Analysis of the anelastic deformation of high-entropy Pd20Pt20Cu20Ni20P20 metallic glass under stress relaxation and recovery

1 Analysis of the anelastic deformation of high-entropy 1 Pd20Pt20Cu20Ni20P20 metallic glass under stress relaxation and 2 recovery 3 4 Y.J. Duana,b, L.T. Zhanga, T. Wadac, H. Katoc, E. Pinedab, D. Crespob, J.M. Pelletierd, 5 J.C. Qiaoa,* 6 aSchool of Mechanics, Civil Engineering and Architecture, Northwestern 7 Polytechnical University, Xi’an 710072, China 8 bDepartment of Physics, Institute of Energy Technologies, Universitat Politècnica de 9 Catalunya, Barcelona 08019, Spain 10 cInstitute for Materials Research, Tohoku University, Sendai 980-8577, Japan 11 d Université de Lyon, MATEIS, UMR CNRS5510, Bat. B. Pascal, INSA-Lyon, F-69621 12 Villeurbanne Cedex, France 13 14 15 16 Submitted to Journal of Materials Science & Technology 17 (Version: July 02, 2021) 18 19 *Corresponding author. 20 Prof. Dr. J.C. Qiao, E-mail address: [email protected] 21 22 23 24 25 2 Abstract 26 The anelastic deformation behavior of Pd20Pt20Cu20Ni20P20 high-entropy metallic 27 glass was probed by monitoring the stress relaxation and recovery processes. The stress 28 relaxation under consecutive strain steps can be described by the Kohlrausch-Williams-29 Watts (KWW) function. In addition, considering a hierarchy of relaxation processes 30 related to the structural heterogeneity, a constitutive model is proposed in order to 31 describe the whole process of stress relaxation and determine the contribution of 32 different time scales. Moreover, a crossover from stochastic activation to percolation of 33 flow defects with the ultimate strain can be observed during stress relaxation process. 34 The anelastic recovery process after a strain step is studied as a function of the initial 35 strain level and characterized by means of a direct spectrum analysis. The peaks in the 36 recovery time-spectra revealed the evolution of flow defects in Pd20Pt20Cu20Ni20P20 37 high-entropy metallic glass. The understanding of the atomic free-volume zones effect 38 and the anelastic deformation provides important insight into how atomic structural 39 features affect the deformation behavior of high-entropy metallic glasses, and may 40 provide a new avenue into the improvement of their mechanical properties. 41 42 Keywords: High-entropy metallic glass; Stress relaxation; Anelastic deformation; 43 Flow defects; Free-volume zones 44 1. Introduction 45 Compared with conventional crystalline alloys, metallic glasses (MGs) present a 46 unique combination of physical, chemical and mechanical properties such as high 47 strength, high hardness, large elastic strain as well as high corrosion and wear resistance 48 [1-3]. Over the past decades, tremendous research efforts have been dedicated to the 49 fundamental issues controlling their various properties [4-7], among which, the 50 understanding of structural heterogeneity in MGs and its link with the mechanical 51 deformation behavior is one of the most challenging issues. 52 Over the past decades, great advances have been achieved from theories [8-10], 53 experiments [11, 12] and simulations [13] to understand the nature of atomic structure 54 3 and structural heterogeneity in MGs. Numerous studies attempted to elucidate the link 55 between structural heterogeneity and mechanical/physical properties of MGs, which is 56 a crucial factor to understand the cryogenic thermal cycling effects [14, 15], elastic 57 properties [16, 17], inelastic deformation [18, 19] and the nano-glass structure [20, 21]. 