Hierarchical heterogeneity and an elastic microstructure observed in a metallic glass alloy

Accepted Manuscript Hierarchical Heterogeneity and an Elastic Microstructure Observed in a Metallic Glass Alloy

Peter Tsai, Kelly Kranjc, Katharine M. Flores PII:

S1359-6454(17)30642-0

DOI:

10.1016/j.actamat.2017.07.061

Reference:

AM 13960

To appear in:

Acta Materialia

Received Date:

27 March 2017

Revised Date:

30 June 2017

Accepted Date:

31 July 2017

Please cite this article as: Peter Tsai, Kelly Kranjc, Katharine M. Flores, Hierarchical Heterogeneity and an Elastic Microstructure Observed in a Metallic Glass Alloy, Acta Materialia (2017), doi: 10.1016/j.actamat.2017.07.061

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Hierarchical Heterogeneity and an Elastic Microstructure Observed in a Metallic Glass Alloy Peter Tsaia, Kelly Kranjca, and Katharine M. Floresa,b a. Washington University in St Louis, Institute of Materials Science & Engineering One Brookings Drive St Louis, MO 63130 b. Washington University in St Louis, Department of Mechanical Engineering & Materials Science One Brookings Drive Campus Box 1185 St Louis, MO 63130 Primary Author: Peter Tsaia Email address: [email protected] Corresponding Author: Katharine M. Floresa,b Email address: [email protected] Phone: (314) 935-3184

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Abstract Heterogeneities in a Zr-based bulk metallic glass (BMG) were investigated using dynamic modulus mapping on a nanoindentation platform, revealing a complex elastic microstructure consisting of interpenetrating locally stiff and compliant regions with characteristic feature lengths on the order of 100 nm. The unique microstructures were observed in as-cast, annealed and laser-processed materials. Surprisingly, at various mapping locations across the cast sample cross sections, the elastic microstructures displayed directional alignment of the features with the mold surface. The results introduce an unprecedented spatial regime of elastic variations in monolithic BMGs that may contribute towards a more complete understanding of structure-property relationships in these materials, especially with regards to global deformation behavior. Keywords: metallic glass; multiscale; microstructure; mechanical properties testing, heterogeneity. 1.0 Introduction Understanding structure-property relationships has long been at the heart of alloy development and design. For crystalline alloys, depending on the complexity of the overall microstructure, variations in structural features could span length scales across many orders of magnitude. Due to the periodic nature of atomic packing in even the most complex crystalline alloys, their underlying structures are readily characterized by conventional techniques such as electron microscopy and x-ray diffraction. In contrast to crystalline alloys, the atomic structure of monolithic metallic glass is amorphous, devoid of long range translational symmetry, although it is known that short and medium range ordering persist [1–3]. For this reason, metallic glasses appear deceptively homogeneous and isotropic when investigated with conventional characterization techniques, without the typical microstructural features that account for complexity and uniqueness in crystalline alloys. Despite the apparent microstructural similarity

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of metallic glasses, however, their deformation behavior can vary drastically with both alloy composition and processing conditions [4–6], implying the existence of a complex underlying structure that is not yet fully understood. On the atomic length scale, the structure of a monolithic metallic glass is by definition heterogeneous, possessing a statistical spread of different atomic cluster configurations, randomly orientated and distributed throughout its volume. Structural heterogeneities extending beyond the size of atomic clusters are less obvious, especially considering the high atomic packing efficiency of bulk amorphous alloys [7]. Recent experimental and molecular dynamics studies have reported nanoscale heterogeneous structure in metallic glasses [8–13]. The presence of such heterogeneities carries profound implications with respect to macroscopic mechanical behavior [14]. In simulated Cu-Zr binary glasses, Ma et al. demonstrated that elastically-soft regions densely populated with unstable cluster motifs are more susceptible to local shear transformations [12,13,15]. The authors proposed that increasing the population of soft spots in a glass would encourage profuse shear banding, resulting in higher fracture toughness and enhanced plastic behavior, both of which are rare among known bulk metallic glasses (BMGs). On the experimental front, using atomic force microscopy (AFM) techniques, nanoscale fluctuations of elastic modulus and energy dissipation have been measured in several amorphous alloys [8–11], but important details such as the characteristic size of the heterogeneous features, their morphology and spatial distribution, and their sensitivity to thermal processing history remain ambiguous. In this work, we apply dynamic modulus mapping (DMM) on a nanoindentation platform, to explore spatial fluctuations of mechanical properties in Zr58.5Cu15.6Ni12.8Al10.3Nb2.8, a BMG with centimeter-scale critical casting thickness [16]. The collected data reveal mechanical heterogeneities on a 100 nm length scale, the characteristics of which have never been reported before. We further explore the influence of laser-pulse melting and thermal annealing

