Polyamorphism mediated by nanoscale incipient concentration wave uncovering hidden amorphous intermediate state with ultrahigh modulus in nanostructured metallic glass

Comprehending the pressure-/temperature-induced structural transition in glasses, as one of the most fascinating issues in material science, is far from being well understood. Here, we report novel polyamorphic transitions in a Cu-based metallic glass (MG) with apparent nanoscale structural heterogeneity relating to proper Y addition. The low-density MG compresses continuously with increasing pressure, and then a compression plateau appears after ∼8.1 GPa, evolving into an intermediate state with an ultrahigh bulk modulus of ∼467 GPa. It then transforms to a high-density MG with significantly decreased structural heterogeneity above ∼14.1 GPa. Three-dimensional atom probe tomography reveals concentration waves of Cu/Zr elements with an average wavelength of ∼5–6 nm, which promote the formation of interconnected ringlike networks composed of Cu-rich and Zr-rich dual-glass domains at nanometer scale. Our experimental and simulation results indicate that steplike polyamorphism may stem from synergic effects of the abnormal compression of the Zr–Zr bond length at the atomic scale and the interplay between the applied pressure and incipient concentration waves (Cu and Zr) at several nanometer scales. The present work provides new insights into polyamorphism in glasses and contributes to the development of high-performance amorphous materials by high-pressure nanostructure engineering.

Here, we report novel steplike polyamorphic transitions in the Cu 46 Zr 42 Al 7 Y 5 MG with nanoscale concentration fluctuations. With increasing pressure, the low-density MG transforms to a high-density MG through nearly constant-volume reorganizations of local structures in the intermediate-density state, which is strikingly different from the electronic polyamorphism in other MGs showing obvious volume reduction during GTG transition due to electronic-configuration variation. Importantly, the new intermediate-density state shows an ultrahigh bulk modulus of ∼467 GPa. Theoretical simulations reveal significant changes in the pair correlation functions in the first three coordination shells upon compression. At larger length scales, by utilizing aberration-corrected high-resolution transmission electron microscopy (HRTEM), atomic-resolution Z-contrast scanning transmission electron microscopy (STEM), and three-dimensional atom probe (3DAP) tomography, pronounced nanoscale heterogeneity and chemical fluctuations with a wavelength (∼5-6 nm) of incipient concentration waves have been observed. We propose a reorganization scheme of the local ring network, as the structural response motif to pressure, composed of several interconnected Cu-rich and Zr-rich domains at the nanoscale embracing a centered domain, to decipher the novel compression behavior of the current Cu-based MG. The ultrahigh bulk modulus of the intermediate MG state may be associated with supra-nanometer dual-glass structures with different compressibilities and the steplike compression of the Zr-Zr bond length. (Supra-nanometer means that the size of each glass droplet is less than 10 nm, and thus 'supra-nanometer dual glass' is used to distinguish it from the conventional phase-separating MGs). The current findings offer a new perspective on polyamorphism in nanostructured glasses and are of importance for designing advanced MGs by modulating the concentration fluctuations at the nanoscale.
Cu 46 Zr 42 Al 7 Y 5 MG was chosen as the main system of the present study because of its enhanced nanoscale heterogeneity due to Y addition (Y-Zr pair has positive enthalpy mixing) and relative 'simplicity' in terms of not having 4f electrons, nonmetal, or any other special elements with distinct change of electronic structure under pressure. The as-quenched ribbon shows typical amorphous features (figures S1 and S2). However, an abnormal exothermic reaction in the differential scanning calorimetry trace between the glass transition and crystallization events (figure S1) is observed (similar to that of the Pd-Ni-P MG), which indicates a unique local structure of the present alloy showing a possible polyamorphous phase transition in the supercooled liquid [27]. In situ synchrotron x-ray diffraction (XRD) patterns during compression and decompression processes for the Cu 46 Zr 42 Al 7 Y 5 MG are shown in figures 1(a) and S3, respectively. The alloy remains in its vitrified state up to 23.0 GPa. The first sharp diffraction peak (FSDP) moves toward larger Q with increasing pressure arising from the compression effect. The FSDP position, Q 1 , can be determined accurately by a Voigt line profile fitting, and its evolution with pressure is shown in figure 1(b). The changes of Q 1 with pressure of several other MGs are also included for comparison, including a Ti-based MG without polyamorphism [38] and a Ce-based MG showing typical polyamorphism [32], a newly investigated Zr 50.7 Cu 28 Ni 9 Al 12.3 MG ( figure S4). With increasing pressure, the Zr-, Ti-, and Ce-based MGs show a continuous increase of Q 1 with decreasing compressibility regardless of whether this MG shows a polyamorphic

Future perspectives
The unique structure of metallic glasses (MGs) with pronounced topological/chemical short-to-medium-range order but no longrange structural order underlies their interesting and excellent properties, which render them attractive for both scientific research and various applications. However, the structure of MGs has been a long-standing mystery, leading to poor understanding of glass formation, deformation, relaxation dynamics, and structure-property relationships. In this work, the observation of a novel steplike polyamorphic transition in an MG with concentration fluctuations is an important contribution toward our fundamental understanding of the heterogeneous structure of MGs under compression. Modulating the chemical/topological heterogeneity at the nanoscale in the future may lead to novel MGs with superb performances and therefore would promote further commercial developments (such as in extreme yet technologically important conditions). A major challenge will be understanding the differences in electronic and structural configurations (at different length scales) that distinguish the different amorphous states of a given MG with polyamorphism. The relationships among glass formation, glass transition, polyamorphism in the glass, and liquid-to-liquid transition in the glass-forming liquid are unresolved issues that offer great opportunities for future study.
