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Dislocations of edge (left) and screw (right) type. Burgers Vector and dislocations (screw and edge type).svg
Dislocations of edge (left) and screw (right) type.

In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to slide over each other at low stress levels and is known as glide or slip. The crystalline order is restored on either side of a glide dislocation but the atoms on one side have moved by one position. The crystalline order is not fully restored with a partial dislocation. A dislocation defines the boundary between slipped and unslipped regions of material and as a result, must either form a complete loop, intersect other dislocations or defects, or extend to the edges of the crystal. [1] [2] A dislocation can be characterised by the distance and direction of movement it causes to atoms which is defined by the Burgers vector. Plastic deformation of a material occurs by the creation and movement of many dislocations. The number and arrangement of dislocations influences many of the properties of materials.


The two primary types of dislocations are sessile dislocations which are immobile and glissile dislocations which are mobile. [3] Examples of sessile dislocations are the stair-rod dislocation and the Lomer–Cottrell junction. The two main types of mobile dislocations are edge and screw dislocations.

Edge dislocations can be visualized 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. This phenomenon is analogous to half of a piece of paper inserted into a stack of paper, where the defect in the stack is noticeable only at the edge of the half sheet.

The theory describing the elastic fields of the defects was originally developed by Vito Volterra in 1907. In 1934, Egon Orowan, Michael Polanyi and G. I. Taylor, proposed that the low stresses observed to produce plastic deformation compared to theoretical predictions at the time could be explained in terms of the theory of dislocations.


The theory describing the elastic fields of the defects was originally developed by Vito Volterra in 1907. [4] The term 'dislocation' referring to a defect on the atomic scale was coined by G. I. Taylor in 1934. [5]

Prior to the 1930s, one of the enduring challenges of materials science was to explain plasticity in microscopic terms. A simplistic 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 , shear strength is given approximately by:

The shear modulus in metals is typically within the range 20 000 to 150 000 MPa indicating a predicted shear stress of 3 000 to 24 000 MPa. This was difficult to reconcile with measured shear stresses in the range of 0.5 to 10 MPa.

In 1934, Egon Orowan, Michael Polanyi and G. I. Taylor, independently proposed 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. In effect, a half plane of atoms is moved in response to shear stress by breaking and reforming a line of bonds, one (or a few) at a time. The energy required to break a row of bonds is far less than that required to break all the bonds on an entire plane of atoms at once. Even this simple model of the force required to move a dislocation shows that plasticity is possible at much lower stresses than in a perfect crystal. In many materials, particularly ductile materials, dislocations are the "carrier" of plastic deformation, and the energy required to move them is less than the energy required to fracture the material.


A dislocation is a linear crystallographic defect or irregularity within a crystal structure which contains an abrupt change in the arrangement of atoms. The crystalline order is restored on either side of a dislocation but the atoms on one side have moved or slipped. Dislocations define the boundary between slipped and unslipped regions of material and cannot end within a lattice and must either extend to a free edge or form a loop within the crystal. [1] A dislocation can be characterised by the distance and direction of movement it causes to atoms in the lattice which is called the Burgers vector. The Burgers vector of a dislocation remains constant even though the shape of the dislocation may change.

A variety of dislocation types exist, with mobile dislocations known as glissile and immobile dislocations called sessile. The movement of mobile dislocations allow atoms to slide over each other at low stress levels and is known as glide or slip. The movement of dislocations may be enhanced or hindered by the presence other elements within the crystal and over time, these elements may diffuse to the dislocation forming a Cottrell atmosphere. The pinning and breakaway from these elements explains some of the unusual yielding behavior seen with steels. The interaction of hydrogen with dislocations is one of the mechanisms proposed to explain hydrogen embrittlement.

Dislocations behave as though they are a distinct entity within a crystalline material where some types of dislocation can move through the material bending, flexing and changing shape and interacting with other dislocations and features within the crystal. Dislocations are generated by deforming a crystalline material such as metals, which can cause them to initiate from surfaces, particularly at stress concentrations or within the material at defects and grain boundaries. The number and arrangement of dislocations give rise to many of the properties of metals such as ductility, hardness and yield strength. Heat treatment, alloy content and cold working can change the number and arrangement of the dislocation population and how they move and interact in order to create useful properties.

