1
Analysis o he anelas ic de o ma ion o high-en opy 1
Pd20P 20Cu20Ni20P20 me allic glass unde s ess elaxa ion and 2
eco e y 3
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Y.J. Duana,b, L.T. Zhanga, T. Wadac, H. Ka oc, E. Pinedab, D. C espob, J.M. Pelle ie d, 5
J.C. Qiaoa,* 6
aSchool o Mechanics, Ci il Enginee ing and A chi ec u e, No hwes e n 7
Poly echnical Uni e si y, Xi’an 710072, China 8
bDepa men o Physics, Ins i u e o Ene gy Technologies, Uni e si a Poli ècnica de 9
Ca alunya, Ba celona 08019, Spain 10
cIns i u e o Ma e ials Resea ch, Tohoku Uni e si y, Sendai 980-8577, Japan 11
d Uni e si é de Lyon, MATEIS, UMR CNRS5510, Ba . B. Pascal, INSA-Lyon, F-69621 12
Villeu banne Cedex, F ance 13
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Submi ed o Jou nal o Ma e ials Science & Technology 17
(Ve sion: July 02, 2021) 18
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*Co esponding au ho . 20
P o . D . J.C. Qiao, E-mail add ess: [email protected] 21
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Abs ac 26
The anelas ic de o ma ion beha io o Pd20P 20Cu20Ni20P20 high-en opy me allic 27
glass was p obed by moni o ing he s ess elaxa ion and eco e y p ocesses. The s ess 28
elaxa ion unde consecu i e s ain s eps can be desc ibed by he Kohl ausch-Williams-29
Wa s (KWW) unc ion. In addi ion, conside ing a hie a chy o elaxa ion p ocesses 30
ela ed o he s uc u al he e ogenei y, a cons i u i e model is p oposed in o de o 31
desc ibe he whole p ocess o s ess elaxa ion and de e mine he con ibu ion o 32
di e en ime scales. Mo eo e , a c osso e om s ochas ic ac i a ion o pe cola ion o 33
low de ec s wi h he ul ima e s ain can be obse ed du ing s ess elaxa ion p ocess. 34
The anelas ic eco e y p ocess a e a s ain s ep is s udied as a unc ion o he ini ial 35
s ain le el and cha ac e ized by means o a di ec spec um analysis. The peaks in he 36
eco e y ime-spec a e ealed he e olu ion o low de ec s in Pd20P 20Cu20Ni20P20 37
high-en opy me allic glass. The unde s anding o he a omic ee- olume zones e ec 38
and he anelas ic de o ma ion p o ides impo an insigh in o how a omic s uc u al 39
ea u es a ec he de o ma ion beha io o high-en opy me allic glasses, and may 40
p o ide a new a enue in o he imp o emen o hei mechanical p ope ies. 41
42
Keywo ds: High-en opy me allic glass; S ess elaxa ion; Anelas ic de o ma ion; 43
Flow de ec s; F ee- olume zones 44
1. In oduc ion 45
Compa ed wi h con en ional c ys alline alloys, me allic glasses (MGs) p esen a 46
unique combina ion o physical, chemical and mechanical p ope ies such as high 47
s eng h, high ha dness, la ge elas ic s ain as well as high co osion and wea esis ance 48
[1-3]. O e he pas decades, emendous esea ch e o s ha e been dedica ed o he 49
undamen al issues con olling hei a ious p ope ies [4-7], among which, he 50
unde s anding o s uc u al he e ogenei y in MGs and i s link wi h he mechanical 51
de o ma ion beha io is one o he mos challenging issues. 52
O e he pas decades, g ea ad ances ha e been achie ed om heo ies [8-10], 53
expe imen s [11, 12] and simula ions [13] o unde s and he na u e o a omic s uc u e 54
3
and s uc u al he e ogenei y in MGs. Nume ous s udies a emp ed o elucida e he link 55
be ween s uc u al he e ogenei y and mechanical/physical p ope ies o MGs, which is 56
a c ucial ac o o unde s and he c yogenic he mal cycling e ec s [14, 15], elas ic 57
p ope ies [16, 17], inelas ic de o ma ion [18, 19] and he nano-glass s uc u e [20, 21]. 58
On he basis o p e ious esea ch, i is known ha MGs consis o igh ly bonded a omic 59
clus e s and loosely bonded ee- olume egions, which ac as so-called “so ” spo s o 60
low de ec s unde mechanical loading [8, 22]. Howe e , he mechanical p ope ies o 61
hese a omis ic egions, which a e he o igin o dynamic he e ogenei y, a e no 62
ho oughly unde s ood up o da e. A comp ehensi e unde s anding o he in e play 63
