Influence of slip and twinning on the crystallographic stability of bimetal interfaces in nanocomposites under deformation

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Influence of slip and twinning on the crystallographic stability of bimetal interfaces in nanocomposites under deformation I.J. Beyerlein a,⇑, J.R. Mayeur a, R.J. McCabe c, S.J. Zheng b, J.S. Carpenter c, N.A. Mara b a Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Materials Physics and Application Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA c Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

b

Received 27 February 2014; received in revised form 13 March 2014; accepted 17 March 2014 Available online 19 April 2014

Abstract In this work, we examine the microstructural development of a bimetal multilayered composite over a broad range of individual layer thicknesses h from microns to nanometers during deformation. We observe two microstructural transitions, one at the submicron scale and another at the nanoscale. Remarkably, each transition is associated with the development of a preferred interface character. We show that the characteristics of these prevailing interfaces are strongly influenced by whether the adjoining crystals are deforming by slip only or by slip and twinning. We present a generalized theory that suggests that, in spite of their different origins, the crystallographic stability of their interface character with respect to deformation depends on the same few basic variables. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Twinning; Nanocomposites; Interfaces; Severe plastic deformation; Crystal plasticity

1. Introduction 1.1. Processing–microstructure relationships It is widely recognized that internal grain boundaries (homophase interfaces) and heterophase interfaces greatly affect the properties of polycrystalline metals [1–7]. Through the control and optimization of these internal interfaces, potentially superior metals with unprecedented strengths and robustness can be developed [4,5,8,9]. For instance, it has been shown that changes in interface properties within nanostructured metals can be made via different processing methods [10–16]. Thermodynamic, near-equilibrium processes, such as solid-state phase transformation, epitaxial growth or solidification processing, can produce highly textured nanostructured single-phase ⇑ Corresponding author.

E-mail address: [email protected] (I.J. Beyerlein).

and composite metals with interfaces that are structurally ordered at the atomic scale [17–21]. They adopt interfaces with nearly the same crystallographic character (narrowly distributed within 15°) throughout the material. By virtue of this near-structural perfection, these materials have shown outstanding thermal stability [22], radiation tolerance [23,24] and strength [25,26]. Far-from-equilibrium mechanical processing, such as severe plastic deformation (SPD) techniques [14,15,27–30], can also produce ultrafine-grained and nanostructural metals comprised of a high density of interfaces. In single-phase SPD metals, while a small fraction of ordered boundaries has been reported [31], most of the grain boundaries are structurally disordered, and are often referred to as “non-equilibrium” boundaries [14,32,33]. Likewise, in bimetal wires fabricated by wire-drawing and bundling, several types of interfaces, both ordered and disordered, can form [29,34,35]. Although imperfect in structure, these SPD nanostructures possess superior strength, and in some cases, ductility

http://dx.doi.org/10.1016/j.actamat.2014.03.041 1359-6454/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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[15,36,37]. However, the disorder renders them microstructurally unstable with respect to heating [38–41]. 1.2. Observation of crystallographically stable interfaces

the Cu–Nb composite is refined via ARB to nanoscale dimensions (<60 nm), the Cu phase is found to deform via slip and twinning. Because of this change in deformation mechanism, the {1 1 2}h1 1 1iCu||{1 1 2}h1 1 0iNb interface becomes unstable. Here, with microstructural characterization and crystal plasticity analyses, we reveal that another stable, predominant interface emerges after twinning, distinct from the one that develops when the crystals deform purely by slip, which remarkably also exhibits a regular atomic structure. We analyze its origin and relationship to deformation twinning. The results enable us to advance the set of stability criteria not only to explain the development of both stable interfaces but also to provide insight into creating other crystallographically stable interfaces via deformation processing.

Recently, it was reported that a well-known SPD process, called accumulative roll bonding (ARB) [28,42– 45], induced the formation of an ordered bimetal Cu–Nb interface that prevailed ubiquitously over the bulk twophase Cu–Nb layered composite. After extreme strains and substantial layer refinement (99.96–99.99% rolling reduction and individual layer thicknesses of h = 200– 700 nm), a predominant bimetal interface emerged with a crystallographic character that was narrowly distributed about {1 1 2}h1 1 1iCu||{1 1 2}h1 1 0i Nb [44] and with a highly ordered atomic structure with little to no detectable defects [44,46,47]. In light of prior reports of interface structures after SPD, the emergence of a highly oriented and atomically ordered predominant interface from ARB is unexpected. The present knowledge base for microstructural evolution in SPD is insufficient for explaining SPDinduced ordering of interface structure. Recently, two variables were proposed to influence the crystallographic stability of this interface [48]. The first variable is plastic stability in co-deformation, which refers to the preservation of interface character during plastic deformation. Crystal plasticity finite-element (CPFE) simulations of a Cu–Nb bicrystal with the {1 1 2}h1 1 1iCu|| {1 1 2}h1 1 0iNb interface under plane strain compression found that its character misoriented only a few degrees to a stable end state [49,50]. Repeating the analysis for other bicrystals in single-crystalline or polycrystalline layers suggested that when an interface is composed of two stable rolling orientations, its character tends to be preserved in rolling [49,50]. This result forecasts that many interface characters could be plastically stable in co-deformation, not only the {1 1 2}h1 1 1iCu||{1 1 2}h1 1 0iNb interface. The second variable is interface formation energy, which can be calculated using molecular dynamics (MD) simulation [47,51]. As layers refine in the ARB process and the interface density increases, a lower formation energy interface would result in lower stored energy in the material. However, while the {1 1 2}h1 1 1iCu||{1 1 2}h1 1 0iNb interface does not have the highest formation energy (825 mJ m2 < 1000 mJ m2), it also does not correspond to the lowest one (Kurdjumov–Sachs or Nishiyama–Wasserman 576–586 mJ m2). The conclusion was that both variables mattered and attaining an optimal combination of both presents a severe constraint that far fewer interfaces satisfy.

