
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39251740
71658
10.1038/s41598-024-71658-y
Article
Deformation behavior of thermally rejuvenated Zr-Cu-Al-(Ti) bulk metallic glass
Ghodki Nandita 1
Jha Shristy 1
Alla Siva Shankar 1
Yang Yu-Chia 1
Pharr George M. 2
Mukherjee Sundeep sundeep.mukherjee@unt.edu

1
1 https://ror.org/00v97ad02 grid.266869.5 0000 0001 1008 957X Department of Materials Science and Engineering, University of North Texas, Denton, TX 76203 USA
2 https://ror.org/01f5ytq51 grid.264756.4 0000 0004 4687 2082 Department of Materials Science and Engineering, Texas A&M University, College Station, TX 77843 USA
5 9 2024
5 9 2024
2024
14 2072925 4 2024
29 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
The deformation behavior of metallic glasses has been shown in prior studies to be often dependent on its structural state, namely higher energy “rejuvenated” state versus lower energy “relaxed” state. Here, the deformation behavior of thermally rejuvenated Zr-Cu-Al-(Ti) bulk metallic glasses (BMGs) was evaluated. Rejuvenation was achieved by cryogenic thermal cycling with increase of free volume measured in terms of enthalpy of relaxation. Hardness, stiffness, and yield strength of the BMGs were all found to decrease while plasticity increased after rejuvenation. More free volume in the rejuvenated BMG resulted in homogeneous plastic deformation as was evident from the high strain rate sensitivity and more pronounced shear band multiplication during uniaxial compression. Shear transformation zone (STZ) volume was calculated by cooperative shear model and correlated well with the change in structural state after rejuvenation. The enhanced plasticity with the addition of 1 at. % Ti as well as after cryogenic thermal cycling was explained by lower activation energy for shear flow initiation due to increased heterogeneity induced in the system. Molecular dynamics simulation demonstrated that the variation in plastic deformation behavior is correlated with local atomic structure changes.

Keywords

Bulk metallic glass
Rejuvenation
Free volume
Shear transformation zone
Subject terms

Engineering
Materials science
http://dx.doi.org/10.13039/100000001 National Science Foundation 1919220 1919220 1919220 1919220 1919220 Ghodki Nandita Jha Shristy Alla Siva Shankar Pharr George M. Mukherjee Sundeep issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

Bulk Metallic Glasses (BMGs) represent a relatively new class of multi-component alloys with amorphous atomic structure and remarkable properties. These include exceptionally high strength and elastic limit, excellent wear and corrosion resistance1–9, soft magnetism, and unique ability for thermoplastic forming10. BMGs have a distinct disordered microstructure with structural changes induced by a variation in their free volume content, in contrast to the long-range atomic order in crystalline counterparts5. The different structural states of a BMG on a potential energy landscape are shown schematically in Fig. 1. A BMG in its “rejuvenated” state has higher energy and more loosely packed atoms compared to its as-cast state. On the contrary, the BMG in its “relaxed” state has relatively lower potential energy and higher atomic packing density as shown in Fig. 1. Structural relaxation typically leads to embrittlement of metallic glasses with plasticity reduction and decrease in fracture toughness11,12. Rejuvenation, in contrast, has been shown to improve the plasticity of metallic glasses by introducing atomic-scale defects and preventing brittle failure13–20. BMGs often exhibit limited plasticity because of the lack of dislocation-based deformation mechanisms when deformed at temperatures below their glass transition. Enhancement of ductility in BMGs, significant for structural applications, continues to be a challenge. Several thermomechanical processing routes have been explored to this end, including shot-peening21, cold rolling22,23, high-pressure treatment24–30, and triaxial compression31. Annealing below the glass transition temperature (Tg) may lead to embrittlement in some cases due to structural relaxation11,32,33. However, annealing above Tg34–36 and cryogenic thermal cycling37–40 has been shown to enhance plasticity. In addition, micro-alloying approach has also been explored for improving the mechanical properties of BMGs, such as with the addition of a small fraction of Ag41, Nb42, Hf43, Ti44, and Fe45. Substitution of Ti with Ag improved the glass forming ability (GFA) and mechanical properties of Zr-based BMGs46. Ti addition was found to change the short-range order in Zr-Al-Ni-Cu glass-forming alloys47 and in some cases enhance GFA and plasticity44,48.Fig. 1 Potential energy landscape illustrating the various structural states in bulk metallic glasses. Rejuvenation leads to an increase in potential energy and higher free volume content while relaxation leads to decrease in potential energy and lower free volume content compared to its as-cast state.

Here, we report on the deformation mechanisms of a model Zr-Cu-Al BMG after cryogenic temperature cycling (thermal rejuvenation) studied with and without the addition of 1 at. % titanium. The Zr-Cu-Al system was chosen because it is the basis for development of numerous alloys in the Zr-based bulk metallic glass family and is a canonical example of a good glass former with a large processing window (wide supercooled liquid region)49,50. Moreover, it is free from toxic Be and does not have expensive noble metals like Pt, Pd, or rare earth elements, making it appealing for widespread applications. A small addition of Ti was investigated for further improvement in glass forming ability (GFA) and plasticity. Mechanical behavior of the Zr-Cu-Al-(Ti) BMGs was characterized in terms of changes in hardness, modulus, uniaxial compression response, shear band formation, and time dependent deformation. There are no reports in literature on simultaneously looking at rejuvenation of BMGs from cryogenic thermal cycling and microalloying. In addition, the time-dependent deformation behavior of BMGs after cryogenic thermal cycling has not been studied. We evaluated the effect of loading rate and report on the strain rate sensitivity (SRS) and relate it to the tendency for flow localization in the Zr-Cu-Al-(Ti) BMGs. Using nanoindentation and micropillar compression, we relate several aspects of the deformation behavior to the changes in structural state after cryogenic thermal cycling. Finally, using molecular dynamics (MD) simulation, we demonstrate that cryogenic thermal cycling leads to decrease in dense packing clusters and increase in loosely packed short range order clusters.

Methods

BMG ingots with the nominal composition of Zr47Cu46Al7 and Zr47Cu45Al7Ti1 were prepared by arc-melting a mixture of pure elements with a purity of 99.9% under a titanium gettered argon atmosphere in water-cooled copper crucibles. Each ingot was melted four times to ensure uniformity in composition. Plate samples in the dimensions of 3 mm × 10 mm × 10 mm was fabricated by suction casting into a copper mold under a purified Ar atmosphere. For thermal rejuvenation, cryogenic cycling was carried out by immersing the plate samples into liquid nitrogen for 12 h followed by holding at room temperature for 12 h for a total of 30 cycles. A schematic for thermal rejuvenation is shown in Fig. 1. The as-cast and rejuvenated samples were mechanically polished to a mirror finish and then cleaned in acetone and distilled water ultrasonically for 15 min for nano-mechanical tests. Rigaku III Ultima X-ray diffractometer (XRD, Rigaku Corporation, Tokyo, Japan) with 1.54 Å wavelength Cu-Kα radiation was used to confirm the amorphous structure of the samples. Differential scanning calorimetry (DSC) (NETZSCH DSC 404C) was conducted at a constant heating rate of 20 K/min to determine the characteristic temperatures and heat flow for the as-cast (AC) and rejuvenated (Rej) BMGs. Poisson`s ratio was measured for all the BMGs using resonant ultrasonic transducers. Rectangular samples in the dimensions of 10 mm × 10 mm × 2 mm were placed between ultrasonic transducers and the longitudinal and shear velocities were measured for each alloy to determine its Poisson`s ratio.

Hardness measurements and creep tests were performed using TI-Premier Triboindenter (Bruker, Minneapolis, MN, USA) with a Diamond Berkovich tip having an included angle of 142.30° and a tip radius of 150 nm. The nanoindentation hardness of the alloys in various structural states were measured using Oliver and Pharr method51. Fused quartz was used as a standard reference sample for initial tip calibration. Static constant load hold (CLH) creep tests were performed at room temperature by ramping to a maximum load of 1000 mN at two different loading rates of 10 mN/s and 100 mN/s. The samples were held at the peak load for 600 s, followed by unloading. The high load was used to minimize surface effects and avoid the indentation size effect (ISE) on hardness. A fast loading-rate was chosen to ensure that creep primarily occurred during the dwell time. At least fifteen indents were performed in each test condition and the distance between two neighboring indents was kept greater than 100 μm to avoid the overlap of their plastic zones. Thermal drift rate was maintained below 0.05 nm/s for all the tests.