Simulation of dislocations in aluminium. Only non-crystalline atoms are shown.

Generating dislocations

When metals are subjected to cold working (deformation at temperatures which are relatively low as compared to the material's absolute melting temperature, i.e., typically less than ) the dislocation density increases due to the formation of new dislocations. 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 or work hardening.

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 homogeneous nucleation, grain boundary initiation, and interfaces between the lattice and the surface, precipitates, dispersed phases, or reinforcing fibers.

Homogeneous nucleation

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 through 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 is the shear modulus of copper (46 GPa). Solving for , 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.

Frank–Read source

The Frank–Read source is a mechanism that is able to produce a stream of dislocations from a pinned segment of a dislocation. Stress bows the dislocation segment, expanding until it creates a dislocation loop that breaks free from the source.


The surface of a crystal can produce dislocations in the crystal. Due to the small steps on the surface of most crystals, stress in some regions on the surface is much larger than the average stress in the lattice. This stress leads to dislocations. The dislocations are then propagated into the lattice in the same manner as in grain boundary initiation. In single crystals, the majority of dislocations are formed at the surface. The dislocation density 200 micrometres 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 do not 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 in dislocations formed and emitted from the interface. [6]

Dislocations may also form and remain in the interface plane between two crystals. This occurs when the lattice spacing of the two crystals do not match, resulting in a misfit of the lattices at the interface. The stress caused by the lattice misfit is released by forming regularly spaced misfit dislocations. Misfit dislocations are edge dislocations with the dislocation line in the interface plane and the Burgers vector in the direction of the interface normal. Interfaces with misfit dislocations may form e.g. as a result of epitaxial crystal growth on a substrate. [7]


Dislocation loops may form in the damage created by energetic irradiation. [8] [9] A prismatic dislocation loop can be understood as an extra (or missing) collapsed disk of atoms, and can form when interstitial atoms or vacancies cluster together. This may happen directly as a result of single or multiple collision cascades, [10] which results in locally high densities of interstitial atoms and vacancies. In most metals, prismatic dislocation loops are the energetically most preferred clusters of self-interstitial atoms.

Interaction and arrangement

Geometrically necessary dislocations

Geometrically necessary dislocations are arrangements of dislocations that can accommodate a limited degree of plastic bending in a crystalline material. 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 15° (low angle grain boundaries).


Adding pinning points that inhibit the motion of dislocations, such as alloying elements, can introduce stress fields that ultimately strengthen the material by requiring a higher applied stress to overcome the pinning stress and continue dislocation motion.

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 recrystallization of the material.

The combined processing techniques of work hardening and annealing allow for control over dislocation density, the degree of dislocation entanglement, and ultimately the yield strength of the material.

Persistent slip bands

Repeated cycling of a material can lead to the generation and bunching of dislocations surrounded by regions that are relatively dislocation free. This pattern forms a ladder like structure known as a persistent slip band (PSB). [11] PSB's are so-called, because they leave marks on the surface of metals that even when removed by polishing, return at the same place with continued cycling.

PSB walls are predominately made up of edge dislocations. In between the walls, plasticity is transmitted by screw dislocations. [11]

Where PSB's meet the surface, extrusions and intrusions form, which under repeated cyclic loading, can lead to the initiation of a fatigue crack. [12]



Dislocations can slip in planes containing both the dislocation line and the Burgers vector, the so called glide plane. [13] For a screw dislocation, the dislocation line and the Burgers vector are parallel, so the dislocation may slip in any plane containing the dislocation. For an edge dislocation, the dislocation and the Burgers vector are perpendicular, so there is one plane in which the dislocation can slip.


Dislocation climb is an alternative mechanism of dislocation motion that allows an edge dislocation to move out of 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 dependence. 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 dependence on temperature.

Dislocation avalanches

Dislocation avalanches occur when multiple simultaneous movement of dislocations occur.