be ween he dynamic s uc u al he e ogenei y and he mechanical de o ma ion 64
p ope ies is s ill lacking. The deep comp ehension o such dynamic and s uc u al 65
he e ogenei y may p o ide key knowledge o imp o e he mechanical p ope ies o 66
MGs. 67
Based on a p incipal me allic elemen (e.g. Z , Cu, Pd, Mg o Ti), adi ional MGs 68
show a limi ed glass- o ming abili y (GFA) [23]. High-en opy alloys (HEAs), 69
con aining equia omic o nea -equia omic composi ions, ha e been de eloped ecen ly 70
[3, 24, 25]. HEAs exhibi supe io p ope ies, i.e. high con igu a ional en opy, la ge 71
la ice dis o ion, sluggish di usion and cock ail e ec [25-27]. Inhe i ing some dis inc 72
p ope ies o bo h MGs and HEAs, high-en opy me allic glasses (HE-MGs) exhibi 73
supe io p ope ies (e.g. ul ahigh s eng h a oom empe a u e [28] and sluggish 74
di usion [29, 30]). HE-MGs a e impo an candida es o be applied as unc ional and 75
s uc u al ma e ials and can help us o unde s and he me allic glass s a e, acili a ing 76
he cons uc ion o a co ela ion be ween a omic ee- olume zones and he mechanical 77
beha io . 78
The Pd20P 20Cu20Ni20P20 HE-MG is de i ed om Pd40Ni40P20 MG, a p o o ypical 79
MG which has been widely in es iga ed in many aspec s, such as he yield c i e ion 80
[31], he e ec o high-p essu e o sion [32], he o ma ion o shea bands [33], as well 81
as he a omic di usi i y and iscosi y [34]. Among he de eloped HE-MGs, 82
Pd20P 20Cu20Ni20P20 has ela i ely la ge GFA, wi h a 10 mm c i ical diame e o ully 83
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amo phous s uc u e [35]. Due o he wide supe cooled liquid empe a u e ange o 65 84
K and la ge GFA, as well as a educed glass ansi ion empe a u e o 0.71 [35], he 85
Pd20P 20Cu20Ni20P20 HE-MG is a po en ial model alloy o s udy he s uc u al 86
he e ogenei y and mechanical beha io o MGs. 87
The long- e m mechanical e olu ion o MGs has been in ensely in es iga ed by 88
c eep [36, 37], s ess elaxa ion [38-40], and eco e y expe imen s [41]. In pa icula , 89
s ess elaxa ion is pe o med a a cons an s ain by he applica ion o uniaxial ension 90
o comp ession on he specimen, and moni o ing how he s ess g adually dec ease wi h 91
elaxa ion ime [38]. Cha ac e izing and unde s anding such ime e olu ion is a key 92
ac o when using he ma e ials in enginee ing applica ions. As a iscoelas ic ma e ial, 93
MGs show a u he ime dependen beha io once he applied loading is emo ed, as 94
he uns ained s a e is no achie ed immedia ely. Such anelas ic eco e y is ypically 95
ac i e, du ing long imes. De i ed om he e na y Pd40Ni40P20 MG, he 96
cha ac e iza ion o a omic ee- olume zones o Pd20P 20Cu20Ni20P20 HE-MG and hei 97
possible ela ionship wi h anelas ic de o ma ion a e unknown issues a he p esen ime. 98
In he cu en wo k, he s ess elaxa ion and eco e y p ocesses a e used o p obe 99
he de o ma ion beha io o Pd20P 20Cu20Ni20P20 HE-MG. The s ess elaxa ion du ing 100
s ep s ain condi ions is desc ibed by he Kohl ausch-Williams-Wa s (KWW) unc ion 101
and, subsequen ly, by a cons i u i e model conside ing a hie a chy o elaxa ion ime 102
scales. The cons i u i e model is p oposed wi hin he ame o a omic ee olume zones 103
and s uc u al he e ogenei y o MGs. And a c osso e om s ochas ic ac i a ion o 104
pe cola ion o low de ec s e eals ha he a omic/molecula le el mechanisms o he 105
s ess elaxa ion beha io o Pd20P 20Cu20Ni20P20 HE-MG a e s ongly dependen on he 106
ul ima e s ain. Following, a di ec spec um analysis is conside ed in o de o 107
in es iga e he impac o ini ial s ain le el on he anelas ic eco e y p ocess. Finally, 108
he physical explana ion o he dis inc phenomena obse ed unde s ess elaxa ion and 109
eco e y is p oposed o come om he low de ec s ela ed o ee- olume zones in 110
Pd20P 20Cu20Ni20P20 HE-MG. 111
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2. Expe imen al 113
