# Fileset

[Intermetallics_Manuscript.pdf](https://mdr.nims.go.jp/filesets/6f4a5679-7f04-43f8-8098-e77b1df38ea3/download)

## Creator

[Silvia Pomes](https://orcid.org/0000-0002-0536-9427), Nozomu Adachi, [Masato Wakeda](https://orcid.org/0000-0002-6377-1318), [Takahito Ohmura](https://orcid.org/0000-0001-7528-566X)

## Rights

[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

## Other metadata

[Comparative analysis of nanoindentation-induced incipient deformation of zirconium-based bulk metallic glass in various structural states](https://mdr.nims.go.jp/datasets/0ab9d714-0ba4-4d66-9dac-3fab274d26ff)

## Fulltext

1  Comparative analysis of nanoindentation-induced incipient 1 deformation of zirconium-based bulk metallic glass in various 2 structural states 3  4 Silvia Pomesa,b, Nozomu Adachic, Masato Wakedab, Takahito Ohmuraa,b 5 aDepartment of Materials Science and Engineering, Graduate School of Engineering, 6 Kyushu University, 774 Motooka, Nishi-ku, Fukuoka 819-0395, Japan 7 bResearch Center for Structural materials, National Institute for Materials Science, 1-2-8 1 Sengen, Tsukuba 305-0047, Japan 9 cDepartment of Mechanical Engineering, Toyohashi University of Technology, 1-1 10 Hibarigaoka, Tempaku, Aichi, 441-8580, Japan 11 E-mail addresses:  12 Silvia Pomes pomes.silvia@nims.go.jp 13 Nozomu Adachi adachi.nozomu.tq@tut.jp  14 Masato Wakeda wakeda.masato@nims.go.jp 15 Corresponding author: Takahito Ohmura ohmura.takahito@nims.go.jp  16  17 The incipient plastic deformation behaviour of as-cast and annealed 18 samples of Zr50Cu40Al10 (atom %) bulk metallic glass was investigated by 19 nanoindentation. A validated load-over-displacement versus displacement 20 plot showed the existence of a precursor event to incipient plasticity in 21 both samples. The activation stress remained consistent in both samples, 22 indicating that the event corresponds to local behaviour in regions with the 23 same energy state, and it is not influenced by the overall microstructure. 24 Conversely, the first serration detected in the as-relaxed sample exhibited a 25 greater magnitude, potentially arising from a distinct energy-dissipation 26 rate related to larger-scale microstructural characteristics. 27 mailto:pomes.silvia@nims.go.jpmailto:adachi.nozomu.tq@tut.jpmailto:wakeda.masato@nims.go.jpmailto:ohmura.takahito@nims.go.jp2   28 Keywords: A. metallic glass, B. mechanical properties, B. inhomogeneous 29 transformation, D.  free volume, F.  nanoindentation 30 1. Introduction 31 Instrumented nanoindentation testing is extensively used in the nanomechanical 32 characterization of bulk metallic glasses (BMG) because of its ability to probe small 33 volumes, enabling the study of local responses to applied loads, and the investigation of 34 the underlying deformation processes [1,2]. Upon testing BMG, a close examination of 35 the loading segment on the load–displacement (P–h) curve initially reveals the presence 36 of an elastic deformation, in accordance with the Hertzian equation [3]. Subsequently, a 37 distinctive serrated flow is observed [4–8]. Schuh and Nieh [9] demonstrated that these 38 serrations correspond to the formation of shear bands. This finding was further 39 supported by Mukhopadhyay et al. [10] and was confirmed by atomic-force microscopy. 40 Indeed, deformation through shearing is a widely accepted concept in BMG and is 41 regarded as a stress-activated process occurring among atoms susceptible to structural 42 relaxation [11,12]. In the analysis of the loading segment, the P/h–h plot [13] is a state-43 of-the-art tool for the nanomechanical characterization of metallic materials [14] and it 44 has proved essential in detecting the occurrence of precursor events to incipient 45 plasticity in BMG [15]. 