Editing Dislocation (section)

=== Generating dislocations ===
When metals are subjected to [[cold forming|cold working]] (deformation at temperatures which are relatively low as compared to the material's absolute melting temperature, <math>T_m</math> i.e., typically less than <math>0.4T_m</math>) 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 <math>\rho</math> in a material can be increased by plastic deformation by the following relationship:

::<math>\tau \propto \sqrt{\rho}</math>.

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 <math> \frac {\tau_{\text{hom}}}{G}=7.4\times10^{-2}</math>, where <math>G</math> is the shear modulus of copper (46 GPa).  Solving for <math>\tau_{\text{hom}} \,\!</math>, 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 ====
{{main article|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.

==== Surfaces ====
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.

==== Interfaces ====
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.<ref>[[Marc A. Meyers|Marc André Meyers]], Krishan Kumar Chawla (1999) ''Mechanical Behaviors of Materials.'' Prentice Hall, pp. 228–31, {{ISBN|0132628171}}.</ref>

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 [[Epitaxy|epitaxial crystal growth]] on a substrate.<ref>{{Cite journal|last1=Schober|first1=T.|last2=Balluffi|first2=R. W.|date=1970-01-01|title=Quantitative observation of misfit dislocation arrays in low and high angle twist grain boundaries|journal=The Philosophical Magazine|volume=21|issue=169|pages=109–123|doi=10.1080/14786437008238400|bibcode=1970PMag...21..109S|issn=0031-8086}}</ref>

==== Irradiation ====
Dislocation loops may form in the damage created by [[Radiation damage|energetic irradiation]].<ref>{{Cite journal|last=Eyre|first=B. L.|date=February 1973|title=Transmission electron microscope studies of point defect clusters in fcc and bcc metals|journal=Journal of Physics F: Metal Physics|language=en|volume=3|issue=2|pages=422–470|doi=10.1088/0305-4608/3/2/009|bibcode=1973JPhF....3..422E|issn=0305-4608}}</ref><ref>{{Cite journal|last=Masters|first=B. C.|date=1965-05-01|title=Dislocation loops in irradiated iron|journal=The Philosophical Magazine|volume=11|issue=113|pages=881–893|doi=10.1080/14786436508223952|bibcode=1965PMag...11..881M|s2cid=4205189 |issn=0031-8086}}</ref> A prismatic dislocation loop can be understood as an extra (or missing) collapsed disk of atoms, and can form when [[Interstitial defect|interstitial atoms]] or vacancies cluster together. This may happen directly as a result of single or multiple [[collision cascade]]s,<ref>{{Cite journal|last1=Kirk|first1=M. A.|last2=Robertson|first2=I. M.|last3=Jenkins|first3=M. L.|last4=English|first4=C. A.|last5=Black|first5=T. J.|last6=Vetrano|first6=J. S.|date=1987-06-01|title=The collapse of defect cascades to dislocation loops|journal=Journal of Nuclear Materials|language=en|volume=149|issue=1|pages=21–28|doi=10.1016/0022-3115(87)90494-6|bibcode=1987JNuM..149...21K|issn=0022-3115|url=https://digital.library.unt.edu/ark:/67531/metadc1095269/}}</ref> 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.