transition or not, just as observed in many other MGs [32][33][34][35][36][37][38][39][40]. In contrast, the as-quenched Cu 46 Zr 42 Al 7 Y 5 MG shows a novel compression behavior, that is, it first undergoes normal compression up to around 8.1 GPa, and then it transforms to an intermediate MG state that is hard to compress. When the pressure is further increased to around 14.1 GPa, the alloy evolves further into a high-density state. Moreover, hysteresis between decompression and compression is observed as a typical feature of polyamorphic transition [21]. The lower right inset of figure 1(b) shows the pressure dependence of Q 1 for another piece of sample, indicating the repeatability of the steplike polyamorphic transitions.
It has been recognized that the FSDP embodies the statistical information of the MRO and average interatomic spacing of a glass [1,27]. The cubic power law, i.e. (Q 1 /Q 10 ) 3 ∝ V 0 /V 1 based on the Ehrenfest relation, has been widely used to characterize the density/volume change of MGs [47], where Q 10 and V 0 are the FSDP position and volume at the initial condition, respectively. (Q 1 and V 1 are values at a given pressure.) Recently, the cluster packing of MGs was found to follow the self-similar rule on a fractal network with a dimension of 2.31, and later a dimensionality crossover at an intermediate length scale was suggested [5]. In particular, from the high pressure investigations of Ce-, La-, Cu-, and Ti-based MGs, it has been found that the density of an MG follows a 5/2 power of the FSDP position [38,48,49]. Here, we use both the cubic (3) and fractional noncubic (5/2) laws to estimate the relative volume change. As shown in figure 2(a), the volume of the present Cu-based MG shows an abnormal steplike compression behavior with increasing pressure. In most MGs, the compressibility decreases gradually with increasing pressure, as shown in the inset of figure 2(a) for the Ce-based MG as an example. While in some rare earth-based MGs and a Pdbased MG showing a polyamorphic transition, the compressibility may show a slight increase with pressure after a certain pressure around 1.5-3.0 GPa [42,50]. This could be associated with f-electron delocalization-induced bond shortening in the former case and change of covalent-like bonds into metallic bonds in the latter. In the present sample, we also found that the compressibility between 2 and 7 GPa is larger than that between 0 and 2 GPa [42,50]. The key points we stress here are the steplike behavior and the intermediate glassy state with the smallest compressibility in a wide pressure range of ∼4 GPa. To illustrate this, we depict the bulk modulus, derived from K = −V(dP/dV), as a function of pressure for the Cu-and Cebased MGs in figure 2(b). Linear fitting of every five adjacent data was used to obtain the slope (dP/dV) of the center point.
The Ce-based MG shows a continuous increase in bulk modulus with increasing pressure with three distinct change rates, which is according to the hierarchical densification behavior [32]. In contrast, the Cu 46 Zr 42 Al 7 Y 5 MG shows an abnormal sharp peak between 8.1 and 14.1 GPa, which is consistent with the trend revealed in figure 1(b). In the intermediate state, the bulk modulus can reach up to 467 GPa (using the 5/2 power law), which is much larger than those of typical MGs in the as-quenched state (the marked green pillar in figure 2(b)) [2,25].
