Emergence of stable interfaces under extreme plastic deformation Irene J. Beyerleina,1, Jason R. Mayeura, Shijian Zhengb, Nathan A. Marab, Jian Wangc, and Amit Misrab a Theoretical Division, bMaterials Physics and Application Division, and cMaterials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545
Atomically ordered bimetal interfaces typically develop in nearequilibrium epitaxial growth (bottom-up processing) of nanolayered composite films and have been considered responsible for a number of intriguing material properties. Here, we discover that interfaces of such atomic level order can also emerge ubiquitously in large-scale layered nanocomposites fabricated by extreme strain (top down) processing. This is a counterintuitive result, which we propose occurs because extreme plastic straining creates new interfaces separated by single crystal layers of nanometer thickness. On this basis, with atomic-scale modeling and crystal plasticity theory, we prove that the preferred bimetal interface arising from extreme strains corresponds to a unique stable state, which can be predicted by two controlling stability conditions. As another testament to its stability, we provide experimental evidence showing 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 in the fabrication of stable nanomaterials with severe plastic deformation techniques. texture
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nlike traditional materials, nanomaterials contain an unusually high density of interfaces that give rise to unprecedented properties such as ultrahigh strengths (1–5). Further, nanomaterials with nearly perfect, atomically ordered low-energy interfaces have been found to possess extraordinary thermal stability and radiation tolerance (1, 6–10). However, nanomaterials with disordered, high-energy interfaces are not stable in these same extreme conditions (11, 12). The integrity of the interface is tied to how the nanomaterial was made. Near-equilibrium processes generate perfect interfaces prevailing across the material but only produce small amounts of material, such as epitaxial thin films (13, 14). Ordinary large-scale metal-working (far from equilibrium) processes produce large amounts of nanostructured material suitable for technical application, but the interface types can vary within the same sample. For single-phase metals, the heavy straining can drive dislocations generated during deformation to organize into low-energy boundary structures (15, 16), some of which can be ordered (17) and others disordered (12, 18–20). Likewise, in heavily drawn two-phase composites, several kinds of bimetal interface structures have been reported, both ordered and disordered (21). Achieving uniformly ordered interfaces in bulk nanostructured metals presents a grand challenge in the design of materials that can be stable in the harsh environments demanded by 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 a preferred bimetal interface with perfect atomic order. Most remarkably, experimental evidence shows that this preferred interface occurs ubiquitously throughout the volume (>cm3) of the nanocomposite. This interface is shown to be stable with respect to further straining, high-temperature exposure, and irradiation, giving the nanomaterial extraordinary tolerances in other extreme situations. This finding has the exciting potential of eliminating the aforementioned tradeoff and permitting the creation of materials www.pnas.org/cgi/doi/10.1073/pnas.1319436111
with pristine interfaces in stable nanocomposites of unlimited quantities. However, although such bulk deformation techniques may offer flexibility in processing path, current approaches for linking strain path to the resulting metallic microstructures have been empirical. To fundamentally rationalize this seemingly counterintuitive result, we use theory, atomic-scale modeling, and experimental characterization to identify the stability conditions that govern the emergence of a preferred interface at extreme strains. We reveal that the observed interface indeed corresponds to a special stable state. On a grander scale, this insight can be used to create other stable interfaces and open a new frontier of deformation processing for extreme-tolerant materials. To impose extreme strains, we fabricated Cu–Nb nanolayered materials in bulk form (>cm3) with a severe plastic deformation processing (SPD) technique called accumulative roll bonding (ARB; refs. 22–24). We begin with an alternating stack of sheets of these two dissimilar, immiscible metals, and then carry out the ARB process. Unlike conventional rolling, ARB strains the sample via a cycle of rolling, cutting, and restacking, and maintains the original sample dimensions. To prevent oxide contamination at the interfaces during the entire ARB process, we use a specially designed method (SI Text and Fig. S1). The individual layer thickness h can be easily refined and controlled with increasing strain (Fig. S1). Previously SPD techniques, like ARB, have been used to make fine-layered material (h = 10–102 μm) using large strains but a significant fraction of the interfaces was reported to be disordered 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 transformation, epitaxial growth, or solidification, can make nanocomposite materials with preferred crystallographic orientation relationships at internal interfaces. On the other hand, metalworking techniques can make composites in bulk quantities for structural applications but typically the resulting bimetal interfaces lack crystallographic order and are unstable with respect to heating. Using a metal-working roll-bonding technique, we find that at extreme plastic strains, the bimetal interfaces develop a remarkably ordered, preferred atomic structure. Using atomic-scale and crystal-plasticity simulations, we study the dynamical stability conditions responsible for this counterintuitive phenomenon. We show that the emergent interface corresponds to a unique stable state, which leads to exceptional mechanical, thermal, and irradiation stability of the 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. 1
To whom correspondence should be addressed. E-mail: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1319436111/-/DCSupplemental.