ARB processing of the Cu–Nb layered composite begins with an alternating stack of 2 mm sheets of coarse-grained polycrystalline Cu and Nb in equal fractions [45,52]. Prior to ARB processing, the as-received Cu (99.99% purity) sheets were rolled to 60% reduction to 2 mm and subsequently annealed at 450 °C for 1 h. The as-received Nb sheets (99.94% purity) were rolled to 30% reduction to 2 mm and annealed afterwards at 950 °C for 1 h. To prevent exposure of the Cu–Nb interfaces to air during ARB processing, the stack was clad on the top and bottom by two half-thick layers of Cu (1 mm). Through repeated rolling, cutting and restacking, the process imposes radically extreme strains, achieving three to six orders of magnitude refinement in the individual layer thickness, h, from 2 mm to 10 nm [45,52]. As the layers are refined, they remain continuous and the bimetal interfaces remain chemically sharp due to the immiscibility of these two metals [46,53]. For h from 45 lm to 200 nm, scanning electron microscopy (SEM) was used to gather statistical data on layer thickness [52]. For h from 135 to 10 nm, transmission electron microscopy (TEM) was used for this purpose [52]. The analyses showed that the average thickness of the Cu and Nb layers at each strain level corresponded well to the nominal value calculated from the applied rolling reduction. This indicates that as h is refined from 45 lm to 10 nm, the two metals plastically co-deformed [54]. The above is a brief account of the materials and processing used and more information can be found in prior works [45,55].

1.3. Objectives: role of deformation twinning

2.2. Theoretical textures of monolithic Cu and monolithic Nb

These ideas were developed assuming that both metals deform by slip only. In this work, we investigate the evolution of interfaces when the face centered cubic (fcc) Cu phase undergoes twinning in addition to slip. When h in

The ARB process imposes the same deformation state as conventional rolling. It is, therefore, worthwhile to compare the textures of the individual phases within the composite with textures that develop when each phase is

2. Observations of evolution in texture and interface character 2.1. ARB processing

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rolled monolithically. The classic rolling textures of fcc and body centered cubic (bcc) metals contain many stable texture components [56,57]. Under extremely large rolling strains, a subset of these components, h1, h2, . . . , hm, increases in volume fraction at the expense of others [56– 60]. Table 1 lists the stable texture components particular to fcc and bcc metals that deform by slip only (RS) under very large strains, denoted by gfcc(h, RS) for fcc Cu and gbcc(h, RS) for bcc Nb. For materials that accommodate rolling strains by slip and twinning, the peak texture components are different. In Table 1, we designate the special set of stable orientations generated in Cu in rolling mediated by slip and twinning (RST) by gfcc(h, RST) [61–63]. 2.3. Interface-induced texture transitions Neutron diffraction was used to measure the texture of each phase in the ARB composite for different layer thicknesses from h  45 lm to 10 nm. As h decreases over this wide span of length scales, we observe two clear transitions in texture evolution. The first is correlated with a reduction in the number of grains spanning the layer thickness to just one or two (h  1 lm to 500 nm) and the second is associated with the onset of deformation twinning in the Cu phase (h  60 nm). These texture transitions and their correlation with interface evolution are discussed below. 2.3.1. Texture in micron-sized composites When h ranges from 45 to 1 lm (via 99.90% rolling reduction), it was observed that the deformation texture closely resembles the rolling texture expected of its constituents, Cu and Nb [42,43,55]. For these length scales, many grains span the thickness of the individual layers and the crystallographic orientation distributions (textures) of the Cu and Nb phases in the composite correspond to those expected of severely rolled monolithic Cu and Nb. They comprised the stable texture components gfcc(h, RS) for fcc Cu and gbcc(h, RS) for bcc Nb (Table 1) known to develop in rolling mediated by slip only (RS). Similar results have been reported for other severely deformed composites with micron-size microstructural dimensions [64]. Texture evolution in such “coarse” composites have been adequately modeled using mean-field polycrystalline plasticity modeling [42,64,65] and spatially resolved twophase CPFE modeling [55,66]. 2.3.2. Emergence of stable interfaces in slip-only-fcc/bcc composites An unexpected change in texture development occurs when the material is further refined to layer thicknesses h below 1 lm to 500 nm. The textures no longer resemble those of gfcc(h, RS) for Cu and gbcc(h, RS) for Nb, as shown for example in Fig. 1, which is a bulk neutron diffraction measurement of the h = 200 nm composite (Fig. 1). Electron backscattered diffraction (EBSD) was used to link these phase textures with microstructure and interface crystallography. Our microstructural characterization in