46 Owing to the limitations of experimental research, numerical protocols have been 47 proposed for quantitatively assessing the features of the underlying deformation 48 mechanisms in BMG. From a theoretical perspective, serrated flow observed in BMG, 49 considered a signature of the activation and propagation of a shear band[16], has been 50 3  connected to the overcoming of a specific potential energy barrier [17,18]. By 51 considering the potential energy landscape theory [17], a universal criterion for plastic 52 yielding at room temperature was formulated by Johnson and Samwer [18] as the 53 cooperative shear model (CSM). On the basis of this model and nanoindentation data, 54 Schuh and Lund [19] formulated a mathematical method to estimate the activation 55 volume for the stress-assisted nucleation of defects, characterizing the incipient plastic 56 flow in a crystalline material. The method was successfully applied by Choi et al. [20] 57 to estimate the volume of the shear-transformation zone (STZ) in a BMG, by 58 performing a statistical analysis of the maximum shear stress associated with the onset 59 of the first serration. In our earlier investigation of a Zr-based BMG [15], which 60 involved the use of nanoindentation P/h–h plots and a statistical analysis, we 61 successfully detected a pre-serration deformation, corresponding to a deviation of the 62 data from the Hertz curve for elastic contact. This phenomenon was identified as a 63 thermally activated process, followed by a similarly thermally activated serration. 64 In the present study, we explored the influence of the bulk microstructure on the early 65 stages of deformation by probing pre-serration processes and the first serration in a Zr-66 based metallic glass in various structural states, through nanoindentation.  67 By employing experimental, theoretical, and statistical analyses, this work unveils the 68 potential physical mechanisms governing early-stage deformation and elucidates the 69 influence of the bulk configuration on the incipient deformation dynamics.  70 4  2. Experimental 71 Two samples, as-cast and as-relaxed, of Zr50Cu40Al10 (atom %) BMG were investigated. 72 The alloy was produced by arc-melting and tilt-casting in the form of rods with a 73 diameter of 10 mm [21,22]. The as-relaxed state was obtained from the as-cast rod by 74 annealing for three hours at 659 K, which is 40° below the glass-transition temperature 75 (Tg = 693 K). Each sample was sectioned into 2-mm-thick discs from the rod. Then, the 76 disc samples were polished using sandpaper with a grit size of up to #4000 and diamond 77 suspension with particle sizes up to 1 µm. A sol–gel Al2O3 suspension with a particle 78 size of 0.05 µm was used to remove the damaged surface layer produced by the 79 mechanical polishing. The final surface roughness (RMS) was 1 nm. 80 A Hysitron Triboindenter TI950 (Bruker Co., Minneapolis, MN, USA), equipped with a 81 Berkovich indenter, was employed to perform nanoindentation testing in the load-82 control mode with a peak load of 300 µN, a loading rate of 10 µN/s, and an acquisition 83 rate of 300 points/s. To prevent any interaction between induced strain fields, a spatial 84 separation of 3 µm was maintained between the test locations. To ensure statistical 85 significance, 130 tests were performed on each sample [23]. Nanoindentation tests were 86 analyzed on a P/h–h plot, as described previously [15], and were complemented by 87 statistical and numerical analyses [18–20]. 88  89 5  3. Results and Discussion 90 Figure 1(a) shows typical P–h plots for the two samples: the curve corresponding to the 91 as-relaxed sample has been shifted horizontally to facilitate visualization. The data 92 obtained from the as-cast and as-relaxed samples are shown in yellow and blue, 93 respectively; this colour coding is used consistently throughout this report. A typical 94 image of an indentation mark, obtained by using an atomic-force microscope embedded 95 in the nanoindentation machine, is shown in the inset of Figure 1(a). As estimated by 96 using the Oliver–Pharr method [24], the as-cast and as-relaxed samples exhibited an 97 average hardness H of 4.21 ± 0.36 GPa and 4.39 ± 0.30 GPa, respectively, and reduced 98 moduli Er of 86.5 ± 5.6 GPa and 92.8 ± 5.3 GPa, respectively. Serrations were slightly 99 observable in both loading segments; hence, to detect them more clearly, the loading 100 segments were replotted in the form of a P/h–h graph in Figure 1(b). Notably, the as-101 relaxed curve has been shifted vertically for easier visualization. 