What are dislocations?

How do crystalline materials deform?  When you try to shear or stretch a crystalline solid, in the elastic regime the atoms just slightly readjust their positions (at right).  The "spring constant" that determines the amount of deformation originates from the chemical bonds - how and to what extent the electrons are shared between the neighboring atoms.  In this elastic regime, if the applied stress is removed, the atoms return to their original positions.  Now imagine cranking up the applied stress.  In the "brittle" limit, eventually bonds rupture and the material fractures abruptly in a runaway process.  (You may never have thought about this, but crack propagation is a form of mechanochemistry, in that bonds are broken and other chemical processes then have to take place to make up for those changes.) 

In many materials, especially metals, rather than abruptly ripping apart, materials can deform plastically, so that even when the external stress is removed, the atoms remain displaced somehow.  The material has been deformed "irreversibly", meaning that the microscopic bonding of at least some of the atoms has been modified.  The mechanism here is the presence and propagation of defects in the crystal stacking called dislocations, the existence of which was deduced back in the 1930s when people first came to appreciate that metals are generally far easier to deform than expectations from a simple calculation assuming perfect bonding.    

(a) Edge dislocation, where the copper-colored spheres

are an "extra" plane of atoms.  (b) A (red) path enclosing 

the edge dislocation; the Burgers vector is shown with 

the black arrow. (c) A screw dislocation.  (Images from 

my textbook.)

Dislocations are topological line defects (as opposed to point defects like vacancies, impurities, or interstitials), characterized by a vector along the line of the defect, and a Burgers vector.  Imagine taking some number of lattice site steps going around a closed loop in a crystal plane of the material.   For example, in the \(x-y\) plane, you go 4 sites in the \(+x\) direction, 4 sites in the \(+y\) direction, 4 sites in the \(-x\) direction, and 4 sites in the \(-y\) direction.  If you ended up back where you started, then you have not enclosed a dislocation.  If you end up shifted sideways in the plane relative to your starting point, your path has enclosed an edge dislocation (see (a) and (b) to the right).  The Burgers vector connects the endpoint of the path with the beginning point of the path.  An edge dislocation is the end of an "extra" plane of atoms in a crystal (the orange atoms in (a)).  If you go around the path in the \(x-y\) plane and end up shifted out of the initial plane (so that the Burgers vector is pointing along \(z\), parallel to the dislocation line), your path enclosed a screw dislocation (see (c) in the figure).   Edge and screw dislocations are the two major classes of mobile dislocations.  There are also mixed dislocations, in which the dislocation line meanders around, so that displacements can look screw-like along some orientations of the line and edge-like along others.  (Here is some nice educational material on this, albeit dated in its web presentation.)  

A few key points:

• Mobile dislocations are the key to plastic deformation and the "low" yield strength of ductile materials compared to the idea situation.  Edge dislocations propagate sideways along their Burgers vectors when shear stresses are applied to the plane in which the dislocation lies.  This is analogous to moving a rug across the floor by propagating a lump rather than trying to shift the entire rug at once.  Shearing the material by propagating an edge dislocation involves breaking and reforming bonds along the line, which is much cheaper energetically than breaking all the bonds in the shear plane at once.  To picture how a screw dislocation propagates in the presence of shear, imagine trying to tear a stack of paper.  (I was taught to picture tearing a phone book, which shows how ancient I am.)  
• A dislocation is a great example of an emergent object.  Materials scientists and mechanical engineers interested in this talk about dislocations as entities that have positions, can move, and can interact.  One could describe everything in terms of the positions of the individual atoms in the solid, but it is often much more compact and helpful to think about dislocations as objects unto themselves. 
• Dislocations can multiply under deformation.  Here is a low-tech but very clear video about one way this can happen, the Frank-Read source (more discussion here, and here is the original theory paper by Frank and Read).  In case you think this is just some hand-wavy theoretical idea, here is a video from a transmission electron microscopy showing one of these sources in action.
• Dislocations are associated with local strain (and therefore stress). This is easiest for me to see in the end-on look at the edge dislocation in (a), where clearly there is compressive strain below where the "extra" orange plane of atoms starts, and tensile strain above there where the lattice is spreading to make room for that plane.   Because of these strain fields and the topological nature of dislocations, they can tangle with each other and hinder their propagation.  When this happens, a material becomes more difficult to deform plastically, a phenomenon called work hardening that you have seen if you've ever tried to break a paperclip by bending the metal back and forth.
• Controlling the nucleation and pinning of dislocations is key to the engineering of tough, strong materials.  This paper is an example of this, where in a particular alloy, crystal rotation makes it possible to accommodate a lot of strain from dislocations in "kink bands".