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on the observed heterogeneous microstructures, and based on the results, discuss possible origins and the implications of their existence on macroscopic deformation behavior. 2.0 Experimental Methods The Zr58.5Cu15.6Ni12.8Al10.3Nb2.8 BMG specimens used for this study were prepared by arc melting pure elements with minimum purities of 99.9 at% in an argon atmosphere. The resulting ingot was flipped and remelted 3 times to ensure homogeneity prior to casting into a copper mold to produce two 3 mm diameter rod specimens. Two discs, each approximately 1 mm thick, were prepared from one of the rods and polished to a mirror finish with colloidal silica. Modulus maps, described below, were acquired from the polished surface of both discs in their as-cast state. One disc was then annealed at 370 °C (0.95Tg, where Tg is the glass transition temperature) in an inert atmosphere for 2 hours prior to repeating the mapping experiments. Following modulus mapping, TEM foils were prepared by conventional ion milling to confirm the amorphous structure of both the as-cast and annealed BMG samples. DMM was also performed on laser-pulse-melted samples prepared from the second rod specimen. Our group has previously shown that laser melting of metallic glasses results in an exceptionally smooth surface suitable for nanoindentation measurements without further polishing [17]. For these experiments, the rod was sectioned into 7 cylindrical segments, each 1.6 mm thick. The circular cross sections of the segments were ground with 600 grit SiC paper and sonicated in a methanol bath to remove surface contaminants. Each segment was then pulsed with a laser for a duration of 100 milliseconds at the central location of the polished and cleaned cross section. Laser power was increased from one sample to the next over the range 100 – 220 W in stepwise increments of 20 W. All laser-pulse processing was performed within the argon-filled glovebox of an Optomec MR-7 LENSTM, with an oxygen concentration maintained below 3 ppm. After confirming the exceptional smoothness of the laser-melted spots, DMM maps were collected directly from the center of each spot without further polishing.

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As with the bulk samples, TEM foils were prepared after mapping to confirm amorphous structure. Similar to AFM methods, DMM combines scanning probe microscopy with dynamic mechanical analysis to map the indentation modulus over a region of interest on a sample’s surface. In the present study, all maps were collected over 3 μm x 3 μm areas at various locations of interest. During mapping, a sinusoidal load function is applied such that contact is maintained between the nanoindenter tip (diamond Berkovich) and the BMG surface throughout the experiment. An appropriate load amplitude was chosen to achieve a tip displacement amplitude between 1-2 nm, resulting in good image contrast while ensuring all deformation remains elastic. A load frequency of 200 Hz was used for all mapping experiments conducted in this study. Accounting for the mass (mT) and stiffness (kT) of the force transducer, the indentation storage stiffness (k’) of the sample can be calculated from the following expression:

k' 

FD cos( )  mT   2  kT dD

where FD, dD, ϕ, and ω are the dynamic load, dynamic displacement, phase shift, and angular frequency, respectively. For the small dynamic displacements in DMM experiments, the Berkovich tip can be approximated as spherical with a radius of curvature r. The storage modulus (Er’) is then obtained from the stiffness values according to classical Hertzian contact theory:

(k ' )3 6 FD r

E  ' r

3.0 Results 3.1 As-cast and annealed samples

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Figure 1a-b shows 9 of the 3 μm x 3 μm storage modulus maps and their respective surface topography images collected from 13 locations on the circular cross section of one of the polished slices in the as-cast state. Despite having distinct topography, the roughness of the polished surface was minor, with root mean square (RMS) values of 1.5-2.0 nm, well within the acceptable range for DMM measurements. For ease of comparison between different mapping locations, the modulus values are represented as a normalized deviation from average rather than their absolute values. Spatial fluctuations of local elastic properties are clearly evident in each of the maps, forming an “elastic microstructure” with an interpenetrating network of locally stiffer and compliant regions. Dynamic modulus maps collected from the annealed sample used for studying the effects of thermal relaxation featured elastic microstructures very similar to those from the ascast state (Fig. 2a) and corresponding histograms of the modulus data displayed Gaussian-like profiles, with the statistical distribution of several locations near the edge suggesting a bi-modal or mixed character (Fig. 2b). Comparison of histograms before and after sub-Tg annealing revealed a consistent narrowing in the normalized statistical spread of Er’ as a result of the heat treatment. 3.2 Laser-pulsed samples Figure 3a shows a differential interference contrast (DIC) optical microscopy image of one of the laser-pulsed spots, treated with a 140 W laser. As expected for an amorphous alloy, the free surface of the melted material appears exceptionally smooth with no detectable asperities that would indicate crystalline features. Figure 3b are modulus maps collected from each laser-pulsed sample, each color-scaled to maximize visual contrast of the elastic heterogeneities. Similar to the modulus maps collected from the as-cast and annealed specimens, elastic microstructures are clearly evident at the center of each of the laser-melted spots. The Gaussian-like statistical spread of normalized Er’ values for the first five samples (100 – 180 W) 6

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are considerably narrower than those from the as-cast specimen, while the final two maps (200 and 220 W) displayed comparable spread (Fig. 4a). To compare the evolution of elastic microstructure and topography with increasing laser heat input, the RMS surface roughness as well as the statistical variation (2σ) of the data in each modulus map are shown in Figure 4b. The trend in both values exhibit an abrupt increase transitioning from the 180 W sample to the 200 W sample, but neither trend is perfectly correlated with the other; while the topography maps developed sequentially rougher surfaces with increasing heat input from the laser, the statistical spread in normalized Er’ reaches a local maximum at 140 W and again at 200 W. Also noteworthy is that despite the statistical variation in the modulus being of the same order, the unpolished laser melted samples were substantially smoother (0.4-1.4 nm RMS roughness) compared to the polished cross sections of the as-cast and annealed specimens. High resolution TEM confirmed that each of the laser-processed samples was amorphous, although some crystallinity confined to an isolated location was found in the 200 W sample but not in the following 220 W sample. Further study is necessary to ascertain whether the crystalline features are anomalous or reproducible under the same processing conditions. 4.0 Discussion 4.1 Characteristics of the elastic microstructure DMM provides the opportunity to investigate variations of the local storage modulus at a spatial resolution between instrumented nanoindentation, which requires a spacing of several microns between measurements, and the finer AFM mapping techniques used elsewhere [8– 11]. Because the average storage modulus varies from map to map, for comparison purposes, we focus solely on variations around the mean within each map. Heterogeneity is observed (Fig. 1a, 2a, and 3b), manifested as nanometer-scale fluctuations of the storage modulus which are clearly interconnected. Although a Gaussian or Gaussian-like distribution of elastic moduli in metallic glass is consistent with previous computational and experimental studies of nanometer-scale 7

