Emergence of stable interfaces under extremeplastic deformationIrene J. Beyerleina,1, Jason R. Mayeura, Shijian Zhengb, Nathan A. Marab, Jian Wangc, and Amit Misrab

aTheoretical Division, bMaterials Physics and Application Division, and cMaterials Science and Technology Division, Los Alamos National Laboratory,Los Alamos, NM 87545

Edited* by William D. Nix, Stanford University, Stanford, CA, and approved February 13, 2014 (received for review October 15, 2013)

Atomically ordered bimetal interfaces typically develop in near-equilibrium epitaxial growth (bottom-up processing) of nanolay-ered composite films and have been considered responsible fora number of intriguing material properties. Here, we discover thatinterfaces of such atomic level order can also emerge ubiquitouslyin large-scale layered nanocomposites fabricated by extreme strain(top down) processing. This is a counterintuitive result, which wepropose occurs because extreme plastic straining creates newinterfaces separated by single crystal layers of nanometer thickness.On this basis, with atomic-scale modeling and crystal plasticitytheory, we prove that the preferred bimetal interface arising fromextreme strains corresponds to a unique stable state, which can bepredicted by two controlling stability conditions. As anothertestament to its stability, we provide experimental evidence show-ing that this interface maintains its integrity in further straining(strains > 12), elevated temperatures (> 0.45 Tm of a constituent),and irradiation (light ion). These results open a new frontier inthe fabrication of stable nanomaterials with severe plasticdeformation techniques.

texture | atomistic simulation | radiation resistance | thermal stability

Unlike traditional materials, nanomaterials contain an un-usually high density of interfaces that give rise to un-

precedented properties such as ultrahigh strengths (1–5).Further, nanomaterials with nearly perfect, atomically orderedlow-energy interfaces have been found to possess extraordinarythermal stability and radiation tolerance (1, 6–10). However,nanomaterials with disordered, high-energy interfaces are not stablein these same extreme conditions (11, 12). The integrity of the in-terface is tied to how the nanomaterial was made. Near-equilibriumprocesses generate perfect interfaces prevailing across the materialbut only produce small amounts of material, such as epitaxial thinfilms (13, 14). Ordinary large-scale metal-working (far from equi-librium) processes produce large amounts of nanostructured ma-terial suitable for technical application, but the interface types canvary within the same sample. For single-phase metals, the heavystraining can drive dislocations generated during deformation toorganize into low-energy boundary structures (15, 16), some ofwhich can be ordered (17) and others disordered (12, 18–20).Likewise, in heavily drawn two-phase composites, several kinds ofbimetal interface structures have been reported, both ordered anddisordered (21). Achieving uniformly ordered interfaces in bulknanostructured metals presents a grand challenge in the design ofmaterials that can be stable in the harsh environments demandedby the next generation of highly energy-efficient systems.Here we discover that a bulk metal-working technique that

imposes extreme amounts of plastic strains can give rise to apreferred bimetal interface with perfect atomic order. Mostremarkably, experimental evidence shows that this preferredinterface occurs ubiquitously throughout the volume (>cm3) of thenanocomposite. This interface is shown to be stable with respect tofurther straining, high-temperature exposure, and irradiation, giv-ing the nanomaterial extraordinary tolerances in other extremesituations. This finding has the exciting potential of eliminating theaforementioned tradeoff and permitting the creation of materials

with pristine interfaces in stable nanocomposites of unlimitedquantities. However, although such bulk deformation techni-ques may offer flexibility in processing path, current approachesfor linking strain path to the resulting metallic microstructureshave been empirical. To fundamentally rationalize this seeminglycounterintuitive result, we use theory, atomic-scale modeling, andexperimental characterization to identify the stability conditionsthat govern the emergence of a preferred interface at extremestrains. We reveal that the observed interface indeed correspondsto a special stable state. On a grander scale, this insight can beused to create other stable interfaces and open a new frontier ofdeformation processing for extreme-tolerant materials.To impose extreme strains, we fabricated Cu–Nb nanolayered

materials in bulk form (>cm3) with a severe plastic deformationprocessing (SPD) technique called accumulative roll bonding(ARB; refs. 22–24). We begin with an alternating stack of sheets ofthese two dissimilar, immiscible metals, and then carry out theARB process. Unlike conventional rolling, ARB strains the samplevia a cycle of rolling, cutting, and restacking, and maintains theoriginal sample dimensions. To prevent oxide contamination at theinterfaces during the entire ARB process, we use a speciallydesigned method (SI Text and Fig. S1). The individual layerthickness h can be easily refined and controlled with increasingstrain (Fig. S1).Previously SPD techniques, like ARB, have been used to make

fine-layered material (h = 10–102 μm) using large strains buta significant fraction of the interfaces was reported to be disor-dered and dispersed (18–22). Here we impose extreme strains,decreasing h by 5–6 orders of magnitude, from 2 mm to 20 nm.