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Edited* by William D. Nix, Stanford University, Stanford, CA, and approved February 13, 2014 (received for review October 15, 2013)
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 measure the distribution of crystallographic orientations (texture) of all grains in the entire ARB sheet. To investigate size effects, these measurements were repeated for samples with different internal layer dimension h, ranging from h = 100 μm to 20 nm. The results revealed 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 to the range of orientations that usually stabilize in Cu or Nb when rolled 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 coincident with attainment of layers that are spanned by only one grain. The grains are exceedingly wide, with an average aspect ratio of 30, about 5–10 times that expected in conventional rolling. This length scale is also below that (∼1 μm) at which dislocation density and substructure development within the layers between interfaces gradually decrease (23, 24) until, at fine layers (200 nm and below), they were no longer observed (refs. 30, 32; see Fig. 4A). This means that at the transition point, individual grains have become bounded by interfaces and not ordinary grain boundaries. These measurements suggest that the unexpectedly, highly oriented microstructure is influenced by the close proximity of the bimetal interfaces. To determine whether preferred orientations correlate with preferred interfaces; that is, whether certain Cu and Nb orientations prefer to be joined, we carried out a correlation analysis of the paired Cu and Nb orientations on either side of the interfaces. For statistical significance, we obtained the data from numerous Cu–Nb pairs from several EBSD maps of samples with h below but near the transition point (29). The extraordinary outcome was that the Cu and Nb orientations were highly correlated. Most of the Cu and Nb grains have assembled such that they are bonded at their mutual {112} planes and the direction of Cu is aligned with the direction of Nb. This means that the Cu orientation on one side of the interface is {112} and the Nb orientation on the other side is {112} . These measurements find that the distribution about these preferred orientations is narrow, such that each crystal varies within 0.1–0.2% of the entire orientation space. Such a highly oriented state is peculiar because many orientations in Cu and Nb are expected to be stable in rolling (25–28) and hence the number of possible Cu–Nb orientation combinations among them is expected to be large. In contradiction, we find that a singular interface character, as defined by this pairing of a particular Cu and Nb orientation, is strongly preferred. To see whether this preferred interface character is stable with respect to straining, we repeated characterization for samples varying in individual layer thickness from h = 200 nm to h = 20 nm. These samples experienced correspondingly strains of 9–12, above and beyond that of conventional rolling. Because these fine nanoscale dimensions of h reached the limits of EBSD, we used other techniques, such as wedge-mounting EBSD (30) and precession electron diffraction (PED) (31), as well as transmission electron microscopy (TEM) and high-resolution (HR)-TEM (32, 33), to obtain analogous measurements. These measurements revealed that the layers remained one grain thick and their average aspect ratio increased to at least 80, meaning the bimetal interface density increased and the grain boundary density decreased markedly. More importantly, they showed that refinement to nanoscale dimensions strengthened the predominance of this preferred interface. Evidently, this special interface character is stable with 2 of 5 | www.pnas.org/cgi/doi/10.1073/pnas.1319436111
respect to straining. It was remarkable to note that extreme strains invoke a natural selection process for particular interfaces. To assess the atomic structure of this interface, we use HRTEM to observe the interfaces in several nanomaterial samples (different h < 100 nm). Fig. 1 shows HR-TEM micrographs of the preferred interface; two configurations are shown, which are slightly misoriented by ∼7°. The unexpected result is that they are regularly ordered at the atomic level. Typically after severe plastic deformation of metals, a fraction of the grain boundaries are disordered (18–22). The atomic regularity in Fig. 1 is reminiscent of pristine, low-energy bimetal interfaces formed after near-equilibrium, thermodynamic processes (13, 14), not of mechanical processing. Additionally, we noticed that they contain a regular array of atomic-scale facets (i.e., the zig-zag morphology). To better understand their origin we developed an atomic-scale (MD) model of this Cu–Nb interface (Fig. S2). The relaxed undeformed equilibrium structure calculated in MD is identical to the HR-TEM observations (34). The two types of facets shown in Fig. 1, {111} Cu//{101}Nb and {001}Cu//{011}Nb, are a consequence of the faceted topology of the {338}Cu and {112}Nb crystallographic planes being joined. They are determined by the global orientation relationship and small angular deviations in the interface– orientation relationship cause a change in the relative length of these facets. Therefore, the faceted interfaces are not a result of residual defects left from numerous interactions with dislocations during severe plastic deformation, but are an intrinsic part of the interface. In other words, these interfaces are not defective 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 