Complex Stacking Faults in Materials

• Complex stacking fault (CSF) is a planar defect featuring multi-layer interruptions that disturb both atomic stacking and chemical order in materials.
• CSFs impact mechanical, electronic, and optical properties by altering dislocation dynamics and introducing local energy variations.
• Characterization of CSFs relies on high-resolution microscopy and computational models to unravel the coupling between structural, chemical, and magnetic factors.

Complex stacking fault (CSF) denotes a planar defect that is more elaborate than a simple intrinsic or extrinsic stacking fault. In the canonical close-packed description, an ideal fcc crystal follows the sequence $\ldots ABCABCABC \ldots$ along $\langle 111\rangle$, and a simple stacking fault is a local interruption of that sequence. A CSF, by contrast, is typically associated with multi-layer faulting, coupled changes in chemical order, anti-phase boundaries, local hcp- or D0$_{19}$-like sequences, domain walls, or other order-parameter rearrangements that make the defect structurally and energetically richer than a single missing or inserted layer. The term is used most explicitly in ordered alloys and ferroics, but the same underlying idea appears across ordered intermetallics, layered kagome metals, non-close-packed carbides, and semiconductor polytypes (Morgado et al., 2024, Jin et al., 2024, Sjökvist et al., 10 Nov 2025).

1. Definition and crystallographic basis

In fcc crystals, a simple stacking fault is conventionally defined relative to the close-packed sequence $\ldots ABCABC \ldots$. Typical examples are the intrinsic fault, where one close-packed layer is effectively missing, and the extrinsic fault, where an additional layer is inserted. A perfect dislocation with Burgers vector

$\mathbf{b}=\frac{a}{2}\langle 110\rangle$

can dissociate into two Shockley partials,

$$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$

which bound an intrinsic stacking fault on a $\{111\}$ plane. The partial separation is controlled by the stacking fault energy $\gamma_{\mathrm{SF}}$: lower $\gamma_{\mathrm{SF}}$ produces a wider fault ribbon (Morgado et al., 2024).

The distinction between a simple stacking fault and a CSF is clearest in ordered materials. In disordered fcc systems, a simple fault is primarily a local stacking interruption. In ordered systems such as L1$_2$ Ni$\langle 111\rangle$0Al-based $\langle 111\rangle$1, a fault can simultaneously disturb both stacking and chemical order, and may involve superlattice intrinsic or extrinsic faults, anti-phase boundaries, multiple closely spaced partials, or extended hcp-like segments. In that setting, “complex” refers not only to geometry but also to the additional ordering and anti-phase-boundary energies that enter the defect energetics (Morgado et al., 2024).

Terminology is not fully uniform across fields. Several studies describe defects that satisfy this broader definition without using the exact phrase “complex stacking fault.” This is explicit in the Ni–W analytical field-ion microscopy study, in the CsV$\langle 111\rangle$2Sb$\langle 111\rangle$3 kagome study, and in the WC simple-hexagonal study, each of which treats a faulted region as more than a single local registry error even when the term itself is introduced only conceptually or by extension (Morgado et al., 2024, Jin et al., 2024, George et al., 2024).

2. CSFs in ordered alloys and chemically disordered fcc systems

In ordered Ni-based superalloys, CSFs are most closely associated with faulted segments in $\langle 111\rangle$4 where multiple partials glide on successive $\langle 111\rangle$5 planes or interact with anti-phase boundaries, producing extended regions of altered stacking and order. In this literature, CSFs can include superlattice intrinsic faults, superlattice extrinsic faults, APB-plus-SF configurations, and local hcp-like sequences inside the ordered L1$\langle 111\rangle$6 phase. The same dislocation-based physics underlies simpler faults in disordered fcc Ni, but the ordered phase adds chemical-ordering terms that make the resulting faults structurally and energetically more intricate (Morgado et al., 2024).

Chemistry near the fault plane is often decisive. In creep-deformed Ni–2 at.% W, Morgado et al. showed by analytical field ion microscopy and atomistic simulation that W segregates to the center of the stacking fault, especially in the tensile layer directly above the fault plane, whereas earlier work on Re found a preference for partial-dislocation cores rather than the fault center. This difference matters because W-like behavior tends to decorate and potentially stabilize fault planes, whereas Re-like behavior preferentially decorates the cores that generate or bound them. The same study explicitly argued that such differences must be considered when extrapolating from simple SFs in disordered $\langle 111\rangle$7 to CSFs in ordered $\langle 111\rangle$8 (Morgado et al., 2024).

