Tailoring and patterning the grain size of nanocrystalline alloys

Acta Materialia 55 (2007) 371–379 www.actamat-journals.com

Tailoring and patterning the grain size of nanocrystalline alloys Andrew J. Detor, Christopher A. Schuh

*

Department of Materials Science and Engineering, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Received 5 July 2006; received in revised form 4 August 2006; accepted 9 August 2006 Available online 27 October 2006

Abstract Nanocrystalline alloys that exhibit grain boundary segregation can access thermodynamically stable or metastable states with the average grain size dictated by the alloying addition. Here we consider nanocrystalline Ni–W alloys and demonstrate that the W content controls the grain size over a very broad range: 2–140 nm as compared with 2–20 nm in previous work on strongly segregating systems. This trend is attributed to a relatively weak tendency for W segregation to the grain boundaries. Based upon this observation, we introduce a new synthesis technique allowing for precise composition control during the electrodeposition of Ni–W alloys, which, in turn, leads to precise control of the nanocrystalline grain size. This technique offers new possibilities for understanding the structure–property relationships of nanocrystalline solids, such as the breakdown of Hall–Petch strength scaling, and also opens the door to a new class of customizable materials incorporating patterned nanostructures.  2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nanocrystalline; Ni–W alloys; Electrodeposition; Grain boundary segregation

1. Introduction Nanocrystalline materials exhibit impressive properties ranging from high strength and wear resistance, to unique functional characteristics owing to the emergence of grain boundary-dominated physics when the grain size approaches 100 nm or below [1–20]. However, while nanocrystalline materials are desirable for a variety of applications, the introduction of high-energy interfaces is a struggle against the equilibrium tendency for grain coarsening in polycrystals. Accordingly, the synthesis of pure nanocrystalline materials usually involves energetic processes such as mechanical attrition, severe plastic deformation or rapid quenching from vapor [21–25]. In most cases, nanocrystalline grain size cannot be explicitly controlled and is limited by the characteristic kinetics of the processing method. As a result, the finest grain sizes (<20 nm) are often difficult to achieve in pure metals. This makes it difficult to investigate the new and interesting behavior that *

Corresponding author. E-mail address: [email protected] (C.A. Schuh).

has been observed at these length scales, such as the apparent breakdown of Hall–Petch scaling [5,10,12,26–30] and an improvement in soft magnetic properties [31–35]. An alternative technique that has been successful in producing the finest nanocrystalline grain sizes involves alloying of two or more elements. The addition of an alloying element has fundamental thermodynamic implications for nanocrystalline metals, which can explain the unique ability of alloyed systems to exhibit fine-grained structures; this was discussed in the works of Weissmu¨ller [36], Kirchheim [37], Liu and Kirchheim [38], Beke et al. [39] and Cserhati et al. [40], among others [41–44]. These studies have demonstrated the possibility of nanocrystalline structures that are in thermodynamic equilibrium due to the energetics of alloying and, in particular, due to grain boundary segregation. Such stabilized nanostructures have obvious practical advantages for applications and also for fundamental scientific studies of material behavior. The thermodynamic framework that has been used to describe nanostructure stabilization is based upon the change in Gibbs free energy G with respect to the grain boundary area A:

1359-6454/$30.00  2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.08.032

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dG ¼ c dA

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ð1Þ

In a single-component metal the grain boundary energy c is positive, so the system can reduce its free energy by increasing the grain size. This is the usual driving force for grain growth and the reason why processing pure nanocrystalline materials is non-trivial; they are inherently unstable with respect to grain growth. In contrast, a two-component system offers the opportunity to lower the system energy by segregating one species to the grain boundaries so that the boundary energy is reduced via an adsorption isotherm [45]. For example, under certain simplifying assumptions, use of the Gibbs adsorption isotherm gives [36,46] c ¼ c0  CðGseg þ RT ln X Þ;

ð2Þ

where c0 is the grain boundary energy of the pure polycrystalline solvent, C is the specific excess of solute located at the grain boundary, Gseg is the segregation energy, R is the gas constant, T is temperature and X is the global solute composition. The segregation term in Eq. (2) now counters the positive energy penalty term c0 and can stabilize the grain size at a finite value; for sufficiently high Gseg and C, the grain boundary energy can equal zero, leaving no driving force for a change in grain size. The physical basis for thermodynamic stabilization of a nanostructure involves an interplay between the total number of highenergy grain boundary sites available at a particular grain size, and the solute content of the alloy. For relatively dilute alloys of small grain size there are excess grain boundary sites available for solute atoms, each with an energy penalty; grain growth is preferred in order to reduce this penalty. In the opposite scenario, the grain size is too large such that grain boundaries are ‘‘overfull’’ and solute atoms must be rejected from the intercrystalline regions into the energetically unfavorable grain interior sites; thus, grain growth is opposed. At the equilibrium grain size these two effects are perfectly in balance, the system energy is minimized and the grain size is stable. While the concept of complete thermodynamic stability (c = 0) is attractive in its simple theoretical basis, it has not yet been demonstrated that a vanishing grain boundary energy can actually be achieved in experimental alloys. In light of this, Krill et al. [41–43] suggested an alternate but related explanation for nanostructure metastability that focuses on the kinetics of grain growth in relation to the grain boundary energy. This explanation relies on a classical result describing the grain boundary velocity v as [41]: 2c vM d

