FCC Dislocation Dissociation Feasibility

In face-centered cubic (FCC) metals, dislocation dissociation reactions are governed by the principle of conservation of the Burgers vector. A perfect dislocation can split into two or more partial dislocations if the vector sum of the partials equals the original perfect dislocation vector. This dissociation is often driven by the reduction in strain energy, especially when it leads to the formation of a stacking fault.

Verifying Burgers Vector Conservation

The initial dislocation has a Burgers vector denoted as $ \vec{B}_{\text{initial}} = a/2 [0\bar{1}1] $. We need to check which of the proposed dissociation reactions conserves this vector through the sum of the Burgers vectors of the resulting partial dislocations.

• Option 1: $ \vec{B}_1 = a/6 [1\bar{2}1] $ and $ \vec{B}_2 = a/6 [\bar{1}\bar{1}2] $

  Sum: $ \vec{B}_1 + \vec{B}_2 = a/6 [1\bar{2}1] + a/6 [\bar{1}\bar{1}2] = a/6 ([1-1], [-2-1], [1+2]) = a/6 [0, -3, 3] $

  Simplifying: $ a/6 [0, -3, 3] = a/2 [0, -1, 1] $. This matches the initial Burgers vector $ a/2 [0\bar{1}1] $. This reaction involves Shockley partials, which are common in FCC metals and dissociate on {111} planes.

• Option 2: $ \vec{B}_1 = a/6 [112] $ and $ \vec{B}_2 = a/6 [21\bar{1}] $

  Sum: $ \vec{B}_1 + \vec{B}_2 = a/6 [112] + a/6 [21\bar{1}] = a/6 ([1+2], [1+1], [2-1]) = a/6 [3, 2, 1] $. This does not match $ a/2 [0\bar{1}1] $.

• Option 3: $ \vec{B}_1 = a/6 [1\bar{1}2] $ and $ \vec{B}_2 = a/6 [\bar{1}\bar{2}\bar{1}] $

  Sum: $ \vec{B}_1 + \vec{B}_2 = a/6 [1\bar{1}2] + a/6 [\bar{1}\bar{2}\bar{1}] = a/6 ([1-1], [-1-2], [2-1]) = a/6 [0, -3, 1] $. This does not match $ a/2 [0\bar{1}1] $.

• Option 4: $ \vec{B}_1 = a/6 [1\bar{2}1] $ and $ \vec{B}_2 = a/6 [2\bar{1}\bar{1}] $

  Sum: $ \vec{B}_1 + \vec{B}_2 = a/6 [1\bar{2}1] + a/6 [2\bar{1}\bar{1}] = a/6 ([1+2], [-2-1], [1-1]) = a/6 [3, -3, 0] = a/2 [1, -1, 0] $. This does not match $ a/2 [0\bar{1}1] $.

Conclusion on Feasibility

Only Option 1 satisfies the conservation of the Burgers vector, meaning the initial dislocation $ a/2 [0\bar{1}1] $ can indeed dissociate into the partial dislocations $ a/6 [1\bar{2}1] $ and $ a/6 [\bar{1}\bar{1}2] $. This type of dissociation into Shockley partials is a characteristic behaviour in FCC metals, leading to the formation of an intrinsic stacking fault.