domain: chim phys spi

text:
Daniel Soriano
email: dsoriano.dsj@gmail.com

Hongbo Zhou
email: h_zhou04@uni-muenster.de

Sven Hilke

Eloi Pineda
email: eloi.pineda@upc.edu

Beatrice Ruta
email: beatrice.ruta@univ-lyon1.fr

Gerhard Wilde

Relaxation dynamics of Pd-Ni-P metallic glass: Decoupling of anelastic and viscous processes

Keywords: Stress relaxation, Relaxation dynamics, XPCS, Metallic glasses, Mechanical properties

The stress relaxation dynamics of metallic glass Pd 40 Ni 40 P 20 was studied in both supercooled liquid and glassy states. Time-temperature superposition was found in the metastable liquid, implying an invariant shape of the distribution of times involved in the relaxation. Once in the glass state, the distribution of relaxation times broadens as temperature and fictive temperature decrease, eventually leading to a decoupling of the relaxation in two processes. While the slow one keeps a viscous behavior, the fast one shows an anelastic nature and a time scale similar to that of the collective atomic motion measured by X-ray Photon Correlation Spectroscopy (XPCS). These results suggest that the atomic dynamics of metallic glasses, as determined by XPCS at low temperatures in the glass state, can be related to the rearrangements of particles responsible of the macroscopically reversible anelastic behavior.

Introduction

The relaxation dynamics of metallic glasses and liquids is intrinsically linked to their mechanical properties, such as the viscous and plastic behaviors [START_REF] Ketkaew | Mechanical glass transition revealed by the fracture toughness of metallic glasses[END_REF], and to the rejuvenation and aging processes [START_REF] Ruta | Relaxation processes and physical aging in metallic glasses[END_REF]. Above the glass transition temperature (T g ) the supercooled liquid (SCL) is a metastable equilibrium phase which is characterized, among other properties, by a density and a structural relaxation time that change with temperature. The structural relaxation time, , determines how fast the structure returns to the equilibrium configuration after a change of the external conditions, pressure or temperature, or the application of an external stimulus. Therefore, it controls the viscosity of the SCL as well as the relaxation towards the new equilibrium configuration after a sudden change of temperature. This process, so called -relaxation, is characterized by a stretched exponential shape of the time-dependent relaxation curves, often attributed to the presence of a distribution of relaxation times whose average value follows a super-Arrhenius temperature dependence, usually well described by a Vogel-Fulcher-Tammann behavior [START_REF] Angell | Relaxation in glassforming liquids and amorphous solids[END_REF].

During a cooling process from the SCL phase, the super-Arrhenius behavior of  makes that at a given temperature the change of temperature becomes too fast for the system to reach the equilibrium configuration, and the system becomes arrested in a glass state. The specific state of a glass is therefore an out-of-equilibrium configuration which is inherently prone to changes towards the metastable equilibrium by means of structural relaxation, this process is known as physical aging. The relaxation dynamics of the glass are therefore responsible of two processes: the response of the system under the application of external forces and the physical aging, and they become usually mingled in most mechanical experiments below T g . Furthermore, the application of high stresses and deformation rates may also induce rejuvenation of the glass [START_REF] Sun | Thermomechanical processing of metallic glasses: extending the range of the glassy state[END_REF], and subsequent intensification of aging during the experiments [START_REF] Mckenna | Mechanical rejuvenation in polymer glasses: fact or fallacy?[END_REF].

If the glass is well aged and the applied stresses are low enough to do not induce rejuvenation, the relaxation dynamics of isoconfigurational glass states may be tested by mechanical experiments. In the seminal works of Taub and Spaepen [START_REF] Taub | Ideal elastic, anelastic and viscoelastic deformation of a metallic glass[END_REF] [START_REF] Taub | Stress-strain rate dependence of homogeneous flow in metallic glasses[END_REF], creep experiments of metallic glass ribbons showed the presence of anelastic and viscous contributions to the relaxation of isoconfigurational states. The viscous relaxation was found to produce a constant deformation rate proportional to the applied stress, with absolute values of viscosity changing for different isoconfigurational states but with Arrhenius temperature dependences with similar activation energies.

In addition to the subjacent slow viscous flow, the anelastic relaxation was found to dominate the first hours, or even days, of the creep experiments. The intensity of the anelastic relaxation was found to be linear with the applied stress and totally recoverable after unloading, thus showing its total anelastic nature.

Concerning the physical aging of glasses, the relaxation processes involved are a matter of intense debate.

The distribution of relaxation times responsible for the structural relaxation in the SCL state is expected to stem from spatial and dynamical heterogeneities, involving microscopic particle movements with various correlation lengths and diverse degrees of cooperativity. Once the system is arrested in a given glass configuration, some of these processes may become too slow to contribute to a detectable physical aging while others remain active.

The evolution of the distribution of relaxation times as a function of temperature and aging dictates which processes can be observable in a particular experiment. The progressive separation of the characteristic times of the relaxation processes in glasses is manifested by the presence of double step aging [START_REF] Cangialosi | Direct evidence of two equilibration mechanisms in glassy polymers[END_REF] [START_REF] Gallino | Hierarchical aging pathways and reversible fragile-to-strong transition upon annealing of a metallic glass former[END_REF] and the observation of multiple secondary relaxations in mechanical experiments [START_REF] Wang | Unusual fast secondary relaxation in metallic glass[END_REF] [START_REF] Luo | Relaxation Decoupling in Metallic Glasses at Low Temperatures[END_REF]. Despite the important advances in the field done in the last years, the nature of the relaxation processes involved in deep glassy states is still far from being understood due to the difficulty to probe the microscopic details of the systems with both experiments and numerical simulations, and the concomitant lack of a direct connection between atomic scale processes and macroscopic relaxations [START_REF] Ruta | Relaxation processes and physical aging in metallic glasses[END_REF].

Here, we present a detailed characterization of the relaxation dynamics of Pd 40 Ni 40 P 20 metallic glass at both macroscopic and microscopic scale. The macroscopic relaxation was characterized by mechanical stressrelaxation experiments in the SCL and in glasses with different degrees of aging. The evolution of the distribution of relaxation times was analyzed by means of fitting the experimental curve to single and double stretched exponential decays. The microscopic features of the different relaxation processes were investigated by X-ray Photon Correlation Spectroscopy (XPCS). The experimental conditions used in the stress relaxation tests and the control of the aging state allowed us to characterize a wide temperature-time region, in both the glass and the SCL states, showing a clear differentiation between stress-driven, anelastic processes and viscouslike relaxation.

Methods

Pd 40 Ni 40 P 20 master alloys were first prepared by melting Pd plates and Ni 2 P granules in a silica crucible under a Ti-gettered argon atmosphere. The samples in ribbon shape for stress relaxation tests were re-melted and ejected onto a Cu wheel rotating at a surface velocity of 40 m s -1 . The samples for XPCS measurements were re-melted and cast in a copper mold obtaining 5 mm diameter rods. Disk-shape slices of the rod were grinded until obtaining a thickness of 20 m used in the XPCS experiment.

The stress relaxation and mechanical spectroscopy experiments were performed in a DMA Q800 TA Instruments apparatus using ribbon-shape samples of 2 mm width and 30 m thickness. In both, mechanical spectroscopy and stress relaxation tests, a first annealing at 523 K (250 o C) while applying a tensile stress of 0.7 N was performed in order to reduce the as-cast bending of the ribbons. The mechanical spectroscopy tests were performed applying a single frequency and an amplitude of oscillation of =0.01% (approximately 1 m) while heating at a constant rate of 1 K min -1 . Stress relaxation measurements were performed isothermally. During the heating or cooling protocols before reaching the desired temperatures, as well as during temperature stabilization, a static force of 0.01 N was constantly applied in order to maintain the straight shape of the samples. After reaching each temperature, the samples were stabilized during 30 minutes, which is required as it was checked that at least during the first 15 minutes the dimensions of the whole system (clamps and sample) were changing, thus inducing artefacts in the stress measurement. After the temperature stabilization step, a constant deformation of =0.05%, 0.1% or 0.2% was applied; most tests were performed at =0.1% and only some selected cases were performed with the other strain values with the aim of determining if there was any significant effect of the applied initial stress. The length of the samples was approximately 10 mm, which means that for =0.1% the constant deformation was of the order of 10 m, the exact absolute value depending on each sample. The static force needed to maintain the applied deformation was monitored as a function of time thus obtaining the stress relaxation curves.

The mechanical measurements were performed under a nitrogen-rich atmosphere. X-ray diffraction of samples collected after the relaxation experiments did not show detectable traces of oxide or crystalline phases.

In addition, the following procedure was made: After long experiments the samples were reheated above T g and tested in order to check if the response was again in agreement with the equilibrated SCL behavior, thus discarding a change of the mechanical response because of the formation of oxide surface layers or crystallization.

