Dislocation

The offset is in materials science, a model for a one-dimensional lattice defects in a crystal. It can occur, for example

• During crystal growth (for example, from the melt or in the gas phase deposition ),
• Existing in the crystal as a result of residual stresses
• Or in the plastic deformation. Plastic deformation of crystals is usually carried out under generation and movement of dislocations.

The displacement is represented by a dislocation line. They can not end in the interior of a crystal.

• 2.1 Burgers vector

Types

There are two basic types of dislocations and any hybrids between them.

Edge dislocation

Burgers vector and dislocation line are perpendicular to each other. An edge dislocation can be thought of as an extra half-plane of particles (atoms, ions) that is inserted in a perfect crystal. The place where these half-plane ends, called the dislocation core or the dislocation line. There the displacement brings about the greatest distortion of the lattice, which is a high-energy strain field around the dislocation line around results (see figure).

The energy of an edge dislocation per unit length

G = shear modulus.

Screw dislocation

Burgers vector and dislocation line are parallel. A screw dislocation can be thought of as a plane that winds around the dislocation line.

The energy of a screw dislocation per unit length is less than the edge dislocation:

Therefore, the typical dislocation loop has more areas with screw than with levels of character and has elliptical shape.

Properties

Each dislocation has two important parameters: the dislocation line and the Burgers vector.

Burgers vector

The Burgers vector (named after Johannes Martinus Burgers ) describes the direction in which the dislocation motion necessarily exists. Its magnitude corresponds to the distance between two adjacent atoms in this direction, its direction is dictated by the crystal structure of the material.

The Burgers vector can be formed with the following thought experiment:

• With some distance from the transfer connection between the atoms is pulled, so that a closed circulation is formed. This is the Burgers loop shown by the broken line in the left image.
• Now the circulation of the left image is transmitted 1:1 on the right picture of an undisturbed crystal.
• The circulation can not be closed at one point.
• The closing of the circulation necessary connection is the Burgers vector.

The Burgers vector with the lowest energy ( grows with the square of its amount) is located in densely packed planes:

• In a face-centered cubic lattice, it is in the < 110 > direction
• In a body-centered cubic lattice, it is in the < 111 > direction.

The energy of a crystal can decrease when the dislocation into two partial dislocations splits with only half as large Burgers vector. In the fcc lattice especially the Shockley dislocations are interesting. Thus, by combination of two Shockley dislocation turn a so-called Lomer - Cottrell dislocation are formed, which causes a further lowering of the energy. Lomer - Cottrell dislocations are often "settled ", so they can not move on, because they lie in a different plane than the output displacement.

Visualization

The lattice distortion for a transfer line can be made ​​visible by a number of methods. These are suitable in principle for determining the dislocation density ρ ( see there).

• IR microscopy
• Transmission Electron Microscopy ( TEM)
• Field ion microscopy ( FIM)
• X-ray topography

Furthermore, it has been possible in recent years by high-resolution transmission electron microscopy ( HRTEM ) in some semiconductors to make dislocation cores visible in near-atomic resolution.

Dislocation motion as an explanation of the plasticity

Until the 1930s there was a challenge to explain the plasticity and strength of metals at the microscopic level. In a " defect-free " crystal, the theoretical strength is described by the expression? M

(G = shear modulus ). However, the actual observed values ​​are for virtually all metals several times below this estimate.

1934 Egon Orowan described, Michael Polanyi and GI Taylor and independently about the same time as this contradiction can be resolved by displacement concept. Under the effect of a very small in comparison to the theoretical strength shear stress dislocations can "move", that is, the atoms of the neighboring half-plane break their bonds briefly on and bind themselves to the next half-plane. The dislocation line "wanders". This is the basic mechanism of plastic deformation. It always happens only in such slip planes, in which also the Burgers vector lies. Except for pure screw dislocations, which can also cross slip, the slip plane is given already by the position of the dislocation in the lattice. However, the course of the dislocation line can also be due to the interaction with spaces, other dislocations to be disturbed, for example, when climbing, or. These processes lead to an obstruction of the sliding process and thus to an increase in work-hardening of the crystal and the formation of new dislocations (so-called dislocation multiplication).

The hardening is irreversible, so long as the temperature remains ( in Kelvin ) is below about 30 % of the absolute melting temperature Tm. Furthermore it can be used for healing (crystal recovery ) of the dislocations come to each other by recombination or arrangement of dislocations, thereby increasing the strength drops significantly again and the ductility increases. At still higher temperatures, the dislocations are eliminated by structure formation during recrystallization.

Dislocations in semiconductors

In the semiconductor industry, low-dislocation crystals as possible are needed, otherwise the electronic properties of the crystals would be disturbed. Industrially, the lowest dislocation densities (<< 108 cm -2) can be achieved today in silicon and germanium. For all other macroscopic crystals, the dislocation density is higher by orders of magnitude. In gallium arsenide, the displacement Diche is about 108 cm - 2, grown by heteroepitaxial gallium nitride layers at 1010 cm -2. Dislocations in single crystals are mainly due to thermal stress in the cooling process in the material, wherein the semiconductor heterostructure layer systems usually through a lattice mismatch. Possible low-dislocation crystals is therefore obtained by gentle cooling.