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heterogeneities [10,18–20], random errors of measurement may also contribute to a Gaussian distribution. To evaluate the severity of random error contributions, DMM was performed on a polished single-crystal silicon wafer, grown in the <100> direction. The resulting modulus map and histogram are shown in Figure 5a-b. The modulus map from the silicon was much more uniform than the maps collected from the BMG, evidenced by the corresponding histogram showing a 2σ width of 5.3%, compared to a range of 10.6 – 32.5 % for the various as-cast, annealed, and laser processed BMG samples. In order to characterize the morphology of the structure in more detail, we applied an unsupervised machine-learning technique, K-means clustering [21], to unambiguously classify the pixels into three distinct categories: stiff, intermediate, and compliant regions. In addition to Er’, we identify the magnitude of the local gradient vector and local mean curvature as important descriptors of the elastic microstructures. For example, a pixel location in the map having a combination of high modulus, low gradient, and large negative mean curvature likely belongs to the stiff network (a peak on the map). Conversely, a locally compliant region would correspond to lower modulus, low gradient, and large positive mean curvature (a valley). Each pixel location in a modulus map is then described by a 3-d vector rather than a single value, and based on the distances between pixels in the 3-d description space, K-means identifies clustering structure in data space by automatically grouping similar pixels together. Figure 6a-c are tricolor representations of representative maps collected from the ascast, annealed, and laser-pulsed samples, with each color representing a group of pixels identified through K-means analysis. Figure 6d-f are the resulting deconvolved histograms of Er’, showing three overlapping sub-distributions corresponding to the pixels identified as stiff, intermediate, or compliant. Although the overall distribution of Er’ for all three maps resemble a single Gaussian, the clustering algorithm successfully delineated the stiff and compliant regions, lending convincing validation to the visual observations. Notably, the laser processed material has a much higher concentration of “intermediate” pixels than the as-cast and annealed. This 8

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reflects the greater uniformity of the more rapidly quenched material, although an interpenetrating network of stiff and compliant regions is still apparent. In contrast, the as-cast and annealed bulk samples are dominated by the more compliant background. In these maps, the intermediate and stiff pixels form a thinner and more defined network running through this background, with some isolated stiff pixels completely embedded in the compliant regions. Note that these isolated stiff pixels correspond to local maxima, not global; they are simply stiffer than the material in the immediate vicinity. Interestingly, the morphological arrangement of the elastic features in the cast and annealed samples were found to be dependent on mapping location. Specifically, the maps collected near the edge of the samples exhibited pronounced circumferential alignment of elongated features with the circular edge (Fig. 1a). To evaluate and compare the degree of alignment at each mapping location, we calculated the normalized autocorrelation function (Fcorr) for each modulus map. Mathematically, the autocorrelation function is defined as the following: Fcorr  x, y  

 E '  x ', y '  E '  x '  x, y '  y  dx ' dy ' r

r

In essence, Fcorr is the integrated sum of the product between a modulus map, Er’(x’,y’), and a shifted copy of itself, Er’(x’ + x, y’ + y). When the maps are perfectly overlapped, corresponding to Fcorr (0,0), the function produces a maximum value but decreases when the shifts are nonzero, reaching a minimum value at a condition when the two maps are completely out of phase with one another. In the case where the features in the maps are directionally aligned, the image representation of Fcorr accurately reflects the morphology of the microstructure, with contours elongated in the direction of the alignment. Since the actual maps are not continuous functions but 256 x 256 arrays of data, Fcorr takes the discretized form in our study: Fcorr  x, y  

 F  x ', y '  F  x '  x, y '  y  y'

x'

Figure 7 is a collection of normalized autocorrelation functions derived from the 13 modulus maps for the as cast material shown in Figure 1a, highlighting the significant 9

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directionality of the elastic fluctuations near the edge of the circular cross section. The strength of the alignment decreases away from the edge towards an approximately unbiased distribution of heterogeneities at the center of the cross section. Similar to other dynamic probing methods, surface roughness of the sample could adversely affect the accuracy of DMM measurements [9–11]. In our results, directional alignment of features is evident in both the storage modulus maps and accompanying surface topography maps of the as-cast and annealed specimens. (Note that directionally unbiased polishing was applied during sample preparation, which excludes the possibility of polishing causing the observed alignment.) For the maps shown in Figure 1, the average R-squared correlation of the modulus and corresponding topography (height) data sets is low, 0.28, indicating an insignificant correlation between the elastic fluctuations and the surface roughness. To further exclude the potential impact of the surface roughness on our DMM measurements, we compare characteristic feature lengths. A characteristic feature length (Lc) can be approximated from each storage modulus map by measuring the distance from the origin of the autocorrelation image to its nearest local minimum; the same analysis can be repeated for the corresponding topography maps and the two sets of feature lengths compared. For the modulus maps of the as-cast material in Figure 1, the average Lc is 132 nm with a 2σ value of 21 nm. Similar results were obtained for the annealed specimen. Analysis of the topography images revealed both a larger average Lc of 190 nm and statistical spread of 47 nm. As expected, the two sets of computed Lc values were essentially uncorrelated, with an Rsquared coefficient of only 0.07. 4.2 Effect of processing conditions on the elastic microstructure The effect of processing conditions on the elastic microstructure offers some insights into the possible origin of the observed heterogeneities. The sub-micron distribution of the storage moduli became consistently narrower with annealing treatment (Fig. 3b), indicating an 10

