GATE 2019 MT – Question 58

Physical Metallurgy · Nucleation solidification and transformations · 2 marks · Numerical answer

Nickel solidifies at 1673 K. Its equilibrium melting temperature is 1728 K, latent heat per volume 2.65×10⁹ J/m³ and liquid–solid interfacial energy 0.5 J/m². Find critical nucleus radius in nm (one decimal place).

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Correct answer: 11.0 to 12.5

Explanation

Undercooling is ΔT=55 K. The bulk free-energy driving force magnitude is approximately $|\Delta G_v|=L_v\Delta T/T_m$. Thus $r^*=2\gamma/|\Delta G_v|=2(0.5)(1728)/(2.65\times10^9\times55)=1.1856\times10^{-8}$ m =11.9 nm.

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