GATE Overflow for GATE XE - Questions without answers in Defects in Crystalline Materials

GATE XE 2026 | Question: 44

Tue, 24 Feb 2026 15:46:15 +0000

In a cubic crystal, the Burgers vector for a mixed dislocation line is $\dfrac{a}{2}$ $[110]$. The dislocation line lies along the $[011]$ direction. The slip plane of the dislocation is

$(1 \overline{1} 1)$
$(111)$
$(0 \overline{1} 1)$
$(1 \overline{1} 0)$

GATE XE 2026 | Question: 47

Tue, 24 Feb 2026 15:45:59 +0000

Which one of the following statements regarding point defects in ionic solids is correct?

Frenkel defects are dominant in those ionic solids where there is a considerable size difference between the cation and anion.
Schottky defects are dominant in those ionic solids where there is a considerable size difference between the cation and anion.
Schottky defects are the dominant defects in all ionic solids.
Similar density of both Frenkel and Schottky defects is present in all ionic solids.

GATE XE 2025 | Question: 53

Sun, 04 May 2025 19:07:15 +0000

In an $\textsf{FCC}$ crystal with lattice parameter $a$, consider the reaction of two leading partial dislocations, $\text{AB}$ and $\text{CD}$, at the line of intersection of their slip planes $(111)$ and $(11 \overline{1})$, respectively, as shown in the figure below. Dislocations, $\text{AB}$ and $\text{CD}$, 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?

Slip plane is $(001)$ and Burgers vector is $\frac{a}{6}[110]$
Slip plane is $(1 \overline{1} 1)$ and Burgers vector is $\frac{a}{6}[110]$
Slip plane is $(001)$ and Burgers vector is $\frac{a}{2}[110]$
Slip plane is $(\overline{1} 11)$ and Burgers vector is $\frac{a}{2}[110]$

GATE XE 2024 | Question: 45

Sun, 21 Jul 2024 16:42:10 +0000

The Miller indices for the shaded plane shown in the unit cell below is

$[632]$
$[123]$
$(632)$
$(123)$

GATE XE 2024 | Question: 49

Sun, 21 Jul 2024 16:42:07 +0000

Which of the following figures schematically represent(s) either the Frenkel defect or the Schotky defect in ionic solids?

GATE XE 2023 | Question: 39

Wed, 14 Feb 2024 18:09:45 +0000

\begin{tabular}{l|l}
Q. 49 & \begin{tabular}{l}
A screw dislocation in a FCC crystal has Burgers vector of $\frac{a}{2}[110]$, where $a$ is the \\
lattice constant. The possible slip plane(s) is/are:
\end{tabular} \\
\hline

& $(11 \overline{1})$ \\
\hline
& $(111)$ \\
\hline
& $(\overline{1} 11)$ \\
\hline
& $(1 \overline{1} 1)$
\end{tabular}

GATE XE 2023 | Question: 38

Wed, 14 Feb 2024 18:09:45 +0000

\begin{tabular}{|l|l|}
\hline Q.48 & \begin{tabular}{l}
Aliovalent doping of $M g C l_{2}$ in $\mathrm{NaCl}$ leads to the formation of defects. Which one \\
of the following is the correct defect reaction?
\end{tabular} \\
\hline

& $M \dot{g}_{C l}+N a_{N a}+V_{C l}^{\prime}=\emptyset$ \\
\hline
& $M \dot{g}_{N a}^{\bullet}+C l_{c l}+V_{N a}^{\prime}=\emptyset$ \\
\hline
& $M g_{N a}+C l_{C l}=\emptyset$ \\
\hline
& $M g_{N a}^{\prime}+C l_{C l}+V_{N a}^{\bullet}=\emptyset$ \\
\hline
\end{tabular}

GATE XE 2023 | Question: 41

Wed, 14 Feb 2024 18:09:43 +0000

Q. 51 A metal has a certain vacancy fraction at a temperature of $600 \mathrm{~K}$. On increasing the temperature to $900 \mathrm{~K}$, the vacancy fraction increases by a factor of (rounded off to one decimal place)
Given: Gas constant, $\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ and activation energy for vacancy formation, $\mathrm{Q}=68 \mathrm{~kJ} \mathrm{~mol}^{-1}$

GATE XE 2022 | Question: 41

Fri, 17 Feb 2023 06:52:06 +0000

The enthalpy required to create an oxygen vacancy in $\mathrm{CeO}_2$ is $4 \mathrm{eV}$. The number of oxygen vacancies present per mole of $\mathrm{CeO}_2$ at $1000 \mathrm{~K}$ is
$\text{(Round off to the nearest integer)}$
Given:
$$
N_A: \text { Avogadro's number }=6.02 \times 10^{23} \mathrm{~mole}^{-1}
$$
$$
k_B \text { : Boltzmann's constant }=8.62 \times 10^{-5} \mathrm{eV} / \mathrm{K}
$$