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overall increase in uniformity compared to the as-cast state. However, at several locations the mixed character of the statistical profiles became noticeably more defined with annealing, bifurcating into an enhanced primary peak accompanied by a pronounced shoulder. Comparing the 2σ widths of the deconvolved (compliant, intermediate, stiff) distributions before and after annealing treatment, the spread in Er’ of both stiff and compliant regions consistently narrowed across all mapping locations. On average, 2σ decreased 4.7 % and 3.4 % for the two categories, respectively. The separating distance between the two sub-distributions also decreased, but by a lower average value of 2.1%, resulting in the appearance of a more bifurcated structure. That is, the subsets of stiff and compliant regions each become more uniform (narrower distributions) with annealing, while themselves remaining distinct features. This resulted in the narrower, more strongly bifurcated distribution. The stability of the stiff and compliant sub-distributions with annealing suggest the possibility of chemical segregation as the primary cause of the ~130 nm length scale heterogeneous features, driven by differences in the pairwise mixing enthalpies among the atomic species. While it is unlikely that the annealing temperature was high enough to induce additional phase separation, the enhancement of the bifurcated profile would naturally arise from the preservation of preexisting chemically-segregated features on the scale of 100 nanometers, in conjunction with structural relaxation of atomic scale heterogeneity resulting in the independent narrowing of the two distributions. If the origin of the elastic fluctuations was purely topological or a byproduct of quenched-in residual stress [22], the annealing treatment would be expected to homogenize the distributions of Er’ towards a narrower single-Gaussian profile instead of preserving their bifurcated character [9]. Phase separation in monolithic BMGs has been reported previously, and in some cases, has been linked with improved toughness or ductility [23–27]. In known phase-separated alloys, the interface between chemically distinct regions can be either sharp or diffuse, depending on whether the separation in the undercooled liquid occurs by a nucleation and growth mechanism 11

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or by spinodal decomposition [28]. In our modulus maps, the variation in modulus is continuous, indicating spinodal decomposition to be the more probable separation mechanism. It should also be noted that contrast indicative of compositional fluctuations was absent in both conventional bright field and high resolution TEM images collected from the as-cast and annealed specimens. The absence of heterogeneous microstructure in the bright-field images, however, does not absolutely affirm chemical uniformity, as demonstrated in previous atom probe studies of phase-separated BMGs [29–31]. Further study is required to address this question. The rapid quenching attainable with laser surface treatment allows us to study elastic microstructures produced by cooling rates that exceed bulk casting cooling rates by several orders of magnitude. Using a built-in pyrometer housed within the MR-7 LENSTM, we have shown in earlier work that maximum cooling rates on the order of 104 K/s are achieved when processed in the range of laser heat inputs explored in the present work. We have further shown that cooling rates within the melt pool during laser melting scale inversely with heat input [17,32]. In the present work, the BMG samples are treated with a single laser pulse lasting 100 milliseconds, too brief a duration for the pyrometer to capture the temporal progression of the temperature profile. Although the details of heating and cooling history could not be quantified, the inverse relationship between laser power and cooling rate can still be applied in the present study to qualitatively establish the causal effect of quench rate on the elastic microstructure in the BMG. In general, metallic glasses synthesized with higher cooling rates are understood to be topologically less relaxed, possessing more quenched-in free volume, and are therefore structurally more heterogeneous at the atomic scale [14,33–35]. Fan et al. carried out molecular dynamics studies to investigate the effect of quench rate on the statistical distribution of the atomic-level shear modulus [18]; the simulated glass created with a lower quench rate resulted in a narrower, or more homogeneous, distribution of local shear moduli. Similarly, Liu et al. reported reduced spatial variability in the viscoelastic properties of a thin-film metallic glass 12