this to a thermodynamic reduction of c. Regardless of whether the grain boundary energy is actually reduced to zero, grain boundary segregation leads to a reduction in the grain boundary energy and improved stability. In addition to the Pd–Zr system mentioned above [41,43,47], the idea that grain boundary segregation may stabilize nanocrystalline structures has also been explored experimentally in the Y–Fe [48], Ni–P [38,49], Ru–Al [37,38] and Fe–P [38] systems. One of the key observations in all of these systems is a monotonic relationship between grain size and composition; higher additions of the minority, segregating component lead to finer grain sizes that are often below 20 nm, and which are apparently in a stable or metastable state. This trend is expected, as those alloys containing higher amounts of solute will prefer finer grain sizes in order to accommodate the segregating species in the grain boundaries. The true attraction of segregation-based nanostructure stabilization lies in its thermodynamic foundation: nanocrystalline grain sizes can be accessed in a stable state, rather than relying upon highly non-equilibrium processing methods and complex kinetic controls over nanostructure. Nonetheless, to our knowledge this concept has not been exploited as a tool for explicit grain size control during the synthesis of nanocrystalline alloys; our purpose here is to do so, using a scalable and robust processing method that yields high-quality nanocrystalline alloys, and which should be applicable to a broad range of alloy systems. Specifically, we extend the discussion of nanostructure stabilization to binary Ni–W alloys and demonstrate the possibility of explicitly tailoring the grain size in alloys produced by aqueous electrodeposition. We show that, like the other systems listed above, the Ni–W system exhibits a characteristic grain size–composition relationship, in line with segregation-based stabilization of grain boundaries. However, the Ni–W system is distinct from those above in that tungsten has a significant solid solubility in the nickel lattice and, consequently, only a weak segregation tendency [50]. This proves to have important practical consequences on the range of grain sizes that can be accessed. In addition to tailoring of the grain size, our synthesis technique also allows for precise patterning of both the structure and properties in bulk nanocrystalline solids. 2. Nanocrystalline Ni–W alloys 2.1. Conventional synthesis and characterization techniques

ð3Þ

where M is the interface mobility and d is grain size. Like the previous thermodynamic description, c = 0 in Eq. (3) predicts a grain boundary velocity of zero and, hence, complete stability of the structure. However, Eq. (3) also suggests a spectrum of increasingly metastable nanocrystalline structures as c is suppressed, but not necessarily driven completely to zero. Krill et al. [41] showed exceptional thermal stability in the Pd–Zr system experimentally, linking

The aqueous electrodeposition of Ni containing a minority addition of W has been studied by a number of authors, and the details of typical deposition procedures, including bath composition and plating parameters, have been reported elsewhere [51–57]. In the present work we have used the same bath chemistry from Ref. [51] to synthesize alloy sheets of approximately 100 lm thickness using electropolished commercial purity copper as the cathode (substrate) and pure platinum mesh as the anode. Of

