This simulation visualises an edge dislocation — an extra half-plane of atoms wedged into a crystal lattice — and how it lets metals deform far more easily than a perfect crystal would. It animates the dislocation gliding along a slip plane under shear stress, draws the surrounding elastic stress field using the analytical Volterra solution, and plots how grain size governs yield strength through the Hall-Petch relation.
The shear-stress slider sets the applied stress τ in MPa; glide begins only once it exceeds the Peierls stress, with speed scaling as τ/τPeierls. The grain-size slider (1–200 μm) moves the marker along the Hall-Petch curve, and the view buttons switch between the lattice glide, the stress-field heatmap and the chart. Understanding this controls how engineers strengthen alloys by refining grain structure.
What is an edge dislocation?
An edge dislocation is a line defect formed when an extra half-plane of atoms is inserted into an otherwise regular crystal lattice. The edge of that half-plane, marked here with the symbol that looks like an inverted T, is the dislocation core where the lattice is most distorted. Real metals contain enormous densities of such defects.
What does the Burgers vector b represent?
The Burgers vector b measures the magnitude and direction of the lattice displacement caused by a dislocation, found by tracing a closed loop around the core. For an edge dislocation it lies perpendicular to the dislocation line, in the slip direction. The simulation annotates b with a blue arrow along the slip plane.
Why does a dislocation make metals easier to deform?
Gliding a dislocation only breaks and reforms one row of atomic bonds at a time, like moving a ruck across a carpet, rather than sliding a whole atomic plane at once. This requires far less stress than the theoretical strength of a perfect crystal, which is why real metals yield at a fraction of their ideal shear strength.
The Peierls (or Peierls-Nabarro) stress is the minimum shear stress needed to move a dislocation through an otherwise perfect lattice at zero temperature. In this model it is estimated as roughly 1.2% of the shear modulus μ. The dislocation only begins to glide when the applied τ exceeds this value; below it the core stays pinned.
The slider sets the applied shear stress τ from 0 to 200 MPa. If τ is below the Peierls stress the dislocation remains pinned and the label reads "Pinned". Above it the core glides along the slip plane, and the glide speed scales with both the animation-speed control and the ratio τ/τPeierls, so higher stress drives faster motion.
The Hall-Petch relation states that yield strength rises as grains get smaller: σy = σ0 + k/√d, where d is the average grain diameter. Grain boundaries obstruct dislocation motion, so more boundaries per unit volume means stronger material. The chart view plots this curve for mild steel, copper and aluminium, each with its own σ0 and k.
The stress field uses the classic Volterra solution for an edge dislocation in an isotropic elastic medium: σxx = −Dy(3x²+y²)/r⁴, σyy = Dy(x²−y²)/r⁴ and τxy = Dx(x²−y²)/r⁴, with D = μb / 2π(1−ν). The heatmap shows the von Mises combination, blue above the slip plane for tension and red below for compression.
The stress field uses the exact linear-elastic Volterra solution and realistic constants (b ≈ 0.25 nm, ν = 0.30, material shear moduli), and the Hall-Petch curves use literature values of σ0 and k. It is a clear two-dimensional teaching model, so it neglects anisotropy, dislocation interactions, screw components, temperature and the singularity at the core, which is clamped numerically.
The grain-size slider labels the structure as nanocrystalline below 5 μm, fine-grained up to 50 μm, medium up to 150 μm and coarse above that. As you move toward smaller d the Hall-Petch marker climbs the curve to higher yield strength, illustrating why grain refinement is a key strengthening strategy in metallurgy.
Controlling dislocation motion underlies almost all metal strengthening: cold working, grain refinement, alloying and precipitation hardening all work by impeding dislocation glide. The Hall-Petch relation guides processing of structural steels, automotive sheet and nanocrystalline alloys, where finer grains buy higher strength without changing composition.