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when annealed to a more relaxed state [9]. This is also consistent with the narrowing of the stiff and compliant contributions to our DMM measurements for the annealed material relative to the as-cast, as discussed above. In contrast, the rapidly quenched laser-pulsed specimens also exhibit a narrower Er’ distributions than the as-cast materials. Furthermore, the expected evolution towards a more topologically heterogeneous material when processed with progressively lower laser power, corresponding to higher quench rates, is not observed. On the contrary, the mapping data shows that the magnitude of elastic heterogeneity, quantified here as 2σ, generally increases with laser power (lower quench rate, Fig. 4b). The widths of the deconvolved compliant and stiff contributions to the Er’ distributions, as well as the separation between the deconvolved distributions, follow a similar trend (not shown). These observations provide further evidence that chemical segregation, rather than topological heterogeneities from quenched-in free volume, are the primary source of the observed fluctuations in Er’. Slower cooling would permit more time for chemical segregation, and more specifically spinodal decomposition, to create compositional heterogeneities in the undercooled liquid, resulting in a wider Er’ distribution and, in particular, larger separation between the stiff and compliant contributions. While the slower quench would also expectedly produce topologically relaxed atomic-level structures (narrowing the distributions), the small changes to the atomic structure on the short time frame of the laserpulsed processing are likely below the resolution of the DMM technique. To evaluate the morphological evolution of the elastic microstructures with cooling rate, Lc values are computed from the autocorrelation functions associated with each laser-pulsed modulus map. The average Lc was 150 nm, similar to the coarseness of the elastic microstructures seen in the as-cast and annealed samples. Furthermore, no obvious correlation or scaling is found between the applied heat input and Lc. On the basis of Cahn and Hilliard’s theoretical treatment of spinodal decomposition [36–39], coarsening of the phase-separated features transpires over time but mainly during the latter stages of the process; prior to 13

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significant coarsening, the evolution of spinodal microstructures involves mainly spontaneous amplification of the compositional fluctuations. It is conceivable that the temporal regime over which the decomposition transpired in the laser-pulsed spots was confined to the earlier stages of development due to rapid quenching of the melt pool; further investigation is necessary to determine whether significant coarsening is possible, either by further increasing laser heat input or performing isothermal annealing above Tg for an extended period of time. In view of the discussion on spinodal decomposition, it is worthwhile to consider the reason phase separation would be present in the Zr-based alloy explored in this work. Most reported cases of phase separation in BMGs involve the pairwise enthalpy of mixing (ΔHmix) being positive for at least one of the elemental pairs, resulting in a pronounced liquid miscibility gap at undercooled temperatures. For the vast majority of known BMG alloys, including the alloy in the present study, ΔHmix between the major components tends to be strongly negative, seemingly ruling out the possibility of spinodal decomposition. While a positive ΔHmix may be required for a liquid miscibility gap to appear in binary alloys, for multicomponent alloys, the enthalpic preference of one atomic species to be surrounded by another is not equally shared among all elemental pairs; for example, in an A-B-C ternary system, ΔHmix between A and B atoms may be more negative than between A and C atoms. At high temperatures, where there is an entropic advantage to have a homogeneous liquid, phase separation is unlikely. But at the deep undercoolings experienced during synthesis by many multicomponent BMGs, the Gibb’s free energy of the liquid is governed by configurational enthalpy rather than entropy, and the emergence of a non-equilibrium miscibility gap is plausible [31,40]. Our discovery of similar “elastic microstructures” in several other well-known Zr-based BMGs (to be discussed elsewhere) that do not possess substantially positive ΔHmix among any of the elemental pairs suggests that spinodal decomposition may be more common in multicomponent BMGs than previously recognized.