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primary interest in this study is the deposit composition, which we controlled by a variety of means. For example, it is conventional to adjust the bath temperature or cathodic current density in order to manipulate the deposit composition [51,52,54,55] and we used these techniques here as well. In addition, we have also explored the effect of the applied current waveform and, in particular, the introduction of a periodic reverse pulse in the deposition process. The consequences of reverse pulse (RP) plating on the composition of Ni–W alloys will be discussed in detail in a later section. All deposits were sectioned and prepared via traditional metallographic techniques for examination in a Leo 438VP scanning electron microscope (SEM) to gather quantitative information on composition to within ±1 at.% via energy dispersive spectroscopy (EDS) (X-ray Optics/AAT #31002). Structural characterization was conducted by Xray diffraction (XRD), as well as transmission electron microscopy (TEM). The X-ray diffraction measurements were performed on a Rigaku RU300 operating at 300 mA and 60 kV, and grain size was quantified by applying the integral breadth method to the {1 1 1} family of peaks [58]. TEM specimens were prepared via twin-jet electropolishing at 10 V in a 2:1 solution of methanol and nitric acid at a temperature of 60 C and were subsequently examined in a JEOL 2010 operating at 200 kV. Mechanical properties were measured via micro- and nanoindentation techniques. Traditional Vickers microhardness measurements were performed on polished cross-sections using a Clark DMH2 model indenter with an applied load of 100 g for 15 s. Nanoindentation experiments were also performed on polished cross-sections using a Hysitron TriboIndenter. A Berkovich tip was used with a linear loading function reaching a maximum of 10 mN over 10 s; typical indents were 150 nm deep. Hardness was calculated from the load–displacement curves using standard methods and an empirically calibrated tip area function [59]. 2.2. Composition and structure of the deposits In total, 48 unique specimens were produced with W content ranging from 1.2 to 26.5 at.%. Some of these specimens were prepared using conventional cathodic current processing, while others were prepared using reverse pulse plating; at this point we make no distinction between the techniques and only focus on the resultant composition– structure relationship. The composition was found to be homogeneous through the cross-section of every deposit to within the spatial resolution of the EDS system (1 lm). Representative X-ray diffraction patterns for specimens with compositions ranging from 2.5 to 23.0 at.% W are shown in Fig. 1. Several trends can be observed as the W content of the deposit increases. First, the crystal structure is unchanged with composition; all of the peaks in Fig. 1 can be indexed with face-centered cubic (fcc) reflections, as expected for Ni-rich solid solu-

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Fig. 1. Typical X-ray diffraction (XRD) patterns for specimens with global tungsten content from 2.5–23.0 at.%. The XRD grain size calculated using the integral breadth method is also shown for each specimen.

tions. It is interesting to observe that W is dissolved to levels much higher than nominally expected from the equilibrium phase diagram (which indicates a solubility limit near 12 at.% at low temperatures [60]). Second, the addition of W clearly leads to substantial peak broadening, which is quantified through the trend of decreasing grain size reported at the right of Fig. 1. Finally, an increasing W content leads to a clear shift of the fcc reflections to lower Bragg angles; this is consistent with lattice swelling due to the relatively large size of W atoms in solution. In order to verify the grain sizes determined by X-ray diffraction, direct observations of the alloy nanostructure were also conducted via TEM for representative specimens containing 3, 15 and 23 at.% W. Bright field images and selected area diffraction patterns for these specimens are shown in Fig. 2a–c. The bright-field TEM images in Fig. 2a and b reveal average grain sizes of approximately 100 and 20 nm, respectively; these values are in line with those approximated by the X-ray diffraction line broadening measurements which gave d  95 and 21 nm for specimens of similar respective compositions. Fig. 2c is a high-resolution TEM image where lattice fringes can be seen for individual grains with appropriate orientations, two of which have been circled. The individual grains visible here are all 2–4 nm in diameter, which again correlates well with the X-ray diffraction measurement (2 nm). Together, the series of micrographs in Fig. 2 illustrate the same trend suggested by Fig. 1, that a clear refinement of the nanocrystalline structure occurs with increasing W content. This is perhaps the main result of our experiments, and is best illustrated through the compiled data shown in Fig. 2d, which plots the grain size as a function of composition for all Ni–W specimens (shown as solid and open circles); here, the Ni–W results are grouped according to two different processing conditions that will be further distinguished later. The characteristic grain size–composition relationship for a Ni–P alloy, from several separate studies collected in Ref. [38], is also shown in Fig. 2d (solid squares). Note that the Ni–W data span a much broader range of length

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Fig. 2. (a–c) Bright field TEM images and selected area diffraction patterns showing structural refinement with increasing solute content in Ni–W specimens; two grains are outlined in the high-resolution image (c) where lattice fringes are visible. (d) Experimental grain size–composition relationship for Ni–W specimens electrodeposited under cathodic (C) and periodic reverse pulse (RP) current conditions (present study), along with data from Ref. [38] for the Ni–P system.

scales as compared with the Ni–P data, thereby allowing nanocrystalline grain size to be controlled from 140 down to 2 nm over a composition range of 1–27 at.% W. The unique ability to access larger grain sizes in the Ni–W system likely relates to the grain boundary segregation tendency, as will be discussed in the following section. 3. Evidence and consequences of grain boundary segregation By analogy with the Ni–P system, which is known to exhibit a strong tendency for grain boundary segregation [49], one might expect that the data in Fig. 2d also point to grain boundary segregation in the Ni–W system. In what follows, we describe a technique to estimate the extent of W segregation to grain boundaries, followed by a more direct approach to quantitatively confirm the behavior. It has been established both experimentally [61] and through simulations [62] that the lattice parameter in the Ni–W system scales linearly with composition: a ¼ aNi þ kX a

