List of top Engineering Materials Science Questions asked in GATE XE

In an FCC crystal with lattice parameter \(a\), consider the reaction of two leading partial dislocations, AB and CD, at the line of intersection of their slip planes \((111)\) and \((\bar{1}11)\), respectively. Dislocations AB and CD have Burgers vectors \(\vec{b}_1\) and \(\vec{b}_2\), respectively, as given in the figure. Which one of the following options for the slip plane and the Burgers vector of the resulting dislocation is correct?

Corrosion of pure iron takes place in an acidic electrolyte by forming \(Fe^{2+}\) ions at ambient condition. The corrosion current density is measured to be \(2 \times 10^{-4} \, A \, cm^{-2}\). The corrosion rate (in mm per year) of iron is (rounded off to one decimal place). Given: \[ \text{Atomic weight of iron} = 55.85, \rho = 7.86 \, g/cm^3 \] \[ \text{1 year} = 365 \times 24 \times 3600 \, s, 1F = 96500 \, C/mol \]

At 873 K, hydrogen diffuses under steady state through a 5 mm thick palladium sheet with a cross-sectional area of 0.3 m\(^2\). The concentrations of hydrogen at high and low pressure ends of the sheet are 3 kg m\(^{-3}\) and 0.5 kg m\(^{-3}\). The amount of hydrogen (in kg per day) passing through the sheet is (rounded off to two decimal places). Given: At 873 K, diffusivity of hydrogen = \(1.8 \times 10^{-8}\, m^2/s\).

An electric field is applied on a copper plate such that the electrons are displaced by \(1.1 \times 10^{-18}\,\text{m}\) relative to the nucleus. The electronic polarization (in \(\mu C \, m^{-2}\)) is (rounded off to two decimal places). Given: Atomic number of copper = 29, Copper has FCC crystal structure with lattice parameter = 0.362 nm, Electron charge = \(1.6 \times 10^{-19}\, \text{C}\).

An aluminum transmission line of 7 km length is designed to carry 100 A current with no more than 2 MW power loss. The required minimum diameter (in mm) of the transmission line is (rounded off to two decimal places).

The slopes of reduction potential vs. pH plots for the reactions: 1. \(NiO + 2H^+ + 2e^- \rightleftharpoons Ni + H_2O\) 2. \(2H^+ + 2e^- \rightleftharpoons H_2\) at 298 K are \(S_1\) and \(S_2\). The ratio \(\dfrac{S_1}{S_2}\) is (rounded off to one decimal place).

A diffraction pattern is obtained from a powdered sample of a pure element, which has FCC crystal structure. If \(x\) and \(y\) are the Bragg angles of the first and the third peaks, respectively, then the ratio \(\dfrac{\sin y}{\sin x}\) is (rounded off to one decimal place).

The TTT diagram for eutectoid steel is shown below. The steel after complete austenitization at 1073 K is rapidly cooled to different temperatures and held for varying times (as indicated in Column I) followed by quenching to 300 K. Assuming isothermal transformation, match the heat treatment conditions in Column I with the corresponding microstructure in Column II.

For a pure element with a BCC crystal structure, the surface energies per unit area of \(\{100\}\) and \(\{110\}\) free surfaces are \(S_{100}\) and \(S_{110}\), respectively. The ratio \(\dfrac{S_{100}}{S_{110}}\) is (rounded off to one decimal place).

On applying 10 V across the two ends of a 100 cm long copper wire, the average drift velocity (in cm/s) in the wire is (rounded off to two decimal places).

Which of the following phenomenon/phenomena contribute to intensity loss of electromagnetic radiation during transmission through a medium?

A GaP–GaAs semiconductor LED display has a band gap of 1.9 eV. The wavelength of emitted light in \(\mu m\) is (rounded off to two decimal places) ..............

Match the detector for a scanning electron microscope (SEM) in Column I with the resulting output in Column II. SE: Secondary electrons; BSE: Backscattered electrons; EDS: Energy Dispersive Spectroscopy; EBSD: Electron Backscatter Diffraction \begin{tabular}{|c|c|} \hline Column I & Column II \\ \hline (P) SE Detector & (1) Elemental composition analysis \\ (Q) BSE Detector & (2) Kikuchi lines \\ (R) EDS Detector & (3) Topographic image \\ (S) EBSD Detector & (4) Compositional contrast image \\ \hline \end{tabular}

For a conventional optical microscope, which of the following options regarding the resolution limit and the depth of field is/are correct?

The unit of measurement for magnetic dipole moment of a body is:

The figure below shows a plane PQR in a unit cell. The Miller indices of the plane PQR is ...........

$B$ is the magnetic flux density and $T_c$ is the critical temperature. The Meissner effect is represented by:

For Al – 4.5 wt% Cu alloy, the correct sequence of precipitation during age hardening at room temperature is:

There is NO base-centered cubic lattice among the list of 14 Bravais lattices because of one or more of the following reasons:

Two moles of a monoatomic ideal gas at 10 atm and 300 K is expanded isothermally and reversibly to a pressure of 2 atm. The absolute value of work done by the system is (in kJ) .......... (rounded off to two decimal places).

An electrochemical cell consists of pure Zn electrode (anode) and a hydrogen electrode (cathode) in a dilute Zn$^{+2}$ solution. The overall reaction is: \[ Zn(s) + 2H^+ \rightarrow H_2 + Zn^{+2} \] If the overall cell potential is +0.690 V, then the value of $\ln \left( \frac{[Zn^{+2}]}{[H^+]^2} \right)$ is ........... (rounded off to two decimal places). Given: Pressure of hydrogen gas = 1 atm; Temperature = 298 K; \[ \frac{RT}{F} = 0.0256 \, V \] Standard reduction potentials: \[ Zn^{+2} + 2e^- \rightarrow Zn (E^0 = -0.762 \, V) \] \[ 2H^+ + 2e^- \rightarrow H_2 (E^0 = 0 \, V) \]

In a Raman spectroscopy experiment done at 300 K, a Raman line is observed at $200 \, cm^{-1} \, (\sim 25 \, meV)$. The ratio of the intensity of the Stokes line to that of the Anti-Stokes line is ............ (rounded off to two decimal places). Given: Boltzmann constant, $k = 8.62 \times 10^{-5} \, eV K^{-1}$

Specific heat ($C_v$) of a material was found to depend on temperature as shown below. Which of the following statement(s) is/are true?

A pure Silicon wafer is doped with Boron by exposing it to $B_2O_3$ vapour at an elevated temperature. It takes 1000 seconds to reach a Boron concentration of $10^{20}$ atoms $m^{-3}$ at a depth of $1 \, \mu m$. The time taken to reach the same concentration of Boron at a depth of $2 \, \mu m$ is (in seconds): ................ (rounded off to nearest integer).

The Young’s modulus of a quartz piezoelectric crystal is 100 GPa. The uniaxial stress required to change its polarization by 1% is (give absolute value in GPa) .............. (rounded off to nearest integer).