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2.1 Sample ab ica ion and he mal p ope ies 114
The mas e alloys o Pd20P 20Cu20Ni20P20 HE-MG we e ab ica ed by he B2O3 lux 115
me hod [35]. The alloy was mixed oge he in a sealed and e acua ed qua z ube unde 116
ine a gon in a esis ance hea ing u nace. Ribbons ~0.02mm hick and 1.2mm wide, 117
we e ab ica ed by single-wheel mel -spinning echnique in an a gon a mosphe e. X-118
ay di ac ion (XRD) was employed o con i m he amo phous s uc u e using a 119
comme cial de ice (D8, B uke AXS Gmbh), as shown in Fig. 1 (a). The he mal 120
p ope ies o he Pd20P 20Cu20Ni20P20 HE-MG we e de e mined by di e en ial scanning 121
calo ime y (DSC, Ne zsch 202) in a ni ogen a mosphe e wi h a hea ing a e o 10 122
K/min. The glass ansi ion empe a u e 𝑇𝑇𝑔𝑔= 572 K and he onse c ys alliza ion 123
empe a u e 𝑇𝑇𝑥𝑥= 632 K we e de e mined [27]. The la ge supe cooled liquid egion 124
(SLR) ∆𝑇𝑇 =𝑇𝑇𝑥𝑥−𝑇𝑇𝑔𝑔=60 K indica es an excellen glass o ming abili y. Hence, 125
Pd20P 20Cu20Ni20P20 HE-MG has been selec ed as an excellen model alloy o s udy he 126
s ess elaxa ion and eco e y beha io o HE-MGs. 127
2.2 Dynamic mechanical analysis and uniaxial ensile expe imen s 128
Dynamic mechanical analysis (DMA, TA Q800) was pe o med in Ni ogen 129
a mosphe e using ibbon samples o he HE-MG. Cons an hea ing expe imen s we e 130
conduc ed wi h a d i ing equency o 2 Hz and a hea ing a e o 5 K/min. The s o age 131
modulus 𝐸𝐸′ and loss modulus 𝐸𝐸′′ we e de e mined. Uniaxial ensile expe imen s 132
we e ca ied ou on ibbon samples on DMA. A e eaching he a ge es empe a u e, 133
he ibbon sample was equilib a ed o 10 minu es, and hen he uniaxial ensile 134
expe imen s we e pe o med a a cons an s ain a es (1.5 × 10−4, 3 × 10−4…4.5 ×135
10−4𝑠𝑠−1) and empe a u es (508, 513, 523…563 K). 136
2.3 S ess elaxa ion spec a measu emen s 137
The s ess elaxa ion expe imen s, con aining 20 iso-s ain s ess elaxa ion cu es, 138
we e measu ed du ing consecu i e s ain s eps om 1% o 10% a 508 K. Each s ep 139
inc eased he o al s ain by 0.5% and las ed o 30 minu es. The expe imen s we e 140
pe o med on he TA Q800 DMA using ibbon samples. 141
2.4 Reco e y measu emen a e s ess elaxa ion 142

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Tensile s ess elaxa ion and eco e y expe imen s we e pe o med on he TA 143
Q800 DMA wi h ibbon samples. Samples we e i s cons ained a a cons an s ain 144
(0.4%, 0.6%...7%) o 180 minu es, hen allowed o elax s ess- ee o 600 minu es. 145
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3. Resul s and discussion 147
3.1 Dynamic mechanical analysis and s ess-s ain cu es 148
The empe a u e dependence o he no malized loss modulus 𝐸𝐸′′/𝐸𝐸𝑢𝑢 o 149
Pd20P 20Cu20Ni20P20 HE-MG ibbon sample is shown in Fig. 1 (b). The no malized loss 150
modulus 𝐸𝐸′′/𝐸𝐸𝑢𝑢 is e y small a low empe a u e. Wi h inc easing empe a u e, a la ge 151
inc ease o he no malized loss modulus is obse ed, which co esponds i s o he 152
slow 𝛽𝛽 elaxa ion and, e en ually, he p ima y 𝛼𝛼 elaxa ion. Unlike he La-based 153
MGs, ha show an e iden slow 𝛽𝛽 elaxa ion peak [19, 27], and he Z - and P -based 154
MGs, ha show only an excess wing [27], he Pd20P 20Cu20Ni20P20 HE-MG exhibi a 155
b oad shoulde co esponding o slow 𝛽𝛽 elaxa ion as shown in Fig. 1 (b). Recen 156
in es iga ions showed ha he slow 𝛽𝛽 elaxa ion closely ela es o he plas ic 157
de o ma ion and he na u e o he glass ansi ion o MGs [42]. Besides, 158
Pd20P 20Cu20Ni20P20 HE-MG exhibi s a ul ahigh ac i a ion ene gy o slow 𝛽𝛽 159
elaxa ion, sugges ing ha HE-MGs may possess a highe ene gy ba ie o he 160
dynamic 𝛽𝛽 elaxa ion [27]. 161
Fig. 1 (c) shows he s ess-s ain cu es o Pd20P 20Cu20Ni20P20 HE-MG ibbon as 162
a unc ion o empe a u e wi h a s ain a e o 3 × 10−4𝑠𝑠−1. The low s ess dec eases 163
om 790 MPa o 140 MPa when he empe a u e inc eases by 60 K. The e o e, he low 164