ð4Þ

where a is the lattice parameter of the alloy, aNi = 0.352 nm is the lattice parameter of pure Ni, Xa is the atomic fraction

of W and k is a constant equal to 4.859 · 104 nm. Using Eq. (4) we can estimate the composition Xa from an accurate measure of the alloy lattice parameter a. When this method is applied to a polycrystal, X-ray reflection only occurs from crystalline regions, so the composition extracted from Eq. (4) is an average value for the grain interior regions and can be assumed to include no information about the composition of the grain boundary. In the present work we used X-ray diffraction to measure a for all of the specimens that exhibited multiple clear crystalline reflections; this generally required a global tungsten content of less than 17 at.% (cf. Fig. 1). The standard Nelson–Riley extrapolation was used to obtain as accurate a measure of a as possible through traditional diffractometry [63]. The grain interior composition determined via Eq. (4) is plotted in Fig. 3 as a function of the global composition determined from EDS; the dashed line indicates equality as would be expected for a perfectly homogeneous solid solution (no grain boundary segregation). It is obvious from this figure that increasing the global W content markedly increases the amount of W in solution within the crystalline lattice. This is unlike strongly segregated systems where solute partitions completely to the grain boundaries

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Fig. 3. Composition of the grain interior regions determined using Eq. (4) with X-ray diffraction data, plotted as a function of the global alloy composition determined using EDS for some of the experimental Ni–W alloys. The dotted line is for a one-to-one trend such as would be observed in a perfect homogeneous solid solution; data points below the line suggest some level of grain boundary segregation.

[49,50,64]; in this scenario the data points in Fig. 3 would all lie along the bottom of the plot at low grain interior compositions. Unfortunately, due to the large degree of scatter inherent in this measurement technique, we can not draw unequivocal conclusions as to the presence of, or the exact extent of grain boundary segregation. However, Fig. 3 shows that there can be, at best, only a subtle amount of W segregation to the grain boundaries in nanocrystalline Ni–W alloys. Combining the apparent weak segregation tendency in Ni–W with very fine nanocrystalline grain sizes makes direct observation of composition gradients difficult. For example, methods such as Auger spectroscopy or EDS carried out in a TEM are often used to study grain boundary segregation, but do not have the required combination of spatial and chemical resolution for these nanocrystalline Ni–W specimens. However, at the length scales of interest here, the structure is amenable to other types of analysis, such as atom-probe tomography (APT) [65–67] or computer simulation [68–70]. We recently conducted a combined computer simulation and APT study on these nanocrystalline Ni–W alloys [71] to investigate the segregation behavior in more quantitative detail. Here we will briefly review a main result of that work; the reader is directed to Ref. [71] for more information. One-dimensional composition profiles through two nanocrystalline structures with 3 nm grain size and 18 at.% W addition are shown in Fig. 4. The data in Fig. 4a were obtained by atomistic computer simulation, in which a polycrystalline specimen was constructed from Ni and W atoms interacting via an empirical multi-body potential [62], and a Monte Carlo procedure was used to identify the minimum energy configuration of the alloy. Periodic boundary conditions were applied in this simulation, and the structure is repeated four times in Fig. 4a to clearly show the composition fluctuations. Thick gray vertical lines indicate the positions of the grain boundaries,

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Fig. 4. Composition profiles constructed through: (a) computer simulated and (b) experimental 3 nm grain size structures: the experimental data were acquired using APT. The solid and dashed horizontal lines indicate the mean composition and standard deviation of the data, respectively. A characteristic wavelength consistent with the grain size is observed in both profiles, owing to the grain boundary segregation tendency of the alloy; known grain boundary positions are indicated by thick vertical lines in (a).

which are known exactly in the simulated structure. It is clear that a subtle degree of grain boundary segregation is present in this simulated alloy where the grain boundary compositions are 5 at.% elevated as compared to the crystalline regions of the specimen. We have seen the same basic trend in experimental Ni– W alloys, as illustrated in Fig. 4b. These data were collected using three-dimensional APT [65–67], a technique which allows for atom-by-atom reconstruction of a finite volume. In this case the grain boundary locations are not known a priori, but the data in Fig. 4b show a characteristic oscillation consistent with the known grain size of the specimen (3 nm). This result strongly suggests that W is partitioned at the scale of the grain structure and, in fact, the result in Fig. 4b for a grain size of 3 nm is also mirrored in experiments on alloys with larger grain sizes of 10 and 20 nm [71]. We consistently observe that, in Ni–W alloys, the characteristic composition fluctuations are of the same length scale as the grain size; this supports an interpretation of grain boundary segregation. An important point reflected in both Figs. 3 and 4 is the relatively weak segregation tendency of the Ni–W system. In particular, we observe that the composition oscillations are, on average, only 40% of the mean W concentration in Fig. 4. For comparison, other more prototypical segregating systems, such as Ni–P, exhibit essentially perfect solute partitioning to grain boundaries, because the solid solubility of P in Ni is vanishingly small [49,50,64]. In those systems, the segregation energy is very high, typically assumed to be 100 kJ mol1. Consequently, every solute atom added strongly prefers a grain boundary site and the stable grain size declines rapidly with solute addition; this is evident in the solid squares of Fig. 2d, which are virtually all at grain sizes below 20 nm. In contrast, we