Significance

Many processing techniques, such as solid-state phase trans-formation, epitaxial growth, or solidification, can make nano-composite materials with preferred crystallographic orientationrelationships at internal interfaces. On the other hand, metal-working techniques can make composites in bulk quantities forstructural applications but typically the resulting bimetal inter-faces lack crystallographic order and are unstable with respectto heating. Using a metal-working roll-bonding technique, wefind that at extreme plastic strains, the bimetal interfaces de-velop a remarkably ordered, preferred atomic structure. Usingatomic-scale and crystal-plasticity simulations, we study thedynamical stability conditions responsible for this counterintu-itive phenomenon. We show that the emergent interfacecorresponds to a unique stable state, which leads to ex-ceptional mechanical, thermal, and irradiation stability ofthe nanocomposite.

Author contributions: I.J.B., N.A.M., and A.M. designed research; I.J.B., J.R.M., S.Z., N.A.M.,and J.W. performed research; and I.J.B. wrote the paper.

The authors declare no conflict of interest.

*This Direct Submission article had a prearranged editor.1To whom correspondence should be addressed. E-mail: irene@lanl.gov.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1319436111/-/DCSupplemental.

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This is equivalent to stretching a nickel coin to 2.2 km in length(or strains exceeding 12).As a way of measuring the degree of microstructural ordering,

neutron diffraction was first used to nondestructively measurethe distribution of crystallographic orientations (texture) of allgrains in the entire ARB sheet. To investigate size effects, thesemeasurements were repeated for samples with different internallayer dimension h, ranging from h = 100 μm to 20 nm. The resultsrevealed that a transition from the classical texture distribution(25–28) to an unfamiliar distribution takes place at h = 700 nm(or a strain of 8) (23). The new texture was exceptionally sharp,signifying a highly oriented structure. This is in stark contrast tothe range of orientations that usually stabilize in Cu or Nb whenrolled alone.To help understand the texture transition, we use electron

backscatter diffraction (EBSD), which, in addition to texture,can locate orientations and phases within the microstructure(29–32). With EBSD, we found that the transition is coincidentwith attainment of layers that are spanned by only one grain. Thegrains are exceedingly wide, with an average aspect ratio of 30,about 5–10 times that expected in conventional rolling. Thislength scale is also below that (∼1 μm) at which dislocationdensity and substructure development within the layers betweeninterfaces gradually decrease (23, 24) until, at fine layers (200 nmand below), they were no longer observed (refs. 30, 32; see Fig.4A). This means that at the transition point, individual grainshave become bounded by interfaces and not ordinary grainboundaries. These measurements suggest that the unexpectedly,highly oriented microstructure is influenced by the close prox-imity of the bimetal interfaces.To determine whether preferred orientations correlate with

preferred interfaces; that is, whether certain Cu and Nb ori-entations prefer to be joined, we carried out a correlationanalysis of the paired Cu and Nb orientations on either side ofthe interfaces. For statistical significance, we obtained the datafrom numerous Cu–Nb pairs from several EBSD maps of sam-ples with h below but near the transition point (29). The ex-traordinary outcome was that the Cu and Nb orientations werehighly correlated. Most of the Cu and Nb grains have assembledsuch that they are bonded at their mutual {112} planes and the<111> direction of Cu is aligned with the <110> direction of Nb.This means that the Cu orientation on one side of the interface is{112}<111> and the Nb orientation on the other side is {112}<110>. These measurements find that the distribution aboutthese preferred orientations is narrow, such that each crystal varieswithin 0.1–0.2% of the entire orientation space. Such a highlyoriented state is peculiar because many orientations in Cu and Nbare expected to be stable in rolling (25–28) and hence the numberof possible Cu–Nb orientation combinations among them isexpected to be large. In contradiction, we find that a singular in-terface character, as defined by this pairing of a particular Cu andNb orientation, is strongly preferred.To see whether this preferred interface character is stable with