102 As in our previous study [15], the characteristic deformation parameters are defined as 103 follows: point HZ represents the deviation of the experimental data from the Hertz curve 104 corresponding to an initiation of inelastic behaviour, whereas point A and point B 105 indicate the onset and completion of a serration event, respectively, and the AB event 106 size is the horizontal distance in displacement between point A and point B.  107 The main plots in Figure 2(a) show the load (PHZ) and displacement values 108 corresponding to point HZ, whereas the side histograms show the probability 109 distribution of each variable on the axis. The Hertz curves for the two samples are 110 indicated by red lines and were calculated by using the following equation 111 6  𝑃 =43𝐸𝑟√𝑅ℎ3, ( 1 112 fitting parameter Er with a fixed indenter tip radius R equal to 700 nm. Because every 113 point lies on the curve, this confirms that point HZ represents the initial point of 114 plasticity as a pre-serration deformation [20]. The fitted Er values for the as-cast and as-115 relaxed samples were 83.6 GPa and 89.7 GPa, respectively, which were almost identical 116 to the values obtained independently by the unloading analysis. The side histograms 117 show a Gaussian-like distribution and an almost identical average and deviation in both 118 samples.  119 Figure 2(b) is a plot for point A, akin to Figure 2(a). The primary plot reveals a positive 120 correlation between higher P values and a greater h, echoing the pattern observed in the 121 point HZ distribution of Figure 2(a). However, compared with Figure 2(a), the data 122 exhibit an increased dispersion. This variance might stem from the stochastic nature of 123 plasticity following point HZ. The side histograms in Figure 2(b) display a distribution 124 of P that is reminiscent of a Gaussian-like curve, similar to that featured in Figure 2(a). 125 Furthermore, they show a remarkable difference in the average value that is higher for 126 the as-relaxed sample. 127 Figure 2(c) illustrates the distribution plot of P at point A (PA) relative to the magnitude 128 of the AB event. In this representation, the data points exhibit a scattered pattern devoid 129 of any discernible trend. This observation implies that the size of the AB event size is 130 independent of PA. The accompanying histograms for the AB event size do not exhibit a 131 distinct Gaussian profile. These outcomes collectively suggest a distinct physical basis 132 for points HZ and A in comparison to the AB event in both samples. 133 7  To identify the underlying nature of these phenomena, complementary cumulative 134 distribution functions (CCDF) for PHZ and PA are presented in Figs. 3(a) and 3(b), 135 respectively. Figure 3(c) shows the CCDF for the AB event size: due to the limited data 136 range (0.6–2.5 nm), a further analysis of the distribution would not have been 137 significant and was, therefore, not performed. Across Figures 3(a) and 3(b), all the data 138 points show a Gaussian-like distribution. This alignment reinforces the findings 139 described in Figures 2(a) and 2(b), supporting the notion that these events potentially 140 stem from thermally activated processes. This observation concurs with the work of 141 Tönnies et al. [25], who reported that the triggering dynamics of the first serration are 142 influenced by thermal fluctuations. 