Dislocation Velocity

Dislocation velocity is largely dependent upon shear stress and temperature, and can often be fit using a power law function: [14]

where is a material constant, is the applied shear stress, is a constant that decreases with increasing temperature. Increased shear stress will increase the dislocation velocity, while increased temperature will typically decrease the dislocation velocity. Greater phonon scattering at higher temperatures is hypothesized to be responsible for increased damping forces which slow the dislocation movement.


An edge-dislocation (b = Burgers vector) Edge dislocation 2.svg
An edge-dislocation (b = Burgers vector)

Two main types of mobile dislocations exist: edge and screw. Dislocations found in real materials are typically mixed, meaning that they have characteristics of both.


Schematic diagram (lattice planes) showing an edge dislocation. Burgers vector in black, dislocation line in blue. Dislocation edge d2.svg
Schematic diagram (lattice planes) showing an edge dislocation. Burgers vector in black, dislocation line in blue.

A crystalline material consists of a regular array of atoms, arranged into lattice planes. An edge dislocation is a defect where an extra half-plane of atoms is introduced midway through the crystal, distorting nearby planes of atoms. When enough force is applied from one side of the crystal structure, this extra plane passes through planes of atoms breaking and joining bonds with them until it reaches the grain boundary. The dislocation has two properties, a line direction, which is the direction running along the bottom of the extra half plane, and the Burgers vector which describes the magnitude and direction of distortion to the lattice. In an edge dislocation, the Burgers vector is perpendicular to the line direction.

The stresses caused by an edge dislocation are complex due to its inherent asymmetry. These stresses are described by three equations: [15]

where is the shear modulus of the material, is the Burgers vector, is Poisson's ratio and and are coordinates.

These equations suggest a vertically oriented dumbbell of stresses surrounding the dislocation, with compression experienced by the atoms near the "extra" plane, and tension experienced by those atoms near the "missing" plane. [15]


A screw dislocation can be visualized by cutting a crystal along a plane and slipping one half across the other by a lattice vector, the halves fitting back together without leaving a defect. If the cut only goes part way through the crystal, and then slipped, the boundary of the cut is a screw dislocation. 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. In pure screw dislocations, the Burgers vector is parallel to the line direction. [16]

The stresses caused by a screw dislocation are less complex than those of an edge dislocation and need only one equation, as symmetry allows one radial coordinate to be used: [15]

where is the shear modulus of the material, is the Burgers vector, and is a radial coordinate. This equation suggests a long cylinder of stress radiating outward from the cylinder and decreasing with distance. This simple model results in an infinite value for the core of the dislocation at and so it is only valid for stresses outside of the core of the dislocation. [15] If the Burgers vector is very large, the core may actually be empty resulting in a micropipe, as commonly observed in silicon carbide.


In many materials, dislocations are found where the line direction and Burgers vector are neither perpendicular nor parallel and these dislocations are called mixed dislocations, consisting of both screw and edge character. They are characterized by , the angle between the line direction and Burgers vector, where for pure edge dislocations and for screw dislocations.


Partial dislocations leave behind a stacking fault. Two types of partial dislocation are the Frank partial dislocation which is sessile and the Shockley partial dislocation which is glissile. [3]

A Frank partial dislocation is formed by inserting or removing a layer of atoms on the {111} plane which is then bounded by the Frank partial. Removal of a close packed layer is known as an intrinsic stacking fault and inserting a layer is known as an extrinsic stacking fault. The Burgers vector is normal to the {111} glide plane so the dislocation cannot glide and can only move through climb. [1]

In order to lower the overall energy of the lattice, edge and screw dislocations typically disassociate into a stacking fault bounded by two Shockley partial dislocations. [17] The width of this stacking-fault region is proportional to the stacking-fault energy of the material. The combined effect is known as an extended dislocation and is able to glide as a unit. However, dissociated screw dislocations must recombine before they can cross slip, making it difficult for these dislocations to move around barriers. Materials with low stacking-fault energies have the greatest dislocation dissociation and are therefore more readily cold worked.

Stair-rod and the Lomer–Cottrell junction

If two glide dislocations that lie on different {111} planes split into Shockley partials and intersect, they will produce a stair-rod dislocation with a Lomer-Cottrell dislocation at its apex. [18] It is called a stair-rod because it is analogous to the rod that keeps carpet in-place on a stair.