respect to straining, we repeated characterization for samplesvarying in individual layer thickness from h = 200 nm to h = 20 nm.These samples experienced correspondingly strains of 9–12, aboveand beyond that of conventional rolling. Because these fine nano-scale dimensions of h reached the limits of EBSD, we used othertechniques, such as wedge-mounting EBSD (30) and precessionelectron diffraction (PED) (31), as well as transmission electronmicroscopy (TEM) and high-resolution (HR)-TEM (32, 33), toobtain analogous measurements. These measurements revealedthat the layers remained one grain thick and their average aspectratio increased to at least 80, meaning the bimetal interface densityincreased and the grain boundary density decreased markedly.More importantly, they showed that refinement to nanoscaledimensions strengthened the predominance of this preferred in-terface. Evidently, this special interface character is stable with

respect to straining. It was remarkable to note that extreme strainsinvoke a natural selection process for particular interfaces.To assess the atomic structure of this interface, we use HR-

TEM to observe the interfaces in several nanomaterial samples(different h < 100 nm). Fig. 1 shows HR-TEM micrographs ofthe preferred interface; two configurations are shown, which areslightly misoriented by ∼7°. The unexpected result is that theyare regularly ordered at the atomic level. Typically after severeplastic deformation of metals, a fraction of the grain bound-aries are disordered (18–22). The atomic regularity in Fig. 1 isreminiscent of pristine, low-energy bimetal interfaces formedafter near-equilibrium, thermodynamic processes (13, 14), notof mechanical processing.Additionally, we noticed that they contain a regular array of

atomic-scale facets (i.e., the zig-zag morphology). To better un-derstand their origin we developed an atomic-scale (MD) modelof this Cu–Nb interface (Fig. S2). The relaxed undeformedequilibrium structure calculated in MD is identical to the HR-TEMobservations (34). The two types of facets shown in Fig. 1, {111}Cu//{101}Nb and {001}Cu//{011}Nb, are a consequence of thefaceted topology of the {338}Cu and {112}Nb crystallographicplanes being joined. They are determined by the global orienta-tion relationship and small angular deviations in the interface–orientation relationship cause a change in the relative lengthof these facets. Therefore, the faceted interfaces are not a resultof residual defects left from numerous interactions with dis-locations during severe plastic deformation, but are an intrinsicpart of the interface. In other words, these interfaces are not de-fective with foreign debris as expected, but are atomically perfect.Thus far, we have discovered that extreme mechanical strains

can naturally select a preferred interface that possesses atomicorder. This counterintuitive result raises fundamental questionsof microstructural evolution in plastically deformed metals. Doesthis preferred interface correspond to a stable state and whatvariables determined it? Are there others like it? The answerscannot be found by current idealizations of interfaces as obsta-cles to slip (1, 35, 36) or crystals deforming as part of a poly-crystalline network (28). In the following, we explore the specialstability conditions that would apply to the dynamic creation ofinterfaces separated by one-grain layer.Stability is often associated with states of low energy. We begin

by using the same atomic-scale Cu–Nb interface model to in-vestigate the formation energy γ of other interfaces. Interfacesare designated by the lattice orientation of the two crystals oneither side of the interface with respect to a global frame, ori-entation relationship of this pair, and the interface planes theyjoin, all of which can be varied independently. Collectively, theydescribe the interface character. Here we elect to vary characterby tilting one crystal relative to another, while covering an ori-entation space that includes the preferred interface. Fig. 2 showsthe energetic landscape versus interface character. In the caseshown, the Nb orientation was fixed to {112}<110>, and the Cuorientation was varied. Other similar calculations were per-formed for different Cu–Nb crystallographic combinations (37).Taken together, the calculations reveal that deep wells in the γprofile correspond to observed preferred interfaces. This can beseen in Fig. 2. Within a narrow orientation range (∼7°), we ob-serve two minimum energy cusps, and these correspond to thetwo variants of the preferred interface seen in Fig. 1 A and B.Using our atomistic simulations coupled with theoretical meth-

ods described in ref. 38, we determined the distribution and char-acteristics of the interfacial dislocations for each interface in Fig. 2.We find that an interface at the cusp location is associated with thetilt angle that minimizes the value of the Burgers vector of theinterfacial dislocations because it best aligns the natural facetsof the Cu and Nb planes being joined (37). This is a powerfulnotion that implies that the preferred interfaces emerging in the