XPCS measurements were performed at beamline ID10 at ESRF (France). The sample was placed under vacuum inside a furnace with kapton foil windows and illuminated with a coherent X-ray beam of 10×8 μm (H×V) size with an intensity of about 10 11 photons per second per 200mA at a photon energy of 8 keV. The diffracted speckle patterns were acquired every 5 second by a CCD detector (Andor Ikon-M, 1024×1024 pixels, 13 μm pixel size) in transmission geometry. The detector was placed at a distance of 70 cm from the sample at an angle corresponding to a momentum transfer of q 0 =2.87 Å -1 , which is the maximum of the structure factor S(q) in this material. The measurements were performed isothermally at different temperature steps as detailed below, the heating and cooling rates between isothermal steps were 6 K min -1 . After each isothermal measurement, an angular scan of the diffracted intensity was realized in order to detect any sign of crystallization in the S(q).

Results

Stress relaxation of the supercooled liquid

The stress relaxation curves were measured in different temperature regions. A first series of measurements were performed at temperatures from 560 K to 585 K in the SCL metastable equilibrium. The glass transition temperature of Pd 40 Ni 40 P 20 is detected around 580 K in calorimetric measurements at a heating rate of 20 K min - 1 [12]. Considering the liquid fragility of this material, m=41, the estimation of the onset of the glass transition at a heating rate of 0.1 K min -1 would be at 560 K [START_REF] Perera | Compilation of the fragility parameters for several glass-forming metallic alloys[END_REF]. From equilibrium viscosity measurements, defining the glass transition at =10 12 Pa s, T g was determined at 561 K [START_REF] Kawamura | Newtonian and non-Newtonian viscosity of supercooled liquid in metallic glasses[END_REF]. Therefore, the stress relaxation experiments presented in this work, which were performed isothermally, are considered to probe the SCL state when performed above 560 K. In this temperature range the shape of the stress relaxation curves is well described by a stretched exponential function

                      t t exp 0 . (1)
The fitting of Eq. 1 to the stress relaxation curves gave relaxation times from 70 s at 563 K to 2 s at 583 K.

The stress relaxation curves at some selected temperatures are shown in Figure 1-a, the experimental data is shown by purple circles and Eq. 1 by purple solid lines. Figure 1-b shows the loss modulus obtained from mechanical spectroscopy applying oscillation frequencies of 1 Hz and 0.1 Hz at a constant heating rate. The values of the  exponent and the relaxation times  obtained from the fitting of the stress relaxation curves in the SCL region are plotted with purple circles in Figures 1-c and 1-d, respectively. As shown in Figure 1-c, the shape of the relaxation function in the SCL region is constant with temperature, with a stretched value of the  exponent around 0.5 and without a neat tendency to increase or decrease with temperature. The temperature dependence of  in the SCL state (Figure 1-d) is in good agreement with previous works reporting viscosity [START_REF] Wilde | Calorimetric, thermomechanical, and rheological characterizations of bulk glass-forming Pd40Ni40P20[END_REF] and mechanical spectroscopy measurements [START_REF] Schröter | Shear modulus and compliance in the range of the dynamic glass transition for metallic glasses[END_REF][17] [START_REF] Zhao | Measurements of slow beta-relaxations in metallic glasses and supercooled liquids[END_REF]. Both the free-volume model of Cohen and Grest [START_REF] Cohen | Liquid-glass transition, a free-volume approach[END_REF],

with the parameters obtained from viscosity fits in ref. [START_REF] Wilde | Calorimetric, thermomechanical, and rheological characterizations of bulk glass-forming Pd40Ni40P20[END_REF], and the Vogel-Fulcher-Tammann (VFT) equation, with parameters B=5381 K and T 0 =419 K from mechanical spectroscopy measurements in ref. [START_REF] Zhao | Measurements of slow beta-relaxations in metallic glasses and supercooled liquids[END_REF], can describe reasonably well the temperature dependence of the SCL stress relaxation times measured in this work. The VFT function is shown by a dashed blue line in Figure 1-d. and below T g by cooling at 10 (red), 5 (orange), 1 (yellow), 0.1 (green) and 0.05 (blue) K min -1 . At the lowest temperature, 523 K, and the slowest cooling rates of 0.1 (green) and 0.05 K min -1 (blue), Eq. 2 was used for the fitting, values of  and  2 are shown with triangle and diamond symbols respectively. d) Relaxation times obtained by fitting the stress relaxation curves (same symbols as in Figure 1-c). Star symbols correspond to the relaxation times obtained from mechanical spectroscopy measurements of the loss modulus. The VFT (dashed blue line) and the relaxation times expected for the secondary relaxation (dashed green line) are calculated with the parameters taken from Ref. [START_REF] Zhao | Measurements of slow beta-relaxations in metallic glasses and supercooled liquids[END_REF].

The relaxation times obtained from the maximum of the loss modulus peak are shown with star symbols in Figure 1-d. Here it is pertinent to recall the relationships between the relaxation times obtained from different types of measurements. In this work, all  values will refer to the relaxation time of the Kohlrausch-Williams-Watts (KWW) function (Eq. 1), which is related to the average relaxation time by

  1 1       
. The -peak of the loss modulus corresponds to the transformation of the KWW function into the frequency domain. For a KWW exponent of ≈0.5, this transformation can be well described by a Havriliak-Negami (HN) function,

         HN i 1
, with exponents =0.809 and =0.510, and a relationship between the HN and the KWW times given by  HN = 2.92 KWW [START_REF] Alvarez | Relationship between the time-domain Kohlrausch-Williams-Watts and frequency-domain Havriliak-Negami relaxation functions[END_REF], with  KWW = in this work. The loss modulus peak corresponds to the imaginary part of the HN function, with a maximum found at

      1 1 2 tan                

HN

. Therefore, for ≈0.5, the time corresponding to the inverse frequency at the maximum of the loss peak is related to the KWW time by

     5 . 1 93 . 1 92 . 2 93 . 1 1      HN max max
. This relationship is used here for calculating the values of the relaxation times  from the maximum of the loss peak at temperatures T 0.1Hz =581 K and T 1Hz =596 K. Figure 1d shows that the relaxation times from the stress relaxation curves follow the same VFT line than the ones obtained from mechanical spectroscopy, the latter in agreement with the data reported in other works [START_REF] Schröter | Shear modulus and compliance in the range of the dynamic glass transition for metallic glasses[END_REF] [START_REF] Zhao | Measurements of slow beta-relaxations in metallic glasses and supercooled liquids[END_REF].

The fact that in the SCL state the stress relaxation curves all have the same KWW exponent implies that the time-temperature-superposition (TTS) principle is valid for this metallic glass-forming melt. Figure 2-a shows how all the SCL measurements converge to the same master curve when the time is normalized by the corresponding  at each temperature, the shape of the relaxation being well described by Eq. 1 with ≈0.5 (black solid line). This is in agreement with previous works in mechanical spectroscopy, where it was found that almost all metallic glass-forming systems can be well described by a loss modulus peak corresponding to the frequency domain transformation of a KWW relaxation with ≈0.5 [START_REF] Wang | Relaxation time dispersions in glass forming metallic liquids and glasses[END_REF]

Stress relaxation in the glass state, cooling from above T g

Figure 1 and Figure 2 also show the results obtained by a series of stress relaxation measurements in the glass within the temperature region from 523 K to T g =561 K. In order to control the glass state, this series of experiments were performed with the following thermal protocol. Firstly, the material was heated above T g , in the SCL state, performing a stress relaxation measurement at this temperature and checking that the response was in agreement with the expected VFT behavior and ≈0.5 as discussed above. Secondly, the temperature was decreased following a fixed cooling rate until reaching the desired temperature. Subsequently, a 30 min thermal stabilization step followed by an isothermal stress relaxation measurement was performed. Therefore, the measurements were always performed in samples coming directly from the SCL state at a known cooling rate, in this way the degree of physical aging leading to different glassy configurations was only due to the difference in cooling rates, minimizing the inherent complexity of physical aging induced by the thermal history and the application of temperature steps once the system is below T g . Figure 1-a shows the stress relaxation curves (red circles), and the corresponding fits with Eq. 1 (red solid lines), obtained at 523 K, 533 K, 543 K and 553 K for the case of a cooling rate of 10 K min -1 . Figures 1-c and 1-d show the KWW exponents and the relaxation times obtained for different cooling rates: 0.05, 0.1, 1, 5 and 10 K min -1 . In the case of the slowest cooling rate, 0.05 K min -1 , only the tests at the two extreme temperatures (523 K and 553 K) were realized. In the glass region, Figure 1-d shows how the relaxation time increases for slower cooling rates, at 523 K varying more than one order of magnitude between the fastest and the slowest cooling rates. The corresponding KWW exponents (Figure 1-c) are not constant anymore and show a definite tendency towards lower values as temperature decreases. The change of the relaxation shape is exemplified in Figure 2-b. At 553 K, the fitting gives a  value consistently below 0.5 in all the tests but the relaxation can still be fitted well by Eq. 1 with  =0.5 (solid black line). On the contrary, at 523 K, a value of  =0.5 (dashed black line) is not able to fit the experimental data. The decrease of the KWW exponent of structural relaxation below T g is predicted in theoretical constructions of the glass state, like the random first-order transition [START_REF] Lubchenko | Theory of aging in structural glasses[END_REF]. The stretching of the stress decay observed here may be due to the presence of in-situ aging during the relaxation tests, this producing that the average relaxation time increases along the test. However, as shown in the Discussion section below, the main contribution explaining the decrease of the KWW exponent is due to a widening of the underlying relaxation times distribution as the system goes deep into the glass state.