58 On the basis of previous research, it is known that MGs consist of tightly bonded atomic 59 clusters and loosely bonded free-volume regions, which act as so-called “soft” spots or 60 flow defects under mechanical loading [8, 22]. However, the mechanical properties of 61 these atomistic regions, which are the origin of dynamic heterogeneity, are not 62 thoroughly understood up to date. A comprehensive understanding of the interplay 63 between the dynamic structural heterogeneity and the mechanical deformation 64 properties is still lacking. The deep comprehension of such dynamic and structural 65 heterogeneity may provide key knowledge to improve the mechanical properties of 66 MGs. 67 Based on a principal metallic element (e.g. Zr, Cu, Pd, Mg or Ti), traditional MGs 68 show a limited glass-forming ability (GFA) [23]. High-entropy alloys (HEAs), 69 containing equiatomic or near-equiatomic compositions, have been developed recently 70 [3, 24, 25]. HEAs exhibit superior properties, i.e. high configurational entropy, large 71 lattice distortion, sluggish diffusion and cocktail effect [25-27]. Inheriting some distinct 72 properties of both MGs and HEAs, high-entropy metallic glasses (HE-MGs) exhibit 73 superior properties (e.g. ultrahigh strength at room temperature [28] and sluggish 74 diffusion [29, 30]). HE-MGs are important candidates to be applied as functional and 75 structural materials and can help us to understand the metallic glass state, facilitating 76 the construction of a correlation between atomic free-volume zones and the mechanical 77 behavior. 78 The Pd20Pt20Cu20Ni20P20 HE-MG is derived from Pd40Ni40P20 MG, a prototypical 79 MG which has been widely investigated in many aspects, such as the yield criterion 80 [31], the effect of high-pressure torsion [32], the formation of shear bands [33], as well 81 as the atomic diffusivity and viscosity [34]. Among the developed HE-MGs, 82 Pd20Pt20Cu20Ni20P20 has relatively large GFA, with a 10 mm critical diameter for fully 83 4 amorphous structure [35]. Due to the wide supercooled liquid temperature range of 65 84 K and large GFA, as well as a reduced glass transition temperature of 0.71 [35], the 85 Pd20Pt20Cu20Ni20P20 HE-MG is a potential model alloy to study the structural 86 heterogeneity and mechanical behavior of MGs. 87 The long-term mechanical evolution of MGs has been intensely investigated by 88 creep [36, 37], stress relaxation [38-40], and recovery experiments [41]. In particular, 89 stress relaxation is performed at a constant strain by the application of uniaxial tension 90 or compression on the specimen, and monitoring how the stress gradually decrease with 91 relaxation time [38]. Characterizing and understanding such time evolution is a key 92 factor when using the materials in engineering applications. As a viscoelastic material, 93 MGs show a further time dependent behavior once the applied loading is removed, as 94 the unstrained state is not achieved immediately. Such anelastic recovery is typically 95 active, during long times. Derived from the ternary Pd40Ni40P20 MG, the 96 characterization of atomic free-volume zones of Pd20Pt20Cu20Ni20P20 HE-MG and their 97 possible relationship with anelastic deformation are unknown issues at the present time. 98 In the current work, the stress relaxation and recovery processes are used to probe 99 the deformation behavior of Pd20Pt20Cu20Ni20P20 HE-MG. The stress relaxation during 100 step strain conditions is described by the Kohlrausch-Williams-Watts (KWW) function 101 and, subsequently, by a constitutive model considering a hierarchy of relaxation time 102 scales. The constitutive model is proposed within the frame of atomic free volume zones 103 and structural heterogeneity of MGs. And a crossover from stochastic activation to 104 percolation of flow defects reveals that the atomic/molecular level mechanisms of the 105 stress relaxation behavior of Pd20Pt20Cu20Ni20P20 HE-MG are strongly dependent on the 106 ultimate strain. Following, a direct spectrum analysis is considered in order to 107 investigate the impact of initial strain level on the anelastic recovery process. Finally, 108 the physical explanation of the distinct phenomena observed under stress relaxation and 109 recovery is proposed to come from the flow defects related to free-volume zones in 110 Pd20Pt20Cu20Ni20P20 