Amorphous Interfacial Complexions

• Amorphous interfacial complexions are nanoscale, equilibrium or metastable disordered films confined to grain or interphase boundaries, distinct from bulk amorphous phases.
• They exhibit spatial gradients in structure and chemistry across their finite thickness, influencing mechanical properties, diffusion, and radiation resistance.
• Their formation depends on interfacial thermodynamics, dopant segregation, and alloy design rules, enabling tailored enhancements in material performance.

Amorphous interfacial complexions are equilibrium or metastable interfacial states of finite thickness in which a grain boundary or interphase boundary becomes structurally disordered while the adjoining grains remain crystalline. In metallic systems they are commonly observed as nanoscale amorphous intergranular films or amorphous grain-boundary complexions, and they are distinguished from both ordinary ordered grain boundaries and bulk amorphous phases by their interface-confined geometry, segregation-stabilized chemistry, and spatially varying short-range order through the film thickness (Schuler et al., 2017). Across Cu–Zr, Cu–Hf, Ni–Zr, Cu–Ta, Al–Y, multicomponent Cu-rich alloys, and W-rich design studies, they have been linked to grain-growth resistance, altered diffusion, improved damage tolerance, reduced strain localization, and enhanced radiation resistance, while recent work has also clarified that their properties depend not only on whether a boundary is amorphous, but on thickness, local chemistry, and the patterning of order and disorder within the interfacial layer itself (Garg et al., 2023).

1. Definition, taxonomy, and interfacial status

Complexions are phase-like interfacial states with stable, finite thicknesses that exist only in equilibrium with adjoining crystals, rather than independent bulk phases. Within the standard complexion taxonomy, ordered states occupy the thinner classes, while disordered type V and VI states can be amorphous; the metallic literature often uses “amorphous intergranular films” for nanoscale amorphous grain-boundary films and “amorphous interfacial complexions” as the broader category that includes grain-boundary and interphase-boundary cases (Schuler et al., 2017).

This distinction is central. A true amorphous interfacial complexion is not simply a damaged boundary, a quenched nonequilibrium layer, or a slab of bulk metallic glass inserted between crystals. It is an interface-localized state whose existence depends on interfacial thermodynamics, local segregation, and the adjoining crystal structures. That point is explicit in studies of Cu–Zr, where nanoscale amorphous films are treated as equilibrium or stabilized complexions distinct from thicker wetting films, and in Cu-rich multicomponent alloys, where the films are identified as equilibrium interfacial states rather than arbitrary amorphous layers (Hu et al., 2017).

The literature also distinguishes among several interface classes. Ordered grain boundaries are crystalline boundaries between grains of the same phase. Ordered interphase boundaries separate different crystalline phases. Amorphous grain-boundary complexions are disordered films between grains of the same phase, whereas amorphous interphase complexions are disordered films at crystal/crystal phase boundaries, as shown in Cu–Ta where amorphous grain-boundary and interphase complexions were analyzed separately under irradiation (Aksoy et al., 2023). This suggests that “amorphous interfacial complexion” is best understood as a structural state family rather than a single morphology.

A recurrent misconception is that any amorphous material adjacent to a crystal qualifies as a complexion. That is not the usage in the canonical metallic-grain-boundary literature. For example, Au in contact with bulk amorphous Si or amorphous silica exhibits a crystalline–amorphous interface with important transport consequences, but the amorphous side is a bulk phase rather than a thermodynamically stabilized nanoscale interfacial film, so the result is mechanistically informative yet not a direct complexion-thermodynamics case (Hajj et al., 2024).

2. Internal structure: spatial gradients, transition regions, and local order

A defining result of the field is that amorphous interfacial complexions are structurally heterogeneous across their thickness. In Cu–Zr amorphous intergranular films analyzed by Voronoi tessellation, three distinct regions were identified: an amorphous–crystalline interface region, a transition region, and, when the film is sufficiently thick, an interior region whose short-range order matches a bulk amorphous phase (Pan et al., 2016). The total thickness occupied by the two amorphous–crystalline interface regions was estimated as about $0.8$ nm, or about $0.4$ nm per side, while a fully saturated bulk-like interior did not appear below about $1.8$ nm total film thickness.

The local structure was described with Voronoi indices $\langle n_3,n_4,n_5,n_6,\ldots\rangle$, with weighted tessellation using a Cu/Zr size ratio of $0.804$ in the Cu–Zr study. Interfacial motifs included $\langle 0,10,2,0\rangle$ and $\langle 0,8,4,0\rangle$, whereas bulk-like amorphous interior motifs included $\langle 0,2,10,0\rangle$ and $\langle 0,0,12,0\rangle$ (Pan et al., 2016). Thin films could contain only the interfacial and transition regions, providing direct evidence that confined amorphous films are not miniature bulk metallic glasses.