At this point, it is worth to describe in more detail the results obtained for the lowest temperature (523 K) and the slowest cooling rates (0.05 and 0.1 K min -1 ). For all the other temperatures and cooling rates, a good fitting could be performed with Eq. 1 obtaining KWW exponents decreasing progressively as the temperature goes down below T g . However, for these two slowest cooling rates, the initial shape of the stress decay starts to show a slight bump (see Figure 2b and Figure S1 in supplementary materials). Here, the fitting with Eq. 1 is not any more appropriate and a double relaxation function

                                       2 2 0 exp 1 exp       t A t A t (2)
gives a perfect fit to the initial steps of the relaxation process. In Figure 2-b, the red line shows the fitting with a double relaxation function with  =34800 s,  = 0.402,  2 = 59 s,  2 =0.65 and A =0.89. In this case, the single relaxation fit would give  =24200 s and  = 0.323. For these two conditions (523 K after cooling at 0.1 K min - 1 and 523 K after cooling at 0.05 K min -1 ) Figure 1-c and Figure 1-d show the relaxation times and KWW exponents obtained using Eq. 2 instead of Eq. 1. Differently from the other temperatures, the evident decoupling observed for the samples cooled with the slowest rates leads to a slight increase of the β parameter obtained for the slow process (green and blue triangles in Figure 1-c), due to a less wide relaxation time distribution of the slow process once the contribution of the fast  2 process is subtracted.

Stress relaxation in the glass state, heating from room temperature

In this series of relaxation experiments the samples were heated consecutively in isothermal steps starting at room temperature. At each isothermal step a stabilization of 30 min followed by a stress relaxation experiment was performed. Two types of pre-annealing protocols were applied to the samples, the first protocol (protocol A) consisted in heating to 523 K and immediately cooling down at a heating/cooling rate of 2 K min -1 . At 523 K the structural relaxation of the as-quenched Pd 40 Ni 40 P 20 ribbons is already active and with this protocol the ribbons released part of the residual stresses and lost the bended shape acquired during the quenching process.

The second protocol (protocol B) consisted in pre-annealing at 523 K during 6h. This protocol resulted in a more aged state and a similar protocol was applied also on the disk-shaped samples used in the XPCS experiments.

Figure 3-a shows the initial part of the stress decay curves of samples pre-annealed with protocol A at some selected temperatures (373, 423, 473 and 553 K), the complete curves are shown in Figure S2 in the supplementary materials. The signature of a double relaxation with a short relaxation time,  2 , and a long one, , is observed at the lowest temperatures, as well as the progressive change towards a single relaxation as temperature increases. At the lowest temperatures (373 and 423 K) only the stress relaxation due to the fast process is observable within the test time (2 h); at these temperatures the curves can be well fitted by a partial decay, i.e. with Eq. 2 with →∞, as the relaxation time of the slow process is too long to be determined. From 473 to 523 K the stress decays were fitted by a double relaxation function and above 523 K by a single relaxation.

Table S2 lists the fitted parameters at the different temperatures. the trends obtained for the glasses cooled with the slowest (more aged) and highest (less aged) cooling rates shown in Figure 1, dashed green line is the behavior expected for the secondary relaxation taken from ref. [START_REF] Zhao | Measurements of slow beta-relaxations in metallic glasses and supercooled liquids[END_REF]. The contribution of the fast anelastic process to the total relaxation is found to increase from around 3% at 373 K to a maximum of 15% at 473 and 498 K, and starts decreasing at 523 K when the relaxation time of the viscous process becomes shorter and the two processes overlap in the stress decay curves. At temperatures higher than 523 K it is not possible to separate the two processes anymore (see Figure S2 in supplementary materials). Concerning the shape of the relaxation curves, the values of  2 for samples annealed following protocol A (green diamonds in Figure 3-c) are found lower than 1 at all temperatures. As for the shape of the slow relaxation, the values of  (green triangles in Figure 3-c) are found to follow the same tendency as observed in the glasses obtained by controlled cooling;  is near 0.5 at T g and it decreases with temperature until 523 K where the fast relaxation can be fitted and, therefore, its contribution is not taken into account anymore when analyzing the shape of the slow relaxation. This observation again indicates that the change in the distribution of relaxation times in the glassy state is mainly due to the progressive separation between the fast and the slow processes as temperature decreases, the former with a much smaller activation energy than the latter. to determine it at temperatures below 423 K. The main effect of the change of the pre-annealing treatments is therefore the increase of  in the samples with a higher degree of aging, while  2 shows similar values for the two protocols. The presence of two relaxation processes with different sensitivity to aging has been observed

previously in other out-of-equilibrium materials [START_REF] De Melo Marques | Structural and microscopic relaxations in a colloidal glass[END_REF], and it has been reported recently also in metallic glasses [11][26]. In this work, the absence of appreciable aging of the fast process is evident by looking at the data measured at 523 K. While τ (pink triangles in Figure 3-d) ages approaching the value obtained by cooling the samples from SCL at 0.05 K min -1 (blue dash-dotted line),  2 keeps constant independently on the applied protocol. Compared to previous works [11][26], in which the detected secondary process showed a constant relaxation time of about 10 min, insensitive to either temperature or aging, here the secondary process shows a relaxation time changing with temperature, although with a relatively small activation energy as discussed above.

Microscopic dynamics

The microscopic relaxation dynamics of Pd 40 Ni 40 P 20 were investigated by means of multi-speckle XPCS, from the evaluation of the autocorrelation of the intensity fluctuations, g 2 (q,t), as specified in ref. [27][28]. This quantity is related to the density fluctuations, and thus the dynamics, through the Siegert's relation

      2 2 , 1 , t q f q b t q g  
, with b(q) a set-up dependent parameter and f(q,t) the intermediate scattering function [START_REF] Ruta | Relaxation dynamics and aging in structural glasses 4TH INTERNATIONAL SYMPOSIUM ON SLOW DYNAMICS IN COMPLEX SYSTEMS[END_REF]. XPCS measurements were performed following a temperature program similar to protocol B, with a preannealing of 6h at 533 K followed by a series of consecutive isothermal steps 373, 423, 473 and 523 K heating from room temperature. After the last isotherms at 523 K the system was heated to 573 K, above the glass transition, and cooled back down to 543 K and a last isothermal measurement was performed. The experimental thermal protocol, i.e. the time spent in each isothermal step, was also the same as applied in the stress relaxation experiments. In the same experiment, samples previously subjected to mechanical rejuvenation were also probed, the comparison between aged and rejuvenated samples is described elsewhere [START_REF] Zhou | X-Ray Photon Correlation Spectroscopy Revealing the Change of Relaxation Dynamics of a Severely Deformed Pd-Based Bulk Metallic Glass[END_REF].

The detector was placed at the maximum of the structure factor q 0 =2.87 Å -1 , thus probing the dynamics at the atomic length scale. Considering a KWW decay of the intermediate scattering function

          t T f t q f q   exp ,
, with f q (T) the non-ergodicity factor, the experimental autocorrelation functions were fitted to

          t T q a t q g 2 exp , 1 , 2    (3)
in order to obtain the relaxation time  and the exponent . Figure S4 shows the two-time correlation functions at the different isothermal steps, the width of the diagonal color bands is proportional to the relaxation time and the diagonal direction is the experiment time line. At 423 and 473 K a slight increase of the width is evident, and it implies an increase of the relaxation time due to in-situ aging during the measurements. Figure S4 shows the average autocorrelation functions obtained at each isothermal step and the corresponding fitting functions using Eq. 3. It is observed that the relaxation time  becomes shorter as temperature increases from 373 to 473 K, while at 523 K the relaxation becomes slower and noticeably more stretched. A similar behavior was observed in other metallic glasses in previous studies and it has been associated to the onset of the equilibration in the glass transition region [START_REF] Ruta | Atomic-Scale Relaxation Dynamics and Aging in a Metallic Glass Probed by X-Ray Photon Correlation Spectroscopy[END_REF]. Figures 3-c and3-d display the KWW exponents and relaxation times obtained from the XPCS experiment as yellow circles for the heating steps and a blue circle in the case of the measurement performed after cooling from above T g . The relaxation times at 373, 423 and 473 K overlap with the ones obtained for the fast process in the stress relaxation experiments, while at 523 K the microscopic relaxation time is comparable to those obtained for the slow process. The shape of the relaxation functions is characterized by a high, compressed exponent (>1.5) for the lowest temperatures, which progressively decreases with temperature and becomes stretched ( <1) at 543 K in the glass cooled down from the SCL state.

