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GATE 2023 MT – Question 21

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

Two dislocations with Burgers vectors $(a/2)[101]$ and $(a/2)[0\bar1\bar1]$ react. The magnitude of the resultant Burgers vector is

  1. $a/\sqrt2$
  2. $\sqrt2a$
  3. $a/2$
  4. $2a$

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Show answer and explanation

Correct answer: (A) $a/\sqrt2$

Explanation

Vector addition gives $\mathbf b=(a/2)([1,0,1]+[0,-1,-1])=(a/2)[1,-1,0]$. Its norm is $(a/2)\sqrt{1^2+(-1)^2}=a/\sqrt2$, **A**.