Twins, Stacking Faults, and Antiphase Boundaries

Internal boundaries that keep the structure but break the sequence

The first three guides in this rung dealt with the planar defects that shout. Guide 1 gave you the free surface, where the crystal simply stops and half of every atom's bonds are cut. Guide 2 gave you the grain boundary, the mismatched seam where two crystals of the same phase meet at different orientations, like floor tiles laid at clashing angles. Guide 3 refined that into the coincidence-site picture, showing why a few special misorientations are unusually low in energy. Now we turn to a quieter family — internal boundaries where the crystal structure and even the orientation barely change, yet one subtle thing has gone wrong. There are three headline members: the stacking fault, the twin, and the antiphase boundary.

The single idea that organizes all planar defects is an energy hierarchy, and it is worth carrying in your head. A free surface costs a great deal, roughly 1 to 2 J/m^2 for a metal, because you truly break bonds. A random high-angle grain boundary costs less, roughly 0.5 to 0.9 J/m^2, because atoms on both sides still find most of their neighbours across the mismatched seam. But a coherent twin or a stacking fault costs almost nothing — often just 0.02 to 0.2 J/m^2, ten to a hundred times cheaper than a grain boundary. Why so cheap? Because across these internal boundaries every atom keeps its full, correct set of nearest neighbours. The coordination number stays 12; essentially no bond is broken or stretched. The mistake lives one shell further out.

The stacking fault: a slip in the ABCABC sequence

Recall from the crystal-structures rung how close packing works. Stack close-packed planes of atoms like a grocer's orange pyramid and each new layer nests into the hollows of the one below. Two long-run recipes exist: FCC repeats every three layers as ABCABC, and HCP repeats every two as ABAB. Both fill 74 percent of space with coordination 12; they differ only in the stacking sequence. A stacking fault is simply a plane where that sequence hiccups. An intrinsic fault looks as if one layer were quietly removed, giving ...ABCAB|ABCAB..., and an extrinsic fault as if an extra layer were slipped in, giving ...ABCAB|C|ABCAB.... Either way, right at the fault you get a thin sliver of the other close packing — a two-layer sliver of HCP stranded inside FCC.

CLOSE-PACKED {111} STACKING   (each letter = one close-packed layer)

  Perfect FCC :  ... A B C A B C A B C A B C ...      (period 3)
  Perfect HCP :  ... A B A B A B A B A B A B ...      (period 2)

  Intrinsic stacking fault  (one C layer removed):

                 ... A B C A B [ ] A B C A B ...
               = ... A B C A B  A B C A B ...
                            ^^^^
                            B-A-B  =  a 2-layer HCP sliver in FCC

  Coherent twin  (mirror plane M sits on one close-packed layer):

                 ... A B C A B C B A C B A C ...
                                 M
                 stepping OUT from M either way gives the mirror
                 image; every atom ON M keeps perfect 12-coordination
                 -> this {111} mirror IS the  Sigma = 3  boundary

Because the fault preserves all 12 nearest neighbours and only misplaces the next layer out, it costs a small, well-defined energy per unit area — the stacking-fault energy (SFE). And its value swings enormously between metals: roughly 160 to 200 mJ/m^2 in aluminium, 45 to 70 in copper, around 20 in silver, and often below 20 in austenitic stainless steel or 70/30 brass. These are approximate and shift with alloying and temperature, so treat them as a ladder of rough magnitudes, not exact constants. That ladder governs how a metal deforms: high-SFE metals like aluminium keep their dislocations tight and cross-slip easily, while low-SFE metals like brass spread their dislocations wide, cross-slip poorly, and readily twin — the very behaviour engineers exploit in TWIP steels.

There is a beautiful link back to the dislocations rung here. A stacking fault in FCC does not float free; it is hemmed in by a pair of partial dislocations (the Shockley partials of type (a/6)<112> you met earlier), a strip of fault stretched between them like a stacking-fault ribbon. The width of that ribbon is set by a tug-of-war: the two partials repel each other elastically and want to fly apart, while the fault between them pulls like a soap film wanting to shrink. Lower SFE means a weaker pull, so a wider ribbon — which is the microscopic reason low-SFE metals behave so differently. When faults stack up in ordered ways in materials like silicon carbide or zinc sulphide, the result is polytypism: many long-period stackings of the very same layers.

The twin: a mirror-image crystal, and the cheapest boundary of all

A twin boundary relates two regions of crystal by a mirror reflection across the boundary plane: the atoms on one side are the exact mirror image of those on the other. In FCC this happens most cheaply on a {111} plane, and it is really just the stacking read backwards — ...ABCABC then the sequence reverses to ...BACBA..., as the code sketch above shows. The astonishing thing is that every atom sitting on the mirror plane still finds all 12 of its correct nearest neighbours; nothing is broken, nothing is strained. That makes the coherent twin a textbook coherent interface — the two lattices match perfectly across the plane, which is why it is the very cheapest internal boundary a crystal can own.

This is exactly where guide 3 pays off. The coherent {111} twin IS the Sigma-3 boundary of the coincidence-site lattice — one atom in three sits on a site shared by both crystals, and on the twin plane itself every atom is a coincidence site. That is the archetypal special, low-energy boundary. Put numbers on the hierarchy: a coherent twin boundary in copper costs only about 20 mJ/m^2, roughly half its intrinsic stacking-fault energy, while a random high-angle boundary in the same copper costs around 600 mJ/m^2 of grain-boundary energy. The twin is about thirty times cheaper. That single fact is why twins are so common and why they barely impede dislocations compared with an ordinary grain boundary.

