Emerging medium-range order in deformed Zr-based bulk metallic glasses during sub-T_g relaxation

Sample preparation

Zr_52.5Cu_17.9Ni_14.6Al₁₀Ti₅ BMG (i.e., BAM 11) plates with dimensions of 10 mm in width, 30 mm in length, and 1 mm in thickness, were prepared by arc melting, followed by copper-mold suction casting (Sky Technology Development Co., Ltd., China) under a Ti-gettered high-purity argon (Ar) atmosphere. Plates 10 mm in width and 1 mm in thickness were rolled on a rolling mill (Changzhou Xiechuang Mechanical Technology Co., Ltd., China). During the rolling process, the down-rolling amount was increased by 0.02 mm each time until the thickness of the plates reached 0.3 mm. Disks 1 mm in thickness and 10 mm in diameter were produced from the original BMG plate by electrical discharge machining (Taizhou Jinggong Electromechanical Manufacturing Co. Ltd., China). The BAM 11 disk, 10 mm in diameter and with a thickness of 1 mm, was placed between the HPT anvils (Japan), which had a diameter of 10 mm and contained a 0.3-mm-deep groove. During the HPT process, the discs were deformed for 10 revolutions at a rotation rate of 1 rpm under an applied pressure of 6 GPa at room temperature. To avoid possible errors induced by introducing different fractions of SBs, the HPT specimens used in the thermal and mechanical tests were obtained from the region of uniform shear deformation, ensuring uniform and severe plastic deformation^[48].

Characterization of SBs

Specific heat capacity (C_p) experiments were carried out by differential scanning calorimetry (Mettler-Toledo, DSC-1, Switzerland) in a high-purity N₂ atmosphere at a flow rate of 50 mL·min^-1. The temperature range of the experiment was set to 323-773 K at a heating rate of 20 K min^-1. A sapphire sample was used as a reference for C_p measurement. An FEI Quanta 250 FEG (Oregon, USA) scanning electron microscope (SEM) was used to observe the SBs on the surfaces of the CR and HPT samples and the morphology of the nanoindentation area. High-resolution transmission electron microscopy measurements were performed via transmission electron microscopy (TEM, JEM-2100F, Japan).

Mechanical testing

The nanoindentation tests were carried out using an Agilent Nano Indenter G200 (California, USA) at room temperature with a typical Berkovich diamond indenter. The load was set from 0 to 100 mN at a loading rate of 5 mN s^-1, and the load was held at 100 mN for 10 s and then unloaded at the same rate as the loading process. Subsequently, eight points were measured for each sample to obtain the mean values. Micropillars with nominal diameters of ~2.5 μm and a height of around 5 μm were prepared by a focused ion beam (FIB) system (Zeiss Auriga, Germany) operated at an accelerating voltage of 30 keV using a Ga⁺ focused ion beam. A two-step milling method was then employed with milling currents of 0.79 nA for coarse milling and 40 pA for fine polishing. Two specimens were prepared on the same individual sample, with a distance of more than 100 μm between them to avoid stress interactions. An FT-NMT03 nanomechanical in situ testing system (China) was used in the experiments, capable of performing in situ micropillar compression tests in a Zeiss Auriga FIB/SEM dual beam system. The experiments utilized a conical flat indenter made of diamond, featuring a 10-μm flat tip at its apex, and indentation was performed at a constant loading rate of 10^-3 s^-1.

High-energy X-ray synchrotron diffraction

High-energy X-ray synchrotron diffraction experiments were performed at the beamline 11-ID-C of the Advanced Photon Source (APS), Argonne National Laboratory (ANL, Illinois, USA). AC-BMG with a thickness of ~1 mm, CR- and HPT-BMG with a thickness of ~0.3 mm were mounted in a Linkam THMS600 furnace (United Kingdom) for thermal scanning. Then, high-energy X-rays with a beam size of 500 μm × 500 μm and wavelength of 0.01173 nm were used to perform transmission geometry for data collection. Measurements were conducted in a high-purity argon atmosphere. Two-dimensional (2D) diffraction patterns were obtained using a Perkin Elmer amorphous silicon detector with a data acquisition time of 1 s for each pattern. The time for data readout and storage was approximately 5 s, with a heating rate of 20 K min^-1. The time resolution was about 6 s, and the temperature resolution was 1-2 K. The static structure factor, S(Q), was derived from the two- dimensional diffraction ring patterns by masking bad pixels, integrating images, subtracting the appropriate background, and correcting for oblique incidence, absorption, multiple scattering, fluorescence, Compton scattering, and Laue correction using Fit2D and PDFgetX2^[49]. The reduced pair-distribution function (PDF) G(r) profiles were obtained via the Fourier transform of Q(S(Q)^-1).