s ess is s ongly he mally ac i a ed. A la ge homogeneous de o ma ion (𝜀𝜀 ≈ 18%) 165
can be cap u ed wi hou any ex ensi e s ain ha dening. I has been epo ed ha he 166
homogeneous de o ma ion occu s a a highe empe a u e in MGs ( ypically o 𝑇𝑇>167
0.8𝑇𝑇𝑔𝑔) [43], which is consis en wi h he esul s in Fig. 1 (c). In such cases, he MGs 168
always exhibi p onounced plas ici y [44]. The plas ic de o ma ion o MGs is ela ed o 169
o ma ion o he localized shea bands [45]. Fig. 1 (d) shows he s ess-s ain cu es as 170
a unc ion o s ain a e a 508 K. The s eng h inc eases and he inal elonga ion 171
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dec eases wi h inc easing s ain a e. The de o ma ion mode changes om he 172
homogeneous ype o he inhomogeneous one inc easing he s ain a e abo e 4.0 ×173
10−4𝑠𝑠−1 . And he b i leness inc eases wi h he inc ease o he s ain a e du ing 174
de o ma ion [43]. In he homogeneous de o ma ion egion, he de o ma ion begins o 175
yield wi h a s ess o e shoo , ollowed by s able low, simila esul s has been ound in 176
Z -based me allic glass [46]. 177
178
Fig. 1 (a) XRD cu e o he as-cas Pd20P 20Cu20Ni20P20 HE-MG. (b) No malized loss 179
modulus 𝐸𝐸′′/𝐸𝐸𝑢𝑢 o Pd20P 20Cu20Ni20P20 HE-MG ibbon as a unc ion o empe a u e. 180
The hea ing a e is 5 K/min, and he d i ing equency is 2 Hz. 𝐸𝐸𝑢𝑢 deno es he alue 181
o he s o age modulus a oom empe a u e. (c) S ess-s ain cu es o 182
Pd20P 20Cu20Ni20P20 HE-MG as a unc ion o empe a u e wi h a s ain a e o 3 ×183
10−4𝑠𝑠−1. (d) as a unc ion o s ain a e a 508 K. 184
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3.2 S ess elaxa ion spec a analysis 186
S ess elaxa ion is a powe ul ool o e eal he ime-dependen na u e o low 187
de ec s in amo phous, iscoelas ic solids (i.e. MGs and polyme s) [38, 47]. Fig. 2 (a) 188
shows he s ess elaxa ion esul s o Pd20P 20Cu20Ni20P20 HE-MG consis ing o 20 iso-189
s ain s ess elaxa ion cu es measu ed a s ep s ains om 1% o 10% a 508 K. The 190
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s ain line is shown in Fig. 2 (a), he s ess elaxa ion cu es o Pd20P 20Cu20Ni20P20 191
HE-MG a 508 K we e ob ained du ing each iso-s ain s ep. Typical iso he mal s ess-192
elaxa ion cu e measu ed a 1% a e shown in he inse o Fig. 2 (a) a 508 K, and he 193
empo al-dependen s ess 𝜎𝜎(𝑡𝑡) is no malized by he ini ial s ess 𝜎𝜎0. Gene ally, he 194
no malized 𝜎𝜎(𝑡𝑡)/𝜎𝜎0 shows a apid dec ease om 1 a he beginning o s ess 195
elaxa ion, and hen ob iously slows down and decays sluggishly wi h elaxa ion ime. 196
These p ominen ea u es a e consis en wi h o he expe imen s and simula ion in s ess 197
elaxa ion o MGs [38, 40, 48]. The ini ial s ess 𝜎𝜎onse and e minal s ess 𝜎𝜎end ha e 198
an e ec on he iscoelas ic p ope ies in glassy solids [47]. The ini ial s ess 𝜎𝜎onse , 199
e minal s ess 𝜎𝜎end and s ess d op ∆𝜎𝜎 =𝜎𝜎onse −𝜎𝜎end o each s ess elaxa ion 200
cu e a e shown as open squa es, ci cles and iangles in Fig. 2 (a) and (b), espec i ely. 201
The ini ial s ess 𝜎𝜎onse , e minal s ess 𝜎𝜎end and s ess d op ∆𝜎𝜎 inc ease 202
signi ican ly wi h s epping s ain un il a o al s ain o 5%. As shown in Fig. 1 (b), he 203
c i ical s ain 5% can be ega ded as he ul ima e s ain o Pd20P 20Cu20Ni20P20 HE-MG 204
a 508 K, implying ha he decay o s ess in s ained HE-MG is co ela ed wi h he 205
s ep s ain and a ansi ion o s ess elaxa ion beha io may occu a ound he c i ical 206
s ain, simila esul s ha e been ound in s ess elaxa ion dynamics o glasses wi h 207
molecula dynamic simula ions [48]. I is ound ha he ∆𝜎𝜎 exhibi s app oxima ely 208
linea below 5%, howe e , he change o o 𝜎𝜎onse , 𝜎𝜎end , and ∆𝜎𝜎 is much less 209
p ominen , con i ming ha he s ess elaxa ion p ocess is sensi i e wi h s ep s ain 210
(below 5%), bu insensi i e wi h s ep s ain shown in Fig. 2 (b). The change o he 211
co ela ions be ween s ep s ain and ∆𝜎𝜎 may indica e he c osso e o he elaxa ion 212
beha io s nea o 5%. 213
