GATE Overflow for GATE XE - Recent questions in Classification and Structure of Materials

GATE XE 2026 | Question: 42

Tue, 24 Feb 2026 15:46:34 +0000

The equilibrium vacancy concentration in aluminum at $900$ $\mathrm{K}$ is $1.1 \times 10^{-4}$. The enthalpy of formation of vacancies in $\mathrm{kJ}. \mathrm{mol}^{-1}$ is $\_\_\_\_$ (rounded off to one decimal place).

Given: Universal gas constant $=8.314 \mathrm{~J} \cdot \mathrm{~K}^{-1} \cdot \mathrm{~mol}^{-1}$

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 2026 | Question: 48

Tue, 24 Feb 2026 15:45:55 +0000

Consider $3$ crystals (all having FCC lattice) labelled as $\text{P, Q}$ and $\text{R}$ as described below:

Crystal $\text{P}$: Cu crystal with $4$ $\text{Cu}$ atoms per unit cell
Crystal $\text{Q}$: NaCl crystal with $4 \mathrm{Na}^{+}$ions and $4 \mathrm{Cl}^{-}$ions per unit cell
Crystal $\text{R}$: Diamond crystal with $8$ $\text{C}$ atoms per unit cell

Which of the following options is/are correct?

Only crystal $\text{P}$ is a close packed structure.
Only crystal $\text{Q}$ is a close packed structure.
Crystal $\text{R}$ has the smallest packing factor.
All the crystals $\text{P, Q}$ and $\text{R}$ are close packed structures.

GATE XE 2025 | Question: 44

Sun, 04 May 2025 19:07:33 +0000

The figure below shows a plane $\text{PQR}$ in a unit cell. The Miller indices of the plane $\text{PQR}$ is

$(432)$
$(43 \overline{2})$
$(23 \overline{4})$
$(\overline{2} \overline{3} 4)$

GATE XE 2025 | Question: 48

Sun, 04 May 2025 19:07:25 +0000

There is $\textsf{NO}$ base-centered cubic lattice among the list of $14$ Bravais lattices because of one or more of the following reasons

It does $\textsf{NOT}$ have translational symmetry
It is only compatible with the symmetry of orthorhombic crystal system
It is only compatible with the symmetry of tetragonal crystal system
It does $\textsf{NOT}$ have $3$-fold rotation axes along the body diagonals

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 2025 | Question: 58

Sun, 04 May 2025 19:07:03 +0000

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

GATE XE 2024 | Question: 38

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

Which one of the following unit cell parameters represents a tetragonal crystal system?

$\mathrm{a}=\mathrm{b}=\mathrm{c} ; \quad \alpha=\beta=\gamma \neq 90^{\circ}$
$\mathrm{a} \neq \mathrm{b} \neq \mathrm{c} ; \quad \alpha=\beta=\gamma=90^{\circ}$
$\mathrm{a}=\mathrm{b} \neq \mathrm{c} ; \alpha=\beta=90^{\circ}, \gamma=120^{\circ}$
$\mathrm{a}=\mathrm{b} \neq \mathrm{c} ; \quad \alpha=\beta=\gamma=90^{\circ}$

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: 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: 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: 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 2023 | Question: 43

Wed, 14 Feb 2024 18:09:41 +0000

\begin{tabular}{|l|l|}
\hline Q. 53 & \begin{tabular}{l}
A student performed X-ray diffraction experiment on a FCC polycrystalline pure \\
metal. The following $\sin ^{2} \theta$ values were calculated from the diffraction peaks. \\
\\
$\sin ^{2} \theta=0.136,0.185,0.504,0.544$ \\
However, the student was negligent and missed noting one of the peaks. Which \\
one of the following Miller indices corresponds to the missing peak?
\end{tabular} \\
\hline

& $(200)$ \\
\hline
& $(220)$ \\
\hline
& $(311)$ \\
\hline
& $(222)$ \\
\hline
\end{tabular}

GATE XE 2023 | Question: 45

Wed, 14 Feb 2024 18:09:39 +0000

\begin{tabular}{|c|c|c|}
\hline \multirow[t]{6}{*}{ Q. 55} & \multicolumn{2}{|c|}{ Match the hardness test (in Column I) with its indenter type (in Column II). } \\
\hline & Column I & Column II \\
\hline & (P) Brinell & 1. Diamond pyramidal \\
\hline & (Q) Rockwell & 2. Diamond cone \\
\hline & (R) Vickers & 3. Tungsten carbide sphere \\
\hline & & 4. Steel sphere \\
\hline

