concept

dislocation

A dislocation is a crystallographic defect or irregularity within a crystal structure where atoms are misaligned along a line.
24 related articles · 1 formulas · 1 who worked here

Description

The crystal lattice is a three-dimensional pattern of atoms. A dislocation disrupts this pattern: it is the edge of an incomplete atomic plane wedged between full layers. Around the dislocation line, the crystal is strained. This stress allows the dislocation to move under load, rearranging atomic rows step by step. Thus the metal flows rather than cracks. In fact, any piece of metal contains billions of dislocations per square centimeter; their tangled movement is plasticity.

History

The concept of dislocations was introduced in 1934 by Geoffrey Taylor, Egon Orowan, and Michael Polanyi to resolve the paradox of the low strength of real crystals compared to theoretical estimates. In the 1940s, Jacques Friedel developed the theory of dislocation networks. Direct observation of dislocations in a transmission electron microscope was achieved by Peter Hirsch and colleagues in 1956. Subsequently, William Lawrence Bragg contributed to the understanding of dislocation structure using X-ray diffraction.

How it works

Under shear stress, a dislocation moves in the slip plane, sequentially breaking and reforming interatomic bonds. The Peierls–Nabarro stress determines the lattice resistance to motion. Schmid's law relates the critical resolved shear stress to the plane orientation. When dislocations meet, they can interact elastically, form Lomer–Cottrell barriers, or annihilate. The Orowan equation relates the plastic strain rate to the density of mobile dislocations, their velocity, and the Burgers vector: dε/dt = ρ_m b v. With increasing temperature, dislocation climb becomes possible through vacancy diffusion, which is essential for creep.

In practice

Forging metal, rolling steel, and the strength of alloys rely on the skillful management of dislocations — without them, an aluminum fuselage would crack rather than bend.

Fun fact

The yellow color of gold is partly due to dislocations, which affect light absorption. Without them, gold might be silvery, like most metals.

Concept graph →

Formulas

$$\tau_P = \frac{2G}{1-\nu} \exp\left(-\frac{2\pi W}{b(1-\nu)}\right)$$
Minimum stress to move a dislocation through a crystal lattice.
What is in the formula
τ_PvariablePeierls-Nabarro stress — peierls nabarro stress pascal
Gvariableshear modulus of the crystal — shear modulus pascal
νvariablePoisson's ratio — poissons ratio
Wvariabledislocation width — dislocation width metre
bvariablemagnitude of the Burgers vector — burgers vector magnitude metre
τ_p=\frac{2g}{1-ν}\exp(-\frac{2πw}{b(1-ν)}) · 2606.29061

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