The s ess elaxa ion o Pd20P 20Cu20Ni20P20 HE-MG cu es can be i ed by a 214
phenomenological KWW equa ion [38, 49], 215
𝜎𝜎(𝑡𝑡)=𝜎𝜎0exp (−𝑡𝑡
𝜏𝜏𝑐𝑐)𝛽𝛽KWW (1) 216
whe e 𝜎𝜎0 is he ini ial s ess a each s ain s ep, 𝛽𝛽KWW is he s e ched exponen ial 217
pa ame e , e lec ing he dynamic he e ogenei y, and 𝜏𝜏𝑐𝑐 is he cha ac e is ic ime 218
ela ed o he s ess elaxa ion mechanisms [38, 49]. 219
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The alues o 𝛽𝛽KWW and 𝜏𝜏𝑐𝑐 a e shown in Fig. 2 (b). Smalle 𝛽𝛽KWW implies 220
la ge dynamic he e ogenei y in MGs [50, 51]. The alue o 𝛽𝛽KWW dec eases 221
subs an ially un il he s ain eaches 1.5%, while main ains a cons an alue a highe 222
s epping s ains. The cha ac e is ic elaxa ion ime 𝜏𝜏𝑐𝑐 inc eases om 102 s o 223
106 s wi h inc easing s ain below 5%, while i changes sligh ly a highe s ains. The 224
change o cha ac e is ic elaxa ion ime 𝜏𝜏𝑐𝑐 is e y close o he e olu ion o s ess d op 225
∆𝜎𝜎, indica ing again a c osso e o he elaxa ion beha io s a s ains abo e 5%. La ge 226
s ess d ops ∆𝜎𝜎 imply la ge ac ion o ac i a ed low de ec s, ela ed o ee- olume 227
zones, in he MGs [47, 48]. The indi idual low de ec s a e ac i a ed e en when he 228
applied s ain is less han 2%, which is excellen consis en wi h he p e ious 229
expe imen and simula ion esul s o he exis ence o local a omic ea angemen s in 230
nominal elas ici y de o ma ion egion in MGs [37, 48]. As his i s ype o low de ec s 231
is s ained he elaxa ion in ol es mo e di e en ype o uni s, hus inc easing he 232
dynamic he e ogenei y and cha ac e is ic ime 𝜏𝜏𝑐𝑐. As he s ep s ain inc eases, mo e 233
low de ec s a e ac i a ed, which a e co esponding o a s ochas ic and isola ed 234
ac i a ion o he low de ec s, simila molecula dynamic simula ion esul s we e ound 235
in MGs [48]. Howe e , when he ene gy ba ie o a omic a angemen s in liquid-like 236
egions [52-54] (also called ee- olume zones o low uni s [55, 56]) is il ed o a 237
ce ain le el, he local plas ic lows become easily ac i a ed, and he yielding occu s in 238
amo phous solids [57]. Abo e 5%, he change o 𝜎𝜎onse , 𝜎𝜎end, and ∆𝜎𝜎 is much less 239
p ominen , implying ha he ac i a ion and annihila ion o low de ec s each a 240
dynamic equilib ium. This indica es ha he whole sample o Pd20P 20Cu20Ni20P20 HE-241
MG en e s in o a ela i ely s able s a e a 508 K a e inc easing he s ain abo e 5%, 242
and simila beha io s o a omic ea angemen ha e been epo ed he dynamic 243
he e ogenei y beha io s du ing he s ess elaxa ion [48]. The c osso e om s ochas ic 244
ac i a ion o pe cola ion o low de ec s e eals he a omic/molecula le el mechanisms 245
o he s ess elaxa ion beha io o Pd20P 20Cu20Ni20P20 HE-MG, which a e s ongly 246
dependen on he ul ima e s ain. 247
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anelas ic s ain 𝜀𝜀𝑎𝑎𝑎𝑎 con ibu ions wi h he inc ease o ini ial s ain le el, indica ing 346
signi ican enhancemen o he iscoplas ic s ain 𝜀𝜀𝑣𝑣𝑣𝑣. The dependence on he ini ial 347
s ain o he h ee di e en eco e y de o ma ion con ibu ions can be di ided in o h ee 348
egions as shown in Fig. 6 (b)-(d). Region (Ⅰ), when he ini ial s ain le el is below 1%, 349
is cha ac e ized by a e y la ge dec ease o he elas ic and anelas ic con ibu ions, wi h 350
he co esponding inc ease o he iscoplas ic pa , as ini ial s ain is inc eased. The 351
slopes o anelas ic and iscoplas ic con ibu ions as a unc ion o ini ial s ain a e highe 352
han ha o he elas ic one. These egion co espond o he nominal elas ic egion in 353
MGs [22]. Region (Ⅱ), wi h ini ial s ain le els be ween 1% and 2%, shows a mino 354
dependence o he h ee di e en eco e y con ibu ions on he ini ial applied s ain. 355
The s uc u e o Pd20P 20Cu20Ni20P20 HE-MG seems o emain ela i ely s able. Unlike 356
he yielding s ain o c ys alline alloys, which is gene ally less han 0.005, he elas ic 357
s ain limi o yielding s ain in MGs is dis ibu ed wi hin a na ow ange a ound 0.02, 358