HE-MG. 111 112 2. Experimental 113 5 2.1 Sample fabrication and thermal properties 114 The master alloys of Pd20Pt20Cu20Ni20P20 HE-MG were fabricated by the B2O3 flux 115 method [35]. The alloy was mixed together in a sealed and evacuated quartz tube under 116 inert argon in a resistance heating furnace. Ribbons ~0.02mm thick and 1.2mm wide, 117 were fabricated by single-wheel melt-spinning technique in an argon atmosphere. X-118 ray diffraction (XRD) was employed to confirm the amorphous structure using a 119 commercial device (D8, Bruker AXS Gmbh), as shown in Fig. 1 (a). The thermal 120 properties of the Pd20Pt20Cu20Ni20P20 HE-MG were determined by differential scanning 121 calorimetry (DSC, Netzsch 202) in a nitrogen atmosphere with a heating rate of 10 122 K/min. The glass transition temperature 𝑇𝑇𝑔𝑔= 572 K and the onset crystallization 123 temperature 𝑇𝑇𝑥𝑥= 632 K were determined [27]. The large supercooled liquid region 124 (SLR) ∆𝑇𝑇 =𝑇𝑇𝑥𝑥−𝑇𝑇𝑔𝑔=60 K indicates an excellent glass forming ability. Hence, 125 Pd20Pt20Cu20Ni20P20 HE-MG has been selected as an excellent model alloy to study the 126 stress relaxation and recovery behavior of HE-MGs. 127 2.2 Dynamic mechanical analysis and uniaxial tensile experiments 128 Dynamic mechanical analysis (DMA, TA Q800) was performed in Nitrogen 129 atmosphere using ribbon samples of the HE-MG. Constant heating experiments were 130 conducted with a driving frequency of 2 Hz and a heating rate of 5 K/min. The storage 131 modulus 𝐸𝐸′ and loss modulus 𝐸𝐸′′ were determined. Uniaxial tensile experiments 132 were carried out on ribbon samples on DMA. After reaching the target test temperature, 133 the ribbon sample was equilibrated for 10 minutes, and then the uniaxial tensile 134 experiments were performed at a constant strain rates (1.5 × 10−4, 3 × 10−4…4.5 ×135 10−4𝑠𝑠−1) and temperatures (508, 513, 523…563 K). 136 2.3 Stress relaxation spectra measurements 137 The stress relaxation experiments, containing 20 iso-strain stress relaxation curves, 138 were measured during consecutive strain steps from 1% to 10% at 508 K. Each step 139 increased the total strain by 0.5% and lasted for 30 minutes. The experiments were 140 performed on the TA Q800 DMA using ribbon samples. 141 2.4 Recovery measurement after stress relaxation 142 6 Tensile stress relaxation and recovery experiments were performed on the TA 143 Q800 DMA with ribbon samples. Samples were first constrained at a constant strain 144 (0.4%, 0.6%...7%) for 180 minutes, then allowed to relax stress-free for 600 minutes. 145 146 3. Results and discussion 147 3.1 Dynamic mechanical analysis and stress-strain curves 148 The temperature dependence of the normalized loss modulus 𝐸𝐸′′/𝐸𝐸𝑢𝑢 of 149 Pd20Pt20Cu20Ni20P20 HE-MG ribbon sample is shown in Fig. 1 (b). The normalized loss 150 modulus 𝐸𝐸′′/𝐸𝐸𝑢𝑢 is very small at low temperature. With increasing temperature, a large 151 increase of the normalized loss modulus is observed, which corresponds first to the 152 slow 𝛽𝛽 relaxation and, eventually, the primary 𝛼𝛼 relaxation. Unlike the La-based 153 MGs, that show an evident slow 𝛽𝛽 relaxation peak [19, 27], and the Zrand Pt-based 154 MGs, that show only an excess wing [27], the Pd20Pt20Cu20Ni20P20 HE-MG exhibit a 155 broad shoulder corresponding to slow 𝛽𝛽 relaxation as shown in Fig. 1 (b). Recent 156 investigations showed that the slow 𝛽𝛽 relaxation closely relates to the plastic 157 deformation and the nature of the glass transition of MGs [42]. Besides, 158 Pd20Pt20Cu20Ni20P20 HE-MG exhibits a ultrahigh activation energy of slow 𝛽𝛽 159 relaxation, suggesting that HE-MGs may possess a higher energy barrier for the 160 dynamic 𝛽𝛽 relaxation [27]. 