To analyze Q₁, the first moment indicated the summary of the products of the position of Q and the corresponding intensity, representing the center of the heights of Q₁. The integrated intensity was calculated by the area between the profile and the baseline (y = 0 for S(Q) and y = 1 for G(r)). To analyze the MRO structure, the reduced PDF profile G(r) was transformed to g(r) by 1 + G(r)/4πrρ₀ (ρ₀ denotes the average number density). The second peak of g(r) characterized the connection mode of the SRO clusters on the MRO scale^[50]. The connection modes between the adjacent coordination polyhedrons were divided into four types: 1-atom (vertex sharing), 2-atom (edge sharing), 3-atom (face sharing), and 4-atom (intercross-sharing). To deconvolute the contributions of these connection modes, Gaussian peak fitting was performed on the second coordination shell. First, we calculated the average cluster radius R = 2.969 Å by weighing the bond length of each atom pair of the BAM 11 system^[51]. Based on this value, the center distances of the 1-atom, 2-atom, 3-atom, and 4-atom cluster connection modes were determined as 2R, $$\sqrt{3}$$R, $$\sqrt{8/3}$$R, and $$\sqrt{2}$$R, respectively. The calculation results of the cluster center distances were input as the initial value for the Gaussian fitting of the second peak of PDF with subtle adjustment (up to ±0.1 Å) to the initial value.

Deformation-induced rejuvenation and shear bands

Figure 1A presents the specific heat capacity curves C_p of the AC, CR- and HPT-deformed BMGs measured at a heating rate of 20 K min^-1. The glass transition temperature (T_g), crystallization temperature (T_x), and enthalpy release (ΔH) are summarized in Table 1. Notably, the onset of T_g for the CR- and HPT-deformed BMGs shifted -6 and -7 K, respectively, compared to the AC BMG, suggesting that the glassy states of the deformed BMGs became less stable than those of the AC BMG. Additionally, the relaxation enthalpy before T_g was calculated, indicating that the HPT-deformed BMG exhibited the highest ΔH of 0.656 kJ mol^-1. A greater ΔH value implied a more pronounced rejuvenated state in the HPT-deformed BMG^[52]. The surface morphology of the CR- and HPT-deformed BMGs (unpolished) was assessed by SEM, revealing a significant proliferation of SBs [Figure 1B and C]. The average spacing between the primary SBs in CR BMG was approximately 7-8 μm [Figure 1B]. By contrast, the HPT BMG exhibited a higher density of shear bands, with an average spacing of about 2 μm [Figure 1C], which was consistent with other reports^[41]. Figure 1D-F shows the high-resolution transmission electron microscopy (HRTEM) images of the AC, CR, and HPT BMGs, with insets showing the corresponding selected area electron diffraction (SAED) patterns. As shown in Figure 1D, the HRTEM image of the AC-BMG revealed a lower heterogeneity amorphous structure with no discernible crystalline features, which was further confirmed by a diffuse halo in the SAED pattern. By contrast, after deformation processing, the CR [Figure 1E] and HPT [Figure 1F] BMGs exhibited pronounced contrast variations in their HRTEM images while retaining their amorphous nature, as evidenced by the diffuse halos in their respective SAED patterns. The enhancement of structural heterogeneity was most prominent in the HPT sample, where the introduction of extensive shear bands led to more distinct contrast variations in the HRTEM image.

Figure 1. Rejuvenation of BAM 11 metallic glass by pre-plastic deformation. (A) Specific heat capacity C_p curves of AC, CR, and HPT BMGs. The SEM images of the surface of (B) CR and (C) HPT BMGs. Shear bands are marked by white dashed lines. HRTEM images of (D) AC, (E) CR, and (F) HPT BMGs. The insets are SAED patterns.

Mechanical softening induced by the shear bands

The nanoindentation results of all BMGs are shown in Figure 2A. The indentation depth under identical loads revealed a clear trend of increasing indentation size with an increasing degree of plastic deformation. For the AC BMG, the hardness and modulus were measured as 6.4 ± 0.1 and 107.8 ± 0.6 GPa, respectively. For the deformed BMGs, the hardness and modulus were as low as 6.2 ± 0.1 and 105.0 ± 0.8 GPa for the CR BMG and 5.9 ± 0.3 and 103.2 ± 2.5 GPa for the HPT BMG, indicating that both the hardness and modulus decreased with increased spatial heterogeneity [Figure 2B]. Analysis of the indentation depth revealed that under consistent load conditions, the rejuvenated BMGs exhibited larger indentation areas, indicating a macroscopic softening phenomenon in the metallic glass. Furthermore, a small step adjacent to the indentation on the surface of the AC BMG (inset of Figure 2C) was observed, showing shear band propagation. By contrast, the edges of indentation for the CR- and HPT-deformed BMGs were smooth, suggesting that plasticity was improved. A notable feature of the load-displacement response in the AC BMG was the presence of a distinct discontinuous deformation event (black arrows in Figure 2A), typically related to the activation of a single shear band. The discrete event reflected the inhomogeneous plasticity of metallic glass, indicating that discontinuous yielding occurred during plastic deformation. This inhomogeneous deformation was notably absent in both the CR- and HPT-deformed BMGs, suggesting that pre-plastic deformation processing promoted more homogeneous deformation characteristics.

