Crystallography · Stacking and planar defects
FCC vs HCP stacking, stacking faults and twins
Two layers are already down below. Press A or C to add the third one, and watch the name of the stack change.
1 Build FCC or HCP 2 Faults and twins 3 How a twin grows Takeaways Questions References
What is the difference between FCC and HCP stacking?
FCC and HCP are the same layers of touching spheres, each in spot A, B or C, stacked in a different order.
Try it: press Fill HCP: all 10 inner layers read h and the top view shows open holes at the C sites. Press Fill FCC: all read c and the top view has no open holes. Space filled stays at 74% and neighbours at 12.
What is a stacking fault, and how is a twin different?
Change one thing in 12 perfect FCC layers. Each change can also be made by Shockley partial dislocations, line defects that slide the layers above them one site over (see stacking fault energy).
Try it: press Intrinsic fault: layers 5 and 6 turn h, 2 units, 36 mJ/m² for copper. Press Twin: only layer 6 is h, 1 unit, 18 mJ/m², half as much.
How does a twin grow, and what is an annealing twin?
Each Shockley partial slides the layers above it by a/6⟨112⟩ (A to B, B to C, C to A); one per plane builds a twin.
Try it: press Step +1 once: two h layers in a row, an intrinsic fault. Press Play to 8: the twin thickens one layer per step, and at 8 the top has moved 3.27a with one h layer left.
What to take away
More detail: the equations, the numbers and the limits
The h/c labels. A layer is h or c "according as its neighbouring layers are alike or different" (Pandey and Krishna, International Tables Vol. C). FCC (3C, copper) is all c and HCP (2H, magnesium) all h. ABCB, the same as ABAC (4H, lanthanum), is hc; the 9-layer samarium type (9R) is hhc. In these Ramsdell symbols the number is the layers in one repeat and C, H or R is the lattice type (cubic, hexagonal, rhombohedral). The end layers of a finite stack get no label.
Packing. For hard spheres of diameter d, every layer sits in the hollows of the one below, √(2/3)d = 0.816d higher. The order does not change that, so every close-packed stacking fills π/(3√2) = 0.7405 of space. Each sphere touches 6 in its layer, 3 below and 3 above. For HCP this needs c/a = √(8/3) = 1.633; real hexagonal metals often differ.
The twinning shear. A Shockley partial has b = a/6⟨112⟩, so |b| = a/√6 = 0.408a, the step from an A site to a B site. The {111} spacing is a/√3 = 0.577a. A Shockley partial on each neighbouring {111} plane in turn builds a twin (Mahajan 2013). One partial per layer gives s = |b|/d111 = 1/√2 = 0.707, a tilt of 35.3° (Christian and Mahajan).
Energy by counting h layers. In the Ising-type layer model (Ruffino et al.) with only neighbouring layers interacting, each h layer in FCC costs the same. Then twin : intrinsic : extrinsic = 1 : 2 : 2, the rule of thumb γisf ≈ γesf ≈ 2γtf (Jin et al., citing Hirth and Lothe). Jin et al. used DFT (density functional theory, a quantum-mechanical calculation). Their mJ/m2 (intrinsic, extrinsic, twin): Cu 36, 40, 18; Ag 16, 12, 8; Ni 133, 138, 65; Al 112, 112, 50. These are calculated, not measured. Measured values vary between methods and studies; the stacking fault energy page lists measured ones.
Naming faults. In Frank's scheme an intrinsic fault keeps the perfect order on both sides up to the fault. In an extrinsic fault, the plane at the fault belongs to neither side.
Limits. Rigid hard spheres with no change in spacing near a fault. Side-view atoms are drawn small, but the side views keep the true spacing ratio, so the drawn 35.3° is the real angle. The layer model leaves out longer-range layer interactions, so real intrinsic and extrinsic energies differ (silver by DFT: 16 and 12). The grain pictures are schematics: real twin numbers depend on alloy, strain and annealing.
Questions people ask
What is the difference between FCC and HCP?
Both stack the same close-packed layers. FCC repeats every three layers (ABCABC) on {111}; HCP every two (ABAB) on its basal plane. Both fill 74% of space with 12 neighbours per atom. Copper is FCC; magnesium is HCP.
Why are FCC and HCP both 74 percent packed?
Each layer sits in the hollows of the one below at the same height, 0.816 sphere diameters, whatever the order. So both fill π/(3√2) = 0.7405 of space in the hard-sphere model. The 12 nearest neighbours sit at the same distance in both; only their arrangement and the atoms further out differ.
What is a stacking fault?