In Fe–Mn–Al–C austenite, Medvedeva et al. did not use the term CSF explicitly, but they provided a direct atomistic basis for chemically complex faults. They showed that the influence of Mn, Al, and C on stacking fault energies is highly local: impurities affect the fault mainly when they are located within a few interatomic layers of it, Mn shows a slight tendency for segregation near the fault, carbon prefers to stay away from the fault region, and short-range Al ordering can sharply lower the unstable stacking fault energy while modifying the intrinsic fault energy more weakly. This produces chemically decorated fault planes whose energetics differ strongly from the matrix average, a defining feature of chemically complex stacking faults (Medvedeva et al., 2012).

In low-SFE TWIP systems, simple stacking faults rapidly evolve into more elaborate fault networks. Meta-atom molecular dynamics of Fe–22 wt.% Mn TWIP steel showed overlapping intrinsic faults on adjacent $\langle 111\rangle$9 planes, local four-layer hcp regions, conversion into twin lamellae by twinning partials, stair-rod arrays at fault intersections, and V-shaped secondary twins. Although the paper did not use the CSF label, it explicitly presented these multi-layer, multi-defect configurations as the natural outcome of low-SFE partial-dislocation activity rather than as isolated single faults (Wang et al., 2016).

High-entropy and medium-entropy fcc alloys add another layer of complexity because the fault energy becomes plane-specific. In CoCrNi and CoCrFeNi, a moment tensor potential trained to DFT reproduced intrinsic stacking fault energies near $_{19}$0 for CoCrNi and $_{19}$1 for CoCrFeNi, while also resolving local chemical effects: Co-rich planes reduce the stacking fault energy, whereas Cr-rich planes in CoCrNi and Cr- or Fe-rich planes in related systems increase it. This suggests that in chemically disordered alloys, CSFs should be viewed as fault networks embedded in a heterogeneous local energy landscape rather than as uniform planar defects (Nitol et al., 14 Sep 2025).

3. Manifestations outside close-packed metallic alloys

Layered materials generalize the concept of stacking fault from close-packed atomic planes to interlayer registry or phase relations. In the kagome superconductor CsV$_{19}$2Sb$_{19}$3, the low-temperature CDW phase is described as a $_{19}$4-staggered order with a relative $_{19}$5 phase shift between adjacent layers, three domain types rotated by about $_{19}$6, and a first-order stacking order–disorder transition around $_{19}$7. The paper interpreted the high-temperature state as a statistical ensemble of multiple stacking configurations, including coexistence of different interlayer phase relations and domain walls. This is precisely the kind of multi-configurational, domain-rich interlayer disorder that layered-materials literature treats as a CSF-like state (Jin et al., 2024).

In simple-hexagonal WC, the defect differs fundamentally from close-packed fcc or hcp faults. The parent structure has AAA stacking along $_{19}$8, while the experimentally relevant faults occur on prismatic $_{19}$9 planes with rectangular ABAB stacking. The proposed atomistic mechanism is not a simple layer omission or insertion but double carbon occupancy of pentahedral interstitial sites, accompanied by local dilation of $\ldots ABCABC \ldots$0, glide of W rows, a $\ldots ABCABC \ldots$1 rotation about $\ldots ABCABC \ldots$2, and a local change from six-fold to two-fold symmetry. The paper explicitly argued that, by the standards of close-packed defect nomenclature, this is naturally regarded as a complex stacking fault (George et al., 2024).

In ferroic oxides, the fault can couple to structural order parameters instead of only atomic stacking. In Sr$\ldots ABCABC \ldots$3NaNb$\ldots ABCABC \ldots$4O$\ldots ABCABC \ldots$5, regular faults on $\ldots ABCABC \ldots$6 have fault vector $\ldots ABCABC \ldots$7, annihilate in sets of four, and connect four symmetry-equivalent directions of the $\ldots ABCABC \ldots$8 octahedral-tilt order parameter. Machine-learned force-field calculations yielded an estimated stacking fault energy of $\ldots ABCABC \ldots$9, and symmetry-mode analysis showed that the faults locally suppress one polar mode while enhancing another. Here the “stacking” is a phase shift of a tilt modulation in a large ferroic unit cell, so the resulting defect is complex by virtue of its coupling to multiple order parameters rather than by close-packed sequence alone (Sjökvist et al., 10 Nov 2025).

Semiconductor literature provides two additional variants. In wurtzite GaN nanowires, the cited work focused on the simple I1 intrinsic basal stacking fault rather than a CSF, but it explicitly noted that more complex faults correspond to thicker or more intricate zincblende/wurtzite inclusions and that the same exciton-trapping picture extends to them. In GaAs, by contrast, paired stacking faults were modeled directly as a double-well potential for excitons, and the paper effectively treated such fault pairs as a complex stacking-fault structure with richer electronic behavior than an isolated single fault (Nogues et al., 2014, Durnev et al., 2019). This suggests that in semiconductor contexts the CSF concept often maps to polytypic inclusions, fault pairs, or multi-plane fault complexes rather than to purely mechanical slip defects.