For micro-pillar compression, pillars with aspect ratio of ~ 2 (height of the pillar ~ 6 μm and diameter of the pillar ~ 2.8 μm) were milled using FEI Nova NanoLab 200 focused ion beam SEM (FIB-SEM) in several steps using Ga ion beam current ranging from 5 nA to 10 pA. The top and bottom diameter of the micro-pillars were measured. As the taper angle was small (< 2°), the top diameter was used to calculate the cross-section area for further analysis. Micro-pillar compression tests were done in PI88 SEM Pico-indenter (Bruker, Minneapolis, MN, USA) with a 5 µm diameter flat diamond punch in displacement control mode. The recorded load versus displacement was converted to engineering stress–strain curve. Three to five micro-pillars were made for each sample condition to determine the standard deviation.

MD simulations were performed using a large-scale atomic/molecular massively parallel simulator (LAMMPS) using the embedded atom model (EAM) potential for Zr-Cu-Al BMG52. The alloys were rapidly quenched at the rate of 1013 K/s to obtain amorphous structure in Zr-Cu-Al and Zr-Cu-Al-Ti BMGs. The thermodynamic processes were carried out at isothermal-isobaric (NPT) ensemble based on the Nose–Hoover thermostat and barostat. Post-processing analysis of the MD simulations was carried out using OVITO tool to analyze the type and fraction of coordination polyhedral clusters or short-range ordering.

Results

Structural and thermal characterization

Figure 2(a) shows the XRD patterns obtained for the Zr-Cu-Al and Zr-Cu-Al-Ti alloys in as-cast (AC) and rejuvenated (Rej) states. A broad peak was observed between 2θ = 30°-45° for each of the alloys supporting their fully amorphous structure. Thermal analysis of the samples was done using DSC and heat flow as a function of temperature for all the alloys are shown in Fig. 2(b). The glass transition temperature (Tg) and onset temperature of crystallization (Tx) are marked by arrows in the DSC curves. All the four samples exhibited a small and broad exothermic peak prior to the glass transition, which is attributed to the annihilation of free volume. This was followed by a wide super-cooled liquid region and an exothermic peak associated with crystallization. Figure 2(c) shows the zoomed-in view of specific heat curves obtained using the DSC plots in Fig. 2(b), with the area under the curve for each alloy representing its relaxation enthalpy. Figure 2(d) shows the enthalpy of relaxation measured for each of the four alloys indicating significant increase in free volume with 1 at. % Ti addition. The Tg, Tx, and liquidus temperature (Tl) for the Zr-Cu-Al and Zr-Cu-Al-Ti alloys in as-cast (AC) condition are listed in Table 1. The relaxation enthalpy was 24.6 J/mol for Zr-Cu-Al and increased to 48.6 J/mol after rejuvenation. Similarly, the relaxation enthalpy was 183.8 J/mol for Zr-Cu-Al-Ti and increased to 190.2 J/mol after rejuvenation. The increase in relaxation enthalpy is much lower after rejuvenation for the Zr-Cu-Al-Ti alloy. This may be attributed to the increase in disorder with the addition of the 4th element53. Therefore, further disorder introduced by thermal strain may be relatively small in comparison to that seen for the ternary Zr-Cu-Al alloy. Disorder is related to increased “confusion” resulting from an increased diversity of atomic species and their different sizes with the introduction of the 4th element, Ti. With the addition of 1 at. % Ti, the Tg decreased from 718.8 K to 695.3 K, Tx decreased from 753.5 K to 736.3 K, and Tl decreased slightly. The reduced glass transition temperature (Trg = Tg/Tl), which is sometimes used as an indicator of GFA54, remained about the same with a value of ~ 0.6 for both the alloys.Fig. 2 (a) XRD pattern of as-cast (AC) and rejuvenated (Rej) Zr-Cu-Al and Zr-Cu-Al-Ti BMGs showing fully amorphous structure; (b) DSC plots for the four alloys showing the glass transition temperature (Tg) and onset temperature of crystallization (Tx); (c) Zoomed-in view of the specific heat capacity (CP) curves around glass transition, with shaded area shown for the as-cast samples; (d) Relaxation enthalpy (ΔHRel) calculated from the area under the DSC curves prior to glass transition for the four alloys.

Table 1 Characteristic temperatures for Zr-Cu-Al and Zr-Cu-Al-Ti BMGs in as-cast (AC) condition measured using a DSC, where Tg is the glass transition temperature, Tx is the onset temperature of crystallization, Tl is the liquidus temperature, and Trg is the reduced glass transition temperature.

Amorphous sample	Tg (K)	Tx (K)	Tl (K)	Trg	
Zr-Cu-Al	718.8 ± 8.1	753.5 ± 7.8	1184.1	0.61	
Zr-Cu-Al-Ti	695.3 ± 7.2	736.3 ± 7.5	1176.9	0.59	

Mechanical behavior

The hardness and modulus for the two alloys in their different structural states are listed in Table 2. For Zr-Cu-Al, the hardness and stiffness decreased by 6.3% and 2.4%, respectively, after rejuvenation. However, Zr-Cu-Al-Ti showed smaller changes with a decrease of 2.5% in hardness and around 1% in stiffness after rejuvenation. The decrease in hardness and stiffness for the rejuvenated alloys may be attributed to local atomic rearrangement and increase in free volume as suggested by the increase in their relaxation enthalpy (Fig. 2(d)).Table 2 Hardness, reduced modulus, and yield strength for the Zr-Cu-Al and Zr-Cu-Al-Ti BMGs in different structural states.

Sample	Hardness (GPa)	Reduced Modulus (GPa)	Yield Strength (MPa)	
Zr-Cu-Al (as-cast)	7.2 ± 0.03	125 ± 0.31	1752 ± 26	
Zr-Cu-Al (rejuvenated)	6.74 ± 0.05	122 ± 0.77	1722 ± 28	
Zr-Cu-Al-Ti (as-cast)	6.69 ± 0.03	121 ± 0.41	1671 ± 15	
Zr-Cu-Al-Ti (rejuvenated)	6.52 ± 0.02	120 ± 0.27	1632 ± 16	

Micropillar compression tests allow for in situ observation of deformation behavior and shear band formation, which is not possible in bulk tests. Also, micropillar compression tests minimize the influence of surface defects that can affect bulk sample measurements. We fabricated and tested multiple micropillars across different areas of the sample to account for any variability, which is captured in the standard deviation of the results. Representative engineering stress–strain curves for the Zr-Cu-Al and Zr-Cu-Al-Ti BMGs obtained from micro-pillar compression tests are shown in Fig. 3(a). The yield strength was calculated at the point where the first shear band was observed in situ during the experiment (corresponding to ‘*’ in the Fig. 3 (a)) and correlated with the first load drop in the load–displacement curve and the values are summarized in Table 2 for all the alloys. The average yield strength obtained from the micro-pillar compression tests for the as-cast Zr-Cu-Al was 1752 MPa, which decreased to 1722 MPa after cryogenic thermal cycling (thermal rejuvenation). The average yield strength further decreased for Zr-Cu-Al-Ti as-cast alloy to 1671 MPa and for the corresponding rejuvenated alloy to 1632 MPa. Post-yield serrations observed in the stress–strain curves during compressive deformation of amorphous alloys are related to nucleation and propagation of shear bands, while pre-yield serrations may be attributed to structural rearrangements during elastic strain55,56. Figure 3(b) shows the stress drop magnitude and frequency calculated from the engineering stress–strain plots for all the four alloys. The magnitude of stress drops decreased, and the stress drop frequency increased as the free volume in the alloys increased suggesting the enhancement in plasticity after cryogenic thermal cycling. Figures 3(c1-c16) show the in-situ SEM images during compression for the four alloys at different strain levels as indicated on the figures. The micropillar for as-cast Zr-Cu-Al deformed by accommodation of all the strain in a single major shear band as shown in Figs. 3(c1-c4). Figures 3(c5-c8) show the in-situ SEM images of the micro-pillar for rejuvenated Zr-Cu-Al indicating the formation of a few secondary shear bands in addition to the primary shear band. Similarly, plastic deformation for the as-cast Zr-Cu-Al-Ti alloy was characterized by few secondary shear bands before a major shear band formed (Figs. 3(c9-c12)). The micropillars for rejuvenated Zr-Cu-Al-Ti alloy showed multiple secondary shear bands intersecting with each other as well as with the primary shear bands (Figs. 3(c13-c16)). This indicates significantly better plasticity accommodation for rejuvenated Zr-Cu-Al-Ti as evident from its relatively homogeneous plastic deformation behavior (Fig. 3(a)), smallest magnitude of stress drops, and higher stress drop frequency (Fig. 3(b)) compared to the other cases.Fig. 3 (a) Engineering stress–strain curves for Zr-Cu-Al and Zr-Cu-Al-Ti alloys in as-cast (AC) and rejuvenated (Rej) states, with origin of the curves shifted by arbitrary units (a.u.) for clarity of representation, the ‘*’ corresponds to the yield point of the sample; (b) Stress drop magnitude and stress drop frequency measured from the engineering stress–strain plots for the two alloys in AC and Rej states; (c1-16) In-situ SEM images showing the change in deformation behavior for the four alloys, illustrating primary shear bands (Pri SB) and secondary shear bands (Sec SB).