A plane where the layer order breaks, such as ABCAB|ABC in FCC. Atoms still touch 12 neighbours, but two layers now have HCP-like surroundings (h layers). That costs energy per area, the stacking fault energy: 36 mJ/m2 for copper by DFT.
Intrinsic vs extrinsic stacking fault: what is the difference?
Intrinsic: one layer taken out (ABCAB|ABC), two h layers side by side. Extrinsic: one layer put in (ABCA C BCAB), h c h. One Shockley partial makes the first; two on neighbouring planes make the second, a two-layer twin.
What is a twin boundary?
A mirror plane: the stacking above is the mirror image of the stacking below (ABCAB C BACBA, mirrored about the middle C). In FCC it lies on {111} and has one h layer. In the layer model it costs half an intrinsic fault (copper by DFT: 18 against 36 mJ/m2). In EBSD maps it is a Σ3 boundary, 60° about ⟨111⟩: one lattice site in three is shared by both crystals.
Annealing twin vs deformation twin: what is the difference?
Annealing twins form as grain boundaries move during annealing, mostly during recrystallisation; after grain growth most have straight sides (Bozzolo and Bernacki). Deformation twins form under stress as thin plates, and twinning carries more of the strain at lower temperature and higher strain rate. Both are 60° ⟨111⟩ twins in FCC.
Why does aluminium have so few annealing twins?
Annealing twins are frequent in FCC metals of low or medium stacking fault energy, such as copper. They are comparatively rare in aluminium (Humphreys and Ferry), whose stacking fault energy is high. By DFT a twin boundary costs 50 mJ/m2 in aluminium and 18 in copper.
Can HCP metals have stacking faults?
Yes. On the basal plane ABAB can break as I1 (ABABCBCB), I2 (ABABCACA) or E (ABABCABAB). These put one, two and three c layers into the all-h stack: build them in the first picture. In the layer model with only neighbouring layers (Ruffino et al.) their energies rise as 1 : 2 : 3.
Related: Stacking fault energy (how far partials split) · Dislocations and Burgers vectors · EBSD misorientation and CSL boundaries (finding Σ3 twins) · Interfaces and CSL lab · Lattices and point groups · Interstitial sites in FCC, BCC and HCP · Two-beam defect simulator (stacking fault fringes in TEM)
References
Show the 8 references
- S. Ďurovič, P. Krishna and D. Pandey, Layer stacking, International Tables for Crystallography Vol. C, ed. E. Prince, IUCr (2006), ch. 9.2, pp. 752 to 773 (section 9.2.1 by Pandey and Krishna). doi:10.1107/97809553602060000618. h/c notation, 2H/3C/4H/9R, packing 0.7405, 12 neighbours, Frank's fault types.
- D. Hull and D. J. Bacon, Introduction to Dislocations, 5th ed., Butterworth-Heinemann/Elsevier (2011): section 1.3 (intrinsic and extrinsic stacking faults) and section 5.2 (the Shockley partial).
- J. W. Christian and S. Mahajan, Deformation twinning, Progress in Materials Science 39, 1 to 157 (1995). doi:10.1016/0079-6425(94)00007-7.
- Z. H. Jin, S. T. Dunham, H. Gleiter, H. Hahn and P. Gumbsch, A universal scaling of planar fault energy barriers in face-centered cubic metals, Scripta Materialia 64, 605 to 608 (2011). doi:10.1016/j.scriptamat.2010.11.033. Table 1, DFT fault energies.
- M. Ruffino, G. C. G. Skinner, E. I. Andritsos and A. T. Paxton, Ising-like models for stacking faults in a free electron metal, Proc. R. Soc. A 476, 20200319 (2020). doi:10.1098/rspa.2020.0319.
- N. Bozzolo and M. Bernacki, Viewpoint on the formation and evolution of annealing twins during thermomechanical processing of FCC metals and alloys, Metall. Mater. Trans. A 51, 2665 to 2684 (2020). doi:10.1007/s11661-020-05772-7.
- F. J. Humphreys and M. Ferry, On the role of twinning in the recrystallization of aluminium, Scripta Materialia 35, 99 to 105 (1996). doi:10.1016/1359-6462(96)00105-4.
- S. Mahajan, Critique of mechanisms of formation of deformation, annealing and growth twins: face-centered cubic metals and alloys, Scripta Materialia 68, 95 to 99 (2013). doi:10.1016/j.scriptamat.2012.09.011. Twins built by a Shockley partial on each neighbouring {111} plane.
BibTeX
@misc{tripathy2026stackingfaults,
author = {Tripathy, Manisha},
title = {Stacking Faults and Twins Lab},
year = {2026},
howpublished = {\url{https://untetheredatom.com/crystallography/stacking-faults-and-twins}},
note = {Interactive web tool}
}