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Cu–Nb nanocomposites may arise in other bimetal interfacematerial systems.Thus far, our calculations reveal that low formation energy γ is

a strong criterion for interface stability. This can be understoodon the basis that as strain increases, interface spacing h decrea-ses, and the interface density in the nanomaterial increases; theinfluence of interface-formation energy naturally grows with in-creasing strain. However, previous atomic-scale simulations showthat there are a few other interface characters (e.g., Kurdjumov–Sachs, Nishiyama–Wasserman γKS = 576–586 mJ/m2) that pos-sess even lower formation energies than that associated with thepreferred interface reported here (39). Thus, another equallyimportant variable determining mechanical interface stabilitymust coexist with the criterion of low formation energy.To isolate this second key variable, we examine the dynamics

of crystal deformation and its role in interface formation. Inorder for the new interfaces to have the same crystallographiccharacter as the original ones, the original interface must beplastically stable. This means that both the Cu and Nb crystallayers can plastically deform during rolling without reorienting.Previous modeling and experimental studies indicate that slipdynamics within an individual crystal largely dictate its stabilityagainst reorientation (27, 28, 35). However, in the presence ofinterfaces that join one crystal layer to another of dissimilarmaterial, the slip dynamics and resistance to reorientation in the

two layers are expected to change. However, how this occurs isunknown. The stability of joined dissimilar crystals in sucha highly constrained system has not been modeled before and ischallenging to measure experimentally.To explore the plastic stability of an interface, we develop

a 3D model of an alternating stack of Cu and Nb single-crystallayers and use the crystal plasticity finite element technique tocalculate its dynamic response in deformation (see SupportingInformation for more details). The model geometry is designedto authentically represent the actual material for h below thetransition point (h < 500 nm). The heart of the model consistsof a Cu and Nb crystal joined at a common interface, a bicrystal,with a prescribed crystallographic character (Fig. S3). Applyingperiodic boundary conditions in three dimensions creates a re-peating multilayer architecture with a single interface character.Next, we calculate the lattice rotation of each crystal on eitherside of the interface under plane strain compression, an ideali-zation of rolling, where the elongation direction coincides withthe rolling direction. We use this information to assess stability.To be specific, when straining causes either crystal to rotate, theinterface character is altered and hence plastically unstable. Asa means of comparing the stabilities of different interfaces,a figure of merit for plastic stability of an interface, ω, is calcu-lated from each simulation, which is given by:

Fig. 1. Ordered interfaces after extreme strains. High-resolution transmission electron microscopy micrographs of preferred Cu–Nb interfaces: (A) {338}<443 >Cujj{112}<110 > Nb and (B) {112}<111 > Cujj{112}<110 > Nb. The crystallography of the facet planes is indicated.

Fig. 2. Preferred interfaces correspond to deep wells in interface formation energy. Molecular dynamics calculation of the variation in interface formationenergy with tilt angle about <110 > Cujj<111 > Nb, the direction normal to the micrographs in Fig. 1 (32).

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ω = exp�−ΔΩfcc

Δ«

�exp

�−ΔΩbcc

Δ«

�;

where ΔΩfcc and ΔΩbcc are the rotation angles (radians) of thelattice of the Cu and Nb crystals from their respective startingorientations due to an imposed strain Δ«. In this measure, thelimit ω→ 0 corresponds to an unstable interface, and the limitω→ 1 to a stable one. For instance, permitting at most smalllattice reorientations in each crystal over a large amount ofstrain, i.e., both ΔΩfcc=Δ«≤ 0:1 and ΔΩbcc=Δ«≤ 0:1, correspondsto ω ≥ 0.8.Consistent with experiment, in the model, the two crystals

joined at an interface are forced to codeform; that is, the in-terface does not slide or debond during straining. One advantageof the present modeling technique is that it can capture changesin the development of elastic (anisotropic) strains and crystallo-graphic slip accompanying the added constraint of codeforma-tion. To further clarify the effects of codeformation, we carry outa detailed comparison between the plastic stability of the bicrystalwith two unbounded individual crystals under the same strainingconditions (Supporting Information). The initial orientations ofthe single crystals are the same as the initial orientations of thecrystals on either side of the interface. Like in the calculations ofinterface energy γ, bicrystal plasticity simulations are performedfor a large number of candidate interface characters, chosenbased on theoretical grounds or experimental observation. Ourresults show that the plastic stability of interfaces found incodeforming crystals is not a straightforward superposition of theplastic stabilities of the crystals they join. In fact, most interfacecharacters are not plastically stable (Fig. S4). We find that thereason is that the less stable of the two determines the plasticstability of the interface; the “weaker link” dictates the plasticstability of the pair. This explains why many stable orientationscommon to single-phase metals are not the same orientationsassociated with the preferred interfaces after extreme straining.From our calculations, we find that a symmetric distribution of