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For the as-cast and annealed materials, there is a strong alignment of the elastic microstructure with the edge of the cylindrical rod cross sections. The normalized autocorrelation functions derived from the 13 modulus maps of the as-cast sample (Fig. 7) confirm significant directional arrangement of the elastic fluctuations near the edge of the circular cross section, with the heterogeneous features aligned in the circumferential direction. The strength of the alignment decreases away from the edge towards an approximately isotropic distribution of heterogeneities at the center of the cross section. The predominance of the circumferential alignment near the outer surface of the specimens is reminiscent of surfacedirected spinodal decomposition [41–43], which has been theoretically modeled and extensively observed to occur in polymeric mixtures, but has never been reported for metallic glass systems. The elastic heterogeneities could potentially be organized near the edge to minimize the surface or interfacial energy associated with the mold material, creating a periodic layering of the stiff and compliant features. It should be noted that in reported cases of the phenomenon involving polymer mixtures, the periodic layering effect does not extend beyond several wavelengths from the surface. In contrast, the effect is weakly present even at 100 μm from the edge of the BMG samples, equivalent to upwards of several thousand compositional wavelengths. Although surprising, this apparent discrepancy is not implausible when considering that the entropic resistance to ordering is greater in polymers than for metals, where spatial rearrangement of the atomic species is not impeded by the complexity of long chain molecules. Furthermore, although circumferential alignment was present along the entire circular edge of the sample cross section, some locations exhibited a much stronger alignment of the elastic features, which may be the result of an uneven cooling history caused by convection during the casting process. 4.3 Implications of the elastic microstructure An important difference between the heterogeneous structures we report in the present work and those from previous studies is in the general length scale of the observed fluctuations. 15

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The characteristic length scale of the elastic microstructure, on the order of 130-150 nm, is as much as two orders of magnitude larger than structural heterogeneities discussed in other studies. Johnson and Samwer’s theoretical model based on cooperative shearing estimated a universal diameter of shear transformation zones to be approximately 15 angstroms [44,45]. Similarly, molecular dynamics studies of binary Cu-Zr glasses have reported soft spots with dimensions of a few nanometers [12,13]. Various dynamic AFM studies also reported spatial heterogeneities of internal friction and viscoelastic phase shift with characteristic lengths of a few nanometers [8,9,11]. The elastic microstructure observed in the present work may represent a networked structure of these nanometer-scale heterogeneities. Beyond the scale of interconnected heterogeneities reported in the present work, Tönnies et al. has recently reported continuous spatial variations of indentation modulus on the order of 100 μm in a Pd-SiCu BMG [46]. The diversity of characteristic feature sizes investigated through different methods suggests a hierarchical description of heterogeneity in metallic glass alloys that may span several orders of magnitude in length. A hierarchical description of microstructure would expand the role of heterogeneities beyond merely supplying fertile sites for initiating plastic flow at the atomic level, to potentially controlling the pathway and stability of propagating shear bands. Bharathula and Flores [47] argued that the scatter in the yield strength of microcompression pillars of the Zr58.5Cu15.6Ni12.8Al10.3Nb2.8 could be explained by a distribution of defects ranging 90-190 nm, in excellent agreement with the feature sizes observed here for the same alloy. Work by Jiang and Greer noted that a critical specimen diameter of ~100 nm was required to successfully nucleate a shear band in a similar Zr-based glass [48]; the present work suggests that the elastic modulus is more homogeneous below this length scale. These prior observations raise the possibility that the elastic microstructure may control shear band nucleation and propagation. The current work also indicates that the elastic microstructure is sensitive to processing conditions, particularly the interaction with the mold surface and the 16

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cooling rate of the liquid. Thus, the elastic microstructure is a potentially tunable feature that could be used to optimize the properties of the glass, as well as explain the wide statistical scattering in the measured fracture toughness of monolithic BMGs [49–54]. Further investigation is required to determine if significant coarsening or refinement of the elastic microstructure is possible, and if so, what impact this has on shear banding and subsequent fracture.

