Line Defects: Dislocations

Introduction

An ideal crystal sheared all at once would require many bonds across a plane to move simultaneously. Real crystals deform at much smaller stresses because a line defect can travel through them, changing local bonding one small region at a time. That line is a dislocation . Edge and screw descriptions capture limiting geometries, while most real lines have mixed character. Their motion controls plasticity and interacts with impurities, grain boundaries and other dislocations.

Core explanation

Picture an extra half-plane of atoms ending inside an otherwise regular lattice. The line where that plane terminates is an edge dislocation . Above and below the line, atoms are displaced and the lattice is strained. For a pure edge segment, the Burgers vector b is perpendicular to the dislocation-line direction. The vector records the net mismatch revealed by tracing a closed sequence of equal lattice steps around the line. In a perfect reference lattice the same sequence closes; around a dislocation it fails to close by b, with the sign depending on the tracing convention.

A screw dislocation has a different geometry: atomic planes form a spiral-like ramp around the line. For a pure screw segment, b is parallel to the line direction. Real dislocation lines can curve; a single line may have edge character at one segment and screw character at another. The Burgers vector is conserved along an ordinary continuous dislocation line through a crystal, while the angle between b and the local line direction changes. MIT physical metallurgy notes teach Burgers circuits and edge, screw and mixed lines together; NIST's dislocation method documentation separates edge and screw vector components in a simulation geometry.

Glide is motion within a suitable slip plane under shear stress. As a dislocation sweeps across a plane, atoms behind it end up displaced by b relative to atoms ahead. A macroscopic piece can therefore acquire permanent shear without breaking all bonds across a plane at once. A screw segment may sometimes move between crystallographically equivalent glide planes by cross-slip; an edge segment has a more constrained glide plane. Climb , by contrast, moves an edge component out of its glide plane by absorbing or emitting vacancies or interstitials and usually requires diffusion. It is more temperature-dependent than ordinary glide.

The direction and magnitude of b matter. A short lattice translation commonly has lower dislocation line energy than a longer one because the elastic energy scale contains a factor approximately proportional to b², although exact line energies depend on elastic moduli, geometry and core structure. Crystals often favour slip on densely packed planes and directions because their atomic arrangement permits lower resistance to dislocation movement. Obstacles such as solute atoms, precipitates and grain boundaries hinder motion; this can increase yield strength. Excessive dislocation pinning may reduce ductility, so a material-design tradeoff exists.

Dislocations also affect chemistry. Their cores and strain fields can trap impurity atoms, provide fast diffusion pathways in some materials, and influence corrosion or phase nucleation. A crystal can have many point defects but few dislocations, or vice versa; the two defect classes are not interchangeable. X-ray diffraction broadening, transmission electron microscopy and etch-pit methods can reveal dislocation-related strain or positions, though each method has limits. MIT's introduction to line and interface defects links their movement to mechanical properties.

Step-by-step reasoning

1. Identify the local direction of the dislocation line. 2. Determine the Burgers vector from a circuit referenced to a perfect lattice. 3. Compare b with the line: perpendicular means edge, parallel means screw, otherwise mixed. 4. Identify a possible slip plane containing b and the relevant line segment. 5. Distinguish glide, cross-slip and diffusion-controlled climb before predicting deformation.

Visual explanation

Draw a square grid with an extra half-row ending near the centre; mark the endpoint line and a b arrow perpendicular to it. Next draw a stack of planes forming a spiral stair around a vertical screw line with b parallel to that line. A third sketch shows the dislocation moving across a slip plane, leaving a one-b-vector offset behind it.

Real-world analogy

A wrinkle in a carpet can be pushed across a room one small section at a time. The whole carpet shifts even though one never lifts and translates every point at once. A dislocation moving through a crystal similarly permits large-scale slip through local rearrangements. The carpet analogy captures motion but not the exact atomic and elastic fields.

Real-world example

Cold-working a metal multiplies and tangles dislocations. New lines obstruct old ones, so progressively larger stress is needed for further plastic deformation; this is work hardening. Annealing can allow recovery or recrystallisation that reduces dislocation density and changes hardness and ductility. Alloy design also uses precipitates and solutes to impede dislocation glide.

Why?

Why can a dislocation lower the stress needed for slip? Only atoms near the moving line need to cross a local bonding barrier at each instant. A hypothetical perfect-crystal shear would force an entire plane to move coherently, requiring much higher stress.

Common misconception

"An edge dislocation is an extra whole plane of material added to a crystal." Its sketch shows an extra half-plane ending within the crystal, and the defining object is its termination line plus surrounding displacement field. The apparent extra plane is a geometric way to visualise a registry mismatch.

Worked example

Question: A dislocation segment runs along the z direction. Its Burgers vector has components b = (0.25 nm, 0, 0). Is the segment edge or screw? If another segment of the same line turns to run along x while b remains unchanged, how does its character change?

Reasoning: For the z-directed segment, b points along x, so b is perpendicular to the line: pure edge character in this simple geometry. For the x-directed segment, b is parallel to the line: pure screw character. The Burgers vector did not change; only the local tangent of a curved line changed. This illustrates why one dislocation can contain different local characters.

Answer: The first segment is edge; the turned x-directed segment is screw.

Quick check

1. Which operation moves an edge dislocation out of its original glide plane by absorbing vacancies? Answer: Climb, a process linked to defect diffusion.

Exam focus

Define b by a Burgers circuit, not merely as a direction of stress. State edge as b perpendicular and screw as b parallel to the line. Relate line movement to a permanent b displacement and distinguish glide from climb.

Advanced insight

The elastic field of a dislocation extends far beyond its atomic core, so dislocations interact over distances much larger than one bond. Their interactions can create pile-ups, sources and networks. Crystal plasticity models coarse-grain the motion of many lines into slip-system rates, but the allowed slip systems remain tied to lattice symmetry and chemistry.

Summary

Dislocations are line defects that permit plastic shear by local motion. Edge and screw limits are distinguished by Burgers-vector orientation relative to the line, with mixed segments common. Glide carries a one-b displacement across a slip plane; climb requires point-defect diffusion. Dislocation obstacles control much of mechanical strength.

Practice questions

1. What is the Burgers-vector orientation for a pure screw segment? Answer: Parallel to the dislocation line. 2. What does a Burgers circuit show around a defect? Answer: A closure failure relative to the corresponding circuit in a perfect lattice, measured by b under a chosen sign convention. 3. Why does cold work often harden a metal? Answer: It raises dislocation density and interactions that obstruct later dislocation motion. 4. What distinguishes glide from climb? Answer: Glide moves within a slip plane under shear; climb moves out of it through absorption or emission of point defects.