atomic order. This counterintuitive result raises fundamental questions of microstructural evolution in plastically deformed metals. Does this preferred interface correspond to a stable state and what variables determined it? Are there others like it? The answers cannot be found by current idealizations of interfaces as obstacles to slip (1, 35, 36) or crystals deforming as part of a polycrystalline network (28). In the following, we explore the special stability conditions that would apply to the dynamic creation of interfaces 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 investigate the formation energy γ of other interfaces. Interfaces are designated by the lattice orientation of the two crystals on either side of the interface with respect to a global frame, orientation relationship of this pair, and the interface planes they join, all of which can be varied independently. Collectively, they describe the interface character. Here we elect to vary character by tilting one crystal relative to another, while covering an orientation space that includes the preferred interface. Fig. 2 shows the energetic landscape versus interface character. In the case shown, the Nb orientation was fixed to {112}, and the Cu orientation was varied. Other similar calculations were performed for different Cu–Nb crystallographic combinations (37). Taken together, the calculations reveal that deep wells in the γ profile correspond to observed preferred interfaces. This can be seen in Fig. 2. Within a narrow orientation range (∼7°), we observe two minimum energy cusps, and these correspond to the two variants of the preferred interface seen in Fig. 1 A and B. Using our atomistic simulations coupled with theoretical methods described in ref. 38, we determined the distribution and characteristics of the interfacial dislocations for each interface in Fig. 2. We find that an interface at the cusp location is associated with the tilt angle that minimizes the value of the Burgers vector of the interfacial dislocations because it best aligns the natural facets of the Cu and Nb planes being joined (37). This is a powerful notion that implies that the preferred interfaces emerging in the Beyerlein et al.
Cu–Nb nanocomposites may arise in other bimetal interface material systems. Thus far, our calculations reveal that low formation energy γ is a strong criterion for interface stability. This can be understood on the basis that as strain increases, interface spacing h decreases, and the interface density in the nanomaterial increases; the influence of interface-formation energy naturally grows with increasing strain. However, previous atomic-scale simulations show that there are a few other interface characters (e.g., Kurdjumov– Sachs, Nishiyama–Wasserman γ KS = 576–586 mJ/m2) that possess even lower formation energies than that associated with the preferred interface reported here (39). Thus, another equally important variable determining mechanical interface stability must 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. In order for the new interfaces to have the same crystallographic character as the original ones, the original interface must be plastically stable. This means that both the Cu and Nb crystal layers can plastically deform during rolling without reorienting. Previous modeling and experimental studies indicate that slip dynamics within an individual crystal largely dictate its stability against reorientation (27, 28, 35). However, in the presence of interfaces that join one crystal layer to another of dissimilar material, the slip dynamics and resistance to reorientation in the
two layers are expected to change. However, how this occurs is unknown. The stability of joined dissimilar crystals in such a highly constrained system has not been modeled before and is challenging 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-crystal layers and use the crystal plasticity finite element technique to calculate its dynamic response in deformation (see Supporting Information for more details). The model geometry is designed to authentically represent the actual material for h below the transition point (h < 500 nm). The heart of the model consists of a Cu and Nb crystal joined at a common interface, a bicrystal, with a prescribed crystallographic character (Fig. S3). Applying periodic boundary conditions in three dimensions creates a repeating multilayer architecture with a single interface character. Next, we calculate the lattice rotation of each crystal on either side of the interface under plane strain compression, an idealization of rolling, where the elongation direction coincides with the rolling direction. We use this information to assess stability. To be specific, when straining causes either crystal to rotate, the interface character is altered and hence plastically unstable. As a means of comparing the stabilities of different interfaces, a figure of merit for plastic stability of an interface, ω, is calculated from each simulation, which is given by:
Fig. 2. Preferred interfaces correspond to deep wells in interface formation energy. Molecular dynamics calculation of the variation in interface formation energy with tilt angle about Cujj Nb, the direction normal to the micrographs in Fig. 1 (32).
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Fig. 1. Ordered interfaces after extreme strains. High-resolution transmission electron microscopy micrographs of preferred Cu–Nb interfaces: (A) {338} Cujj{112} Nb and (B) {112} Cujj{112} Nb. The crystallography of the facet planes is indicated.