143 We therefore evaluated the activation volumes involved in the deformation processes at 144 point HZ and point A by applying the stress-biased thermal activation model for 145 indentation-induced deformation [19,20]. The maximum shear stress (τ) underneath the 146 indenter was estimated by means of the Hertz contact theory [3] as follows: 147 𝜏 = 0.18 (𝐸𝑟𝑅)23P𝑐23     ( 2 148 where 𝑃𝑐 denotes PHZ or PA. The cumulative distribution of events f with respect to the 149 maximum shear stress values is given as follows [19]: 150 𝑓 = 1 − exp [−𝑘𝑇𝛾̇0𝑣∗(𝑑𝜏 𝑑𝑡⁄ )exp (−∆𝐹∗𝑘𝑇) exp (𝜏𝑣∗𝑘𝑇)],   ( 3 151 where 𝑣∗ is the activation volume, 𝑘𝑇 is the thermal energy, 𝛾̇0 is the attempt frequency 152 and ∆𝐹∗ is the Helmholtz activation energy. The Helmholtz activation energy is the 153 energy barrier for nucleation in the absence of external stimuli. In our experimental 154 8  setting, the stress rate is almost constant because the loading rate is constant. The plot is 155 displayed in Figure 4(a), in which the results for point HZ and point A are plotted as 156 triangular and circular markers, respectively.  157 To estimate the activation volume, Eq. (2) is rewritten as, 158 ln[ln(1 − 𝑓)−1] = {∆𝐹∗𝑘𝑇+ ln [𝑘𝑇𝑣∗(𝑑𝜏 𝑑𝑡⁄ )]} +𝑣∗𝑘𝑇𝜏.  ( 4 159 By excluding the tails of distributions, the data in Figure 4(a) are replotted in Figure 160 4(b) according to Eq. (4). The activation volumes for the events at points HZ and A are 161 determined from the slopes of the plots by linear regression fitting. The slope values are 162 displayed in Figure 4(b) and the calculated values of 𝑣∗ are listed in Table 1.  163 Based on the CSM, the explicit formulation of the volume of the STZ (Ω) with respect 164 to the activation volume is given as [20]: 165 Ω =𝜏06𝐶𝜉𝐺0𝛾𝑐2(1−𝜏𝜏0)12𝑣∗, ( 5 166 where 𝐶 and 𝜉 are constants equal to 1/4 and 3, respectively; 𝐺0 = 𝐸𝑟 2(1 + 𝜈)⁄  is the 167 shear modulus at 𝑇 = 0 𝐾; 𝜏 and 𝜏0 are the threshold shear strengths at temperatures T 168 and 0 K, respectively; and 𝛾𝑐 = 𝜏/𝐺 is the critical shear strain at yielding. Previous 169 studies have demonstrated that the shear modulus does not affect the estimation of the 170 STZ volume to any major extent, and that it exhibits a weak temperature dependence 171 [20,26]. By integrating Poisson’s ratio (ν) as 0.36 for both samples [27], the G0 values 172 obtained for the as-cast and as-relaxed samples are 32 and 34.2 GPa, respectively. 173 9  Parameters 𝛾𝑐, 𝜏, and 𝜏0 are calculated using the scaling law proposed by Johnson and 174 Samwer [18]. The values obtained for Ω are listed in Table 1.  175 An approximation of the number of atoms (N) involved in the STZ is obtained by 176 considering the microstructure of the sample as a random arrangement of densely 177 packed hard spheres with an average atomic radius (ravg) given by 178 𝑟𝑎𝑣𝑔 ≈  (∑ 𝐴𝑖𝑟𝑖3𝑛𝑖 )13, ( 6 179 where 𝐴𝑖 and 𝑟𝑖 are the atomic fraction and atomic radius, respectively, of each alloying 180 element. The calculated average atomic radius is 0.137 nm, considering the values for 181 the covalent atomic radius reported in the literature [28]. The values of N are listed in 182 Table 1. The calculated values of 𝑣∗, Ω and N are consistent, in terms of their order of 183 magnitude, with results reported in previous studies on Zr-based BMG [20,22,26,27,29].  184  185 Table 1. Estimated values of the activation volume 𝑣∗, the STZ volume Ω, and the 186 number of atoms in STZ N at the points HZ and A in as-cast and as-relaxed samples 187  As-cast As-relaxed  HZ A HZ A 𝑣∗ [𝑛𝑚3] 0.023 0.030 0.022 0.039 10  Ω [𝑛𝑚3] 0.517 0.662 0.486 0.859 N [atom] 48 61 45 79  188 The as-cast and as-relaxed samples showed different behaviours. The average value of 189 PA is higher for the as-relaxed sample than for the as-cast sample, as shown in Figures 190 2(b) and 3(b). In addition, the size of the AB event shifts to a higher range in the 191 distribution, as shown in Figure 3(c). This behaviour is presumably due to the 192 differences in the atomic configuration. 193 Prior to deformation, the as-relaxed sample is presumed to display a denser 194 microstructure, characterized by a reduced volume fraction of unstable regions, owing 195 to the energy input during the annealing treatment, resulting in the formation of stronger 196 bonds. Experimental evidence for the increase in the atomic-packing density after sub-197 Tg annealing has been provided by Pan et al. [30] and confirmed by X-ray diffraction 198 analyses of Zr50Cu40Al10 (atom %) BMG as-cast and annealed samples [31]. 