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GATE 2022 MT – Question 40

Mechanical Behaviour of Materials · Dislocations and strengthening · 2 marks · Multiple choice

Match the dislocation reactions P–R to descriptions 1–3. Here $a_0$ is the lattice parameter.

P. $(a_0/2)[\bar1\bar1 1]+(a_0/2)[111]=a_0[001]$

Q. $(a_0/6)[12\bar1]+(a_0/6)[\bar1\bar1 2]=(a_0/6)[011]$

R. $(a_0/6)[1\bar2 1]+(a_0/6)[\bar1\bar1 2]=(a_0/2)[0\bar1 1]$

1. Leading partials merging into a Lomer–Cottrell lock in an FCC metal

2. Energetically unfavourable dislocation reaction in an FCC metal

3. Typical dislocation reaction in a BCC metal

  1. P − 3, Q − 2, R − 1
  2. P − 3, Q − 1, R − 2
  3. P − 2, Q − 3, R − 1
  4. P − 2, Q − 1, R − 3

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Correct answer: (B) P − 3, Q − 1, R − 2

Explanation

P combines BCC $(a_0/2)\langle111\rangle$ dislocations to $a_0\langle001\rangle$ (3). Q combines FCC leading partials into a sessile $(a_0/6)\langle110\rangle$ stair-rod, a Lomer–Cottrell lock (1). In R the product has $b^2=a_0^2/2$, greater than the reactant sum $a_0^2/3$, so line energy increases (2). Match: **P–3, Q–1, R–2; B**.