161 Fig. 1 (c) shows the stress-strain curves of Pd20Pt20Cu20Ni20P20 HE-MG ribbon as 162 a function of temperature with a strain rate of 3 × 10−4𝑠𝑠−1. The flow stress decreases 163 from 790 MPa to 140 MPa when the temperature increases by 60 K. Therefore, the flow 164 stress is strongly thermally activated. A large homogeneous deformation (𝜀𝜀 ≈ 18%) 165 can be captured without any extensive strain hardening. It has been reported that the 166 homogeneous deformation occurs at a higher temperature in MGs (typically for 𝑇𝑇>167 0.8𝑇𝑇𝑔𝑔) [43], which is consistent with the results in Fig. 1 (c). In such cases, the MGs 168 always exhibit pronounced plasticity [44]. The plastic deformation of MGs is related to 169 formation of the localized shear bands [45]. Fig. 1 (d) shows the stress-strain curves as 170 a function of strain rate at 508 K. The strength increases and the final elongation 171 7 decreases with increasing strain rate. The deformation mode changes from the 172 homogeneous type to the inhomogeneous one increasing the strain rate above 4.0 ×173 10−4𝑠𝑠−1 . And the brittleness increases with the increase of the strain rate during 174 deformation [43]. In the homogeneous deformation region, the deformation begins to 175 yield with a stress overshoot, followed by stable flow, similar results has been found in 176 Zr-based metallic glass [46]. 177 178 Fig. 1 (a) XRD curve of the as-cast Pd20Pt20Cu20Ni20P20 HE-MG. (b) Normalized loss 179 modulus 𝐸𝐸′′/𝐸𝐸𝑢𝑢 of Pd20Pt20Cu20Ni20P20 HE-MG ribbon as a function of temperature. 180 The heating rate is 5 K/min, and the driving frequency is 2 Hz. 𝐸𝐸𝑢𝑢 denotes the value 181 of the storage modulus at room temperature. (c) Stress-strain curves of 182 Pd20Pt20Cu20Ni20P20 HE-MG as a function of temperature with a strain rate of 3 ×183 10−4𝑠𝑠−1. (d) as a function of strain rate at 508 K. 184 185 3.2 Stress relaxation spectra analysis 186 Stress relaxation is a powerful tool to reveal the time-dependent nature of flow 187 defects in amorphous, viscoelastic solids (i.e. MGs and polymers) [38, 47]. Fig. 2 (a) 188 shows the stress relaxation results of Pd20Pt20Cu20Ni20P20 HE-MG consisting of 20 iso-189 strain stress relaxation curves measured at step strains from 1% to 10% at 508 K. The 190 8 strain line is shown in Fig. 2 (a), the stress relaxation curves of Pd20Pt20Cu20Ni20P20 191 HE-MG at 508 K were obtained during each iso-strain step. Typical isothermal stress-192 relaxation curve measured at 1% are shown in the insert of Fig. 2 (a) at 508 K, and the 193 temporal-dependent stress 𝜎𝜎(𝑡𝑡) is normalized by the initial stress 𝜎𝜎0. Generally, the 194 normalized 𝜎𝜎(𝑡𝑡)/𝜎𝜎0 shows a rapid decrease from 1 at the beginning of stress 195 relaxation, and then obviously slows down and decays sluggishly with relaxation time. 196 These prominent features are consistent with other experiments and simulation in stress 197 relaxation of MGs [38, 40, 48]. The initial stress 𝜎𝜎onset and terminal stress 𝜎𝜎end have 198 an effect on the viscoelastic properties in glassy solids [47]. The initial stress 𝜎𝜎onset, 199 terminal stress 𝜎𝜎end and stress drop ∆𝜎𝜎 =𝜎𝜎onset −𝜎𝜎end of each stress relaxation 200 curve are shown as open squares, circles and triangles in Fig. 2 (a) and (b), respectively. 201 The initial stress 𝜎𝜎onset , terminal stress 𝜎𝜎end and stress drop ∆𝜎𝜎 increase 202 significantly with stepping strain until a total strain of 5%. As shown in Fig. 1 (b), the 203 critical strain 5% can be regarded as the ultimate strain of Pd20Pt20Cu20Ni20P20 HE-MG 204 at 508 K, implying that the decay of stress in strained HE-MG is correlated with the 205 step strain and a transition of stress relaxation behavior may occur around the critical 206 strain, similar results have been found in stress relaxation dynamics of glasses with 207 molecular dynamic simulations [48]. It is found that the ∆𝜎𝜎 exhibits approximately 208 linear below 5%, however, the change of of 𝜎𝜎onset , 𝜎𝜎end , and ∆𝜎𝜎 is much less 209 prominent, confirming that the stress relaxation process is sensitive with step strain 210 (below 5%), but insensitive with step strain shown in Fig. 2 (b). The change of the 211 correlations between step strain and ∆𝜎𝜎 may indicate the crossover of the relaxation 212 behaviors near to 5%. 