Compressed exponents are the hallmark of the out-of-equilibrium dynamics of many systems like metallic glasses [START_REF] Ruta | Relaxation processes and physical aging in metallic glasses[END_REF][32], polymer gels and colloidal systems [START_REF] Cipelletti | Universal Aging Features in the Restructuring of Fractal Colloidal Gels[END_REF] and they have been attributed to internal stress driven dynamics [START_REF] Cipelletti | Universal non-diffusive slow dynamics in aging soft matter Faraday Discuss[END_REF].

Discussion

Relaxation of the supercooled liquid, T > 561 K

The stress relaxation of Pd 40 Ni 40 P 20 in the SCL state has been found to be well described by a KWW function with a relaxation time following a VFT temperature dependence and a constant stretching exponent. The time resolution of the static stress relaxation experiments in our equipment is around 0.5 s. At temperatures above T g , where the relaxation time scale is of the order of few seconds, this implies that the first part of the stretched decay is not visible. This fact requires a careful procedure in order to analyze the shape and estimate the parameters of the curve. In this work, the constant value of β is inferred from the superposition of the stress relaxation results in a master curve as shown in Figure 2.

In previous works on stress relaxation of metallic glass-forming melts, the KWW exponents determined in the SCL region near T g were found to increase rapidly with temperature, from values around  =0.5 at T g to values approaching =1 at temperatures just 10-20 K above [START_REF] Wang | Evolution of hidden localized flow during glass-toliquid transition in metallic glass[END_REF]. This increase was in contradiction with mechanical spectroscopy results, where the main -peak of the loss modulus has been consistently found with an invariant in most systems corresponding to the frequency domain transformation of a KWW time decay with an exponent  ≈0.5 [START_REF] Wang | Relaxation time dispersions in glass forming metallic liquids and glasses[END_REF] [START_REF] Qiao | Dynamic universal characteristic of the main (α) relaxation in bulk metallic glasses[END_REF]. It should be taken into account that mechanical spectroscopy is usually performed at frequencies  ranging from 0.01 to 100 Hz, corresponding to characteristic times (1/2) ranging from 15 s to 1.5 ms, meaning that the -relaxation peak is always characterized in the SCL state. The time scaling of the relaxation of various physical properties is observed in different classes of glass-forming liquids [START_REF] Dyre | Hidden Scale Invariance in Condensed Matter[END_REF], and the scaling of the density-density autocorrelation function has been found in metallic SCLs near the glass transition [START_REF] Ruta | Atomic-Scale Relaxation Dynamics and Aging in a Metallic Glass Probed by X-Ray Photon Correlation Spectroscopy[END_REF] [START_REF] Hechler | Microscopic evidence of the connection between liquid-liquid transition and dynamical crossover in an ultraviscous metallic glass former[END_REF]. If the constant relaxation shape (i.e. the validity of the TTS principle in the SCL region) is a peculiarity of some systems or if it is common in metallic glasses, and how far above T g it extends, are interesting points to check by performing accurate stress relaxation measurements in the SCL state of metallic glass-forming systems.

Relaxation of the glass state

In Figure 1-d, the stress relaxation curves of the glasses quenched with controlled cooling rates show the expected increase of  as the degree of aging is increased [START_REF] Mckenna | Mechanical rejuvenation in polymer glasses: fact or fallacy?[END_REF]; the samples cooled down with slower rates being more aged. In addition, the shape of the relaxation is progressively stretched with aging (see Figure 1-c). The decrease of the parameter  in the glass state can be attributed to two effects; the presence of in-situ aging during the relaxation experiments and the evolution of the relaxation times distribution through aging. Of course, both processes may occur simultaneously under some conditions. In the case of the first effect, the stretching of the stress relaxation function is associated to a =(t) changing significantly between the beginning and the end of the experiment. Many phenomenological models have been proposed to describe the evolution of (t), the one proposed by Lunkenheimer et al. [START_REF] Lunkenheimer | Glassy aging dynamics[END_REF], which was able to reproduce the glassy aging dynamics in dielectric experiments of non-metallic glass formers, introduces an aging controlled by the relaxation time itself

      1 1 1 0 1 exp                         VFT VFT t t t       , (3)
with (t) going from initial value  0 =(t=0) towards the equilibrium  VFT =(t→∞). This equation can be solved numerically and introduced in the KWW function,

           t t t   exp
, to model the effects of in-situ aging on the stress decay. Figure S5 in supplementary materials shows the relaxation curve obtained by Eq. 3 considering different initial values of the relaxation time  0 and the corresponding apparent  parameters obtained by fitting the result to Eq. 1. As expected, the system with the higher effect due to in-situ aging is the one with a  0 more distant to  VFT , as it involves faster aging and, therefore, a larger change of (t) throughout the stress relaxation. This result will be qualitatively similar if another aging model was used instead of Eq. 3.

The results obtained for the Pd 40 Ni 40 P 20 glass with different degrees of aging show a decrease of the KWW exponent as the system goes deeper in the glassy landscape of states and  0 becomes longer, which is exactly the contrary behavior as the one shown in Figure S5 if the effects of in-situ aging were significant. Therefore, the change in the shape of the relaxation decay as a function of the cooling rate of the quenching process cannot be attributed to in-situ aging but to the changes of the underlying relaxation time distributions D() of different glassy states, in agreement also with some theoretical work [START_REF] Lubchenko | Theory of aging in structural glasses[END_REF]. Figure 4 shows the relaxation curves obtained

considering different D()s calculated as           0 exp     d t D t . (4)
Figure 4-left shows, qualitatively, the situation in the equilibrium SCL state. The shape of the distribution is invariant and only the average value of  changes with temperature. Consequently, the corresponding relaxation curves are also invariant in shape, the fitting to Eq.1 providing the same value of the KWW exponent. The plots in Figure 4-right are meant to show a conceivable picture of what happens once the system is in the glassy state.

As previously noted when discussing Figure 1, the stress decay curves reflect a wider distribution of times involved in the relaxation both when reducing temperature and increasing aging. In other words, the lower the fictive and real temperatures the lower the value of the KWW exponent. Eventually, the distribution of relaxation times becomes decoupled between the fast and the slow processes, which have different temperature dependences and apparent activation energies. In S2 andS3). This parameter shows a progressive diminution of the relative intensity of the fast contribution as temperature decreases, and it would introduce a further change of the shape of D(), which is not taken into account in the current discussion.

Concerning the effect of aging, the change of D() indicates that aging seems to affect very differently the diverse relaxation times contributing to the stress relaxation, showing a progressive differentiation of D() from the one observed in the equilibrium SCL state. This means that while aging increases the average , making it more close to the equilibrium  VFT value, it differentiates the shape of the  distribution. The latter effect was not anticipated as aging was expected to reduce the spatial and dynamic heterogeneity of the glass. The observed decoupling between the fast and slow relaxations with aging may be due to a different nature, anelastic/stressdriven vs viscous/diffusive, of the processes involved. It could also be conceivable that this effect is associated to a certain stage of the aging process, as the values of  in the glass states tested in this work are all far from the expected equilibrium values indicated by the VFT line in Figures 1-d and3-d.

The presence of decoupling and different aging sensitivities between the fast and slow processes has been reported in other kinds of disordered systems [START_REF] De Melo Marques | Structural and microscopic relaxations in a colloidal glass[END_REF]. As in those cases, while the slow, α-process keeps evolving with aging, the fast relaxation seems independent on the applied protocol. This is in agreement with recently published results in which the microscopic relaxation time was found not dependent on the fictive temperature of the glass [START_REF] Luo | Nonmonotonous atomic motions in metallic glasses[END_REF]. On the other hand, a recently published work [START_REF] Zhou | X-Ray Photon Correlation Spectroscopy Revealing the Change of Relaxation Dynamics of a Severely Deformed Pd-Based Bulk Metallic Glass[END_REF] shows that the dynamics of the stress-driven relaxation process is accelerated by rejuvenation induced by severe plastic deformation, although the activation energy of the relaxation was not found significantly altered. Therefore, the low temperature stress-driven dynamics, here identified with the fast relaxation process, are actually affected by the aged/rejuvenated state of the glass but with much lower sensitivity than the observed for the viscous-like relaxation. Further investigation of the change of the spatial and dynamical heterogeneities through aging is needed to clarify the origin of the observed macroscopic behavior.