Time-dependent deformation

Time-dependent deformation behavior of the alloys was studied at room temperature using nano-indentation. To evaluate the effect of loading rate, the samples were loaded to 1000 mN at the rates of 10 mN/s and 100 mN/s. The creep mechanism was evaluated by determining the creep strain rate sensitivity (SRS), m, which is the reciprocal of stress exponent (n), defined in the conventional power-law creep as57:1 ε˙=Aσn=A′Hn

where ε˙ is the strain rate, σ is the applied stress, and A or A′ is a temperature-dependent material constant. The strain rate ε was calculated as:2 ε=1hdhdt

where dhdt is the first derivative of the instantaneous creep displacement (h). The displacement rate dh/dt was obtained by fitting the displacement-holding time curve during constant load holding as58:3 ht=h0+at-t0p+kt

where h0 and t0 are the indentation depth and time before the holding segment, and a, p and k are fitting constants. The hardness (H) for the self-similar indentation probe like Berkovich was calculated as:4 H=P24.5hc2

where P is the applied load, hc is contact depth given by hc = hmax − 0.75 P/S for Berkovich indenter and hmax and S are maximum penetration depth and material stiffness, respectively. Slope of log (H) versus log ε˙ was used to calculate the strain rate sensitivity, m (reciprocal of stress exponent, n), which gives a measure of the creep deformation mechanism.

The creep displacement curves obtained by fitting the experimental nanoindentation data, using Eq. 3, for the four alloys during the constant holding period are shown in Figs. 4(a) and 4(b) at the loading rate of 10 mN/s and 100 mN/s, respectively. The creep displacement initially increased sharply with time followed by a decrease in the rate of increase. Overall, the creep displacement was higher for the rejuvenated alloys compared to their as-cast counterparts. The maximum creep displacement increased with loading rate, which may be attributed to less time for relaxation process and more free volume creation at the higher loading rates59,60. Similar trend has been reported for Pd-based, Fe-based, and Ce-based BMGs59,61,62 during nanoindentation at room temperature, as well as in some high entropy alloys63. Figures 4 (a) and 4 (b) also show the corresponding creep strain rate on the secondary y-axis plotted using Eq. 2. The strain rate decreased sharply with in the first 40 s reaching values on the order of 10–4/s by the end of the test. Supplementary figures S1 and S2 show that the hardness did not change significantly with depth well before the end of the test, indicating steady state creep64. Figure 4(c) shows the dependence of creep SRS on loading rate, which is related to the tendency for flow localization in a BMG. Higher SRS indicates more resistance to localization during plastic deformation59,65. In crystalline alloys, the creep mechanism is explained in terms of dislocation glide, diffusion, and grain boundary sliding66, which are fundamentally different compared to the mechanisms in amorphous alloys59,67. At lower loading rate, the creep SRS was lower for the rejuvenated alloys compared to their as-cast counterparts, as shown in Fig. 4 (c). Relatively higher free volume content in the rejuvenated samples promotes larger number of shear bands due to easier rearrangement of atoms65. This results in localized deformation as suggested by lower creep SRS for the rejuvenated samples. Increase in loading rate increases the flow stress leading to increased deformation volume or plastic zone size around the indent. Additionally, the shorter loading time does not allow for atomic rearrangement68 and may lead to higher free volume generation59. This higher rate of free volume generation at higher loading rate leads to more homogeneous plastic deformation69 as suggested from the higher creep SRS in Fig. 4(c).Fig. 4 Creep displacement (primary y-axis) and creep strain rate (secondary y-axis) versus holding time curves for Zr-Cu-Al and Zr-Cu-Al-Ti alloys at the loading rate of (a) 10 mN/s and (b) 100 mN/s; higher free volume in rejuvenated alloys led to larger creep displacement at all loading rates; (c) creep strain rate sensitivity of the four alloys at the two different loading rates.

Discussion

Linking the shear transformation zone volume to deformation behavior

Figure 5 shows the measured yield strength (YS) and shear transformation zone (STZ) volume calculated based on the Johnson-Samwer cooperative shear model (CSM) as a function of Poisson’s ratio70. According to CSM, the activation energy is given as:5 W∗=4R0G0γc21-ττc3/2Ωξ

where Ω is the volume of STZ, G0 and τc are shear modulus and threshold shear resistance of the metallic glass at 0 K, respectively, R0 and ξ are constants with approximate values of 0.5 and 3, respectively71 and, γc is the elastic limit with a value of 0.027 for BMGs71,72. Therefore, STZ volume may be calculated in terms of hardness and strain-rate sensitivity (m) as71:6 Ω=kT32G0γc21R0ξ1mHτc(1-τCTτc)12

where τCT is threshold shear resistance at temperature T, τc /G0≈ 0.036. Furthermore,7 τCTτc=1-0.44(T/Tg)23

Fig. 5 Yield strength (primary y-axis, in blue) and shear transformation zone (STZ) volume (secondary y-axis, in green) as a function of Poisson’s ratio for the studied alloys. The data points represent the as-cast (AC) and rejuvenated (Rej) states for Zr-Cu-Al and Zr-Cu-Al-Ti alloys. The figure illustrates that the yield strength decreases while the STZ volume increases with the increase in Poisson's ratio among the studied alloys.

The STZ volume for Zr-Cu-Al BMG increased from ~ 0.6 nm3 in as-cast state to ~ 0.8 nm3 in thermally rejuvenated state. Similarly, the STZ volume for Zr-Cu-Al-Ti BMG increased from ~ 0.9 nm3 in as-cast state to ~ 1.1 nm3 after thermal rejuvenation. The rejuvenated alloys showed larger STZ volume compared to their as-cast counterparts and the STZ volume increased with the addition of 1 at. % Ti to Zr-Cu-Al BMG. Larger STZ volume correlates with enhanced plasticity, as fewer STZs are needed to reach the critical shear strain for shear band formation. This reduction in the number of necessary STZs for shear band nucleation facilitates higher internal stress concentration, activating new flow units and multiple shear bands, thereby enhancing plasticity.

The yield strength decreased while the STZ volume increased with an increase in Poisson’s ratio among the studied alloys. This behavior may be attributed to the large negative heat of mixing among the constituent elements in a bulk metallic glass (BMG), which promotes chemical short-range ordering54,73. For example, the heat of mixing values are 0 kJ/mol for Ti-Zr, − 9 kJ/mol for Ti-Cu, and − 30 kJ/mol for Ti–Al, whereas they are − 23 kJ/mol for Zr-Cu and − 44 kJ/mol for Zr-Al74. These values suggest that Ti atoms preferentially substitute for Zr sites, as shown in recent studies74. Furthermore, the significant atomic size difference between Ti (0.145 nm) and Zr (0.160 nm) can lead to atomic-scale distortions and loosely packed local configurations. This atomic-scale distortion may explain the observed softening and reduction in stiffness with the addition of 1 at. % Ti to the Zr-Cu-Al BMG, as seen in Table 2.

Local atomic ordering

Molecular dynamics (MD) simulations were carried out to explain the pronounced differences in the deformation behavior of Zr-Cu-Al and Zr-Cu-Al-Ti BMGs in their as-cast and rejuvenated states. Figure 6 shows the fraction change in Voronoi index, calculated using spatial tessellation techniques, for the MD-simulated BMGs of composition identical to those used in the experiments75. The Voronoi index distinguishes coordination polyhedral clusters or short-range ordering (SRO) in the BMGs76.Fig. 6 Fraction change of Voronoi polyhedral clusters for Zr-Cu-Al and Zr-Cu-Al-Ti BMGs after cryogenic thermal cycling compared to their as-cast state.

Figure 6 illustrates the distribution of major Voronoi polyhedra with Al, Ti, and Cu as center atoms. Previous reports classified the polyhedral clusters into dense and loose packing types77,78. Dense packing clusters are void-free, while loose packing clusters contain voids. After cryogenic thermal cycling, the Al-centered Voronoi index of < 0,0,12,0 > decreased by 29% and 27.5% in Zr-Cu-Al and Zr-Cu-Al-Ti BMGs, respectively. The dominant coordination polyhedra, < 0,2,8,1 > and < 0,2,8,2 > , correspond to bicapped square antiprism (BSAP) or distorted BSAP55. In Zr-Cu-Al BMG, the fraction of < 0,2,8,1 > polyhedra decreased by 4.2% and < 0,2,8,2 > by 3.1% after thermal rejuvenation. Similarly, in Zr-Cu-Al-Ti BMG, < 0,2,8,1 > decreased by 3.3% and < 0,2,8,2 > by 3.7%. Conversely, the fraction of loose-packed atomic clusters in both alloys mostly increased after cryogenic thermal cycling. This overall decrease in dense packing clusters and increase in loose packing clusters likely contributed to an increase in atomic-scale voids or free volume, thus enhancing plasticity79,80. The decrease in the number of dominant polyhedra increases the disordered regions where shear transformation nucleation is more likely to occur. Thus, the experimental differences in deformation behavior may be attributed to the degree of structural heterogeneity due to specific polyhedra in different structural states of the BMGs.

