# Dislocation

For the syntactic operation, see Dislocation (syntax)
For the medical term, see Dislocation (medicine)

In materials science, a dislocation is a linear crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of real materials. The theory was originally developed by Vito Volterra in 1905.

Some types of dislocations can be visualised as being caused by the termination of a plane of atoms in the middle of a crystal. In such a case, the surrounding planes are not straight, but instead bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side. The analogy with a stack of paper is apt: if a half a piece of paper is inserted in a stack of paper, the defect in the stack is only noticeable at the edge of the half sheet.

There are two major types of dislocations:

1. Edge dislocations; and
2. Screw dislocations.

Figure 1: An edge-dislocation (b = Burgers vector)
 Contents

## Dislocation geometry

Any dislocation can be described by the Burgers vector and the dislocation line. However, an introduction to these and other terms used to describe dislocations can be difficult and it is easer to begin with a simple description of an edge dislocation.

### Edge dislocations

Edge dislocations can be visualised as being formed by adding an extra half-plane of atoms to a perfect crystal, so that a defect is created in the regular crystal structure along the line where the extra half-plane ends (Figure 1). Such visualisations can be difficult to interpret. Initially, it can be helpful to follow the process of simplification involved in arriving at such representations.One approach is to begin by considering a 3-d representation of a perfect crystal lattice, with the atoms represented by spheres (Figure A). The viewer may then start to simplify the representation by visualising planes of atoms instead of the atoms themselves (Figures B and C).

Missing image
Dislocation_edge_a.jpg
Figure A Perfect (simple cubic) crystal lattice of atoms
Missing image
Dislocation_edge_c.jpg
Figure C Simplified Representation of Lattice planes
Missing image
Dislocation_edge_b.jpg
Figure B Crystal lattice showing atom planes

Finally a simple schematic diagram of such atomic planes can be used to illustrate lattice defects such as dislocations. (Figure D represents the "extra half-plane" concept of an edge type dislocation).

Missing image
Dislocation_edge_d2.jpg
Figure D Schematic diagram (lattice planes) showing an edge dislocation. Burgers vector in black, dislocation line in blue.

### Burgers vector

Missing image
Dislocation_screw_e.jpg
Figure E Schematic diagram (lattice planes) showing a screw dislocation.

Once a picture of an edge dislocation has been formed it is possible to begin to explain the important characteristics used to describe it.

The orientation and magnitude of a dislocation is characterised by its Burgers vector (marked in black in Figure D), which is perpendicular to the dislocation line (marked in blue in Figure D) in the case of the edge, and parallel to it in the case of the screw. In metallic materials, b is alligned with close-packed crystallographic directions and its magnitude is equivalent to one interatomic spacing.

### Screw and mixed dislocations

Screw dislocations are more difficult to visualise, but can be considered as being formed by the insertion of a "parking garage ramp" that extends to the "edges of the garage" into an otherwise perfectly layered structure. Basically it comprises a structure in which a helical path is traced around the linear defect (dislocation line) by the atomic planes in the crystal lattice (Figure E).

In fact, the dislocations present in real crystalline solids are rarely of a pure edge nature or pure screw, rather they exhibit aspects of both types, and are therefore termed "mixed" dislocations.

## Observation of Dislocations

Missing image
TEM1.jpg
Transmission Electron Micrograph of Dislocations

When a dislocation line intersects the surface of a metallic material, the associated strain field locally increases the relative susceptibility of the material to acidic etching and an etch pit of regular geometrical format results. If the material is strained (deformed) and repeatedly re-etched, a series of etch pits can be produced which effectively trace the movement of the dislocation in question.

Transmission electron microscopy can be used to observe dislocations within the microstructure of the material. Thin foils of metallic samples are prepared to render them transparent to the electron beam of the microscope. The electron beam suffers diffraction by the regular crystal lattice planes of the metal atoms and the differing relative angles between the beam and the lattice planes of each grain in the metal's microstructure result in image contrast (between grains of diffent crystallographic orientation). The less regular atomic structures of the grain boundaries and in the strain fields around dislocation lines have different diffractive
Missing image
TEM2.jpg
Transmission Electron Micrograph of Dislocations
properties than the regular lattice within the grains, and therefore present different contrast effects in the electron micrographs. (The dislocations are seen as dark lines in the lighter, central region of the micrographs on the right). Transmission electron micrographs of dislocations typically utilise magnifications of 50,000 to 300,000 times (though the equipment itself offers a wider range of magnifications than this). Some microscopes also permit the in-situ heating and/or deformation of samples, thereby permitting the direct observaion of dislocation movement and their interractions.

Field ion microscopy and atom probe techniques offer methods of producing much higher magnifications (typically 3 million times and above) and permit the observation of dislocations at an atomic level.

(By contrast, traditional optical microscopy, which is not appropriate for the observation of dislocations, typically offers magnifications up to a maximum of only around 2000 times).

## Dislocations, slip and plasticity

Until the 1930s, one of the enduring challenges of materials science was to explain plasticity in microscopic terms. A naive attempt to calculate the shear stress at which neighbouring atomic planes slip over each other in a perfect crystal suggests that, for a material with shear modulus G, shear strength τm is given approximately by:

[itex]\tau_m = \frac {G} {2 \pi}[itex]

As shear modulus in metals is typically within the range 20 000 to 150 000 MPa, this is difficult to reconcile with shear stresses in the range 0.5 to 10 MPa observed to produce plastic deformation in experiments.

In 1934, Egon Orowan, Michael Polanyi and G. I. Taylor, roughly simultaneously, realised that plastic deformation could be explained in terms of the theory of dislocations. Dislocations can move if the atoms from one of the surrounding planes break their bonds and rebond with the atoms at the terminating edge. Even a simple model of the force required to move a dislocation shows that shear is possible at much lower stresses than in a perfect crystal. (Hence, the characteristic maleability of metals).

When metals are subjected to "cold work" (deformation at temperatures which are relatively low as compared to the material's absolute melting temperature Tm, ie. typically less than 0.3Tm) the dislocation density increases due to the formation of new dislocations and dislocation multiplication. The consequent increasing overlap between the strain fields of adjacent dislocations gradually increases the resistance to further dislocation motion. This causes a hardening of the metal as deformation progresses. This effect is known as strain hardening (also "work hardening" and "cold working").

The effects of strain hardening can be removed by appropriate heat treatment (annealling) which promotes the recovery and subsequent recrystallisation of the material.

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