199 At point HZ, the same values are found for both the critical load PHZ and the activation 200 volume in the as-cast and as-relaxed samples. This suggests that the atomic 201 rearrangement at point HZ of pre-serration deformation might correspond to a highly 202 localized process occurring in the unstable region. Furthermore, given that both samples 203 are composed of the same alloying elements, the enthalpy of formation associated with 204 the weakest interatomic bond is identical in both samples, as is the potential energy 205 11  barrier associated with their configuration [17]. The absence of differences in point HZ 206 events, both in their physical nature and scale, suggests that the different degrees of 207 microstructural heterogeneity of the bulk samples do not affect the incipient 208 deformation mechanics.  209 At point A, the critical load PA of the as-cast sample is lower than that of the as-relaxed 210 sample. Choi et al. [29] and Tao et al. [31] reported that as-cast Zr-based BMG samples, 211 as well as the sub-Tg annealed samples, exhibited a similar occurrence of smaller critical 212 loads and STZ sizes at the first pop-in. Tao et al. recently confirmed their findings by 213 using nanoindentation creep and strain-rate sensitivity methods [32,33]. In this work, 214 and in line with previous studies, the aforementioned occurrence is explained in terms 215 of the different structural configurations of the samples. In the as-cast sample, the 216 volume fraction of easily movable atoms is higher; consequently, these atoms are nearer 217 to one another, and a smaller applied stress is required to trigger the cooperative 218 shearing phenomenon. From an energetic standpoint, the as-cast microstructure is more 219 unstable overall; consequently, the energy quota required to reach the serration energy 220 barrier is smaller.  221 Regarding the size of the AB event, longer serrations detected in the as-relaxed sample 222 might be due to the larger distance to which the strain is accommodated in the more-223 uniform microstructure and to the slower energy-dissipation rate over smoother 224 potential-energy landscape transition states.  225  226 12  4. Conclusion 227 In brief, we have conducted a comparative analysis of the early stages of deformation in 228 as-cast and as-relaxed Zr50Cu40Al10 (atom %) BMG by nanoindentation testing. Any 229 unstable deformation mode during loading was clearly visualized using a P/h–h plot. 230 The work yielded the following findings. 231 (1) The critical stress value at point HZ, corresponding to the pre-serration event, 232 was consistent between the two samples, indicating that the event represents a 233 local behaviour occurring in regions characterized by the same energy state and 234 that it is not subject to the influence of the overall microstructure.  235 (2) The critical load at point A of the as-cast sample is lower than that of the as-236 relaxed sample. This difference could be attributed to the higher volume fraction 237 of unstable regions in the as-cast sample, so that a smaller applied stress is 238 required to trigger the serration. 239 (3) The magnitude of the AB event detected in the as-relaxed sample was greater 240 than that in the as-cast sample, potentially due to a distinct energy-dissipation 241 rate related to microstructural characteristics on a larger scale.  242  243 Acknowledgements: S.P. is grateful to acknowledge experimental support by Eri 244 Nakagawa. 245  246 CRediT authorship contribution statement  247 13  Silvia Pomes: Conceptualization; Data curation; Formal analysis; Investigation; 248 Methodology; Writing - original draft; Writing - review & editing. Nozomu Adachi: 249 Funding acquisition; Resources; Writing - review & editing. Masato Wakeda: Writing - 250 review & editing. Takahito Ohmura: Conceptualization; Funding acquisition; 251 Methodology; Project administration; Resources; Supervision; Writing - review & 252 editing. 253  254 Declaration of competing interest  255 The authors declare that they have no known competing financial interests or personal 256 relationships that could have appeared to influence the work reported in this paper.  