4. Energetics, thermodynamics, and multiscale descriptions

At the most basic level, stacking fault energy is the excess free energy per fault area,

$\mathbf{b}=\frac{a}{2}\langle 110\rangle$0

or, at finite temperature and pressure for the Ni$\mathbf{b}=\frac{a}{2}\langle 110\rangle$1Al CSF,

$\mathbf{b}=\frac{a}{2}\langle 110\rangle$2

For Ni$\mathbf{b}=\frac{a}{2}\langle 110\rangle$3Al, the full Helmholtz free energy was decomposed into static, quasiharmonic, anharmonic, electronic, and magnetic contributions. The resulting CSF Gibbs energy decreases moderately from $\mathbf{b}=\frac{a}{2}\langle 110\rangle$4 to about $\mathbf{b}=\frac{a}{2}\langle 110\rangle$5 and then drops more strongly, with a total reduction of almost $\mathbf{b}=\frac{a}{2}\langle 110\rangle$6 by the melting point. Anharmonicity and spin fluctuations lower the CSF energy, whereas quasiharmonic and electronic terms raise it; the high-temperature stabilization of the CSF was traced to strongly anharmonic Al–Al and Ni–Ni pair environments at the fault plane and to enhanced magnetic entropy near the CSF (Xu et al., 21 Aug 2025).

Normal stress can also shift fault energetics substantially. DFT calculations for Al, Ni, Cu, Ag, Au, and Pt showed that compression normal to the $\mathbf{b}=\frac{a}{2}\langle 110\rangle$7 plane increases both stable and unstable stacking fault energies, whereas normal tension decreases them. The same work showed that stacking fault formation is accompanied by inelastic expansion in the normal direction, which explains why compression penalizes and tension favors fault creation. Many classical interatomic potentials were reported to fail even qualitatively in reproducing this stress dependence, often predicting the opposite trend (Li et al., 9 Jan 2026).

Local chemistry modifies fault energies with similarly high sensitivity. In Au alloys, the intrinsic SFE decreases for all alloying elements investigated relative to pure Au, but both stable and unstable fault energies vary strongly with solute concentration and, crucially, with the solute’s distance from the fault plane. The calculated compositional dependence was tied to misfit strain through the relaxation volume associated with alloying. In Fe–Mn–Al–C austenite, Mn, Al, and C affect intrinsic and unstable stacking fault energies only when present within a few layers of the fault; in CoCrNi and CoCrFeNi, the fault energy depends on which elements enrich the specific glide plane. Taken together, these results indicate that the energetics of a CSF are often governed more by the local defect chemistry than by the average alloy composition (Goyal et al., 2020, Medvedeva et al., 2012, Nitol et al., 14 Sep 2025).

A mathematically explicit multiscale description was derived for a discrete model of partial edge dislocations and stacking faults. After subtracting the logarithmic core self-energy, the $\mathbf{b}=\frac{a}{2}\langle 110\rangle$8-limit yields a continuum functional

$\mathbf{b}=\frac{a}{2}\langle 110\rangle$9

where $$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$0 is the core energy, $$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$1 the renormalized dislocation-interaction energy, and $$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$2 the minimal total length of the stacking-fault set resolving the partials. This is important because it makes explicit that complex fault configurations are governed simultaneously by atomic-scale core energies, long-range elastic interactions, and the geometric line or area cost of the fault itself (Bach et al., 2024).

5. Experimental and computational characterization

Direct visualization of CSFs and related faulted regions requires methods that resolve both structure and chemistry. In Ni–W, analytical field ion microscopy combined with density-functional-theory-informed image contrast and time-of-flight mass spectrometry directly imaged W segregation along stacking faults. The same study quantified trajectory aberration at approximately $$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$3, explaining why conventional atom probe tomography did not resolve the segregation layers. This is a notable case in which the defect could be seen only by correlating field-ion images with elemental identification and atomistic modeling (Morgado et al., 2024).

Electron microscopy remains the dominant structural probe for complex fault topologies. In WC, HRTEM, HAADF/ABF STEM, and integrated differential phase-contrast imaging established that the fault contains a double carbon layer and produces a $$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$4 lattice rotation. In Sr$$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$5NaNb$$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$6O$$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$7, dark-field TEM, HRTEM, STEM, symmetry-mode analysis, and force-field calculations identified four-fault annihilation events and linked them to the $$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$8 order parameter. In semiconductors, low-temperature cathodoluminescence and micro-PL correlated the $$\frac{a}{2}[110]\rightarrow \frac{a}{6}[1\bar{1}2]+\frac{a}{6}[2\bar{1}1],$$9 line in GaN nanowires with a single basal stacking fault, while state-of-the-art structural imaging plus effective-mass theory in GaAs established that paired faults form a double-well excitonic trap (Nogues et al., 2014, Sjökvist et al., 10 Nov 2025, Durnev et al., 2019).