slip on the active slip systems is required for maintaining code-formation and preserving interface orientation. Prior atomic-scalemodeling indicates that glide dislocations on slip systems withthe highest resolved shear stress can be supplied from facetedinterfaces, such as that in Fig. 1 (40, 41).Thus far, our simulations have demonstrated that low forma-

tion energy and plastic stability are strong criteria for interfacestability. To map out how interfaces compare with respect toboth criteria, we plot them in Fig. 3 with respect to their ω and γon two axes. We find that many interfaces are plastically stable(ω > 0.8), fewer possess relatively low formation energy (γ < 950mJ/m2), and even fewer correspond to energetic minima (γ ∼600–700 mJ/m2). To understand the relative importance of thesecriteria, we use a black triangle to mark the preferred interfaceand its closely neighboring variants. The significant outcome is

that they all lie exclusively in the region corresponding to bothlow formation energy and high plastic stability. Interfaces lyingfarther away from this region are less likely to “survive” extremestraining. From the experimental and simulation results, we con-clude that extreme strains naturally select interfaces that are low information energy and plastically stable in codeformation, a severeconstraint that only a few interfaces satisfy in rolling. This findingalso strongly implies that a ubiquitous preferred bimetal interfaceis an inevitable outcome of extreme straining provided that thereare deep wells in interface energy. Broadly speaking, the stabilityconditions established here are sufficiently fundamental that theycan apply to other strain paths and other material systems, suchthat other emergent interfaces can be forecasted.As a further test of stability, these nanomaterials were exposed

to extreme conditions. We confirmed experimentally that theinterface preserves its regular atomic structure under furtherstraining down to h = 20 nm (Fig. 4A). Experiments have dem-onstrated that the interface structure and parent nanostructureof the h = 20 nm material is retained after 1-h exposure to 0.45,the melting temperature of Cu with little degradation in strength

Fig. 3. Revealing where emergent interfaces lie: a bimetal interface characterstability map. (Top Left) The regime of mechanically stable interfaces. Squaresand circles are simulated Cu–Nb interfaces under rolling strains. Triangles in-dicate those cases corresponding to the observed preferred interfaces. Thedifferent variants of preferred interfaces are associated with different ori-entations of Nb or Cu close in orientation space. Table S1 lists the data cor-responding to the points here.

Fig. 4. Staying stable in extremes. Transmission electron microcopy micrographs displaying the planar Cu–Nb interfaces after (A) extreme plastic strains of∼12, which produces an h = 20 nm composite, (B) elevated temperatures of 500 °C, which is 0.45 times the melting temperature of Cu (32), and (C) helium-ionirradiation, showing no voids in the layer or in the interfaces in an h = 20 nm composite (39).

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(32) (Fig. 4B). We also report that these interfaces do not de-velop damaging voids under He-ion irradiation unlike ordinarygrain boundaries in Cu (42) (Fig. 4C). The forecasted lifetimes ofthese bulk nanomaterials, dense with naturally selected interfaceswould, therefore, significantly exceed those of their constituents.In summary, we demonstrate that a preferred bimetal interface

possessing regular atomic order emerges from extreme mechan-ical straining of layered nanocomposites. Further, experimentalevidence shows that this interface is stable with respect to con-tinued extreme straining, high temperatures, and irradiation.These results are surprising and question current understandingof microstructural evolution during metal working. Using atomic-scale and crystal-plasticity simulation, we reveal that the strongpreference is a result of the formation of interfaces nanometers

apart during straining. The calculations indicate that thepreferred interface is one of few (among the vast space of possibleinterfaces) that under extreme straining can remain plasticallystable while forming interfaces corresponding to a minimum information energy. Most significantly, it points to other interfacesthat could also emerge in extreme straining and exhibit similarstability properties. Our findings demonstrate that extreme strainscan be used as an innovative way toward manipulating inter-faces at will for target material properties.

ACKNOWLEDGMENTS. The authors gratefully acknowledge support bythe Center for Materials at Irradiation and Mechanical Extremes, anEnergy Frontier Research Center funded by the U.S. Department ofEnergy, Office of Science, Office of Basic Energy Sciences under Award2008LANL1026.

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