Twins come in two flavours worth telling apart. Annealing (growth) twins form during recrystallization and grain growth in low-SFE FCC metals such as copper, brass, and austenitic stainless steel; they are the straight-sided parallel bands you see splitting grains in an etched micrograph. Deformation (mechanical) twins form instead by a coordinated homogeneous shear that tilts a whole block of lattice into the mirror position; they matter most where slip has too few systems to do the job — in HCP metals like magnesium, titanium, and zinc, and in BCC iron shocked at low temperature (the classic Neumann bands). A twin closely related to transformation twinning also appears when a crystal changes phase, as in martensite. Honest caveat: twinning delivers a fixed, quantized shear and hence a definite shape change, quite unlike slip, which can proceed by any amount.

The antiphase boundary: right lattice, wrong chemistry

The third defect needs one new idea: chemical order. In a disordered solid solution the two kinds of atom sit on the lattice at random, like salt and pepper shaken together. But many alloys, on cooling, order — each species claims its own sublattice. Copper and gold settle into Cu3Au with gold on the cube corners and copper on the faces; copper and zinc settle into CuZn (beta-brass) with copper on one simple-cubic sublattice and zinc on the other. Such an ordered arrangement is a superlattice: a larger repeating pattern of chemical decoration laid over the ordinary lattice. Building or losing that pattern is an order-disorder transformation, the subject of a later rung — here we only need the ordered state.

Now the antiphase boundary (APB). Imagine ordering starting independently in two nearby patches. Both patches build the same superlattice, perfectly aligned in lattice and orientation, but one happened to put gold where the other put copper — they are out of chemical register by half a step. Where the two patches meet, the atomic positions run through completely undisturbed (no strain, geometrically coherent), yet the chemical decoration is shifted by a vector that is a translation of the plain lattice but NOT of the superlattice. The consequence is a plane lined with wrong-neighbour bonds: A-A and B-B pairs where the ordered crystal wanted A-B. The APB therefore costs a chemical, ordering energy — a completely different origin from the stacking fault's geometric one, even though both are thin, low-energy planar faults.

Make it concrete in beta-brass, CuZn, whose ordered form is two interpenetrating simple-cubic sublattices, one all-copper and one all-zinc. A displacement of (a/2)[111] — the very body-diagonal vector that would be the ordinary Burgers vector in disordered BCC — lands the copper sublattice exactly onto the zinc sublattice. So a single (a/2)[111] dislocation gliding through ordered brass leaves an APB in its wake; it takes a bound pair of them, a superdislocation of total b = a[111], to sweep through and restore perfect order. Those two superpartials drag a strip of APB between them, the ordered-alloy twin of the stacking-fault ribbon. APB energies run from tens to a few hundred mJ/m^2 (the {111} APB in Ni3Al is around 100 to 180), and, like SFE, they set how superdislocations dissociate and how strong the alloy is.

Zoom out and you see the natural pattern APBs make. When an alloy orders on cooling, ordering nucleates in many places at once, and neighbouring nuclei often choose opposite registers; where they finally impinge, an APB is trapped between them. The material ends up as a mosaic of antiphase domains separated by a network of APBs — the chemical cousin of a polycrystal's patchwork of grains, only here the domains share one continuous lattice and differ solely in which sublattice each species chose. In the microscope these domains light up beautifully in TEM dark-field, and over time they coarsen to shed APB area, just as grains grow to shed grain-boundary area.

One family, one principle: interfacial energy shapes the microstructure

Step back and the three defects rhyme. A stacking fault, a twin, and an antiphase boundary are all two-dimensional faults that carry an interfacial energy, ranging from near-nothing for a coherent twin to a substantial chemical price for a stubborn APB. The unifying law is simple: a material lowers its free energy by shrinking the total boundary area, each patch weighted by its own energy. That curvature-driven drive is the engine of grain growth — big grains devour small ones because eating boundary area is thermodynamically profitable — and the same accounting sets how a low-energy second phase wets a boundary, or why a coarsening pattern of antiphase domains slowly simplifies. Interfacial energy is the quiet bookkeeper behind the whole microstructure.

One member of the planar-defect family is still to come. Every boundary in this guide lay between two regions of the same phase — same structure, same composition, differing only in stacking, mirror, or chemical register. Guide 5 crosses the last frontier to the interphase boundary between two genuinely different phases, where even the lattice parameters no longer match. There the very same coherent-to-incoherent energy ladder returns: a coherent match with strained but continuous planes, a semicoherent match relieved by a grid of misfit dislocations, or a fully incoherent match. That is the structural heart of epitaxy and lattice misfit, and it is where this rung on interfaces comes to rest.

1. Ask first: is the crystal structure and composition the same on both sides? If a whole phase changes, it is an interphase boundary (guide 5), not one of these three.
2. Is the orientation different across it? A real change of orientation means a grain boundary (guides 2 to 3), not a stacking fault or APB, both of which keep orientation.
3. If the two sides are mirror images across the plane, it is a twin — coherent and very low energy on a {111} close-packed plane, the Sigma-3 boundary.
4. If the close-packed stacking hiccups (a missing or extra layer, a sliver of the other packing) with no chemical change, it is a stacking fault, bounded by partial dislocations.
5. If the lattice runs through undisturbed but the chemical order is shifted, lining the plane with wrong-neighbour bonds, it is an antiphase boundary — and only ordered superlattices can have one.