257  258 Data availability  259 Data are not available for public access. 260  261 Funding: This research did not receive any specific grant from funding agencies in the 262 public, commercial, or not-for-profit sectors. 263   264  265 References 266 14  [1] Zhang M, Chen Y, Li W. On the origin of softening in the plastic deformation of 267 metallic glasses. Int. J. Plast. 2019;116:24–38:. doi: 268 10.1016/j.ijplas.2018.12.004. 269 [2] Zhang L, Ohmura T. Plasticity initiation and evolution during nanoindentation of 270 an iron–3% silicon crystal. Phys. Rev. Lett. 2014;112:145504. doi: 271 10.1103/PhysRevLett.112.145504. 272 [3] Johnson KL. One hundred years of Hertz contact. Proc. Inst. Mech. Eng. 273 1982;196(1):363–378. doi: 10.1243/pime_proc_1982_196_039_02. 274 [4] Argon AS. Plastic deformation in metallic glasses. Acta Metall. 1979;27(1):47–275 58. doi: 10.1016/0001-6160(79)90055-5. 276 [5] Kimura H, Masumoto T. A model of the mechanics of serrated flow in an 277 amorphous alloy. Acta Metall. 1983;31(2):231–240. doi: 10.1016/0001-278 6160(83)90100-1. 279 [6] Pampillo CA, Chen HS. Comprehensive plastic deformation of a bulk metallic 280 glass. Mater. Sci. Eng. 1974;13(2):181–188. doi: 10.1016/0025-5416(74)90185-281 2. 282 [7] Spaepen F. A microscopic mechanism for steady state inhomogeneous flow in 283 metallic glasses. Acta Metall. 1977;25: doi: 10.1016/0001-6160(77)90232-2. 284 [8] Maaß R. Beyond serrated flow in bulk metallic glasses: what comes next? 285 Metall. Mater. Trans. A. 2020;51:5597–5605. doi: 10.1007/s11661-020-05985-286 w. 287 [9] Schuh CA, Nieh TG. A nanoindentation study of serrated flow in bulk metallic 288 glasses. Acta Mater. 2003;51(1):87–99. doi: 10.1016/S1359-6454(02)00303-8. 289 [10] Mukhopadhyay NK, Belger A, Paufler P, et al. Nanoindentation studies on Cu–290 Ti–Zr–Ni–Si–Sn bulk metallic glasses. Mater. Sci. Eng. A. 2007;449–551:954–291 957. doi: 10.1016/j.msea.2006.02.258. 292 [11] Argon AS. Plastic deformation in metallic glasses. Acta Metall. 1979;27(1):47–293 58. doi: 10.1016/0001-6160(79)90055-5. 294 [12] Argon AS. Strain avalanches in plasticity. Philos. Mag. 2013;93(28–30):3795–295 3808. doi: 10.1080/14786435.2013.798049. 296 15  [13] Sekido K, Ohmura T, Sawaguchi T, et al. Nanoindentation/atomic force 297 microscopy analyses of e-martensitic transformation and shape memory effect in 298 Fe–28Mn–6Si–5Cr alloy. Scr. Mater. 2011;65(11):942–945. doi: 299 10.1016/j.scriptamat.2011.08.010. 300 [14] Ohmura T. Nanomechanical characterization of metallic materials. In: Tanaka I, 301 Tsuji N, Inui H, editors. The plaston concept: Plastic deformation in structural 302 materials. Singapore: Springer Nature Singapore; 2022. p. 157–195. doi: 303 10.1007/978-981-16-7715-1_8. 304 [15] Pomes S, Adachi N, Wakeda M, Ohmura T. Probing pre-serration deformation in 305 Zr-based bulk metallic glass via nanoindentation testing. Scr. Mater. 306 2023;237:115713. doi: 10.1016/j.scriptamat.2023.115713. 307 [16] Maaß R, Klaumünzer D, Löffler JF. Propagation dynamics of individual shear 308 bands during inhomogeneous flow in a Zr-based bulk metallic glass. Acta Mater. 309 2011;59(8):3205–3213. doi: 10.1016/j.actamat.2011.01.060. 310 [17] Wales DJ. A microscopic basis for the global appearance of energy landscapes. 311 Science. 2001;293(5537):2067–2070. doi: 10.1126/science.1062565. 312 [18] Johnson WL, Samwer K. A universal criterion for plastic yielding of metallic 313 glasses with a (T/Tg)2/3 temperature dependence. Phys. Rev. Lett. 314 2005;95:199501. doi: 10.1103/PhysRevLett.95.195501. 315 [19] Schuh CA, Lund AC. Application of nucleation theory to the rate dependence of 316 incipient plasticity during nanoindentation. J. Mater. Res. 2004;19: 2152–2158. 317 doi: 10.1557/JMChoi R2004.0276. 318 [20] Choi I-C, Zhao Y, Yoo B-G, et al. Estimation of the shear transformation zone 319 size in a bulk metallic glass through statistical analysis of the first pop-in 320 stresses during spherical nanoindentation. Scr. Mater. 2012;66(11):923–926. doi: 321 10.1016/j.scriptamat.2012.02.032. 