ΔΩfcc ΔΩbcc exp − ; ω = exp − Δ« Δ« where ΔΩfcc and ΔΩbcc are the rotation angles (radians) of the lattice of the Cu and Nb crystals from their respective starting orientations due to an imposed strain Δ«. In this measure, the limit ω → 0 corresponds to an unstable interface, and the limit ω → 1 to a stable one. For instance, permitting at most small lattice reorientations in each crystal over a large amount of strain, i.e., both ΔΩfcc =Δ« ≤ 0:1 and ΔΩbcc =Δ« ≤ 0:1, corresponds to ω ≥ 0.8. Consistent with experiment, in the model, the two crystals joined at an interface are forced to codeform; that is, the interface does not slide or debond during straining. One advantage of the present modeling technique is that it can capture changes in the development of elastic (anisotropic) strains and crystallographic slip accompanying the added constraint of codeformation. To further clarify the effects of codeformation, we carry out a detailed comparison between the plastic stability of the bicrystal with two unbounded individual crystals under the same straining conditions (Supporting Information). The initial orientations of the single crystals are the same as the initial orientations of the crystals on either side of the interface. Like in the calculations of interface energy γ, bicrystal plasticity simulations are performed for a large number of candidate interface characters, chosen based on theoretical grounds or experimental observation. Our results show that the plastic stability of interfaces found in codeforming crystals is not a straightforward superposition of the plastic stabilities of the crystals they join. In fact, most interface characters are not plastically stable (Fig. S4). We find that the reason is that the less stable of the two determines the plastic stability of the interface; the “weaker link” dictates the plastic stability of the pair. This explains why many stable orientations common to single-phase metals are not the same orientations associated 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 codeformation and preserving interface orientation. Prior atomic-scale modeling indicates that glide dislocations on slip systems with the highest resolved shear stress can be supplied from faceted interfaces, such as that in Fig. 1 (40, 41). Thus far, our simulations have demonstrated that low formation energy and plastic stability are strong criteria for interface stability. To map out how interfaces compare with respect to both criteria, we plot them in Fig. 3 with respect to their ω and γ on two axes. We find that many interfaces are plastically stable (ω > 0.8), fewer possess relatively low formation energy (γ < 950 mJ/m2), and even fewer correspond to energetic minima (γ ∼ 600–700 mJ/m2). To understand the relative importance of these criteria, we use a black triangle to mark the preferred interface and its closely neighboring variants. The significant outcome is
Fig. 3. Revealing where emergent interfaces lie: a bimetal interface character stability map. (Top Left) The regime of mechanically stable interfaces. Squares and circles are simulated Cu–Nb interfaces under rolling strains. Triangles indicate those cases corresponding to the observed preferred interfaces. The different variants of preferred interfaces are associated with different orientations of Nb or Cu close in orientation space. Table S1 lists the data corresponding to the points here.
that they all lie exclusively in the region corresponding to both low formation energy and high plastic stability. Interfaces lying farther away from this region are less likely to “survive” extreme straining. From the experimental and simulation results, we conclude that extreme strains naturally select interfaces that are low in formation energy and plastically stable in codeformation, a severe constraint that only a few interfaces satisfy in rolling. This finding also strongly implies that a ubiquitous preferred bimetal interface is an inevitable outcome of extreme straining provided that there are deep wells in interface energy. Broadly speaking, the stability conditions established here are sufficiently fundamental that they can apply to other strain paths and other material systems, such that other emergent interfaces can be forecasted. As a further test of stability, these nanomaterials were exposed to extreme conditions. We confirmed experimentally that the interface preserves its regular atomic structure under further straining down to h = 20 nm (Fig. 4A). Experiments have demonstrated that the interface structure and parent nanostructure of 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. 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-ion irradiation, showing no voids in the layer or in the interfaces in an h = 20 nm composite (39).
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ACKNOWLEDGMENTS. The authors gratefully acknowledge support by the Center for Materials at Irradiation and Mechanical Extremes, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award 2008LANL1026.
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apart during straining. The calculations indicate that the preferred interface is one of few (among the vast space of possible interfaces) that under extreme straining can remain plastically stable while forming interfaces corresponding to a minimum in formation energy. Most significantly, it points to other interfaces that could also emerge in extreme straining and exhibit similar stability properties. Our findings demonstrate that extreme strains can be used as an innovative way toward manipulating interfaces at will for target material properties.
