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. The Materials Science Tetrahedron Materials science is a multidisciplinary field focusing on functional solids, whether the function served is structural, electronic, thermal, chemical, magnetic, optical, or some combination of these. ... Crystalline solids have a very regular atomic structure: that is, the local positions of atoms with respect to each other are repeated at the atomic scale. ... Rose des Sables (Sand Rose), formed of gypsum crystals In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... Vito Volterra (May 3, 1860 - October 11, 1940) was an Italian mathematician and physicist, best known for his contributions to mathematical biology. ... 1905 was a common year starting on Sunday (see link for calendar). ...

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. Properties For alternative meanings see atom (disambiguation). ... Quartz crystal A crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions. ... In mathematics, a plane is the fundamental two-dimensional object. ...

There are two major types of dislocations:

1. Edge dislocations; and
2. Screw dislocations.

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

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). Crystalline materials (mainly metals and alloys, but also stoichiometric salts and other materials) are made up of solid regions of ordered matter (atoms placed in one of a number of ordered formations called Bravais lattices). ...

Figure A Perfect (simple cubic) crystal lattice of atoms

Figure C Simplified Representation of Lattice planes

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). Simple Cubic Crystal Lattice Image generated by Wikityke File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Simple Cubic Crystal Lattice Image generated by Wikityke File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Cristallographic lattice planes Image generated by Wikityke File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Cristallographic lattice planes Image generated by Wikityke File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Simple Cubic Lattice showing atomic planes (marked in red) Image generated by Wikityke File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Simple Cubic Lattice showing atomic planes (marked in red) Image generated by Wikityke File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

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

Simplified atomic plane diagram of an edge dislocation. ... Simplified atomic plane diagram of an edge dislocation. ...

Burgers vector

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. Simplified atomic plane diagram of a screw dislocation. ... Simplified atomic plane diagram of a screw dislocation. ...

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

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. TEM Micrograph of Dislocations 1 (precipitate and dislocations in austenitic stainless steel) Photomicrograph by Wikityke File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... TEM Micrograph of Dislocations 1 (precipitate and dislocations in austenitic stainless steel) Photomicrograph by Wikityke File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Etching is an intaglio method of printmaking in which the image is incised into the surface of a metal plate using an acid. ...

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 Transmission electron microscopy (TEM) is an imaging technique whereby a beam of electrons is focused onto a specimen causing an enlarged version to appear on a fluorescent screen or layer of photographic film (see electron microscope), or can be detected by a CCD camera. ... Microstructure refers of the microscopic description of the individual constituents of a material. ... Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ... Diffraction is the apparent bending and spreading of waves when they meet an obstruction. ...

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. TEM micrograph of dislocations 2 (precipitate and dislocations in austenitic stainless steel) Photomicrograph by Wikityke File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... TEM micrograph of dislocations 2 (precipitate and dislocations in austenitic stainless steel) Photomicrograph by Wikityke File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

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. Field ion microscopy (FIM) is an analytical technique used in materials science. ... Atom probe is an analysitical technique in materials science. ...

(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, dislocations in silicon can be observed indirectly using an interference microscope. Crystal orientation can be determined by the shape of dislocations - 100 elliptical, 111 - triangular (pyramidal).

Dislocations in silicon, orientation 100

Dislocations in silicon, orientation 111

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: // Events and trends The 1930s were spent struggling for a solution to the global depression. ... In physics and materials science, plasticity is a property of a material to undergo a non-reversible change of shape in response to an applied force. ... Shear stress is a stress state where the shape of a material tends to change (usually by sliding forces - torque by transversely-acting forces) without particular volume change. ... In materials science, shear modulus S, sometimes referred to as the modulus of rigidity, is defined as the ratio of shear stress to the shear strain: S = shear stress/shear strain = (F/A)/Φ. Another commonly accepted symbol is G. Shear modulus is usually measured in ksi (kips per square...

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. Hot metal work from a blacksmith In chemistry, a metal (Greek: Metallon) is an element that readily forms ions (cations) and has metallic bonds, and metals are sometimes described as a lattice of positive ions (cations) in a cloud of electrons. ... MPA is a TLA that may mean: MasterPaulAnne Macedonian Press Agency Marine Protected Area Maryland and Pennsylvania Railroad (AAR reporting mark MPA) Master of Public Administration Motion Picture Association Morgan_Park_Academy This page concerning a three-letter acronym or abbreviation is a disambiguation page — a navigational aid which lists other pages...

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). 1934 was a common year starting on Monday (link will take you to calendar). ... Egon Orowan (in Hungarian Orován Egon) (August 2, 1901 — August 3, 1989) was an Hungarian/US physicist and metallurgist. ... Michael Polanyi (March 11, 1891 - February 22, 1976) was a Hungarian/ British polymath whose thought and work extended across physical chemistry, economics, and philosophy. ... Sir Geoffrey Ingram Taylor (7 March 1886 - 27 June 1975) was a physicist, mathematician and expert on fluid dynamics and wave theory. ...

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"). Cold Work is a quality imparted on a material as a result of plastic deformation. ... Cold Work is a quality imparted on a material as a result of plastic deformation. ...

The effects of strain hardening can be removed by appropriate heat treatment (annealing) which promotes the recovery and subsequent recrystallisation of the material. The word anneal has several meanings: In metallurgy and materials science annealing is a heat treatment wherein the microstructure of a material is altered, causing changes in its properties such as strength and hardness. ... Recrystallization is an essentially physical process that has meanings in chemistry and geology. ...

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