Temperature and boundary crystallography both affect this spatial organization. At $600$ K, transition-region thickness and motif populations depended on total film thickness and on the interfacing crystal plane; at $0.4$0 K, the transition profile became effectively thickness-independent and the dependence on crystal plane largely vanished (Pan et al., 2016). This suggests that crystalline templating of amorphous short-range order weakens at higher temperature.

Later work refined this picture by splitting the film into a complexion interior and two amorphous–crystalline transition regions, or ACTRs, and then asking how local short-range order within those regions controls mechanical response. In Cu–Zr bicrystals with about $0.4$1 nm total complexion thickness, the ACTR edge was defined where the density of ordered motifs exceeded that of ICO-like motifs, giving an ACTR thickness of about $0.4$2 nm. The key result was that the two films had nearly identical complexion interiors but opposite asymmetry in ordered short-range order across the thickness, and that this asymmetry controlled how plasticity spread through the film during dislocation absorption (Garg et al., 2023).

More recent multicomponent Cu-rich work adds a chemistry–structure coupling to this structural gradient. High-resolution STEM and EDS showed that Zr enriches the more disordered complexion interior, while Nb and Ti enrich the more ordered ACTRs; simulation with a custom MACE machine-learning interatomic potential reproduced the same through-thickness partitioning and showed that increasing chemical complexity makes the complexion interior more disordered overall (Hessong et al., 7 Sep 2025). This suggests that the internal architecture of an amorphous complexion is jointly structural and chemical.

3. Formation thermodynamics, segregation, and alloy-selection rules

The most widely used thermodynamic picture treats an amorphous complexion as favorable when the free-energy penalty of an undercooled amorphous film is smaller than the interfacial-energy reduction achieved by replacing one crystalline grain boundary with two crystal–amorphous interfaces. In the notation used for binary metallic alloys,

$0.4$3

where $0.4$4 is the volumetric free-energy penalty for the amorphous layer, $0.4$5 is film thickness, $0.4$6 is the original crystalline grain-boundary energy, and $0.4$7 is the crystalline–amorphous interfacial energy (Schuler et al., 2017). In practice, two linked conditions recur throughout the literature: dopants must segregate strongly enough to enrich the interface, and the enriched boundary chemistry must favor amorphization rather than ordered segregation or precipitation.

For binary metallic alloys, Schuler and Rupert proposed practical selection rules based on a positive enthalpy of segregation,

$0.4$8

and a negative enthalpy of mixing,

$0.4$9

with atomic size mismatch above about $1.8$0 treated as helpful but secondary (Schuler et al., 2017). Their experiments showed that Cu–Zr and Cu–Hf formed nanoscale amorphous intergranular films, whereas Cu–Nb and Cu–Mo retained ordered boundaries despite segregation; the decisive discriminator was enthalpy of mixing rather than size mismatch alone. The same framework successfully predicted a roughly $1.8$1 nm amorphous intergranular film in Ni–5.5 at.% Zr.

A comparable logic appears in atomistic assessments of interatomic potentials. In Cu–Zr, only potentials that reproduced composition-dependent enthalpy of mixing and realistic bond energetics generated the experimentally correct progression from ordered monolayer segregation to gradual disordering and then to nanoscale amorphous intergranular films at higher temperature or dopant concentration (Hu et al., 2017). This suggests that accurate modeling of complexion formation requires correct thermodynamics of both segregation and amorphization, not merely correct lattice constants or bulk elastic properties.

Recent first-principles alloy design for W-rich systems formalizes the same sequence. The framework first screens grain-boundary segregation using

$1.8$2

then evaluates amorphous stabilization with

$1.8$3

and finally compares crystal–amorphous interfacial energies through

$1.8$4

(Sharma et al., 22 Apr 2026). In W-rich binaries, Y was the strongest promoter, with Co and Ni also favorable; the primary discriminator was the amorphous stabilization energy rather than the variation in crystal–amorphous interface energy. This suggests a transferable complexion-design strategy: maximize boundary enrichment, minimize the amorphization penalty, and then verify that the crystal–amorphous interface is not too costly.