Figure 2. (A) Nanoindentation test results for AC, CR, and HPT BMGs. (B) Hardness and modulus of AC, CR and HPT BMGs from nanoindentation. The error bar indicates the standard deviation through eight tests. (C) The surface morphology of the indentation of AC, CR, and HPT BMGs. The scale bar is 5 μm. (D) The load versus displacement curves of BMG pillars. (E) The morphology of the pillars of AC, CR, and HPT BMGs before and after compression tests. The scale bar is 1 μm.

The micropillar compression results, shown in Figure 2D, present the two stress-strain curves (solid and scattered lines) for both the initial and rejuvenated BMGs. This excessive elastic limit beyond the normal level was because the stress-strain curve was not calibrated, highlighting the macro-softening induced by the high volume fraction of SBs. The yield strength of the AC BMG was approximately 2.27 GPa, while the yield strength of the rejuvenated BMGs decreased to 2.25 GPa for CR BMG and 2.11 GPa for HPT BMG. The softening trend was consistent with the hardness trends observed in the nanoindentation tests [Table 1]. Figure 2E reveals the morphologies after compression. The surface of the AC-BMG had only one primary SB, whereas the surface of the rejuvenated BMGs revealed multiple primary SBs accompanied by small secondary shear bands^[53]. These findings further confirmed that the introduction of heterogeneous structures (SBs) through pre-deformation improved inhomogeneous plastic deformation.

Structure relaxation behavior of shear bands at sub-T_g temperatures

Figure 3A-C shows the structure factors, S(Q) patterns, of AC, CR, and HPT BMGs at different temperatures. It was evident that the BMGs retained a glassy feature when heated to T_g. Figure 3D-F presents the corresponding differential structure factor, ΔS(Q) curves, which were obtained by subtracting the S(Q) data at room temperature from that of the corresponding temperature. The variations in ΔS(Q) curves compared to that of 400 K indicated a sub-T_g structure evolution in the rejuvenated BMGs. As marked by the red dashed line in Figure 3D-F, for the AC BMG, the shape of the ΔS(Q) patterns developed consistently below T_g. This indicated a typical thermally driven structural change of an amorphous system approaching its glass transition state. However, the ΔS(Q) curves of the rejuvenated BMGs (CR and HPT) over 400 K exhibited a clear difference from that of the AC BMG. Specifically, they first exhibited a distinct inflection point at lower Q (~2.3 Å^-1), reached a maximum, and then followed a similar decreasing trend. This unique shape of the ΔS(Q) curves in the low-Q region suggested a non-linear, localized ordering process that differed from the uniform evolution observed in the AC BMG.

Figure 3. The in-situ synchrotron X-ray diffraction patterns at different temperatures of the (A) AC, (B) CR, and (C) HPT BMGs during heating. Difference △S(Q) profiles obtained by subtracting the diffraction pattern at RT for the (D) AC, (E) CR, and (F) HPT BMGs.

Further investigations into the in-situ heating process were conducted by analyzing the FSDP (Q₁)^[54,55]. The first peak position in momentum transfer (first moment of Q₁) was positively correlated with the packing density of the MGs^[49,50,56]. As shown in Figure 4A, with an increase in temperature, the first moment of Q₁ for all BMGs initially exhibited an overall decreasing trend due to thermal expansion. The AC BMG exhibited a continuous decrease as the temperature increased to T_g, reflecting a pronounced decrease in packing density. By contrast, the decrease in packing density for the rejuvenated BMGs was suppressed at temperatures far below T_g, implying a competition event in structural evolution that resisted thermal expansion. Due to the introduction of high density of SBs, the atomic mobility was activated in the loosely packed regions, enabling a preferential transition to denser packing during heating. In HPT-BMG, this competition was even more pronounced. This was possibly attributed to the higher volume fraction of SBs in HPT-BMG.

Figure 4. Emergence of medium-range ordering at sub-T_g in different BMGs. (A) First moment and (B) integrated intensity of the first sharp diffraction peak (Q₁) of S(Q) profile of AC, CR and HPT BMGs as a function of temperature. The solid lines are obtained by spline fitting of the raw data. The onset temperature of relaxation (T_r) is marked by the dashed line in the figures.