(32) (Fig. 4B). We also report that these interfaces do not develop damaging voids under He-ion irradiation unlike ordinary grain boundaries in Cu (42) (Fig. 4C). The forecasted lifetimes of these bulk nanomaterials, dense with naturally selected interfaces would, therefore, significantly exceed those of their constituents. In summary, we demonstrate that a preferred bimetal interface possessing regular atomic order emerges from extreme mechanical straining of layered nanocomposites. Further, experimental evidence shows that this interface is stable with respect to continued extreme straining, high temperatures, and irradiation. These results are surprising and question current understanding of microstructural evolution during metal working. Using atomicscale and crystal-plasticity simulation, we reveal that the strong preference is a result of the formation of interfaces nanometers
Atomically ordered bimetal interfaces typically develop in nearequilibrium epitaxial growth (bottom-up processing) of nanolayered composite films and have been considered responsible for a number of intriguing material properties. Here, we discover that interfaces of such atomic level order can also emerge ubiquitously in large-scale layered nanocomposites fabricated by extreme strain (top down) processing. This is a counterintuitive result, which we propose occurs because extreme plastic straining creates new interfaces separated by single crystal layers of nanometer thickness. On this basis, with atomic-scale modeling and crystal plasticity theory, we prove that the preferred bimetal interface arising from extreme strains corresponds to a unique stable state, which can be predicted by two controlling stability conditions. As another testament to its stability, we provide experimental evidence showing 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 in the fabrication of stable nanomaterials with severe plastic deformation techniques. texture
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nlike traditional materials, nanomaterials contain an unusually high density of interfaces that give rise to unprecedented properties such as ultrahigh strengths (1–5). Further, nanomaterials with nearly perfect, atomically ordered low-energy interfaces have been found to possess extraordinary thermal stability and radiation tolerance (1, 6–10). However, nanomaterials with disordered, high-energy interfaces are not stable in these same extreme conditions (11, 12). The integrity of the interface is tied to how the nanomaterial was made. Near-equilibrium processes generate perfect interfaces prevailing across the material but only produce small amounts of material, such as epitaxial thin films (13, 14). Ordinary large-scale metal-working (far from equilibrium) processes produce large amounts of nanostructured material suitable for technical application, but the interface types can vary within the same sample. For single-phase metals, the heavy straining can drive dislocations generated during deformation to organize into low-energy boundary structures (15, 16), some of which can be ordered (17) and others disordered (12, 18–20). Likewise, in heavily drawn two-phase composites, several kinds of bimetal interface structures have been reported, both ordered and disordered (21). Achieving uniformly ordered interfaces in bulk nanostructured metals presents a grand challenge in the design of materials that can be stable in the harsh environments demanded by 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 a preferred bimetal interface with perfect atomic order. Most remarkably, experimental evidence shows that this preferred interface occurs ubiquitously throughout the volume (>cm3) of the nanocomposite. This interface is shown to be stable with respect to further straining, high-temperature exposure, and irradiation, giving the nanomaterial extraordinary tolerances in other extreme situations. This finding has the exciting potential of eliminating the aforementioned tradeoff and permitting the creation of materials www.pnas.org/cgi/doi/10.1073/pnas.1319436111
with pristine interfaces in stable nanocomposites of unlimited quantities. However, although such bulk deformation techniques may offer flexibility in processing path, current approaches for linking strain path to the resulting metallic microstructures have been empirical. To fundamentally rationalize this seemingly counterintuitive result, we use theory, atomic-scale modeling, and experimental characterization to identify the stability conditions that govern the emergence of a preferred interface at extreme strains. We reveal that the observed interface indeed corresponds to a special stable state. On a grander scale, this insight can be used to create other stable interfaces and open a new frontier of deformation processing for extreme-tolerant materials. To impose extreme strains, we fabricated Cu–Nb nanolayered materials in bulk form (>cm3) with a severe plastic deformation processing (SPD) technique called accumulative roll bonding (ARB; refs. 22–24). We begin with an alternating stack of sheets of these two dissimilar, immiscible metals, and then carry out the ARB process. Unlike conventional rolling, ARB strains the sample via a cycle of rolling, cutting, and restacking, and maintains the original sample dimensions. To prevent oxide contamination at the interfaces during the entire ARB process, we use a specially designed method (SI Text and Fig. S1). The individual layer thickness h can be easily refined and controlled with increasing strain (Fig. S1). Previously SPD techniques, like ARB, have been used to make fine-layered material (h = 10–102 μm) using large strains but a significant fraction of the interfaces was reported to be disordered 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 transformation, epitaxial growth, or solidification, can make nanocomposite materials with preferred crystallographic orientation relationships at internal interfaces. On the other hand, metalworking techniques can make composites in bulk quantities for structural applications but typically the resulting bimetal interfaces lack crystallographic order and are unstable with respect to heating. Using a metal-working roll-bonding technique, we find that at extreme plastic strains, the bimetal interfaces develop a remarkably ordered, preferred atomic structure. Using atomic-scale and crystal-plasticity simulations, we study the dynamical stability conditions responsible for this counterintuitive phenomenon. We show that the emergent interface corresponds to a unique stable state, which leads to exceptional mechanical, thermal, and irradiation stability of the 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. 1
To whom correspondence should be addressed. E-mail: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1319436111/-/DCSupplemental.