Recent MD simulations also show that rejuvenated Zr-Cu-Al glasses have a heterogeneous atomic cluster distribution, marked by a reduced presence of icosahedral (icos) and defective icosahedral clusters (deficos) and an increased prevalence of body-centered cubic (bcc) and face-centered cubic (fcc) + hexagonal close-packed (hcp) clusters81. This atomic restructuring leads to enhanced plasticity in metallic glasses, attributed to the higher nucleation sites for facilitating shear flow events. The addition of 1% Ti in Zr-Cu-Al BMG increases microstructural heterogeneity due to increased diversity of atomic species and their different sizes. Zr-Cu-Al-Ti BMG showed a larger STZ volume of 0.9 nm3 leading to enhanced plasticity compared to 0.6 nm3 for Zr-Cu-Al BMG. Thermal rejuvenation further improved these properties due to atomic-level structural changes.

Conclusions

In summary, the effect of thermal rejuvenation (i.e., with cryogenic cycling) on the plastic deformation behavior of Zr-Cu-Al and Zr-Cu-Al-Ti bulk metallic glasses was studied. The relaxation enthalpy increased while the hardness and strength decreased significantly with the addition of 1 at% Ti to Zr-Cu-Al BMG and further with thermal rejuvenation. The magnitude of stress drops during uniaxial compression decreased while their frequency increased after micro-alloying with 1 at. % Ti and further due to thermal rejuvenation, indicating the accommodation of strain in larger number of shear bands. The enhanced plasticity after micro-alloying with Ti and thermal rejuvenation was explained by higher number of sites for shear flow initiation due to increased heterogeneity in the system along with the decrease in dense packing clusters and increase in loosely packed short range order clusters. Time dependent deformation was relatively more homogenous and creep SRS was higher at higher loading rate (100 mN/s) compared to the response seen at lower loading rate (10 mN/s). This was attributed to the generation of excess free volume during loading at higher rates, thereby making the alloy less sensitive to the initial free volume.

Supplementary Information

Supplementary Information.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-71658-y.

Acknowledgements

This work was partly supported by funding from the National Science Foundation (NSF) under grant numbers 1919220 and 1762545. Any opinions, findings, and conclusions expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).

Author contributions

N.G. and S.M. conceived the study. N.G., S.J., and S.S.A. planned and conducted the experiments including sample preparation, processing, structural and thermal characterization, nanoindentation, and micropillar compression. Y.C.Y conducted the MD simulations. N.G. and S.J. analyzed the data and wrote the paper with input from G.M.P and S.M. All authors proofread the article and contributed extensively to the discussion.