Geometrical differences between jogs and kinks Jog-Kink.gif
Geometrical differences between jogs and kinks

A Jog describes the steps of a dislocation line that are not in the glide plane of a crystal structure. [17] A dislocation line is rarely uniformly straight, often containing many curves and steps that can impede or facilitate dislocation movement by acting as pinpoints or nucleation points respectively. Because jogs are out of the glide plane, under shear they cannot move by glide (movement along the glide plane). They instead must rely on vacancy diffusion facilitated climb to move through the lattice. [19] Away from the melting point of a material, vacancy diffusion is a slow process, so jogs act as immobile barriers at room temperature for most metals. [20]

Jogs typically form when two non-parallel dislocations cross during slip. The presence of jogs in a material increases its yield strength by preventing easy glide of dislocations. A pair of immobile jogs in a dislocation will act as a Frank–Read source under shear, increasing the overall dislocation density of a material. [20] When a material's yield strength is increased via dislocation density increase, particularly when done by mechanical work, it is called work hardening. At high temperatures, vacancy facilitated movement of jogs becomes a much faster process, diminishing their overall effectiveness in impeding dislocation movement.


Kinks are steps in a dislocation line parallel to glide planes. Unlike jogs, they facilitate glide by acting as a nucleation point for dislocation movement. The lateral spreading of a kink from the nucleation point allows for forward propagation of the dislocation while only moving a few atoms at a time, reducing the overall energy barrier to slip.

Example in two dimensions (2D)

Dissociation of a pair of dislocations due to shearing (red arrows) of an hexagonal crystal in 2D. A dislocation in 2D consists of a bound pair of five-folded (green) and seven-folded (orange) coordination number. Dislokation Dissoziation.svg
Dissociation of a pair of dislocations due to shearing (red arrows) of an hexagonal crystal in 2D. A dislocation in 2D consists of a bound pair of five-folded (green) and seven-folded (orange) coordination number.

In two dimensions (2D) only the edge dislocations exist, which play a central role in melting of 2D crystals, but not the screw dislocation. Those dislocations are topological point defects which implies that they cannot be created isolated by an affine transformation without cutting the hexagonal crystal up to infinity (or at least up to its boarder). They can only be created in pairs with antiparallel Burgers vector. If a lot of dislocations are e. g. thermally excited, the discrete translational order of the crystal is destroyed. Simultaneously, the shear modulus and the Young's modulus disappear, which implies that the crystal is molten to a fluid phase. The orientational order is not yet destroyed (as indicated by lattice lines in one direction) and one finds - very similar to liquid crystals - a fluid phase with typically a six-folded director field. This so-called hexatic phase still has an orientational stiffness. The isotropic fluid phase appears, if the dislocations dissociate into isolated five-folded and seven-folded disclinations. [21] This two step melting is described within the so-called Kosterlitz-Thouless-Halperin-Nelson-Young-theory (KTHNY theory), based on two transitions of Kosterlitz-Thouless-type.


Transmission electron microscopy (TEM)

Transmission electron micrograph of dislocations TEM micrograph dislocations precipitate stainless steel 1.jpg
Transmission electron micrograph of dislocations
Transmission electron micrograph of dislocations TEM micrograph dislocations precipitate stainless steel 2.jpg
Transmission electron micrograph of dislocations

Transmission electron microscopy can be used to observe dislocations within the microstructure of the material. [22] Thin foils of material are prepared to render them transparent to the electron beam of the microscope. The electron beam undergoes diffraction by the regular crystal lattice planes into a diffraction pattern and contrast is generated in the image by this diffraction (as well as by thickness variations, varying strain, and other mechanisms). Dislocations have different local atomic structure and produce a strain field, and therefore will cause the electrons in the microscope to scatter in different ways. Note the characteristic 'wiggly' contrast of the dislocation lines as they pass through the thickness of the material in the figure (also note that dislocations cannot end in a crystal, and these dislocations are terminating at the surfaces since the image is a 2D projection).