Recently, the higher mobility of the atoms in the surface of metallic glasses [START_REF] Zhang | Spatially heterogeneous dynamics in a metallic glass forming liquid imaged by electron correlation microscopy[END_REF] has also been identified as a source of dynamic decoupling [START_REF] Bi | Multiscale Relaxation Dynamics in Ultrathin Metallic Glass-Forming Films[END_REF]. Structural heterogeneity due to surface effects is expected within a layer of the order of 10 nm, and it has been proven to originate fast relaxation processes that affect the dynamics of ultrathin samples [START_REF] Bi | Multiscale Relaxation Dynamics in Ultrathin Metallic Glass-Forming Films[END_REF]. In our work, the samples were 30 m thick and it is not expected that the structural heterogeneity due to surface effects can modify significantly the intrinsic bulk heterogeneity. The contribution of the fast relaxation process discussed above reaches more than 10% of the total stress decay in some of the test conditions (see Tables S2 andS3), while the total fraction of volume sample affected by surface heterogeneity would be less than 0.1 %. The mechanical spectroscopy results, applying oscillating strain and shown in Figure 1-b, do not show any significant difference with the behavior obtained for thicker samples in single-cantilever mode [START_REF] Zhao | Measurements of slow beta-relaxations in metallic glasses and supercooled liquids[END_REF], indicating that the mechanical response is not affected by a surface effect.

Finally, it is interesting to discuss the coincidences and differences of time scales and shapes between the microscopic relaxation measured by XPCS and the macroscopic stress decay. At the lower isothermal steps (373, 423 and 473 K), the decorrelation of the intensity fluctuations shows the same time scale as the first relaxation process observed in the stress decay curves. This may indicate that the origin of the two observations is the same, and the dynamics observed by XPCS experiments is related to the same movements of the glass structure that lead to a macroscopically anelastic response. The microscopic mechanisms originating such behavior are not clear. The anelastic relaxation times of metallic glasses are long [START_REF] Taub | Ideal elastic, anelastic and viscoelastic deformation of a metallic glass[END_REF], many orders of magnitude away from any time scale attainable in simulations, thus making a theoretical microscopic description difficult.

At these lower temperatures, the shape of the microscopic relaxation function is compressed with  >1 (Yellow circles in Figure 3-c), such high compressed exponents indicate that this relaxation process is not of diffusive nature and may be due to collective dynamics driven by the presence of stress fields [START_REF] Ruta | Relaxation processes and physical aging in metallic glasses[END_REF][33] [START_REF] Cipelletti | Universal non-diffusive slow dynamics in aging soft matter Faraday Discuss[END_REF][44] [START_REF] Trachenko | Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics[END_REF].

In spite of the coincidence in time scales, the values of the macroscopic shape parameter  2 of the fast relaxation (Diamonds in Figure 3-c) are clearly lower than that of the microscopic exponents. Therefore, in this region of temperatures (373, 423 and 473 K), although the time scale of the microscopic dynamics coincides with the decoupled, faster part of the stress relaxation process, the shape of the relaxation is not at all coincident.

The origin of the compressed exponent and the difference between the macroscopic and microscopic shape At 523 K, the XPCS results show an increase of the decorrelation time (Circles in Figure 3-d), orders of magnitude longer than in the previous isothermal step, and a decrease of the stretching exponent (see also Figure S4). Hence, above this temperature the decorrelation of the intensity fluctuations seems to start showing the contribution of the slow diffusion-like process. This diffusive-like mechanism may be active at lower temperatures, but much slower than the stress-driven dynamics that dominate the microscopic XPCS observations in such a temperature region. As seen in Figure 3, increasing the temperature towards the glass transition causes the microscopic dynamics to change from compressed to stretched, while showing a time scale more similar to the overall stress relaxation. At temperatures near and above T g , the macroscopic and microscopic dynamics of metallic glasses have been found coincident in other experiments [START_REF] Ruta | Atomic-Scale Relaxation Dynamics and Aging in a Metallic Glass Probed by X-Ray Photon Correlation Spectroscopy[END_REF][51] [START_REF] Hechler | Microscopic evidence of the connection between liquid-liquid transition and dynamical crossover in an ultraviscous metallic glass former[END_REF].

The results of this work indicate that going down in temperature through the glass transition, the macroscopic stress relaxation progressively stretches, changing from a constant shape (TTS) behavior towards a decoupling between fast and slow parts of the relaxation time distribution. This coincides with the emergence of compressed dynamics in the intermediate scattering function observable by XPCS, suggesting that the movements responsible of the anelastic part of the relaxation in glass are microscopically very different from the diffusion-like hopping mechanism in supercooled liquids [START_REF] Handle | q-Independent Slow Dynamics in Atomic and Molecular Systems[END_REF][53], which is characterized by stretched microscopic dynamics with exponents <1.

This picture has many similarities with a recent model [START_REF] Trachenko | Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics[END_REF]. This model proposes that above T g the activation of a local relaxation event increases the rigidity of the neighboring relaxation zones, thus leading to a stretched relaxation. On the contrary, below T g , the local relaxation changes to avalanche-like events. In the latter case, the relaxation event softens the surroundings accelerating the dynamics and leading to a compressed behavior.

The results of our work, however, point to a low temperature relaxation mechanism which is reversible, as the fast part of the stress relaxation does not introduce a permanent deformation in the sample, and this seems not compatible to an avalanche-like mechanism. The microscopic origin of the anelastic relaxation could be also explained by other models. For instance, it may be similar to the one observed in bead packs, see for instance [START_REF] Murphy | Memory in Nonmonotonic Stress Relaxation of a Granular System[END_REF]. In this picture the relaxation is driven by movements along stress chains or stress fields formed in the amorphous structure, without necessity of local rearrangements implying change of neighbors or breaking of bonds. A collective motion driven by a stress field may generate a compressed exponent similar to the dynamics observed under flow [START_REF] Busch | Dynamics in shear flow studied by X-ray Photon Correlation Spectroscopy[END_REF]. Further studies, with controlled stress conditions could unveil the nature of this glass relaxation mechanism.

Detailed knowledge of the relaxation behavior is an important technological aspect for low temperature forming processes of metallic glasses [START_REF] Wang | Dynamic relaxations and relaxation-property relationships in metallic glasses[END_REF]. In this sense, XPCS is a unique technique to access the microscopic out-of-equilibrium dynamics. For instance, the time scales of the relaxation processes dealt with in this work are many orders of magnitude longer than the ones accessible by molecular dynamics simulations. While in the supercooled liquid state mechanical and XPCS results show an overall agreement in time scale and relaxation shape, the interpretation of XPCS experiments is complicated in the glassy state, where the inherent out-ofequilibrium effects like aging can be merged with the relaxation of internal stress fluctuations or external stress fields. This work presents a first evidence of coincidence between the time scales of the microscopic dynamics in the glass and a macroscopic effect, which will pave the way to further studies.

Conclusion

In summary, the results of stress relaxation experiments have shown that the stress relaxation of Pd 40 Ni 40 P 20 is controlled by a relaxation time distribution with invariant shape above T g , producing a corresponding constant KWW exponent. Below this temperature, the distribution broadens progressively, which indicates different temperature dependences of the microscopic processes involved in the distribution. The decrease of the KWW exponent is also observed as a function of aging, which implies that the different time scales in the relaxation distribution have different aging sensitivity and the dynamic heterogeneity increases. When temperature decreases far from T g and the system ages enough, the distribution of times decouples between fast processes with recoverable, anelastic behavior and slow, irreversible, viscous-like relaxations. While the main slow process evidently ages with time, the fast one is found independent on the specific applied protocol as in some soft glasses [START_REF] De Melo Marques | Structural and microscopic relaxations in a colloidal glass[END_REF]. The coincidence between the macroscopic stress relaxation behavior and the microscopic dynamics suggests that, at the lower temperatures, the microscopic dynamics measured by XPCS show only the effects of the fast process, i.e. the anelastic-like relaxation of the system under the presence of stress fields. This connection would explain the peculiar compressed shape of the intermediate scattering function of metallic glasses at the atomic scale and deserves further studies.

Figure 1 .

 1 Figure 1. a) Stress relaxation curves obtained above T g =561 K (purple symbols) and from 523 K to T g (red symbols), solid lines are the KWW functions of Eq. 1. b) Loss modulus obtained at 1Hz (blue) and 0.1 Hz (orange) at a heating rate of 1 K min -1 . c) Stretching exponents of Eq. 1 obtained by fitting the experimental curves above T g (purple symbols),

  [START_REF] Qiao | Dynamic universal characteristic of the main (α) relaxation in bulk metallic glasses[END_REF][START_REF] Yao | Characterization and modeling of dynamic relaxation of a Zr-based bulk metallic glass[END_REF].

Figure 2 .

