In materials science, a dislocation is a 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, which often also includes Characterization at the center Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ... 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. ... Enargite 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 (MCMV) was a common year starting on Sunday (see link for calendar). ...

Some types of dislocations can be visualised for 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. Atomic redirects here. ... For other senses of this word, see crystal (disambiguation). ... Two intersecting planes in three-dimensional space In mathematics, a plane is a fundamental two-dimensional object. ...

There are two primary types: edge dislocations and screw dislocations. Mixed dislocations are intermediate between these.

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

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. Image File history File links Edge_dislocation. ... Image File history File links Edge_dislocation. ... In cosmology, a topological defect is a (often) stable configuration of matter predicted by some theories to form at phase transitions in the very early universe. ... In mathematics and physics, a soliton is a self-reinforcing solitary wave caused by nonlinear effects in the medium. ... Anneal may refer to: Annealing (metallurgy), a heat treatment wherein the microstructure of a material is altered, causing changes in its properties such as strength and hardness. ...

Dislocation geometry

A dislocation can be visualized by imagining cutting a crystal along a plane and slipping one half across the other by a lattice vector. The halves will fit back together without leaving a defect. But if the cut only goes part way though the crystal, the boundary of the cut will leave a defect, distorting the nearby lattice. This boundary is the line of the dislocation; the direction of the slip is the Burgers vector.

Dislocations are labeled by the angle between the dislocation line and the Burgers vector. The special cases of 90° and 0° are known as edge and screw dislocations. The dislocations present in real crystalline solids are generally mixed rather than edge or screw; the actual angles of dislocations depend on the lattice structure.

The Burgers vector for an edge dislocation is marked in black in Figure D. It 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.

Edge dislocations

Figure A Perfect (simple cubic) crystal lattice of atoms

Figure C Simplified Representation of Lattice planes

Figure B Crystal lattice showing atom planes

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

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

The stresses caused by an edge dislocation are complex due to its inherent asymmetry. These stresses are described by three equations¹:

where μ is the shear modulus of the material, b is the Burgers vector, ν is Poisson's ratio and x and y are coordinates. These equations suggest a vertically oriented dumbbell of strsasesses surrounding the dislocation, with compression experienced by the atoms near the "extra" plane, and tension experienced by those atoms near the "missing" plane¹. 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... In materials science, a dislocation is a linear crystallographic defect, or irregularity, within a crystal structure. ... When a sample of material is stretched in one direction, it tends to get thinner in the other two directions. ...

Screw dislocations

Figure E Schematic diagram (lattice planes) showing a screw dislocation.

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

Despite the difficulty in visualization, the stresses caused by an screw dislocation are less complex than those of an edge dislocation. These stresses need only one equation, as symmetry allows only one radial coordinate to be used¹:

where μ is the shear modulus of the material, b is the Burgers vector, and r is a radial coordinate. This equation suggests a long cylinder of stress radiating outward from the cylinder and decreasing with distance. Please note, this simple model results in an infinite value for the core of the dislocation at r=0 and so it is only valid for stresses outside of the core of the dislocation.¹ 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... In materials science, a dislocation is a linear crystallographic defect, or irregularity, within a crystal structure. ...

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 different 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. ... Al-Si microstructure at 40x magnification Microstructure refers of the microscopic description of the individual constituents of a material. ... The electron is a fundamental subatomic particle that carries an electric charge. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Galvanized surface with visible crystallites of zinc. ...

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 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. Note the charcteristic 'wiggly' contrast of the dislocation lines as they pass through the thickness of the material. Note also that a dislocation cannot end within a crystal; the dislocation lines in these images end at the sample surface. A dislocation can only be contained within a crystal as a complete loop. 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. Where surface relief can be resolved to the level of an atomic step, screw dislocations appear as distinctive spiral features - thus revealing an important mechanism of crystal growth: where there is a surface step, atoms can more easily add to the crystal, and the surface step associated with a screw dislocation is never destroyed no matter how many atoms are added to it. Field ion microscopy (FIM) is an analytical technique used in materials science. ... The atom probe is an atomic-resolution microscope used in materials science that was invented in 1967 by Erwin Müller. ...

(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). A microscope (Greek: micron = small and scopos = aim) is an instrument for viewing objects that are too small to be seen by the naked or unaided eye. ...

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).

Dislocations in silicon, orientation 100 Image File history File links Silicon_dislocation_orientation_100_mag_500x. ...

Dislocations in silicon, orientation 111 Image File history File links Silicon_dislocation_orientation_111_mag_500x. ...

Dislocation in silicon, orientation 111 Image File history File links Silicon_dislocation_orientation_111_mag_500x_2. ...

Sources of Dislocations

Dislocation density in a material can be increased by plastic deformation by the following relationship: . Since the dislocation density increases with plastic deformation, a mechanism for the creation of dislocations must be activated in the material. Three mechanisms for dislocation formation are formed by homogeneous nucleation, grain boundary initiation, and interfaces the lattice and the surface, precipitates, dispersed phases, or reinforcing fibers.

The creation of a dislocation by homogeneous nucleation is a result of the rupture of the atomic bonds along a line in the lattice. A plane in the lattice is sheared, resulting in 2 oppositely faced half planes or dislocations. These dislocations move away from each other trough the lattice. Since homogeneous nucleation forms dislocations from perfect crystals and requires the simultaneous breaking of many bonds, the energy required for homogeneous nucleation is high. For instance the stress required for homogeneous nucleation in copper has been shown to be , where G is the shear modulus of copper (46 GPa). Solving for τ_hom, we see that the required stress is 3.4 GPa, which is very close to the theoretical strength of the crystal. Therefore, in conventional deformation homogeneous nucleation requires a concentrated stress, and is very unlikely. Grain boundary initiation and interface interaction are more common sources of dislocations.