To further verify the abnormal polyamorphic transitions, an in situ electrical resistivity measurement under different pressures was carried out. Figure 3 displays a change of relative resistivity with pressure, where R p and R 0 are the resistivity under high pressure P and ambient pressure, respectively. The resistivity decreases with increasing pressure in the whole investigated pressure range, that is, a negative pressure coefficient of resistivity is obtained. Similar to the volume evolution, the relative resistivity also shows a steplike behavior, and the intermediate MG has the smallest absolute negative pressure coefficient. Since the present Cu-based MG contains no magnetic elements and the experiments were carried out at room temperature, there is no contribution from the effects of Kondo-type s-d exchange scattering, f delocalization, and two-level configurational tunneling. The electrical resistivity mainly arises from disordered atomic scattering described by the structure factor in the framework of the generalized Ziman theory [51] and is thus sensitive to the local structures. Note that the transition pressures of electrical resistivity are similar to those of the FSDP in the XRD patterns. Thus, the abnormal variation of resistivity mainly originates from the complicated three-stage transitions of the local structures of the Cu-based MG. However, at present, the pressure dependence of resistivity of the MG is impossible to illustrate precisely from the detailed change of electronic configuration due to the delicate influence of the Fermi energy E F , the electron-ion interaction, and structure factor.
To determine the coordinated role of short-range order and MRO on the polyamorphic transition, a combination of ab initio molecular dynamics (AIMD) simulations, HRTEM, and 3DAP experiments was performed. Since the AIMD simulations use a box size of ∼1.7 nm, the structures at mediumrange length scales up to ∼2 nm and above cannot be well determined (e.g. from the peak position Q 1 of the static structure factor S(Q)). Thus, we focus on the structural changes on short-range scales. Typical atomic configurations from the simulation and the change of potential energy with the atomic volume upon compression are shown in figure S5. Figures 4(a)-(d) show the total and partial pair correlation functions at different pressures. It is observed that the pair correlation functions in the first three coordination shells undergo significant changes upon compression. (The bond angle distribution functions show a slight change, as indicated in figure S6.) In particular, in the first coordination shell, while the peak height in the average pair correlation function g(r) gets enhanced upon compression, the peak height in Zr-Zr partial pair correlation function g Zr-Zr (r) gets suppressed (figures 4(a) and (b)). Importantly, there seems to be a shoulder ahead of the first peak in Zr-Zr partial pair correlation function g Zr-Zr (r) ( figure 4(b)). These results indicate that the structural changes around Zr and Cu elements upon compression are very different. In addition, it is found that the first peak position r 1 of g Zr-Zr (r) in the AIMD simulations shows a steplike evolution with the lowest compressibility in the intermediate state (the inset of figure 4(b)), similar to the FSDP of the XRD patterns. Figure 4(e) shows the change of coordination numbers (CNs) of each element at different pressures. Obviously, the CNs of Al and Cu atoms are smaller than the average CN, whereas the CNs of Zr and Y are larger than the average CN. Upon compression, the average CN stays almost unchanged, while the CNs of Al and Cu atoms increase subtly, and the CNs of Zr and Y atoms decrease. It seems that the CNs of all elements tend to the average CN with increasing pressure. We then calculated the CSROs as where N α is the CN of α element, N αβ is the partial CN describing the number of β atoms around α element, and x β is the content of β element. While a negative (positive) value of C αβ means that there are more (less) β atoms around α element than expected, a zero value means there is no chemical segregation within the first coordination shell. As shown in figure 4(f), C Cu-Zr is negative, and C Cu-Cu is positive, suggesting that Cu atoms prefer to bond with Zr atoms. Whereas C Zr-Zr is negative, C Zr-Cu is positive, indicating that Zr atoms also prefer to bond with Zr atoms. The negative value of C Zr-Zr implies that possible Zr segregation may occur in this alloy. Importantly, both C Cu-Zr and C Zr-Zr shift slightly toward zero with increasing pressure. This suggests that pressure may help to suppress chemical ordering at short-range scales, promoting uniform mixing and eliminating chemical segregation. We then turn to MRO structures with length scales above 1 nm to further understand the steplike polyamorphic transitions. First, a careful analysis of the HRTEM images was performed to see whether there is contribution from some very fine nanocrystalline clusters or phase separation. Two HRTEM images (one of them is shown in figure S2) were divided into 17 × 17 cells with a size of 1.995 nm × 1.995 nm, and then the image in each cell was transformed into a 2D autocorrelation map to check the local order (figures 5(a) and S7). From the 2D autocorrelation map, a few cells with crystal-like order can be observed (figures 5(b) and (c)), which are marked by red squares in figure 5(a). Figure 5(d) is a typical cell with a totally disordered structure, and its fast Fourier transformation (FFT) pattern is shown in figure 5(e). The area fraction of the crystal-like order regions can be estimated to be ∼2% in the sample. The fraction of the crystal-like regions is lower than that of a Cu 46 Zr 45 Al 7 Y 2 glassy rod of 3 mm diameter [52] due to the better glass-forming ability of the present MG and the larger cooling rate used here to fabricate the ribbon. Therefore, abnormal polyamorphic transitions do not derive from some fine nanocrystalline phases or some special clusters with crystal-like order identified by the presented method. Next, we check whether there exist nanoscale chemical or density fluctuations in the present MG, which are not easy to detect by HRTEM. The aberration-corrected high-angle annular dark field (HAADF)-STEM technique with Z-contrast was thus performed, which shows a strong contrast correlated with the atomic number Z of the detecting area. The atomicresolution HAADF-STEM images in figures 6(a)-(d) show clearly heterogeneous contrast with dark (soft) and bright (hard) domains at the nanometer scale, indicating an inhomogeneous distribution of density and/or chemistry in the present MG. It has been generally accepted that an MG is structurally heterogeneous, which has been revealed from the distribution of modulus, density, and local symmetry [53][54][55]. By combining angstrom-beam electron diffraction with simulation, the dark and bright domains observed in the HAADF-STEM images of a Zr-Cu-Al MG were revealed to arise from the clusters with crystal-like order and icosahedron-like order, respectively [54]. Thus, it is possible that the soft and hard domains in the HAADF-STEM images in figures 6(a)-(d) have different density and local symmetries.