213 The stress relaxation of Pd20Pt20Cu20Ni20P20 HE-MG curves can be fitted by a 214 phenomenological KWW equation [38, 49], 215 𝜎𝜎(𝑡𝑡)=𝜎𝜎0exp (−𝑡𝑡 𝜏𝜏𝑐𝑐)𝛽𝛽KWW (1) 216 where 𝜎𝜎0 is the initial stress at each strain step, 𝛽𝛽KWW is the stretched exponential 217 parameter, reflecting the dynamic heterogeneity, and 𝜏𝜏𝑐𝑐 is the characteristic time 218 related to the stress relaxation mechanisms [38, 49]. 219 9 The values of 𝛽𝛽KWW and 𝜏𝜏𝑐𝑐 are shown in Fig. 2 (b). Smaller 𝛽𝛽KWW implies 220 larger dynamic heterogeneity in MGs [50, 51]. The value of 𝛽𝛽KWW decreases 221 substantially until the strain reaches 1.5%, while maintains a constant value at higher 222 stepping strains. The characteristic relaxation time 𝜏𝜏𝑐𝑐 increases from 102 s to 223 106 s with increasing strain below 5%, while it changes slightly at higher stains. The 224 change of characteristic relaxation time 𝜏𝜏𝑐𝑐 is very close to the evolution of stress drop 225 ∆𝜎𝜎, indicating again a crossover of the relaxation behaviors at strains above 5%. Larger 226 stress drops ∆𝜎𝜎 imply larger fraction of activated flow defects, related to free-volume 227 zones, in the MGs [47, 48]. The individual flow defects are activated even when the 228 applied strain is less than 2%, which is excellent consistent with the previous 229 experiment and simulation results of the existence of local atomic rearrangements in 230 nominal elasticity deformation region in MGs [37, 48]. As this first type of flow defects 231 is strained the relaxation involves more different type of units, thus increasing the 232 dynamic heterogeneity and characteristic time 𝜏𝜏𝑐𝑐. As the step strain increases, more 233 flow defects are activated, which are corresponding to a stochastic and isolated 234 activation of the flow defects, similar molecular dynamic simulation results were found 235 in MGs [48]. However, when the energy barrier of atomic arrangements in liquid-like 236 regions [52-54] (also called free-volume zones or flow units [55, 56]) is tilted to a 237 certain level, the local plastic flows become easily activated, and the yielding occurs in 238 amorphous solids [57]. Above 5%, the change of 𝜎𝜎onset, 𝜎𝜎end, and ∆𝜎𝜎 is much less 239 prominent, implying that the activation and annihilation of flow defects reach a 240 dynamic equilibrium. This indicates that the whole sample of Pd20Pt20Cu20Ni20P20 HE-241 MG enters into a relatively stable state at 508 K after increasing the strain above 5%, 242 and similar behaviors of atomic rearrangement have been reported the dynamic 243 heterogeneity behaviors during the stress relaxation [48]. The crossover from stochastic 244 activation to percolation of flow defects reveals the atomic/molecular level mechanisms 245 of the stress relaxation behavior of Pd20Pt20Cu20Ni20P20 HE-MG, which are strongly 246 dependent on the ultimate strain. 247 16 anelastic strain 𝜀𝜀𝑎𝑎𝑎𝑎 contributions with the increase of initial strain level, indicating 346 significant enhancement of the viscoplastic strain 𝜀𝜀𝑣𝑣𝑣𝑣. The dependence on the initial 347 strain of the three different recovery deformation contributions can be divided into three 348 regions as shown in Fig. 6 (b)-(d). Region (Ⅰ), when the initial strain level is below 1%, 349 is characterized by a very large decrease of the elastic and anelastic contributions, with 350 the corresponding increase of the viscoplastic part, as initial strain is increased. The 351 slopes of anelastic and viscoplastic contributions as a function of initial strain are higher 352 than that of the elastic one. These region correspond to the nominal elastic region in 353 MGs [22]. Region (Ⅱ), with initial strain levels between 1% and 2%, shows a minor 354 dependence of the three different recovery contributions on the initial applied strain. 