Irregularities at the grain boundaries in materials can produce dislocations which propagate into the grain. The steps and ledges at the grain boundary are an important source of dislocations in the early stages of plastic deformation.

The surface of a crystal can produce dislocations in the crystal. Due to the small steps on the surface of most crystals, stress in certain regions on the surface is much larger than the average stress in the lattice. The dislocations are then propagated into the lattice in the same manner as in grain boundary initiation. In monocrystals, the majority of dislocations are formed at the surface. The dislocation density 200 microns into the surface of a material has been shown to be six times higher than the density in the bulk. However, in polycrystalline materials the surface sources cannot have a major effect because most grains are not in contact with the surface.

The interface between a metal and an oxide can greatly increase the number of dislocations created. The oxide layer puts the surface of the metal in tension because the oxygen atoms squeeze into the lattice, and the oxygen atoms are under compression. This greatly increases the stress on the surface of the metal and consequently the amount of dislocations formed at the surface. The increased amount of stress on the surface steps results in an increase of dislocations^[1].

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: This article or section does not cite its references or sources. ... For other uses, see Plasticity. ... Shear stress is a stress state where the stress is parallel to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ... 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 positive ions (cations) and has metallic bonds. ... MPA is a TLA (three-letter acronym) that may mean: Macedonian Press Agency Marine Protected Area Maritime Patrol Aircraft Maryland and Pennsylvania Railroad (AAR reporting mark MPA) Master of Public Administration Master of Public Affairs Max Planck Institute for Astrophysics Metropolitan Police Authority Mid-atlantic Pagan Alliance Motion Picture Association...

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). 1934 (MCMXXXIV) 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 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). It has been suggested that this article or section be merged into work hardening. ... Cold Work is a quality imparted on a material as a result of plastic deformation. ... Recovery is a process by which deformed grains can reduce their stored energy by the removal or rearrangement of defects in their crystal structure. ...

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. Annealing, in metallurgy and materials science, is a heat treatment wherein the microstructure of a material is altered, causing changes in its properties such as strength and hardness. ... Recovery is a process by which deformed grains can reduce their stored energy by the removal or rearrangement of defects in their crystal structure. ... Recrystallization is an essentially physical process that has meanings in chemistry and geology. ...

Dislocation Climb

Dislocations can slip in planes containing both the dislocation and the Burger's Vector. For a screw dislocation, the dislocation and the Burger's vector are parallel, so the dislocation may slip in any plane containing the dislocation. For an edge dislocation, the dislocation and the Burger's vector are perpendicular, so there is only one plane in which the dislocation can slip. There is an alternative mechanism of dislocation motion, fundamentally different from slip, that allows an edge dislocation to move out of its slip plane, known as dislocation climb. Dislocation climb allows an edge dislocation to move perpendicular to its slip plane.

The driving force for dislocation climb is the movement of vacancies through a crystal lattice. If a vacancy moves next to the boundary of the extra half plane of atoms that forms an edge dislocation, the atom in the half plane closest to the vacancy can "jump" and fill the vacancy. This atom shift "moves" the vacancy in line with the half plane of atoms, causing a shift, or positive climb, of the dislocation. The process of a vacancy being absorbed at the boundary of a half plane of atoms, rather than created, is known as negative climb. Since dislocation climb results from individual atoms "jumping" into vacancies, climb occurs in single atom diameter increments.

During positive climb, the crystal shrinks in the direction perpendicular to the extra half plane of atoms because atoms are being removed from the half plane. Since negative climb involves an addition of atoms to the half plane, the crystal grows in the direction perpendicular to the half plane. Therefore, compressive stress in the direction perpendicular to the half plane promotes positive climb, while tensile stress promotes negative climb. This is one main difference between slip and climb, since slip is caused by only shear stress.

One additional difference between dislocation slip and climb is the temperature dependance. Climb occurs much more rapidly at high temperatures than low temperatures due to an increase in vacancy motion. Slip, on the other hand, has only a small dependance on temperature.

Bibliography

• [1]Reed-Hill, R. E. (1994) "Physical Metallurgy Principles" ISBN 0-534-92173-6
• Dieter, G. E. (1988) Mechanical Metallurgy ISBN 0-07-100406-8
• Honeycombe, R.W.K. (1984) The Plastic Deformation of Metals ISBN 0-7131-2181-5
• Hull, D. & Bacon, D. J. (1984) Introduction to Dislocations ISBN 0-08-028720-4
• Read, W. T. Jr. (1953) Dislocations in Crystals ISBN 1-114-49066-0
• Kleinert, Hagen, Gauge Fields in Condensed Matter, Vol. II, "STRESSES AND DEFECTS; Differential Geometry, Crystal Melting", pp. 743-1456, World Scientific (Singapore, 1989); Paperback ISBN 9971-5-0210-0 (readable online here)
• Meyers and Chawla. (1999) Mechanical Behaviors of Materials. Prentice Hall, Inc. 228-231.

Hagen Kleinert, Photo taken in 2004 Hagen Kleinert is the Professor of Theoretical Physics at the Free University of Berlin, Germany, and Honorary Member of the Russian Academy of Creative Endeavors. ... Figure 1  Stress tensor A mature tree trunk may support a greater force than a fine steel wire but intuitively we feel that steel is stronger than wood. ... Defect is the n00b of the animating world, everybody knows that he cannot and will not animate. ... In physics, melting is the process of heating a solid substance to a point (called the melting point) where it turns into a liquid. ...

External links

• Defects in Crystals/ Prof. Dr. Helmut Föll website Chapter 5 contains a wealth of information on dislocations