Processing studies in Al-rich systems underscore that complexion formation and complexion retention are not identical. In Al–Y, amorphous complexions were retained even after cooling slower than $1.8$5, whereas Al–Ni required quenching and Al–Mg retained only ordered boundaries under the same treatments (Lei et al., 2023). This suggests that alloy selection must account not only for high-temperature complexion stability but also for the kinetics of the reverse transition during cooling.

4. Chemistry, thickness, and multicomponent stabilization

Thickness is a central structural descriptor of amorphous complexions. In Cu–3 at.% Zr micropillar experiments, two otherwise similar nanocrystalline materials differed primarily in average amorphous grain-boundary complexion thickness: $1.8$6 nm in the slower-cooled condition and $1.8$7 nm in the faster-quenched condition (Hessong et al., 26 Jan 2026). The thicker-complexion material showed more homogeneous deformation and higher damage tolerance, while the thinner-complexion material was more prone to shear localization.

The same thickness trend appears in earlier simulation-based arguments and in radiation studies. In Cu–Ta, amorphous grain-boundary and interphase complexions with thicknesses from $1.8$8 to $1.8$9 nm showed that thicker films generate fewer defects at peak damage and retain fewer residual defects after cascade cooling; the authors connected this not only to larger sink volume but also to different intrinsic displacement threshold energies within diffuse amorphous interfaces (Aksoy et al., 2023). This suggests that complexion thickness controls both defect annihilation and defect production.

Chemical complexity offers an additional route to thicker and more stable amorphous films. In quinary Cu-based alloys, the Cu–Zr–Hf–Nb–Ti alloy exhibited an average amorphous complexion thickness of $\langle n_3,n_4,n_5,n_6,\ldots\rangle$0 nm, which was $\langle n_3,n_4,n_5,n_6,\ldots\rangle$1 thicker than binary Cu–Zr and $\langle n_3,n_4,n_5,n_6,\ldots\rangle$2 thicker than ternary Cu–Zr–Hf under comparable methodology (Grigorian et al., 2021). About $\langle n_3,n_4,n_5,n_6,\ldots\rangle$3 of the measured amorphous complexions in the quinary alloy exceeded $\langle n_3,n_4,n_5,n_6,\ldots\rangle$4 nm, compared with about $\langle n_3,n_4,n_5,n_6,\ldots\rangle$5 in the earlier binary and ternary systems. The same alloy remained nanocrystalline after one week at $\langle n_3,n_4,n_5,n_6,\ldots\rangle$6, approximately $\langle n_3,n_4,n_5,n_6,\ldots\rangle$7 of the melting temperature, supporting the idea that increased boundary chemical complexity frustrates crystallization and stabilizes thicker amorphous complexions.

Polycrystalline simulations reinforce that segregation and complexion transitions are intrinsically heterogeneous across a boundary network. In a Cu–2 at.% Zr polycrystal with roughly $\langle n_3,n_4,n_5,n_6,\ldots\rangle$8 grains and about $\langle n_3,n_4,n_5,n_6,\ldots\rangle$9 atoms, local grain-boundary concentration at $0.804$0 K ranged from $0.804$1 to $0.804$2 at.% Zr even though the global alloy composition was only $0.804$3 at.% Zr, and only about $0.804$4 of boundaries exceeded the pure-Cu reference thickness range and were classified as amorphous (Garg et al., 2021). At $0.804$5 K, about $0.804$6 of the boundaries were amorphous complexions. This shows that ordered and amorphous complexion types can coexist in one equilibrated polycrystalline network, each with its own composition distribution.

A further refinement is that multicomponent complexions are internally patterned. In Cu–Zr–Nb and Cu–Zr–Nb–Ti, Zr peaks in the complexion interior, while Nb and Ti peak in the ACTRs; simulations showed that, for a given total dopant concentration, increasing the Nb/Zr ratio increased the disorder parameter in metallic-glass proxies for complexion interiors (Hessong et al., 7 Sep 2025). A plausible implication is that “more complex chemistry” does not act only by thickening the film; it also modifies through-thickness and in-plane heterogeneity inside the film.

5. Mechanical consequences: dislocation absorption, strain delocalization, and tensile failure

The most developed mechanical picture treats amorphous complexions as defect-accommodating interfacial phases that can absorb dislocations more efficiently than ordered boundaries. In the Cu–Zr bicrystal study of local short-range order, dislocation absorption and crack nucleation were simulated in two films with similar chemistry and thickness but different through-thickness patterning of order and disorder (Garg et al., 2023). Damage was defined when total void/crack volume exceeded $0.804$7. Complexion 1 nucleated damage at $0.804$8 shear strain after absorbing $0.804$9 dislocations, whereas Complexion 2 nucleated damage at $\langle 0,10,2,0\rangle$0 shear strain after absorbing $\langle 0,10,2,0\rangle$1 dislocations. Ordered grain boundaries with the same grain orientations failed after absorbing only one partial dislocation, that is $\langle 0,10,2,0\rangle$2 dislocations, at shear strains of $\langle 0,10,2,0\rangle$3 and $\langle 0,10,2,0\rangle$4.