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estimated the segregation energy in Ni–W [71] to be of a much lower magnitude (1 kJ mol1), which correlates with a more subtle tendency for solute partitioning and a lesser energy penalty for solute incorporation in the crystalline lattice. Based on the above discussion, we suggest that for the broadest degree of control over nanocrystalline grain sizes, systems with too strong a segregation tendency should be avoided. In Ni–P or any strongly segregating alloy system it is difficult to control the nanocrystalline grain size explicitly, because even a dilute addition of solute leads to exceedingly fine grains on the order of 10 nm. The accessible range of nanocrystalline grain sizes (and associated desirable properties) is therefore very restricted and of limited practical utility. By allowing some accommodation of solute in the crystalline regions, higher levels of solute are required to refine the grains. Because of the relatively high solubility of W in Ni, only a fraction of the W atoms require grain boundary sites. As a result, the variation in grain size with solute concentration is broadened as the lattice can accept an appreciable amount of solute (Fig. 2d), and the full range of nanocrystalline grain sizes from 2 to 140 nm can be readily accessed. 4. Active control of nanostructure We now turn our attention to the two processing techniques distinguished in Fig. 2d as ‘‘C’’ and ‘‘RP’’, noting first the overlap between these two data sets; the nanocrystalline grain size is apparently determined by composition alone and not the particular processing details. Because of this, controlling the composition directly allows for precise control of nanostructure. The open circles labeled ‘‘C’’ in Fig. 2d were synthesized under conventional cathodic current conditions; this encompasses both direct current as well as unipolar cathodic pulse plating where some amount of periodic off-time is incorporated into the current cycle. We group these two techniques here as both involve only cathodic current and neither presents a significant opportunity to tailor the deposit composition beyond the conventional bath temperature or current density adjustments. In line with the results of Ref. [51] we found that an increase in either of these parameters results in higher W incorporation in the deposit, with bath temperature having the most pronounced effect. Hence, the open circle in Fig. 2d with 23 nm grain size and 9 at.% W content was deposited at a relatively low bath temperature of 45 C, while those points to the right, with greater W content and finer grain size, were obtained at a higher plating bath temperature, with all other variables remaining constant. However, it is particularly noteworthy that the full range of grain sizes accessed using conventional cathodic electrodeposition only spans from 2 to 40 nm. In contrast to the purely cathodic deposition methods, the solid circles labeled ‘‘RP’’ in Fig. 2d were deposited using a reverse pulsing technique, as illustrated in Fig. 5. Here we rely on the use of a periodic reverse pulse in the

Fig. 5. The effect of adding a periodic reverse (anodic) pulse during the electrodeposition of Ni–W on the composition and, in turn, grain size of the alloy. The current waveform, shown schematically, consists of a forward (cathodic) pulse of 20 ms duration and 0.2 A cm2 intensity, followed by a 3 ms reverse pulse and intensity ranging from 0 to 0.3 A cm2.

electrodeposition current, the function of which is to anodically strip the more electroactive W atoms from the surface layer of the deposit during deposition. The timing of the pulses is such that they operate roughly on each monolayer as it is deposited, resulting in a homogeneous composition through the deposit thickness, but with a reduced level of W incorporation. We have generally employed a pulsing scheme with a forward (cathodic) pulse of 20 ms duration and 0.2 A cm2 peak current density, followed by a 3 ms reverse (anodic) pulse. As Fig. 5 illustrates, manipulation of the reverse pulse intensity (current density) allows precise control of the specimen composition [72]; incorporating a more intense reverse pulse proportionally removes more W atoms during deposition. Following the relationship in Figs. 1 and 2, this composition control necessarily correlates with a precise control of grain size, as also illustrated in Fig. 5. Using the reverse pulsing technique to control the composition and grain size in nanocrystalline Ni–W alloys has some important practical advantages. First, the adjustment of a single parameter (reverse pulse intensity) allows bulk alloys of a specific composition/grain size to be deposited from a single bath, at a constant temperature. Second, the applied current waveform can be easily adjusted in situ in order to change the composition/structure/properties of the deposit in real time, thereby enabling the production of patterned nanostructures that may be useful in a variety of applications (this will be explored in more detail later). Third, the deposits are observed to be of high quality over the entire grain size/composition range using the reverse pulse technique. Conventionally, deposition of Ni–W with larger grain sizes (100 nm) would necessitate a low bath temperature [51] that leads to highly cracked and voided specimens, as shown in Fig. 6a for a 23 nm grain size alloy containing 9 at.% W processed at 45 C. An alloy of similar composition and grain size produced

