3D Crystal Lattice & Dislocation Glide

Crystal Lattice

Grain size (cell block) 5×5×5

Temperature 300 K

Applied shear stress 0.4

Coordination #

–

Packing factor

–

Vacancy conc.

–

Dislocation glide

–

How it works

Real metals and ceramics pack atoms into repeating unit cells — body-centred cubic (BCC), face-centred cubic (FCC) or hexagonal close-packed (HCP) — each with a different coordination number and packing efficiency. An edge dislocation is an extra half-plane of atoms; under shear it glides through the lattice one atomic row at a time, which is roughly 10,000× easier than sliding a whole plane past its neighbour at once — this is why real metals deform plastically instead of shattering. Vacancies (missing atoms) appear thermally with a concentration that grows exponentially with temperature.

n_v ∝ exp(−Q / kT)     (vacancy concentration)
CN(BCC)=8, CN(FCC)=CN(HCP)=12
packing: BCC 68%, FCC/HCP 74%

BCC / FCC / HCP — switches the unit cell type; changes coordination number, packing factor and how easily the dislocation can glide.
Grain size — how many unit cells make up the visible grain block before hitting a boundary (dashed plane) that stops the dislocation, echoing Hall–Petch strengthening.
Temperature — raises vacancy concentration (missing atoms blink out) and adds atomic jitter, per the Arrhenius relation above.
Applied shear stress — drives the glide speed of the highlighted dislocation through the slip plane; too low and it stalls at the grain boundary.

Real-world relevance: alloy designers choose lattice type and grain size together — FCC metals like aluminium and copper are ductile because their close-packed planes give dislocations many easy glide paths, while grain refinement (smaller blocks here) raises the stress needed to push a dislocation across a grain.

Lattice atom Dislocation core Vacancy (removed)

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