Data availability

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
==== Refs
References

1. Schuh CA Hufnagel TC Ramamurty U Mechanical behavior of amorphous alloys Acta Mater. 2007 55 4067 4109 10.1016/j.actamat.2007.01.052
Schuh, C. A., Hufnagel, T. C. & Ramamurty, U. Mechanical behavior of amorphous alloys. Acta Mater. 55, 4067–4109. 10.1016/j.actamat.2007.01.052 (2007).10.1016/j.actamat.2007.01.052
2. Sarac B Schroers J Designing tensile ductility in metallic glasses Nat. Commun. 2013 4 4 10 10.1038/ncomms3158
Sarac, B. & Schroers, J. Designing tensile ductility in metallic glasses. Nat. Commun. 4, 4–10. 10.1038/ncomms3158 (2013).10.1038/ncomms3158
3. Fornell J Van Steenberge N Varea A Rossinyol E Pellicer E Suriñach S Baró MD Sort J Enhanced mechanical properties and in vitro corrosion behavior of amorphous and devitrified Ti 40Zr 10Cu 38Pd 12 metallic glass J. Mech. Behav. Biomed. Mater. 2011 4 1709 1717 10.1016/j.jmbbm.2011.05.028 22098871
Fornell, J. et al. Enhanced mechanical properties and in vitro corrosion behavior of amorphous and devitrified Ti 40Zr 10Cu 38Pd 12 metallic glass. J. Mech. Behav. Biomed. Mater. 4, 1709–1717. 10.1016/j.jmbbm.2011.05.028 (2011).22098871 10.1016/j.jmbbm.2011.05.028
4. Si JJ Chen XH Cai YH Wu YD Wang T Hui XH Corrosion behavior of Cr-based bulk metallic glasses in hydrochloric acid solutions Corros. Sci. 2016 107 123 132 10.1016/j.corsci.2016.02.026
Si, J. J. et al. Corrosion behavior of Cr-based bulk metallic glasses in hydrochloric acid solutions. Corros. Sci. 107, 123–132. 10.1016/j.corsci.2016.02.026 (2016).10.1016/j.corsci.2016.02.026
5. Suryanarayana C Inoue A Bulk Metallic Glasses 2011 CRC Press
Suryanarayana, C. & Inoue, A. Bulk Metallic Glasses (CRC Press, 2011).
6. Wang WH Bulk metallic glasses with functional physical properties Adv. Mater. 2009 21 4524 4544 10.1002/adma.200901053
Wang, W. H. Bulk metallic glasses with functional physical properties. Adv. Mater. 21, 4524–4544. 10.1002/adma.200901053 (2009).10.1002/adma.200901053
7. Meagher P O’Cearbhaill ED Byrne JH Browne DJ Bulk metallic glasses for implantable medical devices and surgical tools Adv. Mater. 2016 28 5755 5762 10.1002/adma.201505347 27031058
Meagher, P., O’Cearbhaill, E. D., Byrne, J. H. & Browne, D. J. Bulk metallic glasses for implantable medical devices and surgical tools. Adv. Mater. 28, 5755–5762. 10.1002/adma.201505347 (2016).27031058 10.1002/adma.201505347
8. Inoue A Takeuchi A Recent development and application products of bulk glassy alloys Acta Mater. 2011 59 2243 2267 10.1016/j.actamat.2010.11.027
Inoue, A. & Takeuchi, A. Recent development and application products of bulk glassy alloys. Acta Mater. 59, 2243–2267. 10.1016/j.actamat.2010.11.027 (2011).10.1016/j.actamat.2010.11.027
9. Li HF Zheng YF Recent advances in bulk metallic glasses for biomedical applications Acta Biomater. 2016 36 1 20 10.1016/j.actbio.2016.03.047 27045349
Li, H. F. & Zheng, Y. F. Recent advances in bulk metallic glasses for biomedical applications. Acta Biomater. 36, 1–20. 10.1016/j.actbio.2016.03.047 (2016).27045349 10.1016/j.actbio.2016.03.047
10. Chen M A brief overview of bulk metallic glasses NPG Asia Mater. 2011 3 82 90 10.1038/asiamat.2011.30
Chen, M. A brief overview of bulk metallic glasses. NPG Asia Mater. 3, 82–90. 10.1038/asiamat.2011.30 (2011).10.1038/asiamat.2011.30
11. Ramamurty U Lee ML Basu J Li Y Embrittlement of a bulk metallic glass due to low-temperature annealing Scr. Mater. 2002 47 107 111 10.1016/S1359-6462(02)00102-1cgb
Ramamurty, U., Lee, M. L., Basu, J. & Li, Y. Embrittlement of a bulk metallic glass due to low-temperature annealing. Scr. Mater. 47, 107–111. 10.1016/S1359-6462(02)00102-1cgb (2002).10.1016/S1359-6462(02)00102-1cgb
12. Murali P Ramamurty U Embrittlement of a bulk metallic glass due to sub-Tg annealing Acta Mater. 2005 53 1467 1478 10.1016/j.actamat.2004.11.040
Murali, P. & Ramamurty, U. Embrittlement of a bulk metallic glass due to sub-Tg annealing. Acta Mater. 53, 1467–1478. 10.1016/j.actamat.2004.11.040 (2005).10.1016/j.actamat.2004.11.040
13. Guo W Yamada R Saida J Lü S Wu S Various rejuvenation behaviors of Zr-based metallic glass by cryogenic cycling treatment with different casting temperatures Nanoscale Res. Lett. 2018 10.1186/s11671-018-2816-7 30584651
Guo, W., Yamada, R., Saida, J., Lü, S. & Wu, S. Various rejuvenation behaviors of Zr-based metallic glass by cryogenic cycling treatment with different casting temperatures. Nanoscale Res. Lett.10.1186/s11671-018-2816-7 (2018).30584651 10.1186/s11671-018-2816-7
14. Pan J Wang YX Guo Q Zhang D Greer AL Li Y Extreme rejuvenation and softening in a bulk metallic glass Nat. Commun. 2018 10.1038/s41467-018-02943-4 30568162
Pan, J. et al. Extreme rejuvenation and softening in a bulk metallic glass. Nat. Commun.10.1038/s41467-018-02943-4 (2018).30568162 10.1038/s41467-018-02943-4
15. Guo W Yamada R Saida J Rejuvenation and plasticization of metallic glass by deep cryogenic cycling treatment Intermetallics. 2018 93 141 147 10.1016/j.intermet.2017.11.015
Guo, W., Yamada, R. & Saida, J. Rejuvenation and plasticization of metallic glass by deep cryogenic cycling treatment. Intermetallics. 93, 141–147. 10.1016/j.intermet.2017.11.015 (2018).10.1016/j.intermet.2017.11.015
16. Saida J Yamada R Wakeda M Recovery of less relaxed state in Zr-Al-Ni-Cu bulk metallic glass annealed above glass transition temperature Appl. Phys. Lett. 2013 103 221910 10.1063/1.4835076
Saida, J., Yamada, R. & Wakeda, M. Recovery of less relaxed state in Zr-Al-Ni-Cu bulk metallic glass annealed above glass transition temperature. Appl. Phys. Lett. 103, 221910. 10.1063/1.4835076 (2013).10.1063/1.4835076
17. Küchemann S Derlet PM Liu C Rosenthal D Sparks G Larson WS Maaß R Energy storage in metallic glasses via flash annealing Adv. Funct. Mater. 2018 28 1805385 10.1002/adfm.201805385
Küchemann, S. et al. Energy storage in metallic glasses via flash annealing. Adv. Funct. Mater. 28, 1805385. 10.1002/adfm.201805385 (2018).10.1002/adfm.201805385
18. Meylan CM Orava J Greer AL Rejuvenation through plastic deformation of a La-based metallic glass measured by fast-scanning calorimetry J. Non-Crystalline Solids X. 2020 8 100051 10.1016/j.nocx.2020.100051
Meylan, C. M., Orava, J. & Greer, A. L. Rejuvenation through plastic deformation of a La-based metallic glass measured by fast-scanning calorimetry. J. Non-Crystalline Solids X. 8, 100051. 10.1016/j.nocx.2020.100051 (2020).10.1016/j.nocx.2020.100051
19. Hufnagel TC Cryogenic rejuvenation Nat. Mater. 2015 14 867 868 10.1038/nmat4394 26288974
Hufnagel, T. C. Cryogenic rejuvenation. Nat. Mater. 14, 867–868. 10.1038/nmat4394 (2015).26288974 10.1038/nmat4394
20. Guo W Saida J Zhao M Lü S Wu S Unconspicuous rejuvenation of a Pd-based metallic glass upon deep cryogenic cycling treatment Mater. Sci. Eng. A. 2019 759 59 64 10.1016/j.msea.2019.05.019
Guo, W., Saida, J., Zhao, M., Lü, S. & Wu, S. Unconspicuous rejuvenation of a Pd-based metallic glass upon deep cryogenic cycling treatment. Mater. Sci. Eng. A. 759, 59–64. 10.1016/j.msea.2019.05.019 (2019).10.1016/j.msea.2019.05.019
21. Concustell A Méar FO Suriñach S Baró MD Greer AL Structural relaxation and rejuvenation in a metallic glass induced by shot-peening Philos. Mag. Lett. 2009 89 831 840 10.1080/09500830903337919
Concustell, A., Méar, F. O., Suriñach, S., Baró, M. D. & Greer, A. L. Structural relaxation and rejuvenation in a metallic glass induced by shot-peening. Philos. Mag. Lett. 89, 831–840. 10.1080/09500830903337919 (2009).10.1080/09500830903337919
22. Song KK Pauly S Zhang Y Scudino S Gargarella P Surreddi KB Kühn U Eckert J Significant tensile ductility induced by cold rolling in Cu47.5Zr47.5Al5 bulk metallic glass Intermetallics. 2011 19 1394 1398 10.1016/J.INTERMET.2011.05.001
Song, K. K. et al. Significant tensile ductility induced by cold rolling in Cu47.5Zr47.5Al5 bulk metallic glass. Intermetallics. 19, 1394–1398. 10.1016/J.INTERMET.2011.05.001 (2011).10.1016/J.INTERMET.2011.05.001
