Stack fault energy

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Definition of the generalized stacking fault energy
Functional course of the SFE in (111) Cu

The generalized stacking fault energy ("gamma") indicates the energy per area of ​​an ideal, infinitely extensive stacking fault , so it represents an energy surface density . Essential for the characterization of the plastic deformation are the unstable stacking fault energy - the first maximum - and the stable stacking fault energy - the second minimum.

When a stacking fault occurs, the energy barrier of the unstable stacking fault energy must be overcome. The difference between the two energies is a measure of the ductility of a material.

definition

For the definition of the generalized stacking fault energy one considers an infinitely extended defect- free ideal face-centered cubic crystal . Then this crystal is divided into an upper and a lower part along a dividing plane. Now the upper part of the crystal is moved and the energy of the deformed crystal is measured.

Let now be the total energy of the initial configuration of the ideal crystal and denote further and the displacement of the upper half of the crystal in the plane. Then the generalized stacking fault energy is defined as:

It is

  • the energy of the deformed crystal for the given displacement
  • the contact area of ​​the two halves of the crystal in the plane of displacement.

The two coefficients

and

the shift result in a total shift in the plane

Here are the two basis vectors

and

chosen for the relevant (111) level of our systems.

Characterization of stacking faults

The generalized stacking fault energy is a characteristic parameter of a material . Although it is calculated using an idealization , it is nevertheless suitable for describing the generation of stacking faults during plastic deformation. Properties of the dislocations themselves - such as e.g. B. the dislocation core size, the flow behavior of a dislocation and its energetics - can be well described by the generalized stacking fault energy.

For materials with low stacking fault energy, z. B. hindered the crystal recovery by splitting the dislocations , which is why they tend to recrystallize after deformation . This is particularly the case with metals with a face-centered cubic lattice .

literature

  • Gerolf Ziegenhain: Atomistic simulation of nanoindentation . Ed .: TU Kaiserslautern. Kaiserslautern June 2009.