355 The structure of Pd20Pt20Cu20Ni20P20 HE-MG seems to remain relatively stable. Unlike 356 the yielding strain of crystalline alloys, which is generally less than 0.005, the elastic 357 strain limit or yielding strain in MGs is distributed within a narrow range around 0.02, 358 regardless of their chemical compositions [64]. Region (Ⅲ), corresponding to the 359 higher applied strain levels, is characterized by a viscoplastic contribution that increases 360 and the corresponding decrease of the elastic and anelastic parts. In this region, all three 361 recovery contributions change slower than in Region (Ⅰ). The relative trend of the slopes 362 of the three strain contributions is the same as that in Region (Ⅰ). This phenomenon 363 indicates that the difference in anelastic strain with initial applied strains is mainly 364 affected by the flow defects [39]. These results reveal a significant effect of the initial 365 applied strain on the magnitude of the anelastic process. 366 17 367 Fig. 6 (a) The anelastic strain 𝜀𝜀𝑎𝑎𝑎𝑎 ∕ε𝑎𝑎𝑎𝑎 0 response of Pd20Pt20Cu20Ni20P20 HE-MG 368 versus time for different initial strain level (0.4%, 0.6%...7%) during recovery tests at 369 508 K. ε𝑎𝑎𝑎𝑎 0 is the strain at the beginning of the recovery experiments, i.e. after the 370 instantaneous elastic drop. (b) The elastic strain 𝜀𝜀𝑒𝑒𝑒𝑒 ∕𝜀𝜀0, (c) anelastic strain 𝜀𝜀𝑎𝑎𝑎𝑎 ∕𝜀𝜀0 371 and (d) viscoplastic strain 𝜀𝜀𝑣𝑣𝑣𝑣 ∕𝜀𝜀0 behavior of Pd20Pt20Cu20Ni20P20 HE-MG during 372 recovery experiments as a function of the applied strain, 𝜀𝜀0, during the loading stage. 373 374 To further improve the characterization of the recovery behavior, a direct spectrum 375 analysis was considered [65]. A single stretched exponent exp (−(𝑡𝑡/𝜏𝜏)𝛽𝛽) has been 376 used to describe the shape of the recovery spectrum [61]. However, as the recovery 377 deformation in HE-MG involves several processes, the temporal evolution of the 378 anelastic strain can be also modeled with the combination of exponentially decaying 379 terms, exp (−𝑡𝑡/𝜏𝜏𝑖𝑖) , with different time constants, 𝜏𝜏𝑖𝑖 , as shown in the linear 380 constitutive model depicted in Fig. 7 (a). A direct spectrum analysis method is 381 developed by fitting the anelastic strain curves to the equation: 382 18 ε𝑎𝑎𝑎𝑎/ε𝑎𝑎𝑎𝑎 0=𝐴𝐴+∑ε𝑖𝑖exp (−𝑡𝑡/𝜏𝜏𝑖𝑖 𝑎𝑎 𝑖𝑖=1 ) (3) 383 where ε𝑎𝑎𝑎𝑎 0 is the initial anelastic strain during recovery experiments, A and ε𝑖𝑖 are 384 fitting parameters and n is the number of spring-dashpot units in the model of Fig. 7 385 (a). The constant term A in Eq. (3) describes anelastic processes with time longer than 386 the measurement time window as well as the viscoplastic contribution. 387 CONTIN is a general purpose program to solve linear integral equations [66]. 388 CONTIN is often applied to determine the continuous distributions of diffusion 389 coefficients [66], molecular weights [67], relaxation times [39, 68] and electronic 390 densities [69] among other examples. It is often used to analyze the data as an integral 391 over a continuous distribution of exponentials [66, 68]. The continuous recovery time 392 spectra 𝑔𝑔(𝜏𝜏𝑖𝑖)=ε𝑖𝑖/∆𝑙𝑙𝑙𝑙𝜏𝜏 were computed from the normalized strain versus time data 393 using the CONTIN package. As a portable package for inverse problems, CONTIN 394 fitting can eliminate sharp, unphysical variations in the recovery spectra that may occur 395 due to numerical artifacts [70, 71]. The results using CONTIN package are shown in 396 Fig. 7 (b). ∫𝑔𝑔(𝜏𝜏)𝑑𝑑ln𝜏𝜏 𝜏𝜏 2 𝜏𝜏 1 is the anelastic strain with recovery times in the range 397 (𝜏𝜏1,𝜏𝜏2). This latter integral is proportional to the volume fraction occupied by potential 398 flow defects with recovery times in the corresponding range. Therefore, each peak in 399 the spectra can be associated with one type of flow defects differentiated by their 400 relaxation time scale. 