Statistical analysis of the integral intensity of Q₁ was conducted to illustrate the evolution of localized structural ordering in the MGs [Figure 4B]. AC-BMG exhibited a decreasing trend in integral intensity before T_g, followed by an increase after T_g. This evolution in structural ordering has been reported as associated with structural relaxation. The Q₁ integral intensities of all BMGs demonstrated a uniform decreasing trend in the supercooled liquid phase region, followed by a rapid increase after reaching the T_x temperature, signifying the rapid convergence of the structure into an ordered state during crystallization. After heating, the slope of the integrated intensity initially exhibited a decreasing trend. Subsequently, enhanced atomic mobility in the shear-affected zones promoted structural ordering, leading to an opposite shift in both CR BMG and HPT BMG. This trend reversal was more intense in HPT BMG with greater plastic deformation. Also, the temperature at which these two competing mechanisms reached equilibrium was denoted as T_r.

Real space structural analysis was employed to elucidate the structural evolution mechanism in the BMGs. Reduced pair-distribution function, G(r), patterns in Figure 5A-C were derived from the Fourier transformation of the S(Q) profiles. As the temperature approached T_x, all samples exhibited peak splitting, indicating the onset of crystallization. Statistical analysis of the integral intensities, corresponding to the range of G(r) > 0 of r₁ and r₆, provided specific insights regarding structural evolution. A relative coordinate axis was adopted for comparison, with the Y-axis range set to the average value of each curve ±10%. A notable commonality was that as the temperature increased to T_g, the integral intensities of r₁ and r₆ transitioned from a gradual increase (starting at T_r) to a rapid increase, corresponding to a rapid relaxation process. For AC-BMG, the changes in the intensities of r₁ and r₆ were smaller than those in the rejuvenated BMGs, and the temperature at which rapid relaxation occurred was higher [Figure 5D]. Conversely, CR- and HPT-BMG, which possessed a higher volume fraction of SBs, exhibited a lower T_r, indicating that the introduction of SBs directly modulated atomic mobility, thereby influencing rapid relaxation [Figure 5E]. Although the trends of r₁ and r₆ during relaxation remained consistent in HPT-BMG, it was evident that the changes in the r₆ peak, representing MRO, were more pronounced [Figure 5F]. This indicated that the structural relaxation prior to T_g was primarily driven by contributions from medium-range order. Based on the above analysis, we concluded that the introduction of SBs through plastic deformation facilitated the rapid activation of MRO during the relaxation process, thereby promoting structural ordering below T_g.

Figure 5. Pair-distribution function, G(r), of (A) AC, (B) CR, and (C) HPT BMGs during in-situ heating process. Integrated intensity of G(r) over the first (r₁) and sixth (r₆) shell (for regions where G(r) ≥ 0) for (D) AC, (E) CR, and (F) HPT BMGs.

Based on previous studies, the MRO structures could be reflected by correlations among atoms in the second-nearest-neighbor shell and accessed by analyzing the radial distribution of central atoms within local short-range order (SRO) units^[57]. Figure 6A demonstrates the connection models between inter-polyhedra, including 1-atom, 2-atom, 3-atom, and 4-atom sharing configurations, and variations in these connection modes could alter MRO ordering. The cluster center distances for these four connection modes could be calculated geometrically as 2R, $$\sqrt{3}$$R, $$\sqrt{8/3}$$R, and $$\sqrt{2}$$R, where R denotes the average cluster radius (detailed in Materials and Methods). In multi-peak decoupling, the use of Gaussian fitting was justified by the random deviation of atomic positions from their equilibrium distance caused by thermal fluctuations, following normal statistics near the average nearest neighbor distance^[58]. Figure 6B illustrates the Gaussian fitting of the second PDF peak for HPT-BMG at room temperature, while Figure 6C demonstrates the proportional evolutions of each connection mode during in situ heating process. In the overall heating process, a trade-off relationship was observed between the 1- and 4-atom modes and 2- and 3-atom modes. We found that before T_r, the proportion of 1- and 2-atom patterns tended to increase, while the proportion of 3- and 4-atom patterns decreased. The increased fraction of 1- and 2-atom modes indicated looser packing in MRO dominated by thermal expansion. Within a certain temperature range below T_g, the proportion of 1- and 2-atom modes started to decrease, whereas that of the 3- and 4-atom modes increased. This indicated that the overall structural order of the samples before T_r still decreased under the thermal effect, but the rate of decrease started to slow. After T_r, the structural order improved due to the enhanced relaxation behavior, which was possibly promoted by the emergence of more ordered 3- and 4-atom connection modes where the distance between the SRO clusters was shorter.

Figure 6. (A) Schemes of the four different cluster connection modes. (B) Gaussian fitting result for the 2nd shell of the g(r) pattern of HPT BMG at room temperature. (C) The contribution of each connection mode of the HPT BMG during in situ heating process.