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combination of those of prior works collectively find that at this transition point: (1) the individual layers span only one or two crystals [46,67], (2) the substructure dislocation density begins to decrease [42,43] and (3) a preferred Cu– Nb interface develops over the entire material volume [44,67]. Once formed, it remains stable with respect to further rolling reductions up to 10.6 strain (corresponding to h  60 nm) [44,67]. In the regime h > 60 nm, deformation twinning was not prevalent and the Cu and Nb phases deformed primarily via slip. Hence, hereinafter, we refer to this crystallographically stable interface as the slip-fcc/ bcc interface. Using automated analyses of the interface character of EBSD maps [44,67] for h = 600 nm down to 80 nm, it was found that the slip-fcc/bcc interface joins a Cu crystal ranging within an 8° span from the {1 1 2}h1 1 1i orientation (the C component1) to the {4 4 11}h11 11 8i orientation (the D component) with an Nb crystal lying within an even narrower 5° span from the {1 1 2}h1 1 0i to the {2 2 5}h1 1 0i orientations. It is important to note that these few orientations belong to the larger set of gfcc(h, RS) for Cu and gbcc(h, RS) for Nb. Fig. 2 shows a high-resolution transmission electron microscopy (HR-TEM) micrograph of a typical slip-fcc/ bcc interface: the {3 3 8}h4 4 3ifcc||{1 1 2}h1 1 0ibcc interface.2 As shown, it possesses a highly ordered atomic structure with a zigzag morphology. Another interface {1 1 2}h1 1 1ifcc||{1 1 2}h1 1 0ibcc, near in orientation space (7°) to the one in Fig. 2, exhibits similar features [46]. These interfaces and their characteristic faceted structure have also been reported in Ni–Cr cast materials and wiredrawn Cu–Nb filaments [34,35,68]. Several prior atomicscale analyses have shown that the facets seen in Fig. 2 are a consequence of the faceted topology of the {3 3 8}h1 1 0i Cu and {1 1 2}h1 1 1i Nb cut planes that make up the interface [35,51,68,69]. When Cu and Nb are joined and relaxed at these planes, the resulting Cu–Nb interface assumes a regular array of alternating (0 0 1)Cu||(1 1 0)Nb and (1 1 1)Cu||(1 1 0)Nb KS facets (where KS stands for the Kurdjumov–Sachs orientation relationship) [47,51], like the ones seen in Fig. 2. It is remarkable that the slipfcc/bcc interface resembles so closely the MD calculation for an “undeformed” relaxed interface. This implies that this interface has the ability to recover from interactions with dislocations formed during deformation processing and raises questions of dislocation/interface interactions that warrant further study. Another significant aspect is that the slip-fcc/bcc interface occurs ubiquitously across the material. This is not common for grain boundaries and interfaces found in mechanically driven systems, which tend to be dispersed and mostly disordered, with only a small fraction exhibiting order [14,31,34]. Atomic-scale regularity in interface

1 2

The orientations are written in the {ND}hRDi nomenclature. {3 3 8}h4 4 3i lies less than 1° from the D component.

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Table 1 Stable crystal orientations for fcc and bcc crystals. The components are written in the {ND}hRDi nomenclature, wherein {ND} is the crystallographic plane corresponding to the rolling plane and hRDi is the crystallographic direction aligned with the rolling direction. The orientations belonging to each group are obtained from Refs. [56–63]. gfcc(h, RS) gfcc(h, RST) gbcc(h, RS)

Stable orientation group for fcc crystals expected under rolling when mediated by slip Stable orientation group for fcc crystals expected under rolling when mediated by slip and twinning Stable orientation group for bcc crystals expected under rolling mediated by slip

S {1 2 3}h6 3 4i, brass {1 1 0}h1 1 2i, C {1 1 2}h1 1 1i, D {4 4 11}h11 11 8i, orientations between C and D such as K {3 3 8}h4 4 3i Brass {1 1 0}h1 1 2i, Goss {1 1 0}h0 0 1i, Z {5 5 1}h1 1 0i and orientations between Goss and Z {1 1 2}h1 1 0i, {2 2 5}h1 1 0i, {2 2 3}h1 1 0i, {1 1 1}h1 1 2i, and E {1 1 1}h1 1 0i

Fig. 1. Inverse pole figures of the texture of the Cu and Nb phase in the nanocomposite with layer thickness h = 200 nm as measured using neutron diffraction. The measurements show that the axes parallel to the ND range from (a) {1 1 2} to {1 1 0} in the Cu phase and (b) from {1 1 2} to {0 0 1} in the Nb phase. IPFs are shown instead of conventional ODF sections in order to bring out the sharpness of the textures and the crystallographic axes relative to the two-dimensional layered structure RD–TD–ND. Pole figures and ODFs sections can be found in Ref. [45].

MD calculations [35,51] predict that the interface formation energy of the slip-fcc/bcc interface (Fig. 2) is higher, ranging from 672 to 860 mJ m2 (Fig. 3) [35,47]. Evidently, in distinction to deposition, the formation of a ubiquitous slip-fcc/bcc interface under SPD must not be primarily driven by interface formation energy.