ega dless o hei chemical composi ions [64]. Region (Ⅲ), co esponding o he 359
highe applied s ain le els, is cha ac e ized by a iscoplas ic con ibu ion ha inc eases 360
and he co esponding dec ease o he elas ic and anelas ic pa s. In his egion, all h ee 361
eco e y con ibu ions change slowe han in Region (Ⅰ). The ela i e end o he slopes 362
o he h ee s ain con ibu ions is he same as ha in Region (Ⅰ). This phenomenon 363
indica es ha he di e ence in anelas ic s ain wi h ini ial applied s ains is mainly 364
a ec ed by he low de ec s [39]. These esul s e eal a signi ican e ec o he ini ial 365
applied s ain on he magni ude o he anelas ic p ocess. 366

17
367
Fig. 6 (a) The anelas ic s ain 𝜀𝜀𝑎𝑎𝑎𝑎 ∕ε𝑎𝑎𝑎𝑎
0 esponse o Pd20P 20Cu20Ni20P20 HE-MG 368
e sus ime o di e en ini ial s ain le el (0.4%, 0.6%...7%) du ing eco e y es s a 369
508 K. ε𝑎𝑎𝑎𝑎
0 is he s ain a he beginning o he eco e y expe imen s, i.e. a e he 370
ins an aneous elas ic d op. (b) The elas ic s ain 𝜀𝜀𝑒𝑒𝑒𝑒 ∕𝜀𝜀0, (c) anelas ic s ain 𝜀𝜀𝑎𝑎𝑎𝑎 ∕𝜀𝜀0 371
and (d) iscoplas ic s ain 𝜀𝜀𝑣𝑣𝑣𝑣 ∕𝜀𝜀0 beha io o Pd20P 20Cu20Ni20P20 HE-MG du ing 372
eco e y expe imen s as a unc ion o he applied s ain, 𝜀𝜀0, du ing he loading s age. 373
374
To u he imp o e he cha ac e iza ion o he eco e y beha io , a di ec spec um 375
analysis was conside ed [65]. A single s e ched exponen exp (−(𝑡𝑡/𝜏𝜏)𝛽𝛽) has been 376
used o desc ibe he shape o he eco e y spec um [61]. Howe e , as he eco e y 377
de o ma ion in HE-MG in ol es se e al p ocesses, he empo al e olu ion o he 378
anelas ic s ain can be also modeled wi h he combina ion o exponen ially decaying 379
e ms, exp (−𝑡𝑡/𝜏𝜏𝑖𝑖) , wi h di e en ime cons an s, 𝜏𝜏𝑖𝑖 , as shown in he linea 380
cons i u i e model depic ed in Fig. 7 (a). A di ec spec um analysis me hod is 381
de eloped by i ing he anelas ic s ain cu es o he equa ion: 382
18
ε𝑎𝑎𝑎𝑎/ε𝑎𝑎𝑎𝑎
0=𝐴𝐴+∑ε𝑖𝑖exp (−𝑡𝑡/𝜏𝜏𝑖𝑖
𝑎𝑎
𝑖𝑖=1 ) (3) 383
whe e ε𝑎𝑎𝑎𝑎
0 is he ini ial anelas ic s ain du ing eco e y expe imen s, A and ε𝑖𝑖 a e 384
i ing pa ame e s and n is he numbe o sp ing-dashpo uni s in he model o Fig. 7 385
(a). The cons an e m A in Eq. (3) desc ibes anelas ic p ocesses wi h ime longe han 386
he measu emen ime window as well as he iscoplas ic con ibu ion. 387
CONTIN is a gene al pu pose p og am o sol e linea in eg al equa ions [66]. 388
CONTIN is o en applied o de e mine he con inuous dis ibu ions o di usion 389
coe icien s [66], molecula weigh s [67], elaxa ion imes [39, 68] and elec onic 390
densi ies [69] among o he examples. I is o en used o analyze he da a as an in eg al 391
o e a con inuous dis ibu ion o exponen ials [66, 68]. The con inuous eco e y ime 392
spec a 𝑔𝑔(𝜏𝜏𝑖𝑖)=ε𝑖𝑖/∆𝑙𝑙𝑙𝑙𝜏𝜏 we e compu ed om he no malized s ain e sus ime da a 393
using he CONTIN package. As a po able package o in e se p oblems, CONTIN 394
i ing can elimina e sha p, unphysical a ia ions in he eco e y spec a ha may occu 395
due o nume ical a i ac s [70, 71]. The esul s using CONTIN package a e shown in 396
Fig. 7 (b). ∫𝑔𝑔(𝜏𝜏)𝑑𝑑ln𝜏𝜏
𝜏𝜏 2
𝜏𝜏 1 is he anelas ic s ain wi h eco e y imes in he ange 397
(𝜏𝜏1,𝜏𝜏2). This la e in eg al is p opo ional o he olume ac ion occupied by po en ial 398
low de ec s wi h eco e y imes in he co esponding ange. The e o e, each peak in 399
he spec a can be associa ed wi h one ype o low de ec s di e en ia ed by hei 400
elaxa ion ime scale. 401
The ollowing ema kable phenomena can be seen om Fig. 7 (b): (Ⅰ) Fo ini ial 402
s ain le els below 1%. The eco e y spec um o an ini ial s ain le el o 0.4% shows 403
ou peaks, whe e he ou h peak is mo e likely a “shoulde ” o he hi d peak. Wi h 404
he inc ease o he ini ial s ain all peaks a e shi ed o highe alues. A 0.6% ini ial 405
s ain, he hi d and ou h peaks a e o e lapped in con as o 0.4%. As one can no ice, 406
he i ing cu es co esponding o 0.6% and 0.8% a e e y simila , howe e , he second 407
