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GATE 2026 MT – Question 18

Mechanical Behaviour of Materials · Dislocations and strengthening · 1 mark · Multiple choice

Which of the following dislocation dissociation reactions is feasible in face-centered cubic metals?

  1. $\frac a2[0\,\overline1\,1]\to\frac a6[1\,\overline2\,1]+\frac a6[\overline1\,\overline1\,2]$
  2. $\frac a2[0\,\overline1\,1]\to\frac a6[1\,1\,2]+\frac a6[2\,1\,\overline1]$
  3. $\frac a2[0\,\overline1\,1]\to\frac a6[1\,\overline1\,2]+\frac a6[\overline1\,\overline2\,\overline1]$
  4. $\frac a2[0\,\overline1\,1]\to\frac a6[1\,\overline2\,1]+\frac a6[2\,\overline1\,\overline1]$

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Correct answer: (A) $\frac a2[0\,\overline1\,1]\to\frac a6[1\,\overline2\,1]+\frac a6[\overline1\,\overline1\,2]$

Explanation

Burgers vectors must be conserved. For A, the two partial vectors sum to $(a/6)[0,-3,3]=(a/2)[0,-1,1]$, matching the original vector. The other options do not conserve it.

The parent has $b^2=a^2/2$. Each partial has $b_i^2=a^2/6$, so their sum is $a^2/3<a^2/2$. Frank’s energy criterion therefore favors the dissociation. Select **A**.