Dislocations do not have random structures, the local atomic structure of a dislocation is determined by the Burgers vector. One very useful application of the TEM in dislocation imaging is the ability to experimentally determine the Burgers vector. Determination of the Burgers vector is achieved by what is known as ("g dot b") analysis. [23] When performing dark field microscopy with the TEM, a diffracted spot is selected to form the image (as mentioned before, lattice planes diffract the beam into spots), and the image is formed using only electrons that were diffracted by the plane responsible for that diffraction spot. The vector in the diffraction pattern from the transmitted spot to the diffracted spot is the vector. The contrast of a dislocation is scaled by a factor of the dot product of this vector and the Burgers vector (). As a result, if the Burgers vector and vector are perpendicular, there will be no signal from the dislocation and the dislocation will not appear at all in the image. Therefore, by examining different dark field images formed from spots with different g vectors, the Burgers vector can be determined.

Other methods

Etch Pits formed on the ends of dislocations in silicon, orientation (111) Silicon dislocation orientation 111 mag 500x.png
Etch Pits formed on the ends of dislocations in silicon, orientation (111)

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.

Chemical etching

When a dislocation line intersects the surface of a metallic material, the associated strain field locally increases the relative susceptibility of the material to acid etching and an etch pit of regular geometrical format results. 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 the etch pits associated with the dislocations.

If the material is deformed and repeatedly re-etched, a series of etch pits can be produced which effectively trace the movement of the dislocation in question.

Dislocation forces

Forces on dislocations

Dislocation motion as a result of external stress on a crystal lattice can be described using virtual internal forces which act perpendicular to the dislocation line. The Peach-Koehler equation [24] [25] [26] can be used to calculate the force per unit length on a dislocation as a function of the Burgers vector, , stress, , and the sense vector, .

The force per unit length of dislocation is a function of the general state of stress, , and the sense vector, .

The components of the stress field can be obtained from the Burgers vector, normal stresses, , and shear stresses, .

Forces between dislocations

The force between dislocations can be derived from the energy of interactions of the dislocations, . The work done by displacing cut faces parallel to a chosen axis that creates one dislocation in the stress field of another displacement. For the and directions:

The forces are then found by taking the derivatives.

Free surface forces

Dislocations will also tend to move towards free surfaces due to the lower strain energy. This fictitious force can be expressed for a screw dislocation with the component equal to zero as:

where is the distance from free surface in the direction. The force for an edge dislocation with can be expressed as:

Related Research Articles

Shear stress Component of stress coplanar with a material cross section

Shear stress, often denoted by τ, is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts.

Creep (deformation) Tendency of a solid material to move slowly or deform permanently under mechanical stress

In materials science, creep is the tendency of a solid material to move slowly or deform permanently under the influence of persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increases as they near their melting point.

Miller index Description of crystal lattice planes

Miller indices form a notation system in crystallography for planes in crystal (Bravais) lattices.

Mohrs circle Geometric civil engineering calculation technique

Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor.

Work hardening

Work hardening, also known as strain hardening, is the strengthening of a metal or polymer by plastic deformation. Work hardening may be desirable, undesirable, or inconsequential, depending on the context.

Precipitation hardening, also called age hardening or particle hardening, is a heat treatment technique used to increase the yield strength of malleable materials, including most structural alloys of aluminium, magnesium, nickel, titanium, and some steels and stainless steels. In superalloys, it is known to cause yield strength anomaly providing excellent high-temperature strength.

Cauchy stress tensor Representation of mechanical stress at every point within a deformed 3D object

In continuum mechanics, the Cauchy stress tensor, true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine components that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration. The tensor relates a unit-length direction vector n to the traction vector T(n) across an imaginary surface perpendicular to n:

Yield (engineering) Phenomenon of deformation due to structural stress

In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation.

