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:

Edge dislocations; and
Screw dislocations.

Mathematically, dislocations are a type of topological defect, sometimes called a soliton. The mathematical theory explains why dislocations behave as stable particles: they can be moved about, but maintain their identity as they move. While two dislocations of opposite orientation, when brought together, can cancel each other (this is the process of annealing), there is no way a single dislocation can "disappear" on its own.

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).

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).

Burgers vector

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 aligned with close-packed crystallographic directions and its magnitude is equivalent to one interatomic spacing.

Screw and mixed dislocations

Screw dislocations are more difficult to visualize, 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

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.

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 utilize 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 observation of dislocation movement and their interactions.

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).

After chemical etching, small pits are formed where the etching solution preferentially attacks the more highly strained material around the dislocations. Thus, the image features indicate points at which dislocations intercept the sample surface. In this way, dislocations in silicon, for example, can be observed indirectly using an interference microscope. Crystal orientation can be determined by the shape of dislocations - 100 elliptical, 111 - triangular (pyramidal).

Image:Silicon_dislocation_orientation_100_mag_500x.png|Dislocations in silicon, orientation 100

Image:Silicon_dislocation_orientation_111_mag_500x.png|Dislocations in silicon, orientation 111

Image:Silicon_dislocation_orientation_111_mag_500x_2.png|Dislocation in silicon, orientation 111

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 τ_m is given approximately by:

$\tau_m = \frac {G} {2 \pi\ } \,$

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, realized 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 malleability of metals).

When metals are subjected to "cold working" (deformation at temperatures which are relatively low as compared to the material's absolute melting temperature, T_m, i.e., typically less than 0.3 T_m) 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”). Tangles of dislocations are found at the early stage of deformation and appear as non well-defined boundaries; the process of dynamic recovery leads eventually to the formation of a cellular structure containing boundaries with misorientation lower than 15º (low angle grain boundaries).

The effects of strain hardening by accumulation of dislocations and the grain structure formed at high strain can be removed by appropriate heat treatment (annealing) which promotes the recovery and subsequent recrystallisation of the material.

Bibliography

Dieter, G. E. (1988) Mechanical Metallurgy ISBN 0071004068
Honeycombe, R.W.K. (1984) The Plastic Deformation of Metals ISBN 0713121815
Hull, D. & Bacon, D. J. (1984) Introduction to Dislocations ISBN 0080287204
Read, W. T. Jr. (1953) Dislocations in Crystals ISBN 1114490660

Materials science