GATE 2026 MT – Question 48
An alloy of composition W–20 wt.% Ni is prepared by mixing elemental powders. The mixture is liquid-phase sintered at $1550^\circ\mathrm C$ for 1 hour. The resulting microstructure consists of interconnected spherical tungsten grains dispersed in nickel. The tungsten grain size is $70\ \mu\mathrm m$ and the W–W interparticle neck diameter is $35\ \mu\mathrm m$. If the W–Ni interfacial energy is $0.30\ \mathrm{J/m^2}$, the W–W interfacial energy is ________ $\mathrm{J/m^2}$. (Rounded off to two decimal places.) The melting points of W and Ni are $3410^\circ\mathrm C$ and $1455^\circ\mathrm C$, respectively.
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Correct answer: 0.50 to 0.54
Explanation
In the spherical-grain contact geometry, $\sin(\psi/2)=d_{neck}/d_{grain}=35/70=0.5$, giving $\psi/2=30^\circ$.
Interfacial force balance gives $\gamma_{WW}=2\gamma_{WNi}\cos(\psi/2)=2(0.30)\cos30^\circ=0.519615\ \mathrm{J/m^2}$. The answer is **0.52 J/m²**.