Critical resolved shear stress

Critical resolved shear stress (CRSS) is the component of shear stress, resolved in the direction of slip, necessary to initiate slip in a grain. Resolved shear stress (RSS) is the shear component of an applied tensile or compressive stress resolved along a slip plane that is other than perpendicular or parallel to the stress axis. The RSS is related to the applied stress by a geometrical factor, m, typically the Schmid factor:

Slip (materials science)

In materials science, slip is the large displacement of one part of a crystal relative to another part along crystallographic planes and directions. Slip occurs by the passage of dislocations on close packed planes which are planes containing the greatest number of atoms per area and in close-packed directions. Close-packed planes are known as slip or glide planes. A slip system describes the set of symmetrically identical slip planes and associated family of slip directions for which dislocation motion can easily occur and lead to plastic deformation. The magnitude and direction of slip are represented by the Burgers vector.

Solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element to the crystalline lattice of another element, forming a solid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation more difficult by impeding dislocation motion through stress fields. In contrast, alloying beyond the solubility limit can form a second phase, leading to strengthening via other mechanisms.

Peierls stress is the force needed to move a dislocation within a plane of atoms in the unit cell. The magnitude varies periodically as the dislocation moves within the plane. Peierls stress depends on the size and width of a dislocation and the distance between planes. Because of this, Peierls stress decreases with increasing distance between atomic planes. Yet since the distance between planes increases with planar atomic density, slip of the dislocation is preferred on closely packed planes.

Burgers vector

In materials science, the Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted as b, that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice.

Methods have been devised to modify the yield strength, ductility, and toughness of both crystalline and amorphous materials. These strengthening mechanisms give engineers the ability to tailor the mechanical properties of materials to suit a variety of different applications. For example, the favorable properties of steel result from interstitial incorporation of carbon into the iron lattice. Brass, a binary alloy of copper and zinc, has superior mechanical properties compared to its constituent metals due to solution strengthening. Work hardening has also been used for centuries by blacksmiths to introduce dislocations into materials, increasing their yield strengths.

Frank–Read source

In materials science, a Frank–Read source is a mechanism explaining the generation of multiple dislocations in specific well-spaced slip planes in crystals when they are deformed. When a crystal is deformed, in order for slip to occur, dislocations must be generated in the material. This implies that, during deformation, dislocations must be primarily generated in these planes. Cold working of metal increases the number of dislocations by the Frank–Read mechanism. Higher dislocation density increases yield strength and causes work hardening of metals.

Dislocation creep is a deformation mechanism in crystalline materials. Dislocation creep involves the movement of dislocations through the crystal lattice of the material, in contrast to diffusion creep, in which diffusion is the dominant creep mechanism. It causes plastic deformation of the individual crystals, and thus the material itself.

An antiphase domain (APD) is a type of planar crystallographic defect in which the atoms within a region of a crystal are configured in the opposite order to those in the perfect lattice system. Throughout the entire APD, atoms sit on the sites typically occupied by atoms of a different species. For example, in an ordered AB alloy, if an A atom occupies the site usually occupied by a B atom, a type of crystallographic point defect called an antisite defect is formed. If an entire region of the crystal is translated such that every atom in a region of the plane of atoms sits on its antisite, an antiphase domain is formed. In other words, an APD is a region formed from antisite defects of a parent lattice. On either side of this domain, the lattice is still perfect, and the boundaries of the domain are referred to as antiphase boundaries. Crucially, crystals on either side of an antiphase boundary are related by a translation, rather than a reflection or an inversion.

Geometrically necessary dislocations are like-signed dislocations needed to accommodate for plastic bending in a crystalline material. They are present when a material's plastic deformation is accompanied by internal plastic strain gradients. They are in contrast to statistically stored dislocations, with statistics of equal positive and negative signs, which arise during plastic flow from multiplication processes like the Frank-Read source.

Cross slip

Cross slip is the process by which a screw dislocation moves from one slip plane to another due to local stresses. It allows non-planar movement of screw dislocations. Non-planar movement of edge dislocations is achieved through climb.

Kinks are deviations of a dislocation defect along its glide plane. In edge dislocations, the constant glide plane allows short regions of the dislocation to turn, converting into screw dislocations and producing kinks. Screw dislocations have rotatable glide planes, thus kinks that are generated along screw dislocations act as an anchor for the glide plane. Kinks differ from jogs in that kinks are strictly parallel to the glide plane, while jogs shift away from the glide plane.


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