Fig. 2. High-resolution TEM micrographs of a typical slip-fcc/bcc interface (500 > h > 60 nm): {3 3 8}h4 4 3iCu||{1 1 2}h1 1 0iNb. The crystallography of the facet faces is also shown and agrees with prior MD simulation [47]. The {1 1 2}h1 1 0iCu||{1 1 2}h1 1 0iNb interface (by 7°), which is close in orientation space to this one and also a slip-fcc/bcc interface, shows similar faceted features [46,47].

structure is, however, common for composites formed by thermodynamic processes [18,19,21], which are driven to form interfaces with low formation energy. The Nishiyama–Wasserman (NW) or KS interfaces are characteristic of deposited films [21,44] and have an interface formation energy of 570–580 mJ m2 for the Cu–Nb system [70,71].

2.3.3. Emergence of stable interfaces in twinnable-fcc/bcc composites With neutron diffraction, a second texture transition is observed when h is refined below 60 nm and deformation twins begin to form in the Cu phase [42,46]. With postmortem microscopy, we obtained some indirect evidence on where twins form and grow. Because of the fine nanoscale dimensions (h 6 60 nm), standard EBSD could not be used and thus we employed a special high-resolution EBSD analysis, called wedge-mounting (WM) EBSD [45,67], to associate grain orientations with their twin. In addition, for an even closer look, particularly at the interface where these twins originate [46], TEM and HR-TEM analyses were carried out (Fig. 4). With these methods, twins were observed to form ubiquitously in the Cu layers. With WM-EBSD, they could be associated with the C and D orientations, predominantly occurring throughout the material. Less frequently occurring orientations, such as the B orientation, did not form twins. Both analyses also

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Fig. 3. Variation in interface formation energy with tilt angle about the h1 1 0ifcc||h1 1 1ibcc as calculated using MD simulation [53].

Fig. 4. TEM micrographs showing the evolution of deformation twinning as h decreases from (a) h = 60 nm, (b) h = 30 nm, to (c) h = 10 nm [46,53]. (d) A high-resolution TEM micrograph of a typical twin emanating from an {1 1 2}h1 1 1iCu||{1 1 2}h1 1 0iNb interface [46]. The twin has formed on an {1 1 1} plane that is tilted from the interface. Depending on the orientation of the crystal, this tilt angle ranged from 19° to 26°.

indicated that the twin volume fraction increases as h decreases. Using WM-EBSD and texture analyses, we estimate that the Cu phase attains a 6% twin volume fraction in the ARB h = 60 nm samples and a higher fraction 30% as h is reduced to 10 nm. This twin growth is found to progress by increases in both initiation points and twin expansion, as shown in TEM micrographs in Fig. 4a–c. Further, the twins can grow to be much wider than the layer thickness. As seen in the case of h = 10 nm (Fig. 4c), twin boundaries are not even apparent within the range of the micrograph. Both WM-EBSD and TEM also find that nearly all twins formed on {1 1 1} planes slanted 19–26° from the interface plane (Fig. 4d). It has been proposed previously that twinning partials prefer to be emitted from the interface onto this particular plane because (a) it is well

aligned with active {1 1 0} planes in Nb and/or (b) intrinsic defects in the interface can dissociate favorably onto it [46,72]. In tracking the evolution of the interface during twin formation via HR-TEM, it was apparent that the partial emissions at first caused the interface to kink but with further straining the interface flattened out [72]. It should be mentioned that the formation of twins in the Cu phase when h reaches 60 nm is not surprising, even at room temperature and relatively low strain rates. In other nanostructured Cu-based materials, such as Cu–Ag composites, Cu nanowires and nanocrystalline Cu, Cu has been observed to twin when the crystal size decreases below 100 nm [19,69,73]. The enhanced propensity for twinning in nanostructured fcc metals below critical nanograin sizes has been correlated with the emission of

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twinning partials from boundaries (or in the present case, interfaces) that can create stacking faults or multi-layered twin domains that fully cover the grain cross-section without emitting the trailing partial [69,74,75]. The interesting result concerns the unique texture and interfaces that develop as a consequence of twinning. Fig. 5a shows the texture in the Cu phase of the ARB composite with h = 10 nm. It is appreciably sharper and contains far fewer orientations than the theoretical rolling texture for an fcc metal developed from slip and twinning (denoted by gfcc(h, RST) in Table 1). An analysis of the orientation distribution function (ODF) from WM-EBSD and neutron diffraction results finds that the largest volume fractions consist of components collecting in the orientation range of CT {5 5 2}h1 1 0i to Goss {1 1 0}h0 0 1i (within a 16° span). Compared to this group, a secondary component is B {1 1 0}h1 1 2i. The presence of a texture component, whether signified by intensity p > 0 or volume fraction f > 0, alone does not signify stability [76,77]. Stable components also are recognized by an increase in their intensity or volume fraction with strain (dp/de > 0 or df/de > 0). Because Cu texture evolves from h = 60 nm to 10 nm due to twinning, calculations of dp/de are particularly important. Table 2 provides estimates of p and dp/de for the main components in Cu: C, D, CT, DT, B and G, from WM-EBSD and neutron