& P-2, Q-4, R-1 & \\
\hline
& P-4, Q-2, R-3 & \\
\hline
& P-3, Q-4, R-2 & \\
\hline
& P-4, Q-2, R-1 & \\
\hline
\end{tabular}

GATE XE 2023 | Question: 48

Wed, 14 Feb 2024 18:09:36 +0000

\begin{tabular}{|l|l|}
\hline Q. 58 & \begin{tabular}{l}
Among the 14 Bravais lattices, there is no base centred cubic unit cell. Which of \\
the following statement(s) is/are true?
\end{tabular} \\
\hline & \\
\hline

& The base-centred cubic unit cell is same as the simple tetragonal unit cell \\
\hline
& The base-centred cubic unit cell is same as the body centred tetragonal unit cell \\
\hline
& The base-centred cubic unit cell is same as the simple orthorhombic unit cell \\
\hline
& The base-centred cubic unit cell does not have any 3-fold rotation axis \\
\hline
\end{tabular}

GATE XE 2022 | Question: 34

Fri, 17 Feb 2023 06:52:12 +0000

\begin{tabular}{|l|l|}
\hline Q.44 & Number of atoms per unit area of the (110) plane of a body centered cubic crystal, \\
with lattice parameter ' $a$ ', is \\
\hline

& $\frac{1}{a^{2}}$ \\
\hline
& $\frac{\sqrt{2}}{a^{2}}$ \\
\hline
& $\frac{1}{\sqrt{3} a^{2}}$ \\
\hline
& $\frac{1}{\sqrt{2} a^{2}}$ \\
\hline & \\
\hline
\end{tabular}

GATE XE 2022 | Question: 35

Fri, 17 Feb 2023 06:52:11 +0000

Q.45 Match the following materials with their corresponding bonding types.

$\mathrm{P}-4 ; \mathrm{Q}-2 ; \mathrm{R}-3 ; \mathrm{S}-1$
$\mathrm{P}-3 ; \mathrm{Q}-4 ; \mathrm{R}-2 ; \mathrm{S}-1$
$\mathrm{P}-3 ; \mathrm{Q}-2 ; \mathrm{R}-1 ; \mathrm{S}-4$
$\mathrm{P}-3 ; \mathrm{Q}-1 ; \mathrm{R}-4 ; \mathrm{S}-2$

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:
$$
N_A: \text { Avogadro's number }=6.02 \times 10^{23} \mathrm{~mole}^{-1}
$$
$$
k_B \text { : Boltzmann's constant }=8.62 \times 10^{-5} \mathrm{eV} / \mathrm{K}
$$

GATE XE 2022 | Question: 50

Fri, 17 Feb 2023 06:51:59 +0000

A two-phase $(\alpha+\beta)$ mixture of an $\text{A-B}$ binary system has the following properties:

Phase $\alpha$ has equal weight percentages of $\mathrm{A}$ and $\mathrm{B}$.
Phase $\beta$ has twice the mole fraction of $\mathrm{A}$ compared to $\mathrm{B}$.
The two-phase mixture has equal amounts of $\alpha$ and $\beta$.
Atomic mass of $\mathrm{A}$ is twice that of $\mathrm{B}$.

The mole fraction of $\mathrm{A}$ in the resultant two-phase mixture is

$\text{(Round off to one decimal)}$

GATE XE 2022 | Question: 52

Fri, 17 Feb 2023 06:51:57 +0000

A spherical $\beta$ particle nucleates from the $\alpha$ matrix on a non-deformable substrate \end{tabular} $\delta$, forming a contact angle of $\theta$ as shown in the schematic.

The value of $\frac{\Delta G_{\text {het }}^{*}}{\Delta G_{\text {hom }}^{*}}$ is.

$\text{(Round off to three decimal places)}$

$\Delta G_{\text {hom }}^{*}=$ Gibbs free energy change at the critical radius for homogeneous nucleation
$\Delta G_{\text {het }}^{*}=$ Gibbs free energy change at the critical radius for heterogeneous nucleation
$\alpha-\beta$ interfacial energy $=0.4 \mathrm{~J} / \mathrm{m}^{2}$
$\alpha-\delta$ interfacial energy $=0.3 \mathrm{~J} / \mathrm{m}^{2}$
$\beta-\delta$ interfacial energy $=0.02 \mathrm{~J} / \mathrm{m}^{2}$