The mechanistic distinction was not simply that “more disorder is better.” Using Voronoi analysis, non-affine squared displacement with a threshold of $\langle 0,10,2,0\rangle$5, and flexibility volume $\langle 0,10,2,0\rangle$6, the study showed that the more damage-tolerant complexion was the one whose opposite-side ACTR contained a more disordered, high-$\langle 0,10,2,0\rangle$7 network that allowed shear-transformation-zone activity to spread across the full film thickness (Garg et al., 2023). By contrast, when plasticity remained localized near the absorbing side, crack nucleation occurred earlier. The authors concluded that “the damage tolerance of an amorphous complexion is indeed directly determined by its local atomic structure.”

At the scale of nanocrystalline compression, the same interfacial-plasticity logic manifests as suppression of localization. In Cu–3 at.% Zr micropillars, about $\langle 0,10,2,0\rangle$8 of pillars with thinner complexions showed localized deformation, whereas only about $\langle 0,10,2,0\rangle$9 of pillars with thicker complexions did so; conversely, about $\langle 0,8,4,0\rangle$0 of the thicker-complexion pillars deformed homogeneously (Hessong et al., 26 Jan 2026). In taper-free small-strain pillars, the thicker-complexion material had an average plastic asymmetry lower by about a factor of $\langle 0,8,4,0\rangle$1. The mechanistic interpretation was that thicker amorphous complexions provide a larger interfacial volume for absorbing defects and diffusing strain concentrations.

Tensile experiments isolate the effect of complexion type itself. Nanocrystalline Cu–Zr processed to contain amorphous intergranular films interspersed through the boundary network showed an ultimate tensile strength of $\langle 0,8,4,0\rangle$2 MPa, compared with $\langle 0,8,4,0\rangle$3 MPa for the ordered-grain-boundary condition, but the more informative change was in failure mode rather than peak strength (Wardini et al., 2021). Average reduction in area increased from $\langle 0,8,4,0\rangle$4 to $\langle 0,8,4,0\rangle$5, and amorphous-film-containing samples showed less shear-dominated failure, less strain localization, more diffuse necking, and fracture surfaces with more elongated dimple features. The authors argued that amorphous films retard tensile failure by accommodating dislocation absorption and grain-boundary-mediated plasticity over a larger interfacial volume.

Taken together, these studies establish a multi-scale structure–mechanics relation. Ordered boundaries provide discrete sink sites and can remain strongly biased. Amorphous complexions provide a finite-thickness disordered region in which local rearrangements, motif conversion, and distributed shear-transformation-zone activity can relax strain heterogeneity. Thickness, short-range-order patterning, and internal chemistry all modulate how effectively that interfacial plasticity spreads.

6. Radiation response, transport effects, and broader interfacial analogies

Radiation studies extend the complexion concept from mechanical damage to cascade damage. In Cu–Ta, amorphous grain-boundary and amorphous interphase complexions both outperformed their ordered counterparts as sinks for primary-knock-on-atom damage, with the amorphous interphase complexion performing best and acting as an essentially unbiased sink (Aksoy et al., 2023). Relative to the ordered grain boundary, the amorphous grain-boundary complexion reduced residual interstitials by about $\langle 0,8,4,0\rangle$6 and vacancies by about $\langle 0,8,4,0\rangle$7; relative to the ordered interphase boundary, the amorphous interphase complexion reduced residual interstitials by about $\langle 0,8,4,0\rangle$8 and vacancies by about $\langle 0,8,4,0\rangle$9. The paper linked this to excess volume, structural disorder, and, for thicker films, altered defect production rates due to different intrinsic displacement threshold energies.

The Cu–Ta case is notable because it broadens complexion science beyond canonical good glass formers. The amorphous Cu–Ta interfacial films are nanophase-separated rather than chemically homogeneous, and their excess volume is correspondingly heterogeneous. Average Cu atomic volume in bulk amorphous Cu–Ta was reported as $\langle 0,2,10,0\rangle$0 higher than in single-crystal Cu, compared with $\langle 0,2,10,0\rangle$1 for amorphous Cu–Zr; in interfacial films the Cu atomic volume increase was $\langle 0,2,10,0\rangle$2 for amorphous grain-boundary complexions and $\langle 0,2,10,0\rangle$3 for amorphous interphase complexions (Aksoy et al., 2023). This suggests that free volume remains a key descriptor, but its spatial distribution can matter as much as its average magnitude.