diffraction measurements. Volume fraction f shows the same trends. We find that only the DT {5 5 1}h1 1 0i and G {1 1 0}h0 0 1i components undoubtedly satisfy the criteria for stability (i.e., p > 0 and dp/de > 0). The sudden rise in intensity of DT and G in the Cu phase can be directly associated with twinning. When the predominant C and D components of Cu associated with the slip-fcc/bcc interface (Fig. 2) undergo twinning, they reorient to CT {5 5 2}h1 1 0i and approximately to DT {5 5 1}h1 1 0i, respectively. It has been shown numerically that CT is not stable with respect to rolling and reorients to DT and then to G {1 1 0}h0 0 1i [45,63]. Thus it is likely that the rise in DT and G (e.g., dp/de > 0 in Table 2) is initiated by twinning and sustained by subsequent reorientation via slip. While DT and G are stable and prevalent, we note that B has a high intensity in Cu. However, it is less clear whether the B component is also a consequence of twinning. Recent crystal plasticity calculations demonstrate that twinning can cause a transient rise in the B component [45], supporting earlier ideas put forth in Ref. [63]. The twins alter the slip activity in the (untwinned) matrix material in between the twinned regions, making it planar, favorable only parallel to the twin boundaries. Planar slip causes the (untwinned) C and D matrix regions to reorient near B, where reorientation rates become relatively slow. On this

Fig. 5. Inverse pole figures of the texture of the Cu and Nb phase in the nanocomposite with layer thickness h = 10 nm as measured using neutron diffraction [53]. The measurements show that the textures are sharp and a majority of the interface planes range from (a) {5 5 1} to {1 1 0} in the Cu phase and (b) from {2 2 5} to {1 1 2} in the Nb phase. IPFs are shown instead of conventional ODF sections in order to bring out the sharpness of the textures and the crystallographic axes relative to the two-dimensional layered structure RD–TD–ND. Pole figures and ODFs sections can be found in Ref. [45].

Table 2 Changes in intensity (times random) of key components in the nanolayered Cu–Nb composites as calculated from analysis of EBSD texture measurements. Component

{ND}hRDi

60 nm Intensity p

30 nm Intensity p

10 nm Intensity p

Sign of change in p

C D CT DT B G

{1 1 2}h1 1 1i {4 4 11}h11 11 8i {5 5 2}h1 1 5i {5 5 1}h1 1 10i {1 1 0}h1 1 2i {1 1 0}h0 0 1i

17 7.5 2 3 10 3

12 3 4 6 10.5 7

5 1 4 8 10.5 10

Negative Negative Zero Positive Zero Positive

Stable Stable

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basis, the B component generated in this way would not be stable in rolling unless planar slip ceases and multiple slip (characteristic of B crystals in rolling) resumes. Unlike Cu, Nb does not experience an obvious transition in texture. Fig. 5b shows the corresponding Nb texture at h = 10 nm. We observe that as h is refined from 60 nm to 10 nm, the Nb phase progressively sharpens to a narrow distribution, ranging from {1 1 3}h1 1 0i to {1 1 2}h1 1 0i and attaining a peak at {2 2 5}h1 1 0i. The formation of different and unusually sharp (and unexpected) textures in Nb and Cu after twinning gives some hint that a predominant interface may be emerging and this interface would be distinct from the one that develops when both phases are deforming by slip only. Specifically, the foregoing texture analysis suggests that the interfaces are evolving towards a preferred character, comprising Cu crystals in the narrow range of DT {5 5 1}h1 1 10i and G {1 1 0}h0 0 1i (8° apart) and Nb crystals in the even narrower range of {2 2 5}h1 1 0i to {1 1 2}h1 1 0i (5° apart). Note that these orientations belong to the set of gfcc(h, RST) for Cu and gbcc(h, RS) for Nb. Because of the nanoscale composite structure, we used TEM and HR TEM to identify the character of the interfaces after twinning. The results confirm the development of another predominant interface as specified by the texture analysis, which we refer to as the twin-fcc/bcc interface. Fig. 6 shows a typical TEM micrograph of a representative twin-fcc/bcc in the h = 10 nm material with interface character {5 5 1}h1 1 10iCu||{1 1 2}h1 1 0iNb. Remarkably, this interface is structurally ordered and comprises a periodic array of alternating, independently oriented KS facets. The {5 5 1}h1 1 10iCu||{1 1 2}h1 1 0iNb interface and its close neighbor {1 1 0}h0 0 1iCu (Goss)||{1 1 2}h1 1 0iNb in orientation space, has been modeled previously by MD in Refs. [53,69]. As in the {3 3 8}h4 4 3iCu||{1 1 2}h1 1 0iNb interface (Fig. 2), the KS facets seen in Fig. 6 are a natural consequence of the topology of the {5 5 1}h1 1 10iCu plane and {1 1 2}h1 1 0iNb plane being joined. These MD calculations also predict that its formation energy is 739 mJ m2 [53]

Fig. 6. High-resolution TEM micrographs of a typical nano-interface (h = 10 nm) {5 5 1}h1 1 10iCu||{1 1 2}h1 1 0iNb. The crystallography of the facet faces is also shown.