401 The following remarkable phenomena can be seen from Fig. 7 (b): (Ⅰ) For initial 402 strain levels below 1%. The recovery spectrum for an initial strain level of 0.4% shows 403 four peaks, where the fourth peak is more likely a “shoulder” of the third peak. With 404 the increase of the initial strain all peaks are shifted to higher values. At 0.6% initial 405 strain, the third and fourth peaks are overlapped in contrast to 0.4%. As one can notice, 406 the fitting curves corresponding to 0.6% and 0.8% are very similar, however, the second 407 peak at 0.8% is becoming to be a “shoulder” of the third peak. Only two peaks remains 408 for 1% initial strain. (Ⅱ) For initial strain levels between 1% and 2%, the peaks show a 409 broad recovery time distribution. (Ⅲ) When the initial strain levels are higher than 2%, 410 the first peak intensity decreases nearly to zero, while the second peak shows a recovery 411 19 time progressively narrowing with increasing initial strain. Therefore, with the increase 412 of initial strain level, the number of peaks of the recovery time distribution decrease 413 from four peaks to only one peak. Concurrently, the contribution of permanent 414 viscoplastic deformation and anelastic relaxations longer than the experimental time 415 window increases. 416 Based on the above results, the following discussion explains the details of the 417 effect of initial strain level on potential flow defects related to free-volume zones, as 418 resolved by their time constants. Molecular dynamics computer simulations concluded 419 that shear transformation zones (STZs) consist from several atoms [72] to tens or 420 hundreds of atoms depending on the applied strain level, until they eventually percolate 421 to a shear band at the yielding point [73]. In light of our experiments, it appears that the 422 spectrum of anelastic strain during the recovery process, calculated from Eq. (3) and 423 displayed in Fig. 7 (b), reflects the distribution of flow defects related to free-volume 424 zones and not the STZ sizes. Regarded as regions with “liquid-like” atoms [74, 75], 425 flow defects in free-volume zones are structural heterogeneities which generate 426 deformation of MGs under an applied load. Numerous studies [9, 22, 76] have shown 427 that the flow defects in free-volume zones can be considered as loosely packed regions 428 embedded in hard elastic surroundings. Atomistic simulations and experimental results 429 exhibit that the local shear events in MGs occurs in a very small (~1nm) soft spots and 430 are also related to the characteristics of surrounding clusters [7, 18, 77-79]. 431 The physical explanation for the distinct phenomena observed under stress 432 relaxation and recovery processes comes from the flow defects related to free-volume 433 zones. When the applied strain is very limited at the beginning of the loading process, 434 only a small fraction of reversible flow defects are activated, the increase of the number 435 of activated flow zones with strain is responsible of the increase of the stress drop ∆𝜎𝜎 436 in Fig. 2 (b). The structure of HE-MGs is changed by the applied strain, but at these 437 levels of strain, the isolated flow defects can be reversed at the recovery process, as 438 shown in Fig. 6 (a). The peaks in the recovery time spectra imply a quantized hierarchy 439 of flow defects related to free volume zones in MGs, as shown in Fig. 7 (b). With 440 20 increasing applied strain, the flow defects with larger intrinsic relaxation time are 441 gradually activated, and the concentration of flow defects related to free-volume zones 442 proliferates. The initial elastic and anelastic deformation of the HE-MG structure 443 becomes irreversible as the applied strain increase. Egami et al. also argued that the 444 increase in the number of free-volume zones is ascribed to the distribution of atomic 445 level stresses in MGs [80, 81]. This leads to the larger stress drop, shown in Fig. 2 (b), 446 and longer relaxation time of the anelastic recovery process, captured by Fig. 6 and Fig. 447 7 (b). When the applied strain is close to yield state, the adjacent weak-bonded regions 448 around flow defects also gradually transform into soft regions [7, 78, 79], which leads 449 to the rapidly