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Fig. 7. Hardness plotted as a function of grain size for the present Ni–W alloy along with data from the literature for Ni [74–76] and Ni–W [51,77]. The dashed line with a slope of 2 indicates the classical trend of Hall–Petch strengthening with grain refinement; for grain sizes less than 10 nm this relationship is apparently not obeyed. Fig. 6. Cross-sectional SEM images of Ni–W specimens with similar grain size and W content electrodeposited using: (a) conventional cathodic methods and (b) reverse pulsing control. Significant defects are observed in (a) while the reverse pulsing technique results in a high quality deposit the substrate is seen at the bottom of both images. The specimen in (a) was produced at a plating bath temperature of 45 C, while that in (b) was deposited at 75 C using a 0.15 A cm2 reverse pulse current density (see Fig. 5). Both specimens contain 9 at.% W and have a grain size of 23 nm.

using the reverse pulse technique is shown in Fig. 6b, and is typical of the high quality obtained using this approach. The combination of high specimen quality and precise structural control over the finest nanocrystalline grain sizes is clearly desirable for both detailed scientific studies and application of these materials.

number of independent studies on Ni [74–76] and Ni–W alloys [51,77] and no one of these studies presents data that convincingly spans the crossover from conventional scaling to breakdown behavior. With our new degree of control over alloy grain size in the Ni–W system, we can access the full range of grain sizes over which the breakdown is thought to occur (2–100 nm). Our experimental data are shown as solid points in Fig. 7 and capture both the classical Hall–Petch regime as well as an unambiguous demonstration of scaling breakdown in high-quality materials. Furthermore, unlike pure metals, where specimens of relatively finer grain size represent an increasing departure from equilibrium, nanocrystalline alloys such as ours offer the possibility of studying scaling anomalies in systems in a stable or metastable state.

5. Applications of the reverse pulsing technique

5.2. Patterned nanostructures

5.1. Hall–Petch breakdown

In addition to simply controlling grain size in a monolithic specimen, the present approach also opens the door to a new class of nanostructured solids with patterned grain sizes and properties. In principle, traditional deposition procedures could be applied in a series of discrete steps involving different temperatures, current densities, plating bath chemistries, etc., in order to build up a series of layers of different compositions and grain sizes [78]. However, here we have developed an in situ approach to the fabrication of such materials and, to our knowledge, this procedure has not been used to create graded or layered nanocrystalline materials previously. By effecting changes in the reverse pulse conditions in real time, it is possible to deposit a sequence of tailored layers or smooth gradations in composition and grain size. In principle, any conceivable one-dimensional pattern can be produced on scales ranging from nanometers to millimeters. Fig. 8 shows two specimens exemplifying this capability; the specimen in Fig. 8a comprises eight layers of increasing grain

Control of grain size is desirable for tailoring material properties, not only for practical applications where such optimization is important, but also for scientific inquiries of grain size-dependent properties on the nanoscale. For example, the materials community has recently focused much attention on the breakdown of classical structure– property scaling laws in the nanocrystalline regime [1–8,10,73]. Fig. 7 shows one such relationship, plotting hardness as a function of grain size on double-logarithmic scales. The data at larger grain sizes obey the parabolic Hall–Petch relationship, and there has been considerable debate over its potential breakdown at grain sizes near or below 10 nm [4,5,10,12,30,73]. However, experimental support for such a breakdown has been notably sparse, and the uncertain quality and stability of experimental nanocrystalline specimens has fueled controversy. For example, the open points shown in Fig. 7 represent a

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Fig. 8. Patterned nanocrystalline electrodeposits synthesized using the periodic reverse pulsing technique. Backscatter SEM images and composition line scans are shown at the top of both figures. Nanoindentation hardness (circles) and grain size (squares) profiles show the level of structure and property control available using this method. The specimen in (a) comprises eight layers of monotonically decreasing W content, while that in (b) contains alternating layers of low and high W content. The grain size measurements in (a) were obtained from a serial sectioning X-ray diffraction study (Fig. 9), while those in (b) are an estimate based on the composition.