23. Qiao JC Pelletier JM Influence of thermal treatments and plastic deformation on the atomic mobility in Zr50.7Cu28Ni9Al12.3 bulk metallic glass J. Alloys Compd. 2014 615 S85 S89 10.1016/j.jallcom.2013.11.158
Qiao, J. C. & Pelletier, J. M. Influence of thermal treatments and plastic deformation on the atomic mobility in Zr50.7Cu28Ni9Al12.3 bulk metallic glass. J. Alloys Compd. 615, S85–S89. 10.1016/j.jallcom.2013.11.158 (2014).10.1016/j.jallcom.2013.11.158
24. Yamada R Shibazaki Y Abe Y Ryu W Saida J Unveiling a new type of ultradense anomalous metallic glass with improved strength and ductility through a high-pressure heat treatment NPG Asia Mater. 2019 11 72 10.1038/s41427-019-0175-1
Yamada, R., Shibazaki, Y., Abe, Y., Ryu, W. & Saida, J. Unveiling a new type of ultradense anomalous metallic glass with improved strength and ductility through a high-pressure heat treatment. NPG Asia Mater. 11, 72. 10.1038/s41427-019-0175-1 (2019).10.1038/s41427-019-0175-1
25. Dmowski W Yokoyama Y Chuang A Ren Y Umemoto M Tsuchiya K Inoue A Egami T Structural rejuvenation in a bulk metallic glass induced by severe plastic deformation Acta Mater. 2010 58 429 438 10.1016/j.actamat.2009.09.021
Dmowski, W. et al. Structural rejuvenation in a bulk metallic glass induced by severe plastic deformation. Acta Mater. 58, 429–438. 10.1016/j.actamat.2009.09.021 (2010).10.1016/j.actamat.2009.09.021
26. Meng F Tsuchiya K Seiichiro II Yokoyama Y Reversible transition of deformation mode by structural rejuvenation and relaxation in bulk metallic glass Appl. Phys. Lett. 2012 101 121914 10.1063/1.4753998
Meng, F., Tsuchiya, K., Seiichiro, I. I. & Yokoyama, Y. Reversible transition of deformation mode by structural rejuvenation and relaxation in bulk metallic glass. Appl. Phys. Lett. 101, 121914. 10.1063/1.4753998 (2012).10.1063/1.4753998
27. Adachi N Todaka Y Yokoyama Y Umemoto M Cause of hardening and softening in the bulk glassy alloy Zr50Cu40Al10 after high-pressure torsion Mater. Sci. Eng. A. 2015 627 171 181 10.1016/j.msea.2014.12.101
Adachi, N., Todaka, Y., Yokoyama, Y. & Umemoto, M. Cause of hardening and softening in the bulk glassy alloy Zr50Cu40Al10 after high-pressure torsion. Mater. Sci. Eng. A. 627, 171–181. 10.1016/j.msea.2014.12.101 (2015).10.1016/j.msea.2014.12.101
28. Denis P Meylan CM Ebner C Greer AL Zehetbauer M Fecht H-J Rejuvenation decreases shear band sliding velocity in Pt-based metallic glasses Mater. Sci. Eng. A. 2017 684 517 523 10.1016/j.msea.2016.12.075
Denis, P. et al. Rejuvenation decreases shear band sliding velocity in Pt-based metallic glasses. Mater. Sci. Eng. A. 684, 517–523. 10.1016/j.msea.2016.12.075 (2017).10.1016/j.msea.2016.12.075
29. Dmowski W Yoo GH Gierlotka S Wang H Yokoyama Y Park ES Stelmakh S Egami T High pressure quenched glasses: Unique structures and properties Sci. Rep. 2020 10 9497 10.1038/s41598-020-66418-7 32528160
Dmowski, W. et al. High pressure quenched glasses: Unique structures and properties. Sci. Rep. 10, 9497. 10.1038/s41598-020-66418-7 (2020).32528160 10.1038/s41598-020-66418-7
30. Ebner C Pauly S Eckert J Rentenberger C Effect of mechanically induced structural rejuvenation on the deformation behaviour of CuZr based bulk metallic glass Mater. Sci. Eng. A. 2020 773 138848 10.1016/j.msea.2019.138848
Ebner, C., Pauly, S., Eckert, J. & Rentenberger, C. Effect of mechanically induced structural rejuvenation on the deformation behaviour of CuZr based bulk metallic glass. Mater. Sci. Eng. A. 773, 138848. 10.1016/j.msea.2019.138848 (2020).10.1016/j.msea.2019.138848
31. Pan J Ivanov YP Zhou WH Li Y Greer AL Strain-hardening and suppression of shear-banding in rejuvenated bulk metallic glass Nature. 2020 578 559 562 10.1038/s41586-020-2016-3 32103194
Pan, J., Ivanov, Y. P., Zhou, W. H., Li, Y. & Greer, A. L. Strain-hardening and suppression of shear-banding in rejuvenated bulk metallic glass. Nature. 578, 559–562 (2020).32103194 10.1038/s41586-020-2016-3
32. Kumar G Rector D Conner RD Schroers J Embrittlement of Zr-based bulk metallic glasses Acta Mater. 2009 57 3572 3583 10.1016/j.actamat.2009.04.016
Kumar, G., Rector, D., Conner, R. D. & Schroers, J. Embrittlement of Zr-based bulk metallic glasses. Acta Mater. 57, 3572–3583. 10.1016/j.actamat.2009.04.016 (2009).10.1016/j.actamat.2009.04.016
33. Yokoyama Y Yamasaki T Liaw PK Inoue A Study of the structural relaxation-induced embrittlement of hypoeutectic Zr–Cu–Al ternary bulk glassy alloys Acta Mater. 2008 56 6097 6108 10.1016/j.actamat.2008.08.026
Yokoyama, Y., Yamasaki, T., Liaw, P. K. & Inoue, A. Study of the structural relaxation-induced embrittlement of hypoeutectic Zr–Cu–Al ternary bulk glassy alloys. Acta Mater. 56, 6097–6108. 10.1016/j.actamat.2008.08.026 (2008).10.1016/j.actamat.2008.08.026
34. Saida J Yamada R Wakeda M Ogata S Thermal rejuvenation in metallic glasses Sci. Technol. Adv. Mater. 2017 18 152 162 10.1080/14686996.2017.1280369 28458739
Saida, J., Yamada, R., Wakeda, M. & Ogata, S. Thermal rejuvenation in metallic glasses. Sci. Technol. Adv. Mater. 18, 152–162. 10.1080/14686996.2017.1280369 (2017).28458739 10.1080/14686996.2017.1280369
35. Ryu W Yamada R Saida J Tailored hardening of ZrCuAl bulk metallic glass induced by 2D gradient rejuvenation NPG Asia Mater. 2020 12 52 10.1038/s41427-020-0233-8
Ryu, W., Yamada, R. & Saida, J. Tailored hardening of ZrCuAl bulk metallic glass induced by 2D gradient rejuvenation. NPG Asia Mater. 12, 52. 10.1038/s41427-020-0233-8 (2020).10.1038/s41427-020-0233-8
36. Guo W Niiyama T Yamada R Wakeda M Saida J Synthesis and mechanical properties of highly structure-controlled Zr-based metallic glasses by thermal rejuvenation technique J. Phys. Condens. Matter. 2023 35 154004 10.1088/1361-648X/acb8a0
Guo, W., Niiyama, T., Yamada, R., Wakeda, M. & Saida, J. Synthesis and mechanical properties of highly structure-controlled Zr-based metallic glasses by thermal rejuvenation technique. J. Phys. Condens. Matter. 35, 154004. 10.1088/1361-648X/acb8a0 (2023).10.1088/1361-648X/acb8a0
37. Ketov SV Trifonov AS Ivanov YP Churyumov AY Lubenchenko AV Batrakov AA Jiang J Louzguine-Luzgin DV Eckert J Orava J Greer AL On cryothermal cycling as a method for inducing structural changes in metallic glasses NPG Asia Mater. 2018 10 137 145 10.1038/s41427-018-0019-4
Ketov, S. V. et al. On cryothermal cycling as a method for inducing structural changes in metallic glasses. NPG Asia Mater. 10, 137–145. 10.1038/s41427-018-0019-4 (2018).10.1038/s41427-018-0019-4
38. Song W Meng X Wu Y Cao D Wang H Liu X Wang X Lu Z Improving plasticity of the Zr46Cu46Al8 bulk metallic glass via thermal rejuvenation Sci. Bull. 2018 63 840 844 10.1016/j.scib.2018.04.021
Song, W. et al. Improving plasticity of the Zr46Cu46Al8 bulk metallic glass via thermal rejuvenation. Sci. Bull. 63, 840–844. 10.1016/j.scib.2018.04.021 (2018).10.1016/j.scib.2018.04.021
39. Ketkaew J Yamada R Wang H Kuldinow D Schroers BS Dmowski W Egami T Schroers J The effect of thermal cycling on the fracture toughness of metallic glasses Acta Mater. 2020 184 100 108 10.1016/j.actamat.2019.11.046
Ketkaew, J. et al. The effect of thermal cycling on the fracture toughness of metallic glasses. Acta Mater. 184, 100–108. 10.1016/j.actamat.2019.11.046 (2020).10.1016/j.actamat.2019.11.046
40. Ketov SV Sun YH Nachum S Lu Z Checchi A Beraldin AR Bai HY Wang WH Louzguine-Luzgin DV Carpenter MA Greer AL Rejuvenation of metallic glasses by non-affine thermal strain Nature. 2015 524 200 203 10.1038/nature14674 26268190
Ketov, S. V. et al. Rejuvenation of metallic glasses by non-affine thermal strain. Nature. 524, 200–203. 10.1038/nature14674 (2015).26268190 10.1038/nature14674
41. Chung TM Jian SR Hsieh PJ The effect of Ag addition on the enhancement of the thermal and mechanical properties of CuZrAl bulk metallic glasses Met. 2016 6 216 10.3390/MET6090216
Chung, T. M., Jian, S. R. & Hsieh, P. J. The effect of Ag addition on the enhancement of the thermal and mechanical properties of CuZrAl bulk metallic glasses. Met. 6, 216. 10.3390/MET6090216 (2016).10.3390/MET6090216
42. Nie XP Xu XM Jiang QK Chen LY Xu Y Fang YZ Xie GQ Luo MF Wu FM Wang XD Cao QP Jiang JZ Effect of microalloying of Nb on corrosion resistance and thermal stability of ZrCu-based bulk metallic glasses J. Non. Cryst. Solids. 2009 355 203 207 10.1016/J.JNONCRYSOL.2008.10.011