peak a 0.8% is becoming o be a “shoulde ” o he hi d peak. Only wo peaks emains 408
o 1% ini ial s ain. (Ⅱ) Fo ini ial s ain le els be ween 1% and 2%, he peaks show a 409
b oad eco e y ime dis ibu ion. (Ⅲ) When he ini ial s ain le els a e highe han 2%, 410
he i s peak in ensi y dec eases nea ly o ze o, while he second peak shows a eco e y 411
19
ime p og essi ely na owing wi h inc easing ini ial s ain. The e o e, wi h he inc ease 412
o ini ial s ain le el, he numbe o peaks o he eco e y ime dis ibu ion dec ease 413
om ou peaks o only one peak. Concu en ly, he con ibu ion o pe manen 414
iscoplas ic de o ma ion and anelas ic elaxa ions longe han he expe imen al ime 415
window inc eases. 416
Based on he abo e esul s, he ollowing discussion explains he de ails o he 417
e ec o ini ial s ain le el on po en ial low de ec s ela ed o ee- olume zones, as 418
esol ed by hei ime cons an s. Molecula dynamics compu e simula ions concluded 419
ha shea ans o ma ion zones (STZs) consis om se e al a oms [72] o ens o 420
hund eds o a oms depending on he applied s ain le el, un il hey e en ually pe cola e 421
o a shea band a he yielding poin [73]. In ligh o ou expe imen s, i appea s ha he 422
spec um o anelas ic s ain du ing he eco e y p ocess, calcula ed om Eq. (3) and 423
displayed in Fig. 7 (b), e lec s he dis ibu ion o low de ec s ela ed o ee- olume 424
zones and no he STZ sizes. Rega ded as egions wi h “liquid-like” a oms [74, 75], 425
low de ec s in ee- olume zones a e s uc u al he e ogenei ies which gene a e 426
de o ma ion o MGs unde an applied load. Nume ous s udies [9, 22, 76] ha e shown 427
ha he low de ec s in ee- olume zones can be conside ed as loosely packed egions 428
embedded in ha d elas ic su oundings. A omis ic simula ions and expe imen al esul s 429
exhibi ha he local shea e en s in MGs occu s in a e y small (~1nm) so spo s and 430
a e also ela ed o he cha ac e is ics o su ounding clus e s [7, 18, 77-79]. 431
The physical explana ion o he dis inc phenomena obse ed unde s ess 432
elaxa ion and eco e y p ocesses comes om he low de ec s ela ed o ee- olume 433
zones. When he applied s ain is e y limi ed a he beginning o he loading p ocess, 434
only a small ac ion o e e sible low de ec s a e ac i a ed, he inc ease o he numbe 435
o ac i a ed low zones wi h s ain is esponsible o he inc ease o he s ess d op ∆𝜎𝜎 436
in Fig. 2 (b). The s uc u e o HE-MGs is changed by he applied s ain, bu a hese 437
le els o s ain, he isola ed low de ec s can be e e sed a he eco e y p ocess, as 438
shown in Fig. 6 (a). The peaks in he eco e y ime spec a imply a quan ized hie a chy 439
o low de ec s ela ed o ee olume zones in MGs, as shown in Fig. 7 (b). Wi h 440
20
inc easing applied s ain, he low de ec s wi h la ge in insic elaxa ion ime a e 441
g adually ac i a ed, and he concen a ion o low de ec s ela ed o ee- olume zones 442
p oli e a es. The ini ial elas ic and anelas ic de o ma ion o he HE-MG s uc u e 443
becomes i e e sible as he applied s ain inc ease. Egami e al. also a gued ha he 444
inc ease in he numbe o ee- olume zones is asc ibed o he dis ibu ion o a omic 445
le el s esses in MGs [80, 81]. This leads o he la ge s ess d op, shown in Fig. 2 (b), 446
and longe elaxa ion ime o he anelas ic eco e y p ocess, cap u ed by Fig. 6 and Fig. 447
7 (b). When he applied s ain is close o yield s a e, he adjacen weak-bonded egions 448
a ound low de ec s also g adually ans o m in o so egions [7, 78, 79], which leads 449
o he apidly inc ease o ac ion o low de ec s. Following, he annihila ion and 450
ac i a ion p ocess o low de ec s each almos equilib ium and he pe cola ion o low 451
de ec s ela ed o ee- olume zones occu s. Simila esul s can be ound in e s [38, 452
82]. A his s age, he low de ec s o ee- olume zones esul in localized plas ic e en s 453
and homogeneous de o ma ion occu s in HE-MGs. The pe manen de o ma ion 454
