aluminum sample (only in the plastic regime)?(a) Uniform deformation takes place only up to ultimate tensile stress(b) Strain hardening takes places only up to ultimate tensile stress(c) Strain hardening takes place all the way up to fracture point(d) True stress is highest at ultimate tensile stress

Fill in the blanks: (3 X 1 marks)

1. The total number of slip systems in FCC lattice is ___________

2. In fatigue testing, the load ratio (R) for completely reversed cyclic loading is _____________.

3. Plain carbon steel has higher strength than pure iron, because of this strengthening mechanism: ___________________________

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Ph.D. Admission 20XX Semester XX MSE Department IIT Kanpur Section D

Answer the following:

1. Using Schmid’s Law, determine the tensile stress that is applied along the axis of a silver single crystal to cause slip on the slip system. The critical resolved shear stress is 6 MPa. (3 marks)

2. A material shows flow stress of 350 MPa and 450 MPa when deformed to same strain at strain-rates of 10-3 s-1 and 103 s-1. Find ‘C’ and ‘m’ assuming the material follows the behavior: Y = C * ε̇ m (4 marks)

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Web viewYou are not allowed to communicate by word of mouth or ... A zinc electrowinning cell is being operated at a current of ... Both drift and diffusion