Slip Systems in FCC, BCC and HCP Metals: Burgers Vector and Dislocations

Plastic deformation in crystalline metals proceeds almost entirely by dislocation glide on specific crystallographic planes and directions, collectively called slip systems. This article develops the Burgers vector description of dislocations, catalogues the slip systems of FCC, BCC and HCP structures, and applies Schmid’s law to explain why slip system count is the single strongest crystallographic predictor of ductility.

Crystallography of Slip: Planes, Directions and the Burgers Vector

Slip Plane and Slip Direction Selection

Dislocation glide is confined to specific crystallographic planes, called slip planes, along specific crystallographic directions lying within those planes, called slip directions. The combination of one slip plane and one slip direction constitutes a slip system. Two geometric factors determine which plane and direction combinations are favoured: slip planes are almost always the planes of greatest atomic packing density (widest interplanar spacing), because a wider spacing lowers the shear stress needed to displace one plane relative to its neighbour, and slip directions are almost always the directions of shortest repeat distance (highest linear atomic density), because these correspond to the smallest possible Burgers vector.

Burgers Vector Definition and Notation

The Burgers vector b is obtained by constructing a Burgers circuit: starting from a lattice point, an atom-to-atom path is traced by an equal number of steps in each crystallographic direction to form a closed loop in a dislocation-free region of the same crystal. When the identical step sequence is traced around the real dislocation, the circuit fails to close; the vector required to close it, conventionally drawn from finish (F) to start (S), is the Burgers vector. For FCC metals the shortest full (perfect) Burgers vector is a/2<110>, for BCC it is a/2<111>, and for HCP the basal Burgers vector is a/3<11-20>, where a is the lattice parameter.

Dislocation strain energy per unit length:
  E ≈ (G · b²) / 2   (edge and screw differ by a factor involving Poisson's ratio)

where:
  G = shear modulus (Pa)
  b = magnitude of Burgers vector (m)

Because E scales with b², dislocations strongly favour the shortest available Burgers vector, which is exactly why slip directions coincide with close-packed directions and why partial dislocations with smaller Burgers vectors, bounding a stacking fault, are energetically favourable in low stacking-fault-energy FCC metals such as austenitic stainless steel and brass.

Slip Systems in FCC Metals

Face-centred cubic metals, including aluminium, copper, nickel, gold, silver, and austenitic (300-series) stainless steel, slip on the {111} octahedral plane family. There are four distinct {111} planes, and each contains three <110> close-packed directions, giving 4 × 3 = 12 independent {111}<110> slip systems. This large system count, well above the 5 independent systems required by the von Mises compatibility criterion for arbitrary polycrystalline shape change, is the primary crystallographic reason FCC metals exhibit excellent cold formability, high work-hardening capacity through multiple-slip interactions, and comparatively low crystallographic anisotropy after processing (see also grain boundaries guide for how these slip systems interact with boundaries during deformation).

Slip Systems in BCC Metals

Body-centred cubic metals, including alpha-iron, chromium, molybdenum, tungsten, and vanadium, have no plane with the packing density of an FCC {111} plane. Instead, slip is observed on three plane families that all share the single close-packed <111> direction: {110} (6 planes), {112} (12 planes), and {123} (24 planes), each combined with 1 or 2 independent <111> directions per plane, giving a theoretical maximum in the range of 48 potential slip systems, though not all operate simultaneously at a given temperature. Because BCC screw dislocations have a non-planar, three-dimensionally spread core, their glide is thermally activated to a much greater degree than edge dislocations, producing a critical resolved shear stress that rises sharply as temperature falls. This underlies the pronounced ductile-to-brittle transition characteristic of ferritic and martensitic steels, which is a central design consideration alongside Charpy impact testing and is closely linked to the transformation products discussed in martensite formation.

Slip Systems in HCP Metals

Hexagonal close-packed metals slip preferentially on the (0001) basal plane along the <11-20> close-packed direction, but the basal plane alone supplies only 2 independent slip systems, well below the 5 needed for general polycrystalline ductility. Depending on the c/a axial ratio, additional slip can occur on prismatic {10-10} and pyramidal {10-11} or {11-22} planes, and deformation twinning frequently supplements slip to accommodate strain along the c-axis. Metals with c/a close to the ideal value of 1.633, such as magnesium (c/a ≈ 1.624) and cadmium, favour basal slip strongly, while metals with lower c/a, such as titanium (c/a ≈ 1.587) and zirconium, more readily activate prismatic slip, giving titanium noticeably better room-temperature ductility than magnesium despite both being HCP.

Schmid’s Law and Critical Resolved Shear Stress

Schmid’s law relates an externally applied uniaxial stress to the shear stress actually resolved onto a given slip system’s plane and direction. Slip on that system begins only once the resolved shear stress reaches the system’s critical resolved shear stress (CRSS), an intrinsic material property largely independent of the loading geometry.

where σ is the applied tensile stress, φ is the angle between the tensile axis and the slip plane normal, λ is the angle between the tensile axis and the slip direction, and m = cosφ·cosλ is the Schmid factor for that system. The Schmid factor reaches its theoretical maximum of 0.5 when φ = λ = 45°, defining the “soft” orientation that yields at the lowest applied stress; orientations with φ or λ approaching 0° or 90° are “hard” orientations that may never activate that system before fracture or before a competing system activates instead.

Industrial Applications and Significance

Slip system availability governs sheet metal formability directly: deep-drawing and stamping operations on FCC aluminium and low-carbon steel sheet rely on abundant, near-isotropic slip to reach large strains without localised necking or splitting, whereas HCP titanium and magnesium sheet require warm or hot forming, or specific texture control, to activate sufficient secondary slip and twinning systems. In welding and heat-affected-zone metallurgy, grain refinement and control of the phases produced during cooling (see quenching and tempering and bainite microstructure) indirectly manage local slip system activity by controlling grain size, since finer grains raise the effective yield strength through the Hall-Petch relationship without changing the fundamental slip geometry. Hardness testing methods (hardness testing methods) provide an indirect, practical proxy for the resistance to dislocation glide that ultimately traces back to the slip systems discussed here, and texture-sensitive anisotropy from limited HCP slip systems is a routine consideration in the qualification of titanium and zirconium alloy components for aerospace and nuclear service.

Frequently Asked Questions

Recommended Reference Texts

Disclosure: MetallurgyZone participates in the Amazon Associates programme. If you purchase through these links, we may earn a small commission at no extra cost to you. This helps support free technical content on this site.

Further Reading