The structural heterogeneity was further investigated using the 3DAP experiment. Figure 7 presents the elemental maps of the as-quenched Cu-based MG (a slightly crystallized sample was also investigated for comparison, as indicated in figure  S8), from which no second nanocrystalline phase precipitated or an apparent phase separation can be detected within the detected resolution of 3DAP. Nevertheless, an obvious structural inhomogeneity is observed from the 1D concentration depth profiles of the Cu, Zr, Al, and Y elements obtained from the selected volume (5 × 5 × 120 nm 3 ) marked in the map of all elements in figure 7(a). From figure 7(b), region A has lower average Cu concentration and larger average Zr concentration than region B. Moreover, each peak of the Cu profile curve corresponds well to a valley of the Zr profile curve, as seen from the examples marked by magenta arrows in figure 7(b). This clearly indicates the well-correlated periodic fluctuations of the Zr/Cu element distribution in the Cu 46 Zr 42 Al 7 Y 5 MG. The average wavelength of incipient concentration waves can be determined to be ∼5-6 nm for Zr and Cu. This directly results in density fluctuations with Cu-rich (Zr-poor) and Cu-poor (Zr-rich) domains at several nanometers scale. In contrast, Al and Y show random fluctuations, having no apparent correlation with other elements. Thus, the dark and bright domains observed in the HAADF-STEM may be mainly determined by the composition fluctuations of Cu and Zr. However, the contributions from variations of density and cluster symmetry cannot be ruled out. Besides, figures 7(c) and (d) show the statistical binomial frequency distribution analysis of the experimental results, indicating a relatively good match between the fitting binomial curves and It has been generally accepted that solute-centered clusters can serve as the building blocks for MGs, which construct different types of of MRO by different packing schemes of clusters [3][4][5][6]. Especially in the Cu-Zr systems, simulations reveal that a significant fraction of icosahedral clusters exists and tends to form an interpenetrating stringlike backbone network, and the non-interpenetrating connections further promote the connectivity of icosahedral networks, affecting significantly the dynamic heterogeneity and glass formation [56][57][58]. Note that 53% of the atoms were reported from simulation to be involved in icosahedral clusters in the Cu 64 Zr 36 MG [57]; thus, it is possible that a similarly high fraction of atoms participates in the icosahedral-like clusters in the Cu 46 Zr 42 Al 7 Y 5 MG [57], forming stringlike or ringlike networks of these clusters [56,57]. Accordingly, we will mainly illustrate the steplike polyamorphic transitions from the unique network connections among clusters, which correlate well with the Y addition. First, the Y addition enhances the fraction of the clusters with icosahedral-like symmetry because these clusters are mechanically more stable, easier to aggregate forming backbone, and more long-lived than others [56]. These arguments are supported by the experimental observations of the reduced liquid temperature from 1163 K in Cu 46 Zr 47 Al 7 to 1113 K in Cu 46 Zr 42 Al 7 Y 5 and the improved glass-forming ability significantly after 5 at.% Y addition [59]. Second, the Y atoms may increase the local chemical heterogeneity considerably because the Y-Zr pair has positive enthalpy mixing (+35 kJ mol −1 ), which is strikingly different from other pairs having large negative enthalpy of mixing: Zr-Cu (−142 kJ mol −1 ), Cu-Y (−148 kJ mol −1 ), Zr-Al (−169 kJ mol −1 ), and Y-Al (−181 kJ mol −1 ). This results in distinct density and chemical fluctuations on the subnanometer/nanometer scale, as observed experimentally (figures 6 and 7). We argue that chemical heterogeneity, including Curich and Zr-rich dual-glass nanoscale domains, is crucial for the steplike polyamorphism, and that this novel polyamorphism is not observed in the Zr-, Ti-, and Ce-based MGs (having conventional local structural heterogeneity) due to the absence of such kind of chemical heterogeneity.
