GATE XE topic:properties-applications-materials PYQs & Answers — Page 5

Questions 41–50 of 79. Imported answers require independent review unless marked reviewed.

Density of states, D(E), in a three dimensional solid varies with energy (E) as

Your answerChoose one option.

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A ceramic has a fracture toughness (Kᵢc) of 1 MPa·m¹ᐟ². If this ceramic is to be exposed to a maximum stress (σ) of 200 MPa, the maximum value of half crack length ‘a’ (in micrometer, μm), below which the material does not fail, is ______ μm (round off to one decimal place). Loading condition for the sample is shown in the schematic. Assume geometrical factor f = 1.2.

Diagram for Engineering Sciences question 7

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A ceramic material is periodically heated and cooled between 25°C and a higher temperature, Tf. During thermal cycling, the material remains dimensionally constrained. The material can withstand a maximum compressive stress of 200 MPa without failure. Material’s coefficient of thermal expansion is 7.5×10⁻⁶ °C⁻¹ and modulus of elasticity (E) is 200 GPa. The lowest value of Tf (in °C) at which material will fail is ______ °C (round-off to the nearest integer). Assume that there is no plastic deformation during the thermal cycling.

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Pure silicon (Si) has a band gap (Eg) of 1.1 eV. This Si is doped with 1 ppm (parts per million) of phosphor atoms. Si contains 5 × 10²⁸ atoms per m³ in pure form. At temperature T = 300 K, the shift in Fermi energy upon doping with respect to intrinsic Fermi level of pure Si will be ______ eV (with appropriate sign and round-off to two decimal places).

Intrinsic carrier concentration of Si, ni, is given as:

Given: Mass of an electron, m = 9.1 × 10⁻³¹ kg Charge of an electron, e = 1.6 × 10⁻¹⁹ C Boltzmann constant, kB = 1.38 × 10⁻²³ J.K⁻¹ Planck’s constant, h = 6.6 × 10⁻³⁴ J.s⁻¹

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The schematic diagram shows the light of intensity

incident on a material (shaded grey) of thickness,

, which has an absorption coefficient,

and reflectance,

. The intensity of transmitted light is

. The reflection of light (of a particular wavelength) occurs at both the surfaces (surfaces indicated in the diagram). The transmittance is estimated to be ______ (round-off to three decimal places).

Given that for the wavelength used,

and

Diagram for Engineering Sciences question 17

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Fe₃O₄ (also represented as FeO·Fe₂O₃) is a FCC structured inverse spinel (AB₂O₄) material where 1/8 of tetrahedral sites are occupied by half of B cations and 1/2 of the octahedral sites are occupied by remaining B and A cations. The magnetic moments of cations on octahedral sites are antiparallel with respect to those on tetrahedral sites. Atomic number of Fe is 26 and that of O is 8. The saturation magnetic moment of Fe₃O₄ per formula unit in terms of Bohr magnets (μB) will be ______ μB. Ignore contribution from orbital magnetic moments.

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A piezoelectric ceramic with piezoelectric coefficient (

) value of

is subjected to a force,

, of 10 N, applied normal to its x-y face, as shown in the figure. If relative dielectric constant (

) of the material is 100, the voltage developed along the z-direction of the sample will be ______ Volts (round-off to two decimal places). Ignore any nonlinear effects.

Given: Permitivity of free space (

) is

Diagram for Engineering Sciences question 19

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Silicon carbide (SiC) particles are added to Aluminum (Al) matrix to fabricate particle reinforced Al-SiC composite. The resulting composite is required to possess specific modulus (E/ρ; E: elastic modulus, ρ: density) three times that of pure Al. Assuming iso-strain condition, the volume fraction of SiC particles in the composite will be ______ (round-off to two decimal places).

Material	E (GPa)	ρ (g.cm⁻³)
Al	69	2.70
SiC	379	2.36

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Which one of the following is time-independent?

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Elastic deformation

Anelastic deformation

Viscoelastic deformation

Creep deformation

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GaAs has advantage over silicon when used in integrated circuits at low power because it has

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larger band gap

more than one element

higher electron mobility

higher hole mobility

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GATE XE topic:properties-applications-materials PYQs

Question 4

Question 7

Question 8

Question 16

Question 17

Question 18

Question 19

Question 20

Question 4

Question 7