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Edited* by William D. Nix, Stanford University, Stanford, CA, and approved February 13, 2014 (received for review October 15, 2013)
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 measure the distribution of crystallographic orientations (texture) of all grains in the entire ARB sheet. To investigate size effects, these measurements were repeated for samples with different internal layer dimension h, ranging from h = 100 μm to 20 nm. The results revealed 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 to the range of orientations that usually stabilize in Cu or Nb when rolled 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 coincident with attainment of layers that are spanned by only one grain. The grains are exceedingly wide, with an average aspect ratio of 30, about 5–10 times that expected in conventional rolling. This length scale is also below that (∼1 μm) at which dislocation density and substructure development within the layers between interfaces gradually decrease (23, 24) until, at fine layers (200 nm and below), they were no longer observed (refs. 30, 32; see Fig. 4A). This means that at the transition point, individual grains have become bounded by interfaces and not ordinary grain boundaries. These measurements suggest that the unexpectedly, highly oriented microstructure is influenced by the close proximity of the bimetal interfaces. To determine whether preferred orientations correlate with preferred interfaces; that is, whether certain Cu and Nb orientations prefer to be joined, we carried out a correlation analysis of the paired Cu and Nb orientations on either side of the interfaces. For statistical significance, we obtained the data from numerous Cu–Nb pairs from several EBSD maps of samples with h below but near the transition point (29). The extraordinary outcome was that the Cu and Nb orientations were highly correlated. Most of the Cu and Nb grains have assembled such that they are bonded at their mutual {112} planes and the direction of Cu is aligned with the direction of Nb. This means that the Cu orientation on one side of the interface is {112} and the Nb orientation on the other side is {112} . These measurements find that the distribution about these preferred orientations is narrow, such that each crystal varies within 0.1–0.2% of the entire orientation space. Such a highly oriented state is peculiar because many orientations in Cu and Nb are expected to be stable in rolling (25–28) and hence the number of possible Cu–Nb orientation combinations among them is expected to be large. In contradiction, we find that a singular interface character, as defined by this pairing of a particular Cu and Nb orientation, is strongly preferred. To see whether this preferred interface character is stable with respect to straining, we repeated characterization for samples varying in individual layer thickness from h = 200 nm to h = 20 nm. These samples experienced correspondingly strains of 9–12, above and beyond that of conventional rolling. Because these fine nanoscale dimensions of h reached the limits of EBSD, we used other techniques, such as wedge-mounting EBSD (30) and precession electron diffraction (PED) (31), as well as transmission electron microscopy (TEM) and high-resolution (HR)-TEM (32, 33), to obtain analogous measurements. These measurements revealed that the layers remained one grain thick and their average aspect ratio increased to at least 80, meaning the bimetal interface density increased and the grain boundary density decreased markedly. More importantly, they showed that refinement to nanoscale dimensions strengthened the predominance of this preferred interface. Evidently, this special interface character is stable with 2 of 5 | www.pnas.org/cgi/doi/10.1073/pnas.1319436111
respect to straining. It was remarkable to note that extreme strains invoke a natural selection process for particular interfaces. To assess the atomic structure of this interface, we use HRTEM to observe the interfaces in several nanomaterial samples (different h < 100 nm). Fig. 1 shows HR-TEM micrographs of the preferred interface; two configurations are shown, which are slightly misoriented by ∼7°. The unexpected result is that they are regularly ordered at the atomic level. Typically after severe plastic deformation of metals, a fraction of the grain boundaries are disordered (18–22). The atomic regularity in Fig. 1 is reminiscent of pristine, low-energy bimetal interfaces formed after near-equilibrium, thermodynamic processes (13, 14), not of mechanical processing. Additionally, we noticed that they contain a regular array of atomic-scale facets (i.e., the zig-zag morphology). To better understand their origin we developed an atomic-scale (MD) model of this Cu–Nb interface (Fig. S2). The relaxed undeformed equilibrium structure calculated in MD is identical to the HR-TEM observations (34). The two types of facets shown in Fig. 1, {111} Cu//{101}Nb and {001}Cu//{011}Nb, are a consequence of the faceted topology of the {338}Cu and {112}Nb crystallographic planes being joined. They are determined by the global orientation relationship and small angular deviations in the interface– orientation relationship cause a change in the relative length of these facets. Therefore, the faceted interfaces are not a result of residual defects left from numerous interactions with dislocations during severe plastic deformation, but are an intrinsic part of the interface. In other words, these interfaces are not defective 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 