Thermal transport studies provide a more indirect lesson. Au interfaces with amorphous Si or amorphous silica exhibited higher interfacial thermal conductance than the corresponding crystalline interfaces, with values at $\langle 0,2,10,0\rangle$4 K of $\langle 0,2,10,0\rangle$5 for Au/a-Si versus $\langle 0,2,10,0\rangle$6 for Au/c-Si, and $\langle 0,2,10,0\rangle$7 for Au/a-SiO$\langle 0,2,10,0\rangle$8 versus $\langle 0,2,10,0\rangle$9 for Au/c-SiO$\langle 0,0,12,0\rangle$0 (Hajj et al., 2024). Although these are not complexion films in the strict metallic-grain-boundary sense, the atomistic explanation—enhanced bonding, larger cross-interface displacement correlations, and stronger anharmonicity in the amorphous interfacial environment—suggests mechanisms by which true amorphous interfacial complexions could also alter transport.

There are also broader analogies in amorphous–amorphous interfaces. In colloidal glass-forming liquids, interfaces between high- and low-overlap amorphous regions exhibit an effective surface tension that grows rapidly near the mode-coupling crossover (Ganapathi et al., 2017). In amorphous ice, a flat LDA$\langle 0,0,12,0\rangle$1HDA interface at $\langle 0,0,12,0\rangle$2 K was found to have an approximately pressure-invariant Gibbs-type thickness of about $\langle 0,0,12,0\rangle$3 Å and to contain MDA-like local environments localized at the interface rather than in a distinct bulk intermediate phase (Shupletsova et al., 31 May 2026). These systems are not metallic complexions, but they suggest that finite-thickness, structurally distinct amorphous interphases may be a broader interfacial motif.

The caution is terminological. These analogies support the physical idea that disordered interfaces can have their own structure, thickness, and functionality, but they do not replace the thermodynamic complexion framework developed for grain boundaries in segregating crystalline materials.

7. Modeling practice, controversies, and design outlook

A persistent issue in this field is the difference between physically meaningful complexion predictions and simulation artifacts. The Cu–Zr interatomic-potential comparison showed that some potentials produced unrealistically high bulk solubility or unphysical Zr clustering at the boundary, even though they could still generate nominally disordered films (Hu et al., 2017). The broader lesson is that credible complexion modeling requires accurate segregation thermodynamics, composition-dependent enthalpy of mixing, and bond energetics across crystalline, liquid, and amorphous states.

Another important caution is that not every “amorphous boundary” has the same significance. In Al-rich alloys, carbides and intermetallics compete with boundaries for segregants, so complexion stability cannot be inferred from boundary chemistry alone (Lei et al., 2023). In polycrystals, the most highly segregated boundaries are not necessarily the ones that amorphize, so a single universal critical boundary composition is too simplistic (Garg et al., 2021). In multicomponent films, average thickness or average composition can also be insufficient because local patterning across ACTRs and interiors can dominate the response (Hessong et al., 7 Sep 2025).

Even apparently simple design rules therefore remain conditional. “Negative $\langle 0,0,12,0\rangle$4 and positive $\langle 0,0,12,0\rangle$5” is a useful first filter for binary metallic systems (Schuler et al., 2017), but later work shows that complexion retention, second-phase competition, grain-boundary character, dopant ratio, and through-thickness chemistry all matter. Likewise, “thicker is better” is supported in confined few-nanometer Cu–Zr films under compression (Hessong et al., 26 Jan 2026) and in Cu–Ta cascade simulations (Aksoy et al., 2023), yet the Cu–3Zr study explicitly limits that conclusion to the sub-$\langle 0,0,12,0\rangle$6 nm regime, noting that much thicker amorphous regions can behave differently.

The current design outlook is consequently multiscale. Alloy selection identifies dopants that segregate and lower the amorphization penalty. Processing controls whether high-temperature disordered states are retained. Internal chemistry and short-range-order patterning determine whether the film delocalizes strain or localizes it. Thickness controls both sink volume and the fraction of the deformation or cascade process that occurs inside the amorphous state. This suggests that amorphous interfacial complexions are best treated not as a binary attribute of a boundary, but as nanostructured interfacial phases with tunable chemistry, thickness, and internal order architecture (Sharma et al., 22 Apr 2026).