5.0 Conclusions In summary, using dynamic modulus mapping, we revealed elastic heterogeneities permeating a Zr-based BMG at the sub-micron length scale. An “elastic microstructure” consisting of interpenetrating stiff and compliant regions is observed. The elastic microstructure near the edge of as-cast and annealed cross sections displayed prominent directional alignment of the features, a result that was both unexpected and remarkable for monolithic glasses. The ~130-150 nm length scale of the elastic microstructure was in excellent agreement with critical length scales for shear band nucleation and propagation, suggesting that the modulus fluctuations may play a vital role in controlling the plastic deformation of metallic glasses. Isothermal annealing treatment at a temperature below the glass transition reduced the overall degree of heterogeneity in the alloy but also enhanced the distinctness of the features. On the other hand, modulus maps collected from rapidly quenched laser-pulsed samples revealed a general inverse relationship between cooling rate and the degree of elastic inhomogeneity. Based on these observations, we suggest that the elastic microstructure results from chemical segregation, potentially associated with spinodal decomposition. The collective results from this work describes a newly discovered spatial regime of interconnected heterogeneities in multicomponent BMGs, and outlines an experimental approach for studying their complex microstructure, ultimately with a view towards the improvement of their reliability for structural applications. 17

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6.0 Acknowledgements PT and KMF gratefully acknowledge support from the Saigh Mechanical Engineering Fund at Washington University in St. Louis. KK and KMF acknowledge support from the Air Force Office of Scientific Research through award number FA9550-12-1-0059. All electron microscopy was conducted within the facilities of the Institute of Materials Science and Engineering at Washington University. 7.0 References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]

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Figure 1 Elastic heterogeneities observed by dynamic modulus mapping. (a) Selected 3 μm x 3 μm storage modulus (Er’) maps for the BMG in the as-cast condition, collected from various locations (lower right insets) around the cross section of the cylindrical specimen. (b) Corresponding surface topography maps.

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Figure 2 The effect(s) of annealing treatment on the statistical and spatial distribution of elastic heterogeneity. (a) Two sets of storage modulus maps obtained from the same specimen before (left) and after (right) isothermal annealing treatment for 2 hours at 370 °C. Maps were collected from approximately the same locations pre- and post-annealing. (b) Corresponding histograms demonstrating the consistent narrowing of the statistical spread of Er’ values due to thermal annealing.

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Figure 3 Modulus maps collected from laser-pulsed BMG samples. (a) DIC optical microscopy image of the melted spot produced by a 140 W laser, demonstrating the exceptional smoothness of the free surface. (b) Modulus map images color-scaled for maximum visual contrast of the features in each map.

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Figure 4 Effect of laser power on modulus variations and surface roughness in laser pulsed samples. (a) Histograms of the Er’ data; the statistical spread of the 200 W and 220 W samples are comparable to the bulk samples while samples processed with lower laser power are substantially less heterogeneous. (b) The evolution of statistical variation (2σ) and surface roughness with increasing laser heat input. For comparison, the arrows indicate average values for the as-cast sample in Figure 1. 4

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Figure 5 Absence of spatial heterogeneities in a structurally homogeneous material. (a) 3 μm x 3 μm storage modulus map collected from the surface of a singlecrystal silicon wafer grown in the <100> direction and (b) corresponding histogram.

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Figure 6 K-means clustering analysis for characterization of elastic microstructure. (a-c) Example tricolor representations of the modulus maps with the pixels grouped according to the modulus category (blue = compliant, green = intermediate, and yellow = stiff). Image (a) is from the central location of an as-cast sample, (b) is from the central location of the sample post-annealing, and (c) represents the map obtained from the sample pulsed with a 180 W laser. (d-f) Corresponding deconvolved histograms, showing the overlapping distribution of Er’ for the three categories of features.

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Figure 7 Normalized auto-correlation functions derived from the collection of modulus maps in the as cast state (Figure 1). The image representations highlight the circumferential alignment of the elastic features and variation of the alignment with radial position.

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