GATE 2026 MT – Question 52
The lattice parameter of face-centered cubic Ni is 0.35 nm and its shear modulus is 76 GPa. The strain energy per unit length of a screw dislocation is ________ $\times10^{-9}\ \mathrm{J/m}$. (Rounded off to two decimal places.)
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Correct answer: 2.30 to 2.38
Explanation
For a perfect FCC dislocation, $b=a/\sqrt2$. Using the conventional estimate $E/\ell\approx Gb^2/2=Ga^2/4$, substitute $G=76\times10^9\ \mathrm{Pa}$ and $a=0.35\times10^{-9}\ \mathrm m$.
This gives $E/\ell=2.3275\times10^{-9}\ \mathrm{J/m}$, so enter **2.33**. The full elastic expression $Gb^2\ln(R/r_0)/(4\pi)$ requires inner and outer cutoffs not supplied; the official range uses the approximate expression.