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(see Fig. 3). Significantly, this value is comparable to that of the interface in Fig. 2 (672 mJ m2) (see Fig. 3) [35,51,52], suggesting that the formation the twin-fcc/bcc interface does not incur an additional energetic penalty. The regularity in structure at the atomic scale again suggests the possibility that the twin-fcc/bcc interface is able to recover from interactions with dislocations generated in deformation. As one indication of its stability, h 6 20 nm composites exhibit outstanding stability in microstructure and hardness up to temperatures of 0.5 Tm of Cu [53,78,79]. 3. Two key variables for crystallographic stability of an interface under SPD Regarding the origin of the two prevailing interfaces, the slip-fcc/bcc and twin-fcc/bcc, we now turn to the question: Can crystallographically stable interfaces that form in rolled bimetal material systems that deform via different mechanisms depend on the same few basic variables? In spite of their difference in character, these two stable interfaces appear to form from processes that have several aspects in common: (1) both interfaces join two crystals of ideal or nearly ideal rolling components, (2) their interface formation energies are comparable, (3) their energies are larger than those of the lowest energy interfaces, KS and NW, and (4) the two crystals on either side of these interfaces co-deform and refine continuously with applied deformation, meaning that they maintain interface continuity (i.e., they do not slide or debond) [54]. Thus, the processes driving the development of a stable, predominant interface in SPD may in fact be the same for materials deforming by slip and twinning or by slip only. On this basis, we revisit two criteria developed previously for metals that slip. The first criterion is plastic stability in co-deformation, which means that the interface character is maintained because the applied deformation and the co-deformation constraint do not require reorientation of either crystal on each side of the interface. Consequently, the crystals associated with such an interface will reduce in thickness and extend to create a new interface area with the same interface character. The second criterion concerns the energetic penalty for creating the new interfacial area. Previous MD calculations find that for Cu–Nb interfaces, the interface formation energy cint depends on the interface crystallographic character, varying widely from as low as 586 mJ m2 for the Kurdjumov–Sachs {1 1 1}h1 1 0ifcc||{1 1 0}h1 1 1ibcc interface to greater than 1100 mJ m2 for the {1 1 0}h0 0 1ifcc|| {0 0 1}h1 1 0ibcc interface [52,69,70]. Considering such variation, a preference for low-energy interface characters can be expected. The above physical picture qualitatively links the two criteria and gives the sense that while satisfying one of them would not be a strong constraint, satisfying both would impose a severe limitation. Next we quantitatively

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investigate the applicability of these criteria, considering collectively composite systems that slip and twin. 3.1. Plastic stability of an interface in co-deforming phases In the present experimental case, the crystals on each side of the interface co-deform during processing to the nanoscale. Let hfcc||hbcc denote the interface character, where hfcc is the orientation of the Cu crystal on one side and hbcc the orientation of the Nb crystal on the other side of the interface. The character hfcc||hbcc can change in co-deformation if either crystal reorients from hfcc or hbcc. Let DXfcc (De) define the value of the minimum angle through which the fcc crystal reorients from its original orientation hfcc during a strain interval of De (a scalar value of strain in a relevant direction) and correspondingly the same for the bcc crystal. The interface character hfcc||hbcc is considered plastically stable in co-deformation when both DXfcc and DXbcc are approximately zero and unstable when either is non-zero. To capture this relationship, we transform DXfcc and DXbcc into a quantitative measure of plastic stability in co-deformation using the following parameter x [49]:     DXfcc exp  DXbcc ; ð1Þ x ¼ exp  De De which ranges from 0 to 1, where 1 is ideally stable. Assuming a tolerance of 10° reorientation on both sides, we can also consider interfaces lying within 1 > x > 0.8 to be stable. An intermediate (arbitrary) condition of “meta-stability” would correspond to 0.8 > x > 0.75, where interfaces are close in orientation space to a stable end state. Values x < 0.75 are unstable. To calculate DX/De in Eq. (1), we employ a bicrystal finite-element model developed in Ref. [49]. There, details of the model set-up and constitutive laws are provided, and here, for self-consistency, we briefly review the essential physical aspects. The core model geometry is a bicrystal with an initial interface character hfcc||hbcc that is subjected to plane strain compression. Periodic boundary conditions are applied in both in-plane directions in order to represent a multilayer material with single crystalline layers and one prevailing interface character. To account for co-deformation, traction and displacement continuity at the interface is enforced during deformation (formally called a kinematic constraint). Both crystals are finely meshed and thus inhomogeneous stress fields or localization will be captured. Deformation of the material point is realized by a combination of anisotropic elasticity and slip on established crystallographic slip planes ({1 1 1}h1 1 0i systems in fcc and {1 1 0}h1 1 1i and {1 1 2}h1 1 1i in bcc [80]). The hardening model for slip has its roots in the thermodynamic and kinetics theory of plastic slip [81–83]. This classical theory relates the rates of slip to the glide of arrays of dislocations interacting with other groups of dislocations in a network. The rate regime where such kinetics best applies lies above the creep regime (105 s1) and below that of linear drag (104 s1) [84] and matches the laboratory condi-