inc eases and only pa ial applied s ain eco e s. These signa u es a e obse ed he e 455
wi h inc easing ini ial s ain le el. The peak posi ions shi o longe ime, and he peaks 456
o eco e y ime spec a dec ease in in ensi y and numbe , om ou peaks o only one 457
peak, as shown in Fig. 7 (b). 458
459
21
460
Fig. 7 (a) The schema ic diag am o he linea cons i u i e model: n anelas ic p ocesses 461
ac in se ies. (b) Reco e y- ime spec a o Pd20P 20Cu20Ni20P20 HE-MG wi h di e en 462
ini ial s ain le els (0.4%, 0.6%...7%). The peaks o he ime spec a a e indica ed by 463
he a ows. 464
465
4. Conclusion 466
In summa y, he mechanical esponse o Pd20P 20Cu20Ni20P20 high-en opy me allic 467
glass is e ealed and cha ac e ized h ough he s ess elaxa ion and eco e y p ocess. 468
I is ound ha he s ess elaxa ion du ing consecu i e s ain s eps can be well 469
desc ibed by he Kohl ausch-Williams-Wa s (KWW) unc ion. A cons i u i e model is 470
also applied o analyze in de ail he hie a chy o s uc u al and dynamic he e ogenei y, 471
conside ing he p esence o elaxa ion p ocesses wi h di e en ime scales. The 472
c osso e om s ochas ic ac i a ion o pe cola ion o low de ec s e eals ha he 473

22
a omic /molecula le el mechanisms o he s ess elaxa ion beha io o 474
Pd20P 20Cu20Ni20P20 HE-MG a e s ongly dependen on he ul ima e s ain. The 475
eco e y p ocess is cha ac e ized by a di ec spec um analysis, e ealing he e olu ion 476
o low de ec s ela ed o ee- olume zones du ing he eco e y p ocess a e di e en 477
ini ial s ain le els. The esul s in bo h he s ess elaxa ion and eco e y p ocesses 478
show a p og essi e shi o longe elaxa ion ime scales as s ain le els inc ease, as 479
well as an inc ease o dynamical he e ogenei y in ol ing wide elaxa ion ime 480
dis ibu ions. The p oposed expe imen s and models a e capable o dis inguishing he 481
con ibu ion o di e en ypes o low de ec s on he mechanical p ope ies. The 482
unde s anding o he con ibu ion o a omic ee- olume zones o he de o ma ion 483
beha io and he anelas ic eco e y also sheds ligh on he ole o a omic s uc u al 484
he e ogenei y in high-en opy me allic glasses. 485
486
Acknowledgmen s 487
This wo k is suppo ed by he NSFC (G an No. 51971178) and he Na u al 488
Science Founda ion o Shaanxi P o ince (G an No. 2019JM-344). E. Pineda and D. 489
C espo acknowledge inancial suppo om MICINN (g an FIS2017-82625-P) and 490
Gene ali a de Ca alunya (g an 2017SGR0042). The in es iga ion o Y. J. Duan 491
sponso ed by Inno a ion Founda ion o Doc o Disse a ion o No hwes e n 492
Poly echnical Uni e si y (No. CX202031) and China Schola ship Council (CSC) unde 493
G an 202006290092. 494
495
496
497
23
Appendix A: Cons i u i e model o 1 sp ing + 4 sp ing-dashpo uni s 498
The s ess elaxa ion o a cons i u i e model o 1 sp ing + 4 sp ing-dashpo uni s, 499
as shown in Fig. S1, is gi en by, 500
𝜎𝜎=𝐴𝐴1exp �− 𝑡𝑡
𝜏𝜏1�+𝐴𝐴2exp �− 𝑡𝑡
𝜏𝜏2�+𝐴𝐴3exp �− 𝑡𝑡
𝜏𝜏3�+𝐴𝐴4exp �− 𝑡𝑡
𝜏𝜏4� (S1) 501
The elaxa ion imes 𝜏𝜏𝑖𝑖 (𝑖𝑖=1 o 4) and he co esponding in ensi ies 𝐴𝐴𝑖𝑖 (𝑖𝑖=1 o 502
4) i ed wi h Eq. (S2) o he s ess elaxa ion o Pd20P 20Cu20Ni20P20 HE-MG a e shown 503
in Fig. S2. I should be no iced ha he o de s o magni ude o he elaxa ion ime 𝜏𝜏𝑖𝑖 504
(i =3 and 4) a e much longe han ha o expe imen al ime window, which may ha e 505
no clea physical meaning. As a esul , he cons i u i e model o 1 sp ing + 3 sp ing-506
dashpo uni s is he mos adequa e o e eal he hie a chical dis ibu ion o low de ec s 507
ela ed o ee- olume zones ac ing in s ess elaxa ion o Pd20P 20Cu20Ni20P20 HE-MG 508
wi hou including meaningless e ms. 509
510
Fig. S1. Schema ic diag am o he cons i u i e model wi h 1 sp ing + 4 sp ing-dashpo 511
uni s. 512
24
513
Fig. S2. The elaxa ion imes 𝜏𝜏𝑖𝑖 (i =1, 2, 3 and 4) i ed wi h Eq. (S2). The size 514
o he symbol is p opo ional o he co esponding in ensi y 𝐴𝐴𝑖𝑖 (i =1, 2, 3 and 4). 515
516
25
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