Edge & screw motion under shear · slip systems in cubic crystals · the four routes to make a metal harder
A slip system is a slip plane combined with a slip direction inside that plane. Dislocations preferentially glide on planes of highest atomic density (smallest b / largest planar spacing) along directions of shortest b.
The close-packed plane of each structure is preferred because slipping along its close-packed direction requires the smallest atomic rearrangement, lowering the Peierls stress (the lattice resistance to dislocation motion).
where w is the dislocation width (proportional to planar spacing). Wider planes ⇒ wider w ⇒ lower τP.
| Structure | Plane | Direction | Systems |
|---|---|---|---|
| SC | {100} | ⟨100⟩ | 3 |
| BCC | {110}, {112}, {123} | ⟨111⟩ | 48 |
| FCC | {111} | ⟨110⟩ | 12 |
| HCP | (0001) | ⟨11-20⟩ | 3 |
Foreign atoms (solutes) distort the host lattice and impose a strain field. A passing dislocation must either push through that strain field or bow around it — both cost extra stress. Substitutional solutes (different size on a lattice site) and interstitial solutes (C, N in Fe) both work; interstitials are usually 10–100× more potent per atom.
where G is shear modulus, ε is the misfit strain per solute, and c is concentration. The dependence comes from random spacing between solutes scaling as 1/.
| Alloy | Solute | Type | Δσ at 5 at% |
|---|---|---|---|
| Cu–Ni | Ni in Cu | substitutional | ~25 MPa |
| Cu–Zn (brass) | Zn in Cu | substitutional | ~60 MPa |
| Fe–C | C in α-Fe | interstitial | ~300 MPa |
Plastic deformation at room temperature multiplies dislocations (sources like Frank–Read operate as soon as τ rises). The new dislocations interact with one another, forming forests and tangles that pin further glide. As %CW rises, the metal becomes stronger but less ductile.
where ρ is the dislocation density (length / volume). Cold work raises ρ from ~1010 m−2 (annealed) to ~1015 m−2 (heavily worked).
Pull a sample to ε1, unload (elastic recovery), then reload: yielding now occurs at the previous flow stress, not the original σy. The "memory" of prior straining is stored in the dislocation network.