Problem 174

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Problem 174
February 7, 2007 Nina Bordeaux

• The energy necessary to generate a dislocation is
  proportional to the square of the length of the
  Burgers vector . This means that the most
  stable (lowest energy) dislocations have the
  minimum length, b. For the BCC metal structure,
  calculate (relative to Eb 111) the
  dislocation energies for Eb 110 and Eb
  100.

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Motivation

• We have claimed that slip (linear dislocations)
  occurs along closely packed directions and now we
  will find out why.

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Linear Dislocations

• There are two types of linear dislocations, edge
  and screw, but they usually exist as a mix.
• Edge dislocations are as if there are an extra
  half-plane of atoms, so that a defect is created
  in the regular crystal structure along the line
  where the extra half-plane ends
• Screw dislocations are as if a portion of the
  crystal moved laterally compared to a neighboring
  portion.
• Both types of dislocation can be described by a
  Burgers vector.
• In this problem, we do not care whether the
  dislocation is edge or screw.

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Burgers Vectors

• describe the magnitude and direction of the
  lattice distortion associated with a dislocation.
  
• The directions are given in the problem statement
  (111, 110, and 100).
• goes from the center of one atom to the center of
  the next atom.

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Burgers Vectors in BCC
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Eb

• energy required to move an atom along a Burgers
  vector.
• It should not be confused with the energy
  required to create a dislocation, which affects a
  large portion of the lattice and must take into
  account the energy required to disturb many
  atoms.

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Procedure

• Given Eb ? and Burger directions 111,
  110, and 100
• 1) Find for each given Burger direction
• 2) Compare of 110 and 100 to of
  111

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Results

• energy required to dislocate an atom in the 110
  and 100 directions is higher than the energy
  required to dislocate an atom in the 111
  direction.
• Therefore slip is most likely to occur in the
  111 direction.
• These results are expected since the 111
  direction has the greatest linear density.

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Questions?