GATE 2020 MT – Question 37

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

Which dislocation reaction is NOT feasible in an FCC crystal?

$\tfrac12[0\bar11]\to\tfrac16[1\bar21]+\tfrac16[\bar1\bar12]$
$\tfrac12[1\bar10]+\tfrac12[1\bar10]\to[1\bar10]$
$\tfrac16[11\bar2]+\tfrac13[111]\to\tfrac12[110]$
$\tfrac12[\bar101]\to\tfrac16[\bar211]+\tfrac16[\bar1\bar12]$

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Correct answer: (B) $\tfrac12[1\bar10]+\tfrac12[1\bar10]\to[1\bar10]$

Explanation

Frank’s energy criterion compares the sum of squared Burgers-vector magnitudes, since dislocation line energy scales approximately with b². In B, two identical vectors of squared magnitude 1/2 combine into one of squared magnitude 2. The total therefore rises from 1 to 2, making that reaction energetically unfavourable. In the other intended dissociation/combination choices the squared-magnitude sum decreases. Select B. The vectors also conserve Burgers vector: in A, [1,−2,1]+[−1,−1,2]=[0,−3,3], giving the stated half-vector after division by six.

GATE 2020 MT – Question 37

Explanation

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