An edge dislocation is an extra half-plane of atoms inserted into a crystal lattice. Under shear stress τ it glides along the slip plane — atoms near the core switch bonds one at a time, like pushing a ripple through a rug. This enables plastic deformation at stresses hundreds of times lower than the theoretical shear strength of a perfect crystal.
σ_xy = Gb / [2π(1−ν)] · x(x²−y²) / (x²+y²)²
Glide velocity: v = M · (τ − τ_PN) [τ_PN ≈ 2G·exp(−2πw/b)]
Burgers vector magnitude: |b| = a₀/√2 (FCC, ⟨110⟩ slip)The concept of a dislocation was independently proposed by Taylor, Orowan, and Polanyi in 1934 to explain why real metals yield at stresses 10,000× lower than theory predicts. It took until 1956 — when the electron microscope improved sufficiently — for dislocations to be directly observed for the first time.
What is an edge dislocation in a crystal?
An edge dislocation is a line defect in a crystal lattice formed by inserting an extra half-plane of atoms. The boundary of that extra half-plane — where it terminates inside the crystal — is the dislocation line. Atoms near the core are compressed above and stretched below, creating a strong local stress field.
What is the Burgers vector and why is it important?
The Burgers vector b is a lattice vector that quantifies the magnitude and direction of the displacement mismatch caused by a dislocation. For an edge dislocation b is perpendicular to the dislocation line. Its magnitude equals the lattice spacing and determines how far the crystal shears each time a dislocation crosses a slip plane.
Why does dislocation glide require far less stress than the theoretical shear strength?
The theoretical shear strength of a perfect crystal is roughly G/30, because every bond in a plane must break simultaneously. With a dislocation present, only bonds at the core switch one at a time — like moving a rug by pushing a ripple across it. This sequential bond-switching reduces the required stress by several orders of magnitude.
The Volterra solution gives the shear stress component σ_xy = Gb/[2π(1−ν)] · x(x²−y²)/(x²+y²)², where G is the shear modulus, b the Burgers vector magnitude, ν Poisson's ratio, and (x,y) coordinates from the dislocation core. The field is long-range (falls off as 1/r) and has quadrupole symmetry.
The slip plane is the crystallographic plane on which a dislocation moves. For edge dislocations the slip plane contains both the dislocation line and the Burgers vector. Plastic flow is easiest on close-packed planes because atoms are most densely packed there, reducing the Peierls–Nabarro stress needed to move the dislocation.
The Peierls–Nabarro stress τ_PN = 2G·exp(−2πw/b) is the minimum shear stress needed to move a dislocation through the lattice at 0 K, where w is the dislocation core width. Wider cores (covalent vs ionic materials) have lower τ_PN, explaining why metals with metallic bonding deform easily while ceramics are brittle.
Taylor hardening gives Δσ = αGb√ρ, where ρ is dislocation density and α ≈ 0.3. As a metal is cold-worked, dislocations multiply and their stress fields overlap, impeding each other's motion. This raises the flow stress — a mechanism called work hardening or strain hardening.
Glide (conservative motion) is movement of a dislocation within its slip plane under shear stress — the subject of this simulation. Climb is non-conservative motion perpendicular to the slip plane, requiring diffusion of vacancies or interstitials at elevated temperature. Cross-slip allows a screw dislocation to switch to another slip plane with the same Burgers vector.
Grain boundaries are regions of severe lattice mismatch between crystallites of different orientation. A gliding dislocation cannot pass directly through a grain boundary; it piles up against it, creating a back-stress that opposes further dislocation motion. This is the basis of the Hall–Petch relation: smaller grains → more boundaries → higher yield strength.
Metal forming processes — rolling, forging, drawing, stamping — all rely on dislocation glide for permanent shape change. Precipitation hardening (age hardening in aluminium alloys) pins dislocations with nanometre-scale precipitates. Annealing removes stored dislocations by allowing climb and recovery. Understanding glide is central to designing high-strength, high-toughness structural alloys.