tions of ARB processing. For the sole purpose of assessing plastic stability (not to mimic extreme straining), De via Eq. (1) is made sufficiently large (>0.75 strain). Computational strain increments to accumulate De are two orders of magnitude smaller. To demonstrate the utility of the plastic stability metric, we consider the stable interface seen before twinning: the {1 1 2}h1 1 1ifcc||{1 1 2}h1 1 0ibcc interface with a KS orientation relationship. This interface has been studied extensively using MD simulation in prior works [35,47,51,68, 69,71,85]. In plane strain compression, our bicrystal model finds that the Cu crystal reorients about the h1 1 0i  6° and the Nb crystal lattice about the h1 1 1i  2°. The interface character corresponding to this new end state is nearby in orientation space to the starting {1 1 2}h1 1 1ifcc||{1 1 2} h1 1 0ibcc interface, with x = 0.86, and hence the initial interface is considered stable by the current definition. Notably, this end state interface not only lies within the tight distribution of the predominant slip-fcc/bcc interface but corresponds to its peak value. As a further test of stability, we repeated the simulation starting from various 10° perturbations of either crystal from the {1 1 2}h1 1 1ifcc|| {1 1 2}h1 1 0ibcc KS interface and found that all cases reorient to the vicinity of this end state. To gain a broader perspective, we repeat this simulation for a large number of starting interfaces of distinct character. Table A.1 in the Appendix provides a listing of all interfaces tested and their calculated x values. The interfaces investigated can be grouped into two mutually exclusive classes: group 1 (squares) consists of interfaces where both adjoining crystal orientations are stable components in the theoretical rolling texture of the corresponding monolithic material (Table 1) and group 2 (circles) consists of interfaces where one or both crystals do not correspond to a stable rolling texture component. Interfaces that are also experimentally observed stable interfaces are additionally marked by black symbols: triangles and stars respectively for those within a narrow distribution of the slip-fcc/bcc interface and of the twin-fcc/bcc interface. Fig. 7 locates these two groups of interfaces and the experimentally observed stable ones on an interface character plastic (ICP) stability map for rolling deformation [49]. The first important finding is that the predominant interfaces (black symbols) belong to group 1 (squares); that is, they join two crystals that are individually stable in rolling. This map compares x for a co-deforming bicrystal containing a single interface vs. xSX for the same two crystals but deforming independently (not joined at an interface). From Eq. (1), this analogous parameter xSX is defined as:     DXSX DXSX fcc bcc xSX ¼ exp  exp  ð2Þ De De A second important finding revealed in Fig. 7 is that the slip-fcc/bcc interfaces (triangles) and twin-fcc/bcc interfaces (stars) fall in the stable regime (x P 0.8). Thus, the predominant interfaces are plastically stable.

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Table A.1 Calculated stability related quantities for a range of fcc–bcc interfaces. The data listed here correspond to those plotted in Figs. 6 and 7. The interfaces are written in the {ND}hRDi nomenclature, wherein {ND} is the crystallographic plane corresponding to the rolling plane and hRDi is the crystallographic direction aligned with the rolling direction. The units for cint are mJ m2. The symbols are the same symbols used in Figs. 6 and 7: squares are interfaces that join two crystals belonging to their respective theoretical rolling textures for the phase in monolithic form (Table 1 in the main text), the circles are those that do not and the triangles correspond to observed predominant interfaces within a narrow distribution about the slip-fcc/bcc interfaces and the stars correspond to those within a narrow distribution about the twin-fcc/bcc interface. Cu||Nb interface C||{1 1 2}h1 1 0i D||{1 1 2}h1 1 0i K||{1 1 2}h1 1 0i S||{1 1 2}h1 1 0i Brass||{1 1 2}h1 1 0i Goss||{1 1 2}h1 1 0i {5 5 2}h1 1 5i||{1 1 2}h1 1 0i Z||{1 1 2}h1 1 0i C||{1 1 1}h1 1 0i D||{1 1 1}h1 1 0i K||{1 1 1}h1 1 0i S||{1 1 1}h1 1 0i Brass||{1 1 1}h1 1 0i Goss||{1 1 1}h1 1 0i {1 1 0}h1 1 1i||{1 1 1}h1 1 0i {1 1 1}h1 1 2i||{1 1 0}h1 1 2iKS {1 1 1}h1 1 2i||{1 1 0}h1 1 0iNW Z||{1 1 1}h1 1 0i {5 5 2}h1 1 5i||{1 1 1}h1 1 0i C||{2 2 5}h1 1 0i D||{2 2 5}h1 1 0i K||{2 2 5}h1 1 0i Brass||{2 2 5}h1 1 0i Goss||{2 2 5}h1 1 0i Z||{2 2 5}h1 1 0i {5 5 2}h1 1 5i||{2 2 5}h1 1 0i C||{0 0 1}h1 1 0i D||{0 0 1}h1 1 0i K||{0 0 1}h1 1 0i S||{0 0 1}h1 1 0i Brass||{0 0 1}h1 1 0i Goss||{0 0 1}h1 1 0i Z||{0 0 1}h1 1 0i {5 5 2}h5 5 1i||{0 0 1}h1 1 0i

Symbol

x

xSX

cint (mJ m2)

0.855 0.820 0.839 0.834 0.993 0.994 0.714 0.800 0.701 0.559 0.573 0.665 0.780 0.781 0.689 0.340 0.428 0.590 0.539 0.824 0.845 0.862 0.933 0.934 0.770 0.681 0.834 0.736 0.752 0.802 0.999 1.000 0.709 0.687