increase of fraction of flow defects. Following, the annihilation and 450 activation process of flow defects reach almost equilibrium and the percolation of flow 451 defects related to free-volume zones occurs. Similar results can be found in refs [38, 452 82]. At this stage, the flow defects of free-volume zones result in localized plastic events 453 and homogeneous deformation occurs in HE-MGs. The permanent deformation 454 increases and only partial applied strain recovers. These signatures are observed here 455 with increasing initial strain level. The peak positions shift to longer time, and the peaks 456 of recovery time spectra decrease in intensity and number, from four peaks to only one 457 peak, as shown in Fig. 7 (b). 458 459 21 460 Fig. 7 (a) The schematic diagram of the linear constitutive model: n anelastic processes 461 act in series. (b) Recovery-time spectra of Pd20Pt20Cu20Ni20P20 HE-MG with different 462 initial strain levels (0.4%, 0.6%...7%). The peaks of the time spectra are indicated by 463 the arrows. 464 465 4. Conclusion 466 In summary, the mechanical response of Pd20Pt20Cu20Ni20P20 high-entropy metallic 467 glass is revealed and characterized through the stress relaxation and recovery process. 468 It is found that the stress relaxation during consecutive strain steps can be well 469 described by the Kohlrausch-Williams-Watts (KWW) function. A constitutive model is 470 also applied to analyze in detail the hierarchy of structural and dynamic heterogeneity, 471 considering the presence of relaxation processes with different time scales. The 472 crossover from stochastic activation to percolation of flow defects reveals that the 473 22 atomic /molecular level mechanisms of the stress relaxation behavior of 474 Pd20Pt20Cu20Ni20P20 HE-MG are strongly dependent on the ultimate strain. The 475 recovery process is characterized by a direct spectrum analysis, revealing the evolution 476 of flow defects related to free-volume zones during the recovery process after different 477 initial strain levels. The results in both the stress relaxation and recovery processes 478 show a progressive shift to longer relaxation time scales as strain levels increase, as 479 well as an increase of dynamical heterogeneity involving wider relaxation time 480 distributions. The proposed experiments and models are capable of distinguishing the 481 contribution of different types of flow defects on the mechanical properties. The 482 understanding of the contribution of atomic free-volume zones to the deformation 483 behavior and the anelastic recovery also sheds light on the role of atomic structural 484 heterogeneity in high-entropy metallic glasses. 485 486 Acknowledgments 487 This work is supported by the NSFC (Grant No. 51971178) and the Natural 488 Science Foundation of Shaanxi Province (Grant No. 2019JM-344). E. Pineda and D. 489 Crespo acknowledge financial support from MICINN (grant FIS2017-82625-P) and 490 Generalitat de Catalunya (grant 2017SGR0042). The investigation of Y. J. Duan 491 sponsored by Innovation Foundation for Doctor Dissertation of Northwestern 492 Polytechnical University (No. CX202031) and China Scholarship Council (CSC) under 493 Grant 202006290092. 494 495 496 497 23 Appendix A: Constitutive model of 1 spring + 4 spring-dashpot units 498 The stress relaxation of a constitutive model of 1 spring + 4 spring-dashpot units, 499 as shown in Fig. S1, is given by, 500 𝜎𝜎=𝐴𝐴1exp �− 𝑡𝑡 𝜏𝜏1�+𝐴𝐴2exp �− 𝑡𝑡 𝜏𝜏2�+𝐴𝐴3exp �− 𝑡𝑡 𝜏𝜏3�+𝐴𝐴4exp �− 𝑡𝑡 𝜏𝜏4� (S1) 501 The relaxation times 𝜏𝜏𝑖𝑖 (𝑖𝑖=1 to 4) and the corresponding intensities 𝐴𝐴𝑖𝑖 (𝑖𝑖=1 to 502 4) fitted with Eq. (S2) to the stress relaxation of Pd20Pt20Cu20Ni20P20 HE-MG are shown 503 in Fig. S2. It should be noticed that the orders of magnitude of the relaxation time 𝜏𝜏𝑖𝑖 504 (i =3 and 4) are much longer than that of experimental time window, which may have 505 not clear physical meaning. 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