322 [21] Yokoyama Y, Fredriksson H, Yasuda H, et al. Glassy solidification criterion of 323 Zr50Cu40Al10 alloy. Mater. Trans. 2007;48(6):1363–1372. doi: 324 10.2320/matertrans.MF200624. 325 16  [22] Adachi N, Todaka Y, Ohmura T. Macroscopic viscoelastic deformation at room 326 temperature in mechanically rejuvenated Zr-based metallic glass. MRS 327 Commun. 2021;11:330–335. doi: 10.1557/s43579-021-00023-1. 328 [23] Nag S, Narayan RL, Mukhopadhyay Jang J-I, et al. Statistical nature of the 329 incipient plasticity in amorphous alloys. Scr. Mater. 2020;187:360–365. doi: 330 10.1016/j.scriptamat.2020.06.045. 331 [24] Oliver WC, Pharr GM. An improved technique for determining hardness and 332 elastic modulus using load and displacement sensing indentation experiments. J. 333 Mater. Res. 1992;7:1564–1583. doi: 10.1557/jmr.1992.1564. 334 [25] Tönnies D, Samwer K, Derlet PM, et al. Rate-dependent shear-band initiation in 335 a metallic glass. Appl. Phys. Lett. 2015;106:171907. doi: 10.1063/1.4919134. 336 [26] Limbach R, Kosiba K, Pauly S, et al. Serrated flow of CuZr-based bulk metallic 337 glasses probed by nanoindentation: Role of the activation barrier, size and 338 distribution of shear transformation zones. J. Non. Cryst. Solids. 2017;459: 130–339 141. doi: 10.1016/j.jnoncrysol.2017.01.015. 340 [27] Ma Y, Peng GJ, Debela TT, et al., Nanoindentation study on the characteristic of 341 shear transformation zone volume in metallic glassy films. Scr. Mater. 342 2015;108:52–55. doi: 10.1016/j.scriptamat.2015.05.043. 343 [28] Pyykkö P, Atsumi M, Molecular single-bond covalent radii for elements 1–118. 344 Chem. Eur. J. 2008;15(1):186–197. doi: 10.1002/chem.200800987. 345 [29] Choi IC, Zhao Y, Kim YJ, et al., Indentation size effect and shear transformation 346 zone size in a bulk metallic glass in two different structural states. Acta Mater. 347 2012;60(19):6862–6868. doi: 10.1016/j.actamat.2012.08.061. 348 [30] Pan D, Yokoyama Y, Fujita T, et al. Correlation between structural relaxation and 349 shear transformation zone volume of a bulk metallic glass. Appl. Phys. Lett. 350 2009;95:141909. doi: 10.1063/1.3246151. 351 [31] Tao K, Qiao JC, He QF, et al. Revealing the structural heterogeneity of metallic 352 glass: Mechanical spectroscopy and nanoindentation experiments. Int. J. Mech. 353 Sci. 2021;201:106469. doi: 10.1016/j.ijmecsci.2021.106469. 354 17  [32] Pan D, Inoue A, Sakurai T, et al. Experimental characterization of shear 355 transformation zones for plastic flow of bulk metallic glasses. Proc. Natl. Acad. 356 Sci. U. S. A. 2008;105(39): 14769–14772. doi: 10.1073/pnas.0806051105. 357 [33] Tao K, Khonik VA, Qiao JC. Indentation creep dynamics in metallic glasses 358 under different structural states. Int. J. Mech. Sci. 2023;240:107941. doi: 359 10.1016/j.ijmecsci.2022.107941. 360 361 18   362 Figure 1 (a) Representative load–displacement P–h curve for the Zr50Cu40Al10 bulk 363 metallic glass as-cast (yellow) and as-relaxed (blue) samples. Serration is indicated by 364 black arrows. A resulting indentation mark is shown in the inset. (b) P/h–h curves 365 obtained from Figure 1(a): serrations exhibit a negative slope.366 19   367 Figure 2 Distribution plots for as-cast (yellow) and as-relaxed (blue) samples. (a) 368 Distribution of depth versus load at point HZ. Side histogram plots show probability 369 distributions. Hertz curves are displayed in red. (b) Distribution of depth versus load at 370 point A. (c) Distribution of the size at event AB versus the load at point A: the serration 371 size is not related to the activation load. 372 20   373 Figure 3 Log–log plots of complementary cumulative distribution functions for as-cast 374 (yellow) and as-relaxed (blue) samples at (a) point HZ, (b) point A and (c) AB event 375 size.376 21   377 Figure 4 (a) Cumulative distribution of maximum shear stress underneath the indenter 378 at point HZ (triangular marker) and point A (circular marker) for as-cast (AC; yellow) 379 and as-relaxed (AR; blue) samples. (b) Activation volume estimation at points HZ and 380 A.  381