Crystal Dislocations: Why Metals Bend Instead of Snap

The puzzle theoretical strength couldn't explain

A crystal with no defects should require a shear stress of roughly τ ≈ G/(2π), where G is the shear modulus, to slide whole planes of atoms past each other simultaneously. Measured yield stresses in real metals are typically hundreds or thousands of times smaller than that prediction. The resolution, proposed independently by Taylor, Orowan and Polanyi in 1934, is that crystals do not shear all at once — a dislocation lets atoms shift one row at a time, much as a ruck moved along a carpet shifts the whole carpet with little effort. That single insight reconciled theory with experiment and founded modern dislocation theory.

Edge and screw dislocations, and the Burgers vector

A dislocation is a one-dimensional defect where the lattice's regular order is locally interrupted along a line running through the material. The edge dislocation is an extra half-plane of atoms wedged into the lattice; the screw dislocation shears the planes into a continuous helical ramp. Most dislocations in real metals are mixed, with both characters along their length.

Every dislocation is characterised by its Burgers vector b, found by tracing a closed loop around the dislocation line and noting the gap — the closure failure — compared with the same circuit in a perfect crystal. For an edge dislocation, b is perpendicular to the line; for a screw dislocation, b is parallel to it.

Slip systems and Schmid's law

Plastic deformation happens when dislocations glide on specific planes and directions called slip systems — usually the most densely packed planes and closest-packed directions, since these give atoms the smoothest path to rearrange. The stress that actually drives glide is the component resolved onto the slip system, captured by Schmid's law:

τ = σ · cos(φ) · cos(λ)

σ = applied stress
φ = angle between loading axis and slip-plane normal
λ = angle between loading axis and slip direction

Yielding begins once this resolved shear stress τ reaches a critical value for the material.

Multiplication, tangling and work-hardening

Dislocations don't vanish as a metal deforms — they multiply, often via a Frank-Read source in which a pinned segment bows out repeatedly and emits new loops, and dislocation density can rise by several orders of magnitude during heavy working. As they multiply, they tangle and pile up against obstacles, making further glide progressively harder — the microscopic origin of work-hardening. Heating reverses some of this: during annealing, dislocations rearrange and partly annihilate, releasing stored energy and softening the metal. Balancing work-hardening against recovery, through temperature and deformation history, is a principal lever metallurgists use to tailor mechanical behaviour — from cold-rolled car-body steel to precipitation-hardened aerospace aluminium, where dispersed particles obstruct dislocation glide for high strength at low weight.

Frequently asked questions

Try it live

Everything above runs in your browser — open Dislocation & Crystal Slip, apply shear stress to a lattice, and watch an edge dislocation glide along its slip plane under your control.