A cluster-construction model of the present alloy is thus proposed as follows. Many of the Zr-rich clusters (forming the solid-like domain) may have icosahedral-like symmetry and higher density, connecting to form the backbone network [56,57]. These regions (Cu-rich clusters) with lower density form liquid-like structures surrounding the backbone network. Importantly, the Zr-rich domains and the Cu-rich domains (several nanometers in size) are bridged with each other and form an interconnected network. This unique network structure is consistent with the experimental observations in figures 6(a)-(d) and 7(b). To illustrate the unordinary polyamorphic transition, we focus on the reorganization of a local ring network under compression, as illustrated schematically in figure 7(e). Each ring is composed of a central Zrrich domain and several (m on average in the as-quenched state) neighboring Zr-rich domains (with typical size as that of the bright domains in figures 6(a)-(d)), which are connected mainly through the Cu-rich domains. This kind of local ring acts as the structural unit on the MRO length scale responding to the external pressure. Under initial compression, these local rings collapse mainly through densification of the liquid-like (Cu-rich) domains (step 1 in figure 7(e)). Under compression, more and more liquid-like domains transform into solid-like domains. Below 8.1 GPa, the local cluster network transforms into a new configuration with an increased average number (m + 1) of the solid-like domains in the local ring. Further compression (8.1-14.1 GPa) mainly distorts the domains and rearranges their connections while keeping the density slightly changed due to the hard compression of the Zr-Zr bond length (the inset of figure 4(b)). Above ∼14.1 GPa, the MG evolves into a high-density state with the lowest degree of chemical fluctuation (in accord with the simulation), the compression of which is dominated mainly by the solid-like domains (step 3 in figure 7(e)) and takes place more homogeneously than that below 14.1 GPa.
Therefore, the compression plateau is associated with the distortion of and interplay between the Cu-rich and Zr-rich domains in the intermediate state with an increased average number (m + 1) of solid-like domains in each local ring (step 2 in figure 7(e)). This transformation behavior is like the compression plateau of the network glass GeO 2 [60,61]. It was found that the plateau of the FSDP position between 22.6 and 37.9 GPa was related to the formation and stability of sixfold-coordinated structural motifs [62]. The pressure independence of the FSDF between 72.5 and 91.7 GPa arose from the gradual transformation of the sixfold-coordinated structural motifs into stable motifs with higher Ge-O CN [63]. The similar compression behavior between the Cu 46 Zr 42 Al 7 Y 5 MG and GeO 2 implies that they may have some common connection features of their structural motifs. In addition, the different compression behaviors between Cu 46 Zr 42 Al 7 Y 5 and many other MGs indicate the significant impact of the details of structural heterogeneity on the evolution of atomic configuration under compression 50]. Finally, we argue that the ultrahigh bulk modulus (directly related to the compression plateau under high pressure) in the intermediate state of Cu 46 Zr 42 Al 7 Y 5 is rooted in the reorganization of the suprananometer-sized dual-glass network structures at MRO and the lowest coefficient of compressibility of the Zr-Zr bond length (from simulation) at short-range order. At present, the detailed mechanism of this intriguing behavior requires further study in the future.
In summary, novel steplike polyamorphic transitions are observed in a Cu-based nanostructured MG. We have excluded the contributions from the nanocrystalline phase or some special crystal-like clusters and verified the significant role of the concentration waves of Cu/Zr and the corresponding interconnected network composed of Cu-rich and Zr-rich domains at the nanoscale. At short-range-order length scale, the heterogeneous evolution of the bond lengths of different atomic pairs (especially the Zr-Zr bonds) makes a significant impact on the evolution of the Cu-rich and Zr-rich domains and contributes to the polyamorphism. The present polyamorphic transitions unveil a hidden intermediate state with an unusually high modulus, which opens a new avenue toward advanced MGs with super-mechanical performances by tailoring topological/chemical heterogeneity at nanoscale and supra-nanometer structure engineering. Since chemical heterogeneity, local composition fluctuation, and nanoscale phase separation are facile to create in MGs [64][65][66][67][68][69][70][71], the steplike polyamorphism may exist in other systems.