 2 Figure 2. a) Stress relaxation measurements above 560 K plotted as function of t/ (symbols) and Eq. 1 with =0.5 (black solid line). b) Stress relaxation at 553 K and 523 K after cooling from the SCL state at 0.05 K min -1 (blue symbols). Eq. 1 with =0.5 (solid black line for 553 K and dashed line for 523 K). Double relaxation fitting of Eq. 2 for the 523 K measurement (red line).

Figure 3 .

 3 Figure 3. Stress relaxation curves (a) and recovery of the strain after the stress relaxation experiments (b) at 373 K (skyblue), 423 K (greyblue), 473 K (blue) and 553 K (purple) of a sample pre-annealed following protocol A. Solid lines in a) are fits to Eq. 2 (373, 423, 473 K) or Eq. 1 (553 K). KWW exponents (c) and relaxation times (d) obtained from the fits. Green symbols:  2 and  2 (diamonds) and  and  (triangles) for samples pre-annealed with protocol A. Pink symbols:  2 and  2 (diamonds) and  and  (triangles) for samples pre-annealed with protocol B. Yellow circles are  and  from XPCS experiments done similarly to protocol B, while the blue circles are XPCS  and  measured upon

Figure 3 -

 3 Figure 3-b shows the recovery steps after the stress relaxation measurements. In such recovery steps the load on the sample was released and the evolution of the sample length recorded. The figure shows the results at the selected temperatures of 373, 423, 473 K and 553 K. The first three temperatures correspond to stress relaxationexperiments that were able to record basically only the stress decay due to the fast relaxation process, and it is observed that the strain is totally recovered after the test. This indicates a completely anelastic nature of the fast relaxation. On the contrary, at 553 K the stress relaxation is completed during the experiment and the deformation becomes permanent, which indicates the viscous nature of the relaxation process at this temperature.

Figures 3 -

 3 Figures 3-c and 3-d also show the results of relaxation times and stretching exponents obtained from the samples pre-annealed according to protocol B (6 h at 523 K). Pink diamonds correspond to  2 and  2 while pink triangles to  and . A comparison of the stress relaxation curves between glasses pre-annealed following protocols A or B is shown in FigureS3in the supplementary materials. It is observed that the long pre-annealing at 523 K induced a more aged state in which the contribution of the fast process is reduced and the relaxation time of the slow process becomes longer. The reduction of the contribution of the fast process made it impossible

Figure 4 -

 4 right, this effect is qualitatively represented by shifting the D() with different activation energies between the fast and the slow contributions. In the case of the Figure 4 a ratio of E fast / E slow = 0.5 has been chosen. It is shown how the fitting to Eq. 1 provides a stretching exponent of the relaxation function which is progressively reduced and, finally, how the decoupling between the fast and the slow parts of the distribution becomes evident.

Figure 4 .

 4 Figure 4. Relaxation time distributions (Top plots) and corresponding decay functions (Symbols in the bottom plots) with the value of  obtained by fitting Eq. 1 (lines in the bottom plots). Left: Invariant shift of the relaxation time distribution. Right: Shift of the relaxation function applying different activation energies for the fast and the slow processes, the plots correspond to E fast /E slow = 0.5.

  parameters, which is observed in many systems, is still controversial and remains an open question and a matter of intense research[45][46][47][START_REF] Wu | Stretched and compressed exponentials in the relaxation dynamics of a metallic glass-forming melt[END_REF][49][START_REF] Zaccone | Relaxation and vibrational properties in metal alloys and other disordered systems[END_REF]. The XPCS measurements showed in this work were performed at the maximum of the structure factor, thus probing the decorrelation of atomic scale configurations. The coincidence of time scales suggests that the atomic scale dynamics control the relaxation process, but the macroscopic response may have contributions of time scales associated to other length scales.

Acknowledgements

We acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities and we would like to thank Y. Chushkin and F. Zontone for assistance in using beamline ID10. E.P. acknowledges financial support from MINECO (grant FIS2017-82625-P) and Generalitat de Catalunya (grant 2017SGR0042). G.W. and S.H. acknowledge funding by DFG (WI 1899/29-1). H.Z. acknowledges the China Scholarship Council for its financial support.


domain: spi chim phys

text:
Peng Luo
email: pengluo@iphy.ac.cn

Fan Zhu

Yu-Miao Lv

Zhen Lu

Lai-Quan Shen

Rui Zhao

Yi-Tao Sun

Gavin Vaughan

Marco Di Michiel

Beatrice Ruta

Hai-Yang Bai
email: hybai@iphy.ac.cn

Wei-Hua Wang

Microscopic structural evolution during ultrastable metallic glass formation

By decreasing the rate of physical vapor deposition, ZrCuAl metallic glass with improved stability and mechanical performances can be formed. With scanning transmission electron microscopy, we found that the glass deposited at higher rate exhibits a heterogeneous structure with compositional fluctuations at distances of a few nanometers, which gradually disappear on decreasing the deposition rate and eventually a homogeneous, featureless structure is developed approaching ultrastability. This microscopic structural evolution suggests the existence of two dynamical processes: the faster diffusion driven by the kinetic energy of the depositing atoms, which leads to nanoscale compositional fluctuations, and the slower collective rearrangements that equilibrate the deposited atoms and eliminate the compositional and structural heterogeneity.

Table of Contents

Unlike crystalline materials having well-defined periodic order and structural defects, the structure and property of glasses obtained from liquid quenching are generally only tunable in a limited range. In 2007 it was demonstrated that organic molecular glasses with extraordinary thermodynamic and kinetic stability [START_REF] Swallen | Organic Glasses with Exceptional Thermodynamic and Kinetic Stability[END_REF] and exceptional mechanical and functional properties [START_REF] Kearns | High-Modulus Organic Glasses Prepared by Physical Vapor Deposition[END_REF][START_REF] Gujral | Structural Characterization of Vapor-Deposited Glasses of an Organic Hole Transport Material with X-Ray Scattering[END_REF][START_REF] Ràfols-Ribé | High-Performance Organic Light-Emitting Diodes Comprising Ultrastable Glass Layers[END_REF][START_REF] Dalal | Tunable Molecular Orientation and Elevated Thermal Stability of Vapor-Deposited Organic Semiconductors[END_REF] compared to their liquid-quenched counterparts can be produced by physical vapor deposition (PVD). These glasses, termed as ultrastable glasses, have received much attention due to both their fundamental importance for understanding the nature of glass and their potentials for broad technological applications. [START_REF] Gujral | Structural Characterization of Vapor-Deposited Glasses of an Organic Hole Transport Material with X-Ray Scattering[END_REF][START_REF] Ràfols-Ribé | High-Performance Organic Light-Emitting Diodes Comprising Ultrastable Glass Layers[END_REF][START_REF] Dalal | Tunable Molecular Orientation and Elevated Thermal Stability of Vapor-Deposited Organic Semiconductors[END_REF][START_REF] Léonard | Macroscopic Facilitation of Glassy Relaxation Kinetics: Ultrastable Glass Films with Frontlike Thermal Response[END_REF][START_REF] Vila-Costa | Nucleation and Growth of the Supercooled Liquid Phase Control Glass Transition in Bulk Ultrastable Glasses[END_REF][START_REF] Rodríguez-Tinoco | Surface-Bulk Interplay in Vapor-Deposited Glasses: Crossover Length and the Origin of Front Transformation[END_REF][START_REF] Wang | Low-Frequency Vibrational Modes of Stable Glasses[END_REF][START_REF] Seoane | Low-Temperature Anomalies of a Vapor Deposited Glass[END_REF][START_REF] Angell | On the Uncertain Distinction between Fast Landscape Exploration and Second Amorphous Phase (Ideal Glass) Interpretations of the Ultrastable Glass Phenomenon[END_REF][START_REF] Lüttich | Anti-Aging in Ultrastable Metallic Glasses[END_REF][START_REF] Khomenko | Depletion of Two-Level Systems in Ultrastable Computer-Generated Glasses[END_REF][START_REF] Perez-Castaneda | Suppression of Tunneling Two-Level Systems in Ultrastable Glasses of Indomethacin[END_REF][START_REF] Yu | Suppression of β Relaxation in Vapor-Deposited Ultrastable Glasses[END_REF] In the past decades, more species of ultrastable glasses, including metallic glasses (MGs) [START_REF] Yu | Ultrastable Metallic Glass[END_REF][START_REF] Aji | Ultrastrong and Ultrastable Metallic Glass[END_REF] and polymeric glasses [START_REF] Guo | Ultrastable Nanostructured Polymer Glasses[END_REF] have been fabricated by PVD, as well as Lennard-Jones glasses in computer simulations. [START_REF] Singh | Ultrastable Glasses from in Silico Vapour Deposition[END_REF] In all these works, the general consensus is that the substrate temperature (Tsub) during deposition is a critical variable and the optimal Tsub for creating an ultrastable glass is near the glass transition temperature (Tg), at 0.8~0.9Tg, [START_REF] Yu | Ultrastable Metallic Glass[END_REF][START_REF] Aji | Ultrastrong and Ultrastable Metallic Glass[END_REF][START_REF] Guo | Ultrastable Nanostructured Polymer Glasses[END_REF][START_REF] Singh | Ultrastable Glasses from in Silico Vapour Deposition[END_REF][START_REF] Kearns | Influence of Substrate Temperature on the Stability of Glasses Prepared by Vapor Deposition[END_REF][START_REF] Kearns | Hiking down the Energy Landscape: Progress Toward the Kauzmann Temperature via Vapor Deposition[END_REF] associated with the enhanced surface mobility that gives rise to a more relaxed structure. [START_REF] Berthier | Origin of Ultrastability in Vapor-Deposited Glasses[END_REF] Very recently, it was found that ultrastable MGs with substantial Tg enhancement can be fabricated by PVD on room temperature substrates corresponding to Tsub ≈ 0.43Tg, with reduced deposition rate (R). [START_REF] Sun | Transition towards Ultrastable Metallic Glasses in Zr-Based Thin Films[END_REF][START_REF] Luo | Ultrastable Metallic Glasses Formed on Cold Substrates[END_REF] Moreover, molecular dynamics (MD) simulations [START_REF] Bokas | Increased Stability of CuZrAl Metallic Glasses Prepared by Physical Vapor Deposition[END_REF] revealed that the optimal Tsub for the formation of ultrastable Zr49Cu45Al6 MG is 0.625Tg at constant R, already far below the empirical 0.8~0.9Tg. These findings suggest that the surface atoms of MGs retain high mobility even at low temperatures. [START_REF] Luo | Ultrastable Metallic Glasses Formed on Cold Substrates[END_REF] However, the microscopic structural and dynamical processes occurring in the material on approaching ultrastability is still unclear. As a multicomponent material with nondirectional metallic bonds, the micromechanisms relevant to ultrastable MG formation are intrinsically challenging.