Nie, X. P. et al. Effect of microalloying of Nb on corrosion resistance and thermal stability of ZrCu-based bulk metallic glasses. J. Non. Cryst. Solids. 355, 203–207. 10.1016/J.JNONCRYSOL.2008.10.011 (2009).10.1016/J.JNONCRYSOL.2008.10.011
43. Jia P Guo H Li Y Xu J Ma E A new Cu–Hf–Al ternary bulk metallic glass with high glass forming ability and ductility Scr. Mater. 2006 54 2165 2168 10.1016/J.SCRIPTAMAT.2006.02.042
Jia, P., Guo, H., Li, Y., Xu, J. & Ma, E. A new Cu–Hf–Al ternary bulk metallic glass with high glass forming ability and ductility. Scr. Mater. 54, 2165–2168. 10.1016/J.SCRIPTAMAT.2006.02.042 (2006).10.1016/J.SCRIPTAMAT.2006.02.042
44. Shi H Zhao W Wei X Ding Y Shen X Liu W Effect of Ti addition on mechanical properties and corrosion resistance of Ni-free Zr-based bulk metallic glasses for potential biomedical applications J. Alloys Compd. 2020 815 152636 10.1016/j.jallcom.2019.152636
Shi, H. et al. Effect of Ti addition on mechanical properties and corrosion resistance of Ni-free Zr-based bulk metallic glasses for potential biomedical applications. J. Alloys Compd. 815, 152636. 10.1016/j.jallcom.2019.152636 (2020).10.1016/j.jallcom.2019.152636
45. Pan J Chan KC Chen Q Li N Guo SF Liu L The effect of microalloying on mechanical properties in CuZrAl bulk metallic glass J. Alloys Compd. 2010 504 S74 S77 10.1016/J.JALLCOM.2010.02.064
Pan, J. et al. The effect of microalloying on mechanical properties in CuZrAl bulk metallic glass. J. Alloys Compd. 504, S74–S77. 10.1016/J.JALLCOM.2010.02.064 (2010).10.1016/J.JALLCOM.2010.02.064
46. Zhang Y Cheng H Du W Shen Y Effect of Ag substitution for Ti on the deformation behaviors of in-situ Ti-based bulk metallic glass composites J. Mater. Res. Technol. 2022 5 69 10.1016/j.jmrt.2022.08.167
Zhang, Y., Cheng, H., Du, W. & Shen, Y. Effect of Ag substitution for Ti on the deformation behaviors of in-situ Ti-based bulk metallic glass composites. J. Mater. Res. Technol. 5, 69 (2022).10.1016/j.jmrt.2022.08.167
47. Ding DW Tan J Cai AH Liu Y Wu H An Q Li PW Zhang Y Yang Q Effect of Ti addition on properties of Zr54Al10.2Ni9.4Cu26.4 glass forming alloy J. Alloys Compd. 2021 864 6580 10.1016/j.jallcom.2021.158911
Ding, D. W. et al. Effect of Ti addition on properties of Zr54Al10.2Ni9.4Cu26.4 glass forming alloy. J. Alloys Compd. 864, 6580. 10.1016/j.jallcom.2021.158911 (2021).10.1016/j.jallcom.2021.158911
48. Ma GZ Sun BA Pauly S Song KK Kühn U Chen D Eckert J Effect of Ti substitution on glass-forming ability and mechanical properties of a brittle Cu-Zr-Al bulk metallic glass Mater. Sci. Eng. A. 2013 563 112 116 10.1016/j.msea.2012.11.036
Ma, G. Z. et al. Effect of Ti substitution on glass-forming ability and mechanical properties of a brittle Cu-Zr-Al bulk metallic glass. Mater. Sci. Eng. A. 563, 112–116. 10.1016/j.msea.2012.11.036 (2013).10.1016/j.msea.2012.11.036
49. Wang D Tan H Li Y Multiple maxima of GFA in three adjacent eutectics in Zr–Cu–Al alloy system–a metallographic way to pinpoint the best glass forming alloys Acta Mater. 2005 53 2969 2979 10.1016/j.actamat.2005.03.012
Wang, D., Tan, H. & Li, Y. Multiple maxima of GFA in three adjacent eutectics in Zr–Cu–Al alloy system–a metallographic way to pinpoint the best glass forming alloys. Acta Mater. 53, 2969–2979. 10.1016/j.actamat.2005.03.012 (2005).10.1016/j.actamat.2005.03.012
50. Zhang L Cheng Y-Q Cao A-J Xu J Ma E Bulk metallic glasses with large plasticity: Composition design from the structural perspective Acta Mater. 2009 57 1154 1164 10.1016/j.actamat.2008.11.002
Zhang, L., Cheng, Y.-Q., Cao, A.-J., Xu, J. & Ma, E. Bulk metallic glasses with large plasticity: Composition design from the structural perspective. Acta Mater. 57, 1154–1164. 10.1016/j.actamat.2008.11.002 (2009).10.1016/j.actamat.2008.11.002
51. Oliver WC Pharr GM An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments J. Mater. Res. 1992 7 1564 1583 10.1557/JMR.1992.1564
Oliver, W. C. & Pharr, G. M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583. 10.1557/JMR.1992.1564 (1992).10.1557/JMR.1992.1564
52. Cheng YQ Ma E Sheng HW Atomic level structure in multicomponent bulk metallic glass Phys. Rev. Lett. 2009 102 245501 10.1103/PHYSREVLETT.102.245501/FIGURES/4/MEDIUM 19659024
Cheng, Y. Q., Ma, E. & Sheng, H. W. Atomic level structure in multicomponent bulk metallic glass. Phys. Rev. Lett. 102, 245501. 10.1103/PHYSREVLETT.102.245501/FIGURES/4/MEDIUM (2009).19659024 10.1103/PHYSREVLETT.102.245501/FIGURES/4/MEDIUM
53. Stiehler ME Panagiotopoulos NT Keeble DS Ivanov YP Menelaou M Jolly MR Lindsay Greer A Georgarakis K The effect of Ni or Co additions on the structure of Zr60Cu30Al10 bulk metallic glass revealed by high-energy synchrotron radiation Mater. Today Commun. 2022 31 103531 10.1016/j.mtcomm.2022.103531
Stiehler, M. E. et al. The effect of Ni or Co additions on the structure of Zr60Cu30Al10 bulk metallic glass revealed by high-energy synchrotron radiation. Mater. Today Commun. 31, 103531. 10.1016/j.mtcomm.2022.103531 (2022).10.1016/j.mtcomm.2022.103531
54. Hua N Zhang T Glass-forming ability, crystallization kinetics, mechanical property, and corrosion behavior of Zr-Al-Ni-Ag glassy alloys J. Alloys Compd. 2014 602 339 345 10.1016/j.jallcom.2014.03.015
Hua, N. & Zhang, T. Glass-forming ability, crystallization kinetics, mechanical property, and corrosion behavior of Zr-Al-Ni-Ag glassy alloys. J. Alloys Compd. 602, 339–345. 10.1016/j.jallcom.2014.03.015 (2014).10.1016/j.jallcom.2014.03.015
55. Chen Y Bo Z-X Sun YH Sun B-A Wang WH Pre-yield serrations in a Mg-based bulk metallic glass during compression J. Alloys Compd. 2023 945 169268 10.1016/j.jallcom.2023.169268
Chen, Y., Bo, Z.-X., Sun, Y. H., Sun, B.-A. & Wang, W. H. Pre-yield serrations in a Mg-based bulk metallic glass during compression. J. Alloys Compd. 945, 169268 (2023).10.1016/j.jallcom.2023.169268
56. Gan K Zhu S Jiang S Huang Y Study on stochastic nature of plasticity of Cu/Zr metallic glass micropillars J. Alloys Compd. 2020 831 154719 10.1016/j.jallcom.2020.154719
Gan, K., Zhu, S., Jiang, S. & Huang, Y. Study on stochastic nature of plasticity of Cu/Zr metallic glass micropillars. J. Alloys Compd. 831, 154719 (2020).10.1016/j.jallcom.2020.154719
57. Bower AF Fleck NA Needleman A Ogbonna N Indentation of a power law creeping solid Proc. R. Soc. London A. 1993 441 97 124 10.1098/rspa.1993.0050
Bower, A. F., Fleck, N. A., Needleman, A. & Ogbonna, N. Indentation of a power law creeping solid. Proc. R. Soc. London A. 441, 97–124. 10.1098/rspa.1993.0050 (1993).10.1098/rspa.1993.0050
58. Li H Ngan AHW Size effects of nanoindentation creep J. Mater. Res. 2004 19 513 522 10.1557/jmr.2004.19.2.513
Li, H. & Ngan, A. H. W. Size effects of nanoindentation creep. J. Mater. Res. 19, 513–522. 10.1557/jmr.2004.19.2.513 (2004).10.1557/jmr.2004.19.2.513
59. Xu F Long ZL Deng XH Zhang P Loading rate sensitivity of nanoindentation creep behavior in a Fe-based bulk metallic glass Trans. Nonferrous Met. Soc. China 2013 23 1646 1651 10.1016/S1003-6326(13)62643-6
Xu, F., Long, Z. L., Deng, X. H. & Zhang, P. Loading rate sensitivity of nanoindentation creep behavior in a Fe-based bulk metallic glass. Trans. Nonferrous Met. Soc. China 23, 1646–1651. 10.1016/S1003-6326(13)62643-6 (2013).10.1016/S1003-6326(13)62643-6
60. Cao QP Sun LJ Wang C Fu Y Liu SY Qu SX Wang XD Zhang DX Jiang JZ Effect of loading rate on creep behavior and shear transformation zone in amorphous alloy thin films, and its correlation with deformation mode transition Thin Solid Films. 2019 681 23 31 10.1016/j.tsf.2019.04.050
Cao, Q. P. et al. Effect of loading rate on creep behavior and shear transformation zone in amorphous alloy thin films, and its correlation with deformation mode transition. Thin Solid Films. 681, 23–31. 10.1016/j.tsf.2019.04.050 (2019).10.1016/j.tsf.2019.04.050
61. Wei B Zhang T Li W Xing D Zhang L Wang Y Indentation creep behavior in Ce-based bulk metallic glasses at room temperature Mater. Trans. 2005 46 2959 2962 10.2320/matertrans.46.2959