size (from 10 to 60 nm), while that in Fig. 8(b) has a composite structure of alternating 7 and 70 nm grain size regions. A serial-sectioning XRD study was undertaken for the graded specimen in Fig. 8a in order to profile the grain size of the deposit through its thickness (see Fig. 9). For this study, layers 10 lm in thickness were successively removed from the surface of the deposit by

mechanical polishing. After each polishing step, an X-ray diffraction scan was performed on the polished surface; the penetration depth of the X-rays was 10–15 lm. In addition to the change in composition and structure, grain size patterning permits customizable material properties, such as the nanoindentation hardness measurements also shown in Fig. 8. Six hardness profiles through the deposit thickness were obtained on each specimen by indenting along a line from the substrate to the surface, with the indents spaced 6 lm apart. Each data point is an average of several tests performed at the same relative position from the substrate. Such patterned structures may be ‘‘functionally graded’’, as in Fig. 8a, to impart superior surface characteristics and allow smooth property transitions to the bulk. Alternatively, laminate structures such as that shown in Fig. 8b may be useful for balancing two desirable properties individually optimal at different grain sizes. 6. Conclusions

Fig. 9. A serial X-ray diffraction (XRD) study conducted on the eightlayer specimen in Fig. 8a. The grain size calculated using the integral breadth method is shown along with the corresponding distance from the substrate. The star symbol (*) on the pattern closest to the substrate indicates the emergence of a copper diffraction peak as the X-rays penetrate the Ni–W specimen and begin to sample the substrate.

The control of grain size has posed a considerable barrier to the scientific understanding and practical exploitation of the enhanced properties of bulk nanocrystalline materials. By selecting an alloy with a weak tendency for grain boundary segregation and building on the strengths of existing synthesis methods for nanocrystalline solids, we have demonstrated significant potential for explicitly

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controlling and patterning grain size. Specifically, we have found that the Ni–W system exhibits a much broader range of accessible grain sizes over a similar range of solute content, as compared with other more strongly segregating systems like Ni–P. Our simulations and atom-probe experiments suggest that this may be a consequence of weak segregation tendency in the Ni–W system, and partial accommodation of solute in the crystalline lattice. Understanding the composition–structure relationship suggests a technique for explicit control of alloy nanostructure and properties. Here we have shown that incorporating a periodic reverse pulse in the applied current waveform allows for precise composition control during the electrodeposition of Ni–W alloys; this composition, in turn, dictates a stable nanocrystalline grain size. In principle, this technique may be applied to a number of different alloy systems to control composition, structure and properties. Such methods also allow for the synthesis of layered composites, functionally graded nanocrystalline materials, and other patterned nanocrystalline structures.

[28] [29] [30] [31]

Acknowledgements

[47] [48]

The US Army Research Office supported this work under contract DAAD19-03-1-0235; the sponsor does not endorse the views presented herein. The authors gratefully acknowledge the assistance of Mr. V. Brunini (MIT) with the graded and layered specimen preparation. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

Weertman JR, Farkas D, Hemker K, et al. MRS Bull 1999;24:44. Gleiter H. Acta Mater 2000;48:1. Lu L, Sui ML, Lu K. Science 2000;287:1463. Schiotz J, Jacobsen KW. Science 2003;301:1357. Kumar KS, Van Swygenhoven H, Suresh S. Acta Mater 2003;51:5743. Jiles DC. Acta Mater 2003;51:5907. Herzer G. J Magn Magn Mater 2005;294:99. Wang Y, Chen M, Zhou F, et al. Nature 2002;419:912. Chen M, Ma E, Hemker KJ, et al. Science 2003;300:1275. Gutkin MY, Ovid’ko IA, Pande CS. Philos Mag 2004;84:847. Mohamed FA, Li Y. Mater Sci Engng 2001;A298:1. Van Vliet KJ, Tsikata S, Suresh S. Appl Phys Lett 2003;83:1441. Cheng S, Spencer JA, Milligan WW. Acta Mater 2003;51:4505. Wang YM, Ma E. Mater Sci Engng 2004;A375–A377:46. Wang YM, Hamza AV, Ma E. Appl Phys Lett 2005;86:241917. Ma E. Scripta Mater 2003;49:663. Suryanarayana C, Koch CC. Hyper Int 2000;130:5. Schwaiger R, Moser B, Dao M, et al. Acta Mater 2003;51:5159. Lund AC, Nieh TG, Schuh CA. Phys Rev B 2004;69:12101. Lund AC, Schuh CA. Acta Mater 2005;53:3193. Koch CC. Rev Adv Mater Sci 2003;5:91. Valiev R. Nat Mater 2004;3:511. Koch CC, Youssef KM, Scattergood RO, et al. Adv Engng Mater 2005;7:787. Khan AS, Zhang HY, Takacs L. Int J Plasticity 2000;16:1459. Dalla Torre F, Spatig P, Schaublin R, et al. Acta Mater 2005;53:2337. Schuh CA, Nieh TG, Yamasaki T. Scripta Mater 2002;46:735. El-Sherik AM, Erb U, Palumbo G, et al. Scripta Metall Mater 1992;27:1185.