In this letter, we investigated the microscopic structure evolution of a prototypical Zr46Cu46Al8 (at.%) MG prepared by PVD with different deposition rates, combining spherical aberration corrected scanning transmission electron microscopy (Cs-STEM) and high-energy synchrotron X-ray diffraction (XRD). The results reveal the gradual transformation from a nanoscale heterogeneous structure to a homogeneous one with concomitant increasing prevalence of Zr-Zr bonds on decreasing R, providing novel insights on the microscopic processes relevant to ultrastable MG formation.

The MGs were prepared by single-target ion beam deposition without heating the substrates. More details for sample preparation and characterizations are included in the Experimental Methods. The samples were firstly examined by in-house XRD, which reveals diffuse patterns indicative of fully amorphous structure (see Fig. S1 in the Supporting Information). The Differential scanning calorimetry (DSC) curves adapted from our previous work [START_REF] Luo | Ultrastable Metallic Glasses Formed on Cold Substrates[END_REF] are shown in Fig. 1(a). For the glass deposited at 5.7 nm min -1 , Tg is measured to be 706 K, close to that of the liquid-quenched ordinary glass (698 K). [START_REF] Luo | Ultrastable Metallic Glasses Formed on Cold Substrates[END_REF] When R is lowered to 2.8 nm min -1 , Tg increases to 724 K. For the glass deposited at the slowest rate of 0.8 nm min -1 , Tg reaches 757 K. These results indicate the evolution towards ultrastable glass state through reducing R.

An instrumented nanoindentation is employed to examine the mechanical performances of the vapor-deposited MG films. The samples were deposited on Si(001) substrates to a thickness of 2 µm, with root mean square roughness less than 0.2 nm independent of R (Fig. S2). Such good surface quality eliminates the possible effects of surface defects and roughness on nanoindentation measurements. With sequential nanoindentation tests, indentation size effect [START_REF] Jang | Indentation Size Effect in Bulk Metallic Glass[END_REF][START_REF] Lu | Shear-Banding Induced Indentation Size Effect in Metallic Glasses[END_REF] is observed at small contact depth (h < 150 nm), and substrate effect [START_REF] Chu | Thin Film Metallic Glasses: Unique Properties and Potential Applications[END_REF][START_REF] Liu | Rate-Dependent Deformation Behavior of Zr-Based Metallic-Glass Coatings Examined by Nanoindentation[END_REF] shows up when h is larger than 200 nm (Fig. S3).

To circumvent these effects, we chose a peak load of 5 mN that yields a penetration depth around 180-200 nm. The inset in Fig. 1(b) displays the representative nanoindentation load-depth curves. The lower R, the smaller penetration depth is under the same load, thus higher resistance against deformation. The hardness and Young's modulus evaluated by Olive-Pharr method [START_REF] Oliver | An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments[END_REF] show the same deposition rate dependence as Tg [Fig. 1(b)]. As R decreases from 5.7 nm min -1 to 0.8 nm min -1 , the hardness and Young's modulus increase from, respectively, 126.40±1.71 GPa and 6.71±0.14 GPa to 139.48±1.36 GPa and 7.48±0.05 GPa, by ≈11%. These results demonstrate that the mechanical performances can be substantially improved with slower deposition, in good agreement with the Tg enhancement. The heterogeneous contrast in the STEM images implies an inhomogeneous distribution of chemistry and/or density. As shown in Fig. 3(a-d prepared by PVD at R = 30~60 nm min -1 by Barbee et al. [START_REF] Barbee | Phase Separation in Vapor Quench Synthesized Noncrystalline Copper Zirconium Alloys[END_REF] However, contradictory results were observed on the occurrence of phase separation in liquid-quenched ZrCu(Al) MGs. [START_REF] Kim | Phase Separation in Metallic Glasses[END_REF] Here, our observation of nanoscale phase separation in ZrCuAl MGs prepared by PVD strengthens the idea that PVD is less effective in suppressing phase separation compared to liquid quenching. [START_REF] Barbee | Phase Separation in Vapor Quench Synthesized Noncrystalline Copper Zirconium Alloys[END_REF] For ZrCu and ZrCuAl MGs containing no atom pair with positive heat of mixing (Table S1), [START_REF] Takeuchi | Classification of Bulk Metallic Glasses by Atomic Size Difference, Heat of Mixing and Period of Constituent Elements and Its Application to Characterization of the Main Alloying Element[END_REF] phase separation is thermodynamically unfavored and thus metastable. Figure 2(e-g) reveal the gradual transformation from a phase-separated nanostructure to a single-phase structure upon decreasing R. As R is the only variable for the sample preparation, these observations can be ascribed to the different surface residence time of the deposited atoms before being buried deeper, where their dynamics are orders of magnitude slower. Therefore, our results suggest that the depositing atoms experience two dynamic processes after arriving at the substrate: the faster diffusion process that leads to nanoscale compositional fluctuations and the slower collective rearrangements that equilibrate the deposited atoms and eliminate the compositional and structural heterogeneity.

During vapor-deposition, individual atom species are deposited onto the substrate, as the deposition parameters were maintained constant and the substrates were rotating at a constant speed (15 r/min), a uniform deposition process is expected. For all deposited MGs, atomically smooth surfaces are obtained independent of R (Fig. S2), indicating the absence of transition in growth modes. [START_REF] Liu | Deposition of Multicomponent Metallic Glass Films by Single-Target Magnetron Sputtering[END_REF] In a recent experimental and simulation study on vapor-deposited atomically thin MG membranes, it was found that after arriving at the substrate the atoms aggregate to form a fractal structure on a length scale comparable to the phase separations of our observation. [START_REF] Jiang | Direct Observation of Atomic-Level Fractal Structure in a Metallic Glass Membrane[END_REF] On the other hand, our results and those of Barbee et al [START_REF] Barbee | Phase Separation in Vapor Quench Synthesized Noncrystalline Copper Zirconium Alloys[END_REF] indicate that phase separation is pronounced at higher R. Therefore, it can be concluded that the phase separation in vapor-deposited ZrCu(Al) MGs occurs rapidly during the aggregation process, driven by the kinetic energy of the depositing atoms. However, for ZrCu(Al) MGs with negative heat of mixing (Table S1), [START_REF] Takeuchi | Classification of Bulk Metallic Glasses by Atomic Size Difference, Heat of Mixing and Period of Constituent Elements and Its Application to Characterization of the Main Alloying Element[END_REF] a homogeneous structure without decomposition is thermodynamically more favored. [START_REF] Kim | Phase Separation in Metallic Glasses[END_REF] Hence, with longer surface residence time allowed by slower deposition, the deposited atoms can undergo further rearrangements driving the glass towards homogenization, during which the atoms will adopt more stable structural configurations.