Spectroscopic probes are especially important when stacking involves an order parameter rather than only atom positions. In CsV$\{111\}$0Sb$\{111\}$1, polarization- and temperature-dependent Raman spectroscopy detected splitting of the $\{111\}$2 phonon, twofold and fourfold intensity modulations consistent with $\{111\}$3 symmetry, and a hysteretic transformation of a Cs-related mode around $\{111\}$4. These signatures identified domain structure and a stacking order–disorder transition even though the fault itself is an interlayer CDW configuration rather than a simple crystallographic misregistry (Jin et al., 2024).

Theory spans atomistic, mesoscale, and continuum levels. Bond-order-potential simulations were used to map W binding energies around a dissociated edge dislocation in Ni; meta-atom molecular dynamics resolved the conversion of overlapping stacking faults into twins and stair-rod arrays in TWIP steels; phase-field crystal models stabilized intrinsic faults and split Shockley partials while reproducing dissociation widths and Peierls strains; moment tensor potentials enabled near-DFT predictions of plane-resolved fault energetics in medium-entropy alloys; and rigorous $\{111\}$5-convergence established continuum energies involving both partial dislocations and stacking-fault length terms (Wang et al., 2016, Berry et al., 2012, Nitol et al., 14 Sep 2025, Bach et al., 2024). Across these methods, the consistent theme is that a CSF cannot be characterized solely by an isolated $\{111\}$6-surface point; one must also resolve chemical order, defect geometry, and the interactions of multiple partials.

6. Mechanical, electronic, and optical consequences

In structural alloys, CSFs matter because they modify how dislocations move. Solute segregation to faults or their bounding partials can pin the faulted configuration, change the local stacking fault energy, and alter the competition among compact glide, extended partial glide, twinning, and transformation. In Ni-based systems, W segregation to fault centers and Re segregation to partial cores imply different strengthening modes; in TWIP steels, overlapping faults, twin embryos, and stair-rod arrays explain why deformation twins act both as barriers and as dislocation-storage sites; in Ni$\{111\}$7Al, the decrease of CSF Gibbs energy with temperature increases the cross-slip barrier and therefore requires refinement of existing analytical models for the anomalous yield behavior (Morgado et al., 2024, Wang et al., 2016, Xu et al., 21 Aug 2025).

In chemically complex fcc alloys, SFE engineering turns CSFs into an alloy-design variable. DFT plus machine learning in Co–Cr–Fe–Mn–Ni–V–Al predicted a broad range of SFEs and used a target value of about $\{111\}$8 to search for alloys likely to display TWIP/TRIP behavior. Because low or negative intrinsic SFE promotes wide partial separation, hcp-like lamellae, and micro-faulting, a plausible implication is that the same design strategy also tunes the propensity for extended and complex faulted microstructures, not only the average width of a single intrinsic fault (Khan et al., 2021). In Au alloys, the strong dependence of SFE on solute position near the fault supports the same conclusion from a different chemical system (Goyal et al., 2020).

CSFs also have non-mechanical consequences. In CsV$\{111\}$9Sb$\gamma_{\mathrm{SF}}$0, stacking disorder modulates the coherence of the three-dimensional CDW and is linked in the discussion to superconductivity, nematicity, and possible time-reversal-symmetry-breaking phenomena. In Ag thin films, periodic stacking-fault arrays confine Ag(111) surface states into decoupled one-dimensional stripe states. In GaN and GaAs, stacking-fault-bound excitons demonstrate that faulted polytypic segments act as atomically thin or double-well quantum structures that trap carriers and reshape local optical response (Jin et al., 2024, Uchihashi et al., 2011, Durnev et al., 2019).

A recurrent misconception is to treat CSF as a single universal crystallographic object. The literature summarized here shows instead that CSF is a family of defect states whose concrete realization depends on the host lattice and the active order parameters. In ordered superalloys it refers to APB-coupled and chemically reordered fault packets; in layered kagome materials it refers to domain-rich interlayer phase disorder; in WC it refers to an interstitial-driven rotational fault; in ferroics it is a topological defect of a tilt modulation; and in semiconductors it can mean a paired or polytypic fault complex. Several of the cited studies do not use the term explicitly, but their structures match this broader definition. This suggests that the unifying feature of a CSF is not a particular stacking sequence alone, but the coexistence of faulted stacking with additional structural, chemical, magnetic, ferroic, or electronic complexity (Morgado et al., 2024, Jin et al., 2024, George et al., 2024).