[32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]

[43] [44] [45] [46]

[49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61]

[62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78]

379

Masumura RA, Hazzledine PM, Pande CS. Acta Mater 1998;46:4527. Jang D, Atzmon M. J Appl Phys 2003;93:9282. Fan GJ, Choo H, Liaw PK, et al. Mater Sci Engng 2005;A409:243. Aus MJ, Szpunar B, El-Sherik AM, et al. Scripta Metall Mater 1992;27:1639. Beke DL. Mater Sci Forum 1996;225–227:701. Herzer G. IEEE Trans Magn 1990;26:1397. Makino A, Inoue A, Hatanai T, et al. Mater Sci Forum 1997;235– 238:723. Yamauchi K, Yoshizawa Y. Nanostruct Mater 1995;6:247. Weissmuller J. Nanostruct Mater 1993;3:261. Kirchheim R. Acta Mater 2002;50:413. Liu F, Kirchheim R. J Cryst Growth 2004;264:385. Beke DL, Cserhati C, Szabo IA. J Appl Phys 2004;95:4996. Cserhati C, Szabo IA, Beke DL. J Appl Phys 1998;83:3021. Krill CE, Ehrhardt H, Birringer R. Z Metallk 2005;96:1134. Krill CE, Ehrhardt H, Birringer R. In: Ma E et al., editors. Chemistry and physics of nanostructures and related non-equilibrium materials. Warrendale (PA): The Minerals, Metals, and Materials Society; 1997. Krill CE, Klein R, Janes S, et al. Mater Sci Forum 1995;179–181:443. Swaminarayan S, Srolovitz DJ. Acta Mater 1996;44:2067. Gupta D. Met Trans 1977;8A:1431. Gibbs JW. The collected works of J. Willard Gibbs. New Haven (CT): Yale University Press; 1928. p. 55. Liu F, Kirchheim R. Scripta Mater 2004;51:521. Weissmuller J, Krauss W, Haubold T, et al. Nanostruct Mater 1992;1:439. Farber B, Cadel E, Menand A, et al. Acta Mater 2000;48:789. Seah MP. J Phys F 1980;10:1043. Yamasaki T, Tomohira R, Ogino Y, et al. Plat Surf Finish 2000;87:148. Younes O, Gileadi E. J Electrochem Soc 2002;149:100. Atanassov N, Gencheva K, Bratoeva M. Plat Surf Finish 1997;84:67. Wu Y, Chang D, Kim D, et al. Surf Coat Tech 2003;173:259. Wu YY, Chang DY, Kwon SC, et al. Plat Surf Finish 2003;90:46. Younes O, Gileadi E. Electrochem Solid-State Lett 2000;3:543. Obradovic MD, Stevanovic RM, Despic AR. J Electroanal Chem 2003;552:185. Zhang Z, Zhou F, Lavernia EJ. Met Trans 2003;34A:1349. Oliver WC, Pharr GM. J Mater Res 1992;7:1564. Gabriel A, Lukas HL, Allibert CH, et al. Z Metallk 1985;76:589. Nagender Naidu SV, Sriramamurthy AM, Rama Rao P. Phase diagrams of binary tungsten alloys. Calcutta: Indian Institute of Metals; 1991. p. 170. Kong LT, Liu JB, Lal WS, et al. J Alloys Comp 2002;337:143. Cullity BD. Elements of X-ray diffraction. 2nd ed. Reading (MA): Addison-Wesley; 1978. p. 99. Hentschel T, Isheim D, Kirchheim R, et al. Acta Mater 2000;48:933. Miller MK. Atom probe tomography: analysis at the atomic level. Boston (MA): Kluwer Academic/Plenum Publishers; 2000. Miller MK, Cerezo A, Hetherington MG, et al. In: Brook RJ, editor. Atom probe field ion microscopy. Oxford: Clarendon Press; 1996. Miller MK, Smith GDW. Appl Surf Sci 1995;87–88:243. Seidman DN. Ann Rev Mater Sci 2002;32:235. Rittner JD, Udler D, Seidman DN, et al. Phys Rev Lett 1995;74:1115. Xie X, Mishin Y. Acta Mater 2002;50:4303. Detor AJ, Schuh CA. Phil Mag 2006;86:4459. Detor AJ, Schuh CA. US Patent Application No. 11/147,146; 2006. Nieh TG, Wadsworth J. Scripta Metall Mater 1991;25:955. Erb U. Nanostruct Mater 1995;6:533. Ebrahimi F, Bourne GR, Kelly MS, et al. Nanostruct Mater 1999;11:343. Hughes GD, Smith SD, Pande CS, et al. Scripta Metall 1986;20:93. Schuh CA, Nieh TG, Iwasaki H. Acta Mater 2003;51:431. Wang H, Yao S, Matsumura S. Surf Coat Tech 2002;157:166.