atomic order. This counterintuitive result raises fundamental questions of microstructural evolution in plastically deformed metals. Does this preferred interface correspond to a stable state and what variables determined it? Are there others like it? The answers cannot be found by current idealizations of interfaces as obstacles to slip (1, 35, 36) or crystals deforming as part of a polycrystalline network (28). In the following, we explore the special stability conditions that would apply to the dynamic creation of interfaces 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 investigate the formation energy γ of other interfaces. Interfaces are designated by the lattice orientation of the two crystals on either side of the interface with respect to a global frame, orientation relationship of this pair, and the interface planes they join, all of which can be varied independently. Collectively, they describe the interface character. Here we elect to vary character by tilting one crystal relative to another, while covering an orientation space that includes the preferred interface. Fig. 2 shows the energetic landscape versus interface character. In the case shown, the Nb orientation was fixed to {112}, and the Cu orientation was varied. Other similar calculations were performed for different Cu–Nb crystallographic combinations (37). Taken together, the calculations reveal that deep wells in the γ profile correspond to observed preferred interfaces. This can be seen in Fig. 2. Within a narrow orientation range (∼7°), we observe two minimum energy cusps, and these correspond to the two variants of the preferred interface seen in Fig. 1 A and B. Using our atomistic simulations coupled with theoretical methods described in ref. 38, we determined the distribution and characteristics of the interfacial dislocations for each interface in Fig. 2. We find that an interface at the cusp location is associated with the tilt angle that minimizes the value of the Burgers vector of the interfacial dislocations because it best aligns the natural facets of the Cu and Nb planes being joined (37). This is a powerful notion that implies that the preferred interfaces emerging in the Beyerlein et al.
Cu–Nb nanocomposites may arise in other bimetal interface material systems. Thus far, our calculations reveal that low formation energy γ is a strong criterion for interface stability. This can be understood on the basis that as strain increases, interface spacing h decreases, and the interface density in the nanomaterial increases; the influence of interface-formation energy naturally grows with increasing strain. However, previous atomic-scale simulations show that there are a few other interface characters (e.g., Kurdjumov– Sachs, Nishiyama–Wasserman γ KS = 576–586 mJ/m2) that possess even lower formation energies than that associated with the preferred interface reported here (39). Thus, another equally important variable determining mechanical interface stability must 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. In order for the new interfaces to have the same crystallographic character as the original ones, the original interface must be plastically stable. This means that both the Cu and Nb crystal layers can plastically deform during rolling without reorienting. Previous modeling and experimental studies indicate that slip dynamics within an individual crystal largely dictate its stability against reorientation (27, 28, 35). However, in the presence of interfaces that join one crystal layer to another of dissimilar material, the slip dynamics and resistance to reorientation in the
two layers are expected to change. However, how this occurs is unknown. The stability of joined dissimilar crystals in such a highly constrained system has not been modeled before and is challenging 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-crystal layers and use the crystal plasticity finite element technique to calculate its dynamic response in deformation (see Supporting Information for more details). The model geometry is designed to authentically represent the actual material for h below the transition point (h < 500 nm). The heart of the model consists of a Cu and Nb crystal joined at a common interface, a bicrystal, with a prescribed crystallographic character (Fig. S3). Applying periodic boundary conditions in three dimensions creates a repeating multilayer architecture with a single interface character. Next, we calculate the lattice rotation of each crystal on either side of the interface under plane strain compression, an idealization of rolling, where the elongation direction coincides with the rolling direction. We use this information to assess stability. To be specific, when straining causes either crystal to rotate, the interface character is altered and hence plastically unstable. As a means of comparing the stabilities of different interfaces, a figure of merit for plastic stability of an interface, ω, is calculated from each simulation, which is given by:
Fig. 2. Preferred interfaces correspond to deep wells in interface formation energy. Molecular dynamics calculation of the variation in interface formation energy with tilt angle about Cujj Nb, the direction normal to the micrographs in Fig. 1 (32).
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Fig. 1. Ordered interfaces after extreme strains. High-resolution transmission electron microscopy micrographs of preferred Cu–Nb interfaces: (A) {338} Cujj{112} Nb and (B) {112} Cujj{112} Nb. The crystallography of the facet planes is indicated.