Wei, B. et al. Indentation creep behavior in Ce-based bulk metallic glasses at room temperature. Mater. Trans. 46, 2959–2962. 10.2320/matertrans.46.2959 (2005).10.2320/matertrans.46.2959
62. Huang YJ Chiu YL Shen J Chen JJJ Sun JF Indentation creep of a Ti-based metallic glass J. Mater. Res. 2009 24 993 997 10.1557/JMR.2009.0119
Huang, Y. J., Chiu, Y. L., Shen, J., Chen, J. J. J. & Sun, J. F. Indentation creep of a Ti-based metallic glass. J. Mater. Res. 24, 993–997. 10.1557/JMR.2009.0119 (2009).10.1557/JMR.2009.0119
63. Sadeghilaridjani M Muskeri S Hasannaeimi V Pole M Mukherjee S Strain rate sensitivity of a novel refractory high entropy alloy: Intrinsic versus extrinsic effects Mater. Sci. Eng. A. 2019 766 138326 10.1016/j.msea.2019.138326
Sadeghilaridjani, M., Muskeri, S., Hasannaeimi, V., Pole, M. & Mukherjee, S. Strain rate sensitivity of a novel refractory high entropy alloy: Intrinsic versus extrinsic effects. Mater. Sci. Eng. A. 766, 138326. 10.1016/j.msea.2019.138326 (2019).10.1016/j.msea.2019.138326
64. Ginder RS Nix WD Pharr GM A simple model for indentation creep J. Mech. Phys. Solids. 2018 112 552 562 10.1016/j.jmps.2018.01.001
Ginder, R. S., Nix, W. D. & Pharr, G. M. A simple model for indentation creep. J. Mech. Phys. Solids. 112, 552–562. 10.1016/j.jmps.2018.01.001 (2018).10.1016/j.jmps.2018.01.001
65. Ghodki N Sadeghilaridjani M Mukherjee S Time-dependent deformation mechanism of metallic glass in different structural states at different temperatures J. Non. Cryst. Solids. 2022 576 121221 10.1016/J.JNONCRYSOL.2021.121221
Ghodki, N., Sadeghilaridjani, M. & Mukherjee, S. Time-dependent deformation mechanism of metallic glass in different structural states at different temperatures. J. Non. Cryst. Solids. 576, 121221. 10.1016/J.JNONCRYSOL.2021.121221 (2022).10.1016/J.JNONCRYSOL.2021.121221
66. Sadeghilaridjani M Mukherjee S High-temperature nano-indentation creep behavior of multi-principal element alloys under static and dynamic loads Metals (Basel). 2020 10.3390/met10020250
Sadeghilaridjani, M. & Mukherjee, S. High-temperature nano-indentation creep behavior of multi-principal element alloys under static and dynamic loads. Metals (Basel).10.3390/met10020250 (2020).10.3390/met10020250
67. Wang C Cao QP Wang XD Zhang DX Qu SX Jiang JZ Time-dependent shear transformation zone in thin film metallic glasses revealed by nanoindentation creep J. Alloys Compd. 2017 696 239 245 10.1016/j.jallcom.2016.11.264
Wang, C. et al. Time-dependent shear transformation zone in thin film metallic glasses revealed by nanoindentation creep. J. Alloys Compd. 696, 239–245. 10.1016/j.jallcom.2016.11.264 (2017).10.1016/j.jallcom.2016.11.264
68. Dong Q Tan J Huang R Wang HL Song P Li CJ Feng ZX Calin M Eckert J Nanoindentation creep behavior of an Fe–Cr–Mo–B–C amorphous coating via atmospheric plasma spraying Intermetallics. 2022 141 107411 10.1016/j.intermet.2021.107411
Dong, Q. et al. Nanoindentation creep behavior of an Fe–Cr–Mo–B–C amorphous coating via atmospheric plasma spraying. Intermetallics. 141, 107411 (2022).10.1016/j.intermet.2021.107411
69. Yuan CC Lv ZW Pang CM Zhu WW Wang X-L Shen BL Pronounced nanoindentation creep deformation in Cu-doped CoFe-based metallic glasses J. Alloys Compd. 2019 806 246 253 10.1016/j.jallcom.2019.07.226
Yuan, C. C. et al. Pronounced nanoindentation creep deformation in Cu-doped CoFe-based metallic glasses. J. Alloys Compd. 806, 246–253. 10.1016/j.jallcom.2019.07.226 (2019).10.1016/j.jallcom.2019.07.226
70. Johnson WL Samwer K A universal criterion for plastic yielding of metallic glasses with a (T/Tg)2/3 temperature dependence Phys. Rev. Lett. 2005 10.1103/PhysRevLett.95.195501 16486408
Johnson, W. L. & Samwer, K. A universal criterion for plastic yielding of metallic glasses with a (T/Tg)2/3 temperature dependence. Phys. Rev. Lett.10.1103/PhysRevLett.95.195501 (2005).16486408 10.1103/PhysRevLett.95.195501
71. Pan D Inoue A Sakurai T Chen MW Experimental characterization of shear transformation zones for plastic flow of bulk metallic glasses Proc. Natl. Acad. Sci. U. S. A. 2008 105 14769 14772 10.1073/pnas.0806051105 18815377
Pan, D., Inoue, A., Sakurai, T. & Chen, M. W. Experimental characterization of shear transformation zones for plastic flow of bulk metallic glasses. Proc. Natl. Acad. Sci. U. S. A. 105, 14769–14772. 10.1073/pnas.0806051105 (2008).18815377 10.1073/pnas.0806051105
72. Sahu BP Dutta A Mitra R Mechanism of negative strain rate sensitivity in metallic glass film J. Alloys Compd. 2019 784 488 499 10.1016/j.jallcom.2019.01.024
Sahu, B. P., Dutta, A. & Mitra, R. Mechanism of negative strain rate sensitivity in metallic glass film. J. Alloys Compd. 784, 488–499. 10.1016/j.jallcom.2019.01.024 (2019).10.1016/j.jallcom.2019.01.024
73. Zhu SL Wang XM Inoue A Glass-forming ability and mechanical properties of Ti-based bulk glassy alloys with large diameters of up to 1 cm Intermetallics. 2008 16 1031 1035 10.1016/j.intermet.2008.05.006
Zhu, S. L., Wang, X. M. & Inoue, A. Glass-forming ability and mechanical properties of Ti-based bulk glassy alloys with large diameters of up to 1 cm. Intermetallics. 16, 1031–1035. 10.1016/j.intermet.2008.05.006 (2008).10.1016/j.intermet.2008.05.006
74. Chen LY Fu ZD Zhang GQ Hao XP Jiang QK Wang XD Cao QP Franz H Liu YG Xie HS Zhang SL Wang BY Zeng YW Jiang JZ New class of plastic bulk metallic glass Phys. Rev. Lett. 2008 100 1 4 10.1103/PhysRevLett.100.075501
Chen, L. Y. et al. New class of plastic bulk metallic glass. Phys. Rev. Lett. 100, 1–4. 10.1103/PhysRevLett.100.075501 (2008).10.1103/PhysRevLett.100.075501
75. Hirata A Guan P Fujita T Hirotsu Y Inoue A Yavari AR Sakurai T Chen M Direct observation of local atomic order in a metallic glass Nat. Mater. 2011 10 28 33 10.1038/NMAT2897 21102454
Hirata, A. et al. Direct observation of local atomic order in a metallic glass. Nat. Mater. 10, 28–33. 10.1038/NMAT2897 (2011).21102454 10.1038/NMAT2897
76. Sheng HW Luo WK Alamgir FM Bai JM Ma E Atomic packing and short-to-medium-range order in metallic glasses Nature. 2006 439 419 425 10.1038/NATURE04421 16437105
Sheng, H. W., Luo, W. K., Alamgir, F. M., Bai, J. M. & Ma, E. Atomic packing and short-to-medium-range order in metallic glasses. Nature. 439, 419–425. 10.1038/NATURE04421 (2006).16437105 10.1038/NATURE04421
77. Sheng HW Ma E Kramer MJ Relating dynamic properties to atomic structure in metallic glasses JOM. 2012 64 856 881 10.1007/s11837-012-0360-y
Sheng, H. W., Ma, E. & Kramer, M. J. Relating dynamic properties to atomic structure in metallic glasses. JOM. 64, 856–881 (2012).10.1007/s11837-012-0360-y
78. Yang Y-C Xia Z Mukherjee S Unraveling the structural statistics and its relationship with mechanical properties in metallic glasses Nano Lett. 2021 21 9108 9114 10.1021/acs.nanolett.1c02869 34669420
Yang, Y.-C., Xia, Z. & Mukherjee, S. Unraveling the structural statistics and its relationship with mechanical properties in metallic glasses. Nano Lett. 21, 9108–9114. 10.1021/acs.nanolett.1c02869 (2021).34669420 10.1021/acs.nanolett.1c02869
79. Spaepen F A microscopic mechanism for steady state inhomogeneous flow in metallic glasses Acta Metall. 1977 25 407 415 10.1016/0001-6160(77)90232-2
Spaepen, F. A microscopic mechanism for steady state inhomogeneous flow in metallic glasses. Acta Metall. 25, 407–415. 10.1016/0001-6160(77)90232-2 (1977).10.1016/0001-6160(77)90232-2
80. Argon AS Plastic deformation in metallic glasses Acta Metall. 1979 27 47 58 10.1016/0001-6160(79)90055-5
Argon, A. S. Plastic deformation in metallic glasses. Acta Metall. 27, 47–58. 10.1016/0001-6160(79)90055-5 (1979).10.1016/0001-6160(79)90055-5
81. Wang M Lü S Wu S Guo W Rejuvenation behavior of Cu-Zr-Al metallic glass under different thermal treatment: Experiments and simulation J. Alloys Compd. 2023 934 168058 10.1016/j.jallcom.2022.168058
Wang, M., Lü, S., Wu, S. & Guo, W. Rejuvenation behavior of Cu-Zr-Al metallic glass under different thermal treatment: Experiments and simulation. J. Alloys Compd. 934, 168058. 10.1016/j.jallcom.2022.168058 (2023).10.1016/j.jallcom.2022.168058