0.866 0.915 0.924 0.851 0.993 0.994 0.737 0.853 0.680 0.718 0.725 0.668 0.779 0.781 0.653 0.593 0.596 0.670 0.579 0.814 0.859 0.868 0.933 0.934 0.802 0.692 0.871 0.920 0.929 0.856 0.999 1.000 0.858 0.741

825 739 672 982 1090 949 939 739 1107 1070 1069 1098 972 1058 1098 586 586 1082 1066 948 936 919 1082 985 955 980 1038 1034 1033 942 941 1115 1076 1078

The role of co-deformation in plastic stability is revealed by the location of the interfaces on this map with respect to the solid line in Fig. 7, which marks where x and xSX are equivalent. Co-deformation improves plastic stability when the interface lies above the line, has no effect when it lies on the line and decreases stability when it lies below the line. Fig. 7 shows that plastically stable interfaces (x P 0.8) tend to lie arbitrarily “close” to the solid line, indicating that two independently stable orientations tend to maintain stability when constrained to co-deform with each other. Unstable interfaces (x  0.8) lie far below the line, revealing that co-deformation does not have a stabilizing effect. This result leads to our third point: plastic interface stability is dictated by the less stable orientation of the two

Fig. 7. Plastic stability dependence on bimetal interface character. The solid line corresponds to x = xSX. Interfaces lying along this line correspond to the situation when the stability of the co-deforming bicrystal equals that of its constituents when deformed alone. Square and circle symbols correspond to simulated fcc/bcc interfaces under rolling strains. Interfaces with black triangles represent the observed predominant slip-fcc/bcc interfaces and with black stars the twin-fcc/bcc interfaces. The significance of the observation that many interfaces lie below the x = xSX line is stability is limited by the less stable of the two crystals (see Table A.1 in the Appendix for a list of all interfaces tested and along with their values for xSX and x).

adjoining crystals. When an unstable orientation is joined to a stable one, the bicrystal is unstable. Evidently, co-deformation imposes a severe constraint on stability, substantially reducing the number of plastically stable interfaces. 3.2. Mechanical stability map In spite of being a strong constraint, many interfaces are still found to be plastically stable in co-deformation (i.e., x P 0.8). Furthermore, many of these are not experimentally observed (i.e., those interfaces lying x P 0.8 but not marked by a black solid symbol). Thus while plastic stability appears to be an important variable in interface selection under SPD, it is not sufficient to consider it alone. A second variable of influence is the interface formation energy, which is not considered in the ICP map in Fig. 7. Fig. 3 shows an MD calculation of the variation in interface formation energy, cint, with the tilt angle of the Cu crystal about the h1 1 0ifcc||h1 1 1ibcc axis taken from Ref. [53]. In this calculation Nb was fixed to {1 1 2}h1 1 0i. The narrow range of stable slip-fcc/bcc interfaces and twinfcc/bcc interfaces correspond to relatively low energy interfaces and some even to local energy minima, such as the {3 3 8}h4 4 3iCu||{1 1 2}h1 1 0iNb in Fig. 2 and the {5 5 1}h1 1 10iCu||{1 1 2}h1 1 0iNb interface in Fig. 6. To account for both factors, Fig. 8 plots these same two groups of interfaces according to their crystallographic stability x and their interface formation energy cint, provided

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Fig. 8. Bimetal interface character stability map. Squares represent interfaces created by pairing orientations from the stable orientation distribution (i.e., well-developed rolling texture for the single-phase metal) of the deformed crystals hfcc||hbcc where hfcc 2 gfcc(h) and hbcc 2 gbcc(h) (Table 1). Circles represent interfaces formed when one or both orientations do not belong to the theoretical single-phase rolling texture (Table 1). Interfaces with black triangles represent the observed predominant slipfcc/bcc interfaces and with black stars the twin-fcc/bcc interfaces (see Table A.1 in the Appendix for the cint of all interfaces tested taken from Refs. [52,53,69]).

in Refs. [53,69] and normalized by c = cint/cKS. Table A.1 in the Appendix contains the calculated values for x and cint. As shown, the experimentally observed predominant interfaces, both before and after twinning, exclusively collect in the region bounded by x P 0.8 and c < 1.6. Put another way, no unstable candidate interface lies within this region and none of the observed stable ones lies outside this region. The map confirms the hypothesis that an interface stable in crystallography with respect to deformation: (1) joins two crystals belonging to the group of stable orientations expected for the applied deformation, (2) maintains plastic stability while co-deforming and (3) forms a relatively low formation energy interface. When the material system and deformation mode permit satisfaction of these criteria simultaneously, then a crystallographically stable bimetal interface can emerge. 4. Summary In ARB processing of a 50/50 Cu–Nb layered composite, when h is refined to the submicron range, 1 lm to 500 nm (8–9 strain), a crystallographically stable interface emerges predominantly over the entire material. The interface remains stable with respect to continued extreme straining to h = 60 nm (10.6 strain). The evolution of textures and interfaces over the corresponding strain regime involves primarily slip in both layers. Upon further straining to reductions in h below 60 nm, the Cu phase begins to twin, a common occurrence seen in other nanostructured Cu systems. We find that another

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