ΔΩfcc ΔΩbcc exp − ; ω = exp − Δ« Δ« where ΔΩfcc and ΔΩbcc are the rotation angles (radians) of the lattice of the Cu and Nb crystals from their respective starting orientations due to an imposed strain Δ«. In this measure, the limit ω → 0 corresponds to an unstable interface, and the limit ω → 1 to a stable one. For instance, permitting at most small lattice reorientations in each crystal over a large amount of strain, i.e., both ΔΩfcc =Δ« ≤ 0:1 and ΔΩbcc =Δ« ≤ 0:1, corresponds to ω ≥ 0.8. Consistent with experiment, in the model, the two crystals joined at an interface are forced to codeform; that is, the interface does not slide or debond during straining. One advantage of the present modeling technique is that it can capture changes in the development of elastic (anisotropic) strains and crystallographic slip accompanying the added constraint of codeformation. To further clarify the effects of codeformation, we carry out a detailed comparison between the plastic stability of the bicrystal with two unbounded individual crystals under the same straining conditions (Supporting Information). The initial orientations of the single crystals are the same as the initial orientations of the crystals on either side of the interface. Like in the calculations of interface energy γ, bicrystal plasticity simulations are performed for a large number of candidate interface characters, chosen based on theoretical grounds or experimental observation. Our results show that the plastic stability of interfaces found in codeforming crystals is not a straightforward superposition of the plastic stabilities of the crystals they join. In fact, most interface characters are not plastically stable (Fig. S4). We find that the reason is that the less stable of the two determines the plastic stability of the interface; the “weaker link” dictates the plastic stability of the pair. This explains why many stable orientations common to single-phase metals are not the same orientations associated 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 codeformation and preserving interface orientation. Prior atomic-scale modeling indicates that glide dislocations on slip systems with the highest resolved shear stress can be supplied from faceted interfaces, such as that in Fig. 1 (40, 41). Thus far, our simulations have demonstrated that low formation energy and plastic stability are strong criteria for interface stability. To map out how interfaces compare with respect to both criteria, we plot them in Fig. 3 with respect to their ω and γ on two axes. We find that many interfaces are plastically stable (ω > 0.8), fewer possess relatively low formation energy (γ < 950 mJ/m2), and even fewer correspond to energetic minima (γ ∼ 600–700 mJ/m2). To understand the relative importance of these criteria, we use a black triangle to mark the preferred interface and its closely neighboring variants. The significant outcome is
Fig. 3. Revealing where emergent interfaces lie: a bimetal interface character stability map. (Top Left) The regime of mechanically stable interfaces. Squares and circles are simulated Cu–Nb interfaces under rolling strains. Triangles indicate those cases corresponding to the observed preferred interfaces. The different variants of preferred interfaces are associated with different orientations of Nb or Cu close in orientation space. Table S1 lists the data corresponding to the points here.
that they all lie exclusively in the region corresponding to both low formation energy and high plastic stability. Interfaces lying farther away from this region are less likely to “survive” extreme straining. From the experimental and simulation results, we conclude that extreme strains naturally select interfaces that are low in formation energy and plastically stable in codeformation, a severe constraint that only a few interfaces satisfy in rolling. This finding also strongly implies that a ubiquitous preferred bimetal interface is an inevitable outcome of extreme straining provided that there are deep wells in interface energy. Broadly speaking, the stability conditions established here are sufficiently fundamental that they can apply to other strain paths and other material systems, such that other emergent interfaces can be forecasted. As a further test of stability, these nanomaterials were exposed to extreme conditions. We confirmed experimentally that the interface preserves its regular atomic structure under further straining down to h = 20 nm (Fig. 4A). Experiments have demonstrated that the interface structure and parent nanostructure of 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. 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-ion irradiation, showing no voids in the layer or in the interfaces in an h = 20 nm composite (39).
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ACKNOWLEDGMENTS. The authors gratefully acknowledge support by the Center for Materials at Irradiation and Mechanical Extremes, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award 2008LANL1026.
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apart during straining. The calculations indicate that the preferred interface is one of few (among the vast space of possible interfaces) that under extreme straining can remain plastically stable while forming interfaces corresponding to a minimum in formation energy. Most significantly, it points to other interfaces that could also emerge in extreme straining and exhibit similar stability properties. Our findings demonstrate that extreme strains can be used as an innovative way toward manipulating interfaces at will for target material properties.
(32) (Fig. 4B). We also report that these interfaces do not develop damaging voids under He-ion irradiation unlike ordinary grain boundaries in Cu (42) (Fig. 4C). The forecasted lifetimes of these bulk nanomaterials, dense with naturally selected interfaces would, therefore, significantly exceed those of their constituents. In summary, we demonstrate that a preferred bimetal interface possessing regular atomic order emerges from extreme mechanical straining of layered nanocomposites. Further, experimental evidence shows that this interface is stable with respect to continued extreme straining, high temperatures, and irradiation. These results are surprising and question current understanding of microstructural evolution during metal working. Using atomicscale and crystal-plasticity simulation, we reveal that the strong preference is a result of the formation of interfaces nanometers