More detailed structural difference between the vapor-deposited MGs at different rates and the liquid-quenched MG were revealed by high-energy synchrotron XRD. S1). The first peaks split into a sub-peak located at r = 2.82 Å and a shoulder around 3.20 Å due to the discrete bonding length distribution of the nearestneighbor atoms. According to the interatomic distances and weight factors, Cu-Cu, Zr-Cu and Zr-Zr atom pairs dominate the first peak. The sub-peak at 2.82 Å can be assigned mainly to Zr-Cu pairs, while the shoulder around 3.20 Å originates mostly from Zr-Zr pairs. The PDF of the 4.4 nm min -1 deposited MG basically overlap that of the liquidquenched MG, while at 3.0 Å < r < 3.5 Å the 0.8 nm min -1 deposited MG exhibits higher G(r)Zr-Zr/G(r)Zr-Cu ratio. This indicates more Zr-Zr pairs and lesser Zr-Cu pairs in the ultrastable MG, in agreement with previous results from MD simulation. [START_REF] Bokas | Increased Stability of CuZrAl Metallic Glasses Prepared by Physical Vapor Deposition[END_REF] Since the heat of mixing between Zr and Cu is negative, the occurrence of phase separation does not mean an increase in the like near-neighbor pairs (Zr-Zr and Cu-Cu) and a decrease in the unlike near-neighbor pair (Zr-Cu), in agreement with our results.

Based on the model of local configurational excitations in the atomic connectivity network proposed by Egami and co-workers [START_REF] Iwashita | Elementary Excitations and Crossover Phenomenon in Liquids[END_REF] , and the experimental fact of the much slower diffusion of Zr atoms than the other atoms in liquid alloy, [START_REF] Basuki | Decoupling of Component Diffusion in a Glass-Forming Zr46.75Ti8.25Cu7.5Ni10Be27.5 Melt Far above the Liquidus Temperature[END_REF] it was proposed that Zr atoms form significantly stronger temporary nearest-neighbor bonds that have to be broken by thermal activation than the other atoms. [START_REF] Basuki | Decoupling of Component Diffusion in a Glass-Forming Zr46.75Ti8.25Cu7.5Ni10Be27.5 Melt Far above the Liquidus Temperature[END_REF] The observation of increased prevalence of Zr-Zr bonds in ultrastable MGs in our experiments and previous MD simulations [START_REF] Bokas | Increased Stability of CuZrAl Metallic Glasses Prepared by Physical Vapor Deposition[END_REF] further confirms this presumption and reveals the importance of Zr-Zr bonds in strengthening the atomic connectivity and enhancing the stability of MGs. well-defined correlation peaks till r = 22 Å are seen in the latter, while no discernable oscillations can be observed in the 4.4 nm min -1 deposited MG above r = 16 Å [Fig. 4(d)]. For the 0.8 nm min -1 deposited MG, the G(r) peaks are stronger than that deposited at 4.4 nm min -1 and retained to larger distance around r = 18 Å. This increased medium-range ordering on decreasing R is consistent with the increased compositional and structural homogeneity in the vapor-deposited MGs (Fig. 2), but even at the slowest deposition, medium-range ordering comparable to the liquid-quenched MG is not developed in the vapor-deposited MGs, suggesting the intrinsic difference between these two glass forming paths experiencing or not the liquid state.

By looking at the heat flow curves in Fig. 1

(a), an inflection is observed between

Tg and the crystallization temperature (Tx) in the 5.7 nm min -1 deposited MG, which becomes less obvious in the 2.8 nm min -1 deposited MG and eventually disappears in the 0.8 nm min -1 deposited ultrastable MG. This is more observable in the derivatives of the heat flow (see Fig. S4). Such a deposition rate dependent two-stage-like endothermic behavior is in agreement with the chemical ordering (phase separation) of the glass as revealed by STEM [Fig. 2(e-g)]. On the other hand, it has been shown in our previous work [START_REF] Luo | Ultrastable Metallic Glasses Formed on Cold Substrates[END_REF] that, while the Tg of the vapor-deposited MGs is always larger than that of the liquid-quenched MG the Tx of the MG deposited at R ≲ 2 nm min -1 is even lower than that of the liquid-quenched MG. This is analogous to the previous observation that vapor-deposited, phase-separated ZrCu MG shows lower Tx than that of liquid-quenched, single-phase MG. [START_REF] Barbee | Phase Separation in Vapor Quench Synthesized Noncrystalline Copper Zirconium Alloys[END_REF] Hence, our results confirm this phenomenon and further demonstrate that with reduced phase separation by lowering R the Tx of the vapor-deposited MG will increase and become less different from that of the liquid-quenched, single-phase MG. These results suggest that the development of phase separation during vapor-deposition of materials with negative heat of mixing could be thermodynamically related to the propensity to crystallize of the depositing atoms having remnant kinetic energy.

These experimental facts shed new lights on the microscopic processes the atoms experience before achieving ultrastable state. After arriving at the substrate, the kinetic energy of the depositing atoms enables their faster diffusion towards the development of nanoscale chemical ordering. If the deposition is slow, long free surface residence time is allowed and the atoms undergo surface-mediated equilibration, during which both the compositional and the structural fluctuations will be eliminated as they are not thermodynamically favored for an amorphous system with negative heat of mixing, at the same time the atoms can adopt more stable structural configurations. The increased structural homogeneity with less soft sites and the strengthened atomic network with increased prevalence of Zr-Zr bonds make the glass stronger against deformation [Fig.

1(b)]. The herein observed structural and chemical homogenization may also account for the recent observations of reduced nanoscale elasticity fluctuations in ultrastable

MGs. [START_REF] Sun | Transition towards Ultrastable Metallic Glasses in Zr-Based Thin Films[END_REF][START_REF] Dziuba | Local Mechanical Properties of an Ultrastable Metallic Glass[END_REF] The changed local structure leads to increased kinetic stability as manifested by the enhanced Tg, but differently from molecular systems [START_REF] Liu | Birefringent Stable Glass with Predominantly Isotropic Molecular Orientation[END_REF] and aged MGs, [START_REF] Luo | Nonmonotonous Atomic Motions in Metallic Glasses[END_REF] on the DSC up-scans no discernable enthalpy recovery following glass transition is observed for ultrastable MGs in the present or the previous studies. [START_REF] Yu | Ultrastable Metallic Glass[END_REF][START_REF] Aji | Ultrastrong and Ultrastable Metallic Glass[END_REF][START_REF] Sun | Transition towards Ultrastable Metallic Glasses in Zr-Based Thin Films[END_REF][START_REF] Luo | Ultrastable Metallic Glasses Formed on Cold Substrates[END_REF] The absence of enthalpy recovery above Tg and the experimental fact that ultrastable MGs are more resistant against crystallization [START_REF] Sun | Transition towards Ultrastable Metallic Glasses in Zr-Based Thin Films[END_REF][START_REF] Luo | Ultrastable Metallic Glasses Formed on Cold Substrates[END_REF] suggest that the local structure modification cannot be erased before crystallization sets in. Therefore, the total amount of enthalpy change (∆H), during heating from glassy state to fully crystallized state can reflect the energy state of the glass. Compared to the liquid-quenched MG, this enthalpy change in the vapordeposited MGs is much less and exhibits a continuous decrease with lower R [Fig. S5].

If not considering the difference between the potential energy of the crystallization phases [START_REF] Sun | Transition towards Ultrastable Metallic Glasses in Zr-Based Thin Films[END_REF][START_REF] Luo | Ultrastable Metallic Glasses Formed on Cold Substrates[END_REF] , the reduced ∆H roughly indicates the increased thermodynamic stability of ultrastable MGs.

To summarize, combining start-of-the-art structure characterizations, we revealed that MGs prepared by fast vapor-deposition show highly heterogeneous structure with nanoscale compositional fluctuations, which gradually transform into a homogeneous, featureless structure accompanied by increased prevalence of Zr-Zr atom pairs on decreasing R. This observations explain the inflections on the DSC curves above Tg and the reduced Tx of the MGs deposited at R ≲ 2 nm min -1 , [START_REF] Luo | Ultrastable Metallic Glasses Formed on Cold Substrates[END_REF] and suggest that two dynamical processes are responsible for the microscopic structural evolution: the faster diffusion driven by the kinetic energy of the depositing atoms, which leads to nanoscale compositional fluctuations, and the slower collective rearrangements that equilibrate the deposited atoms and eliminate the compositional and structural heterogeneity.

EXPERIMENTAL METHODS

Preparation of metallic glasses

MG films were prepared by ion beam deposition using a high purity Zr46Cu46Al8 alloy target 100 mm in diameter. To remove the oxide layer on the target surface, presputtering was carried out for 200 s. Prior to the deposition of the MG, 100 nm thick Aluminum was deposited on a flat polycarbonate (PC) substrate 12 cm in diameter.

During the deposition, the substrate is rotated at a constant rotating speed (15 r/min), making a uniform deposition process. The ion beam energy was 750 eV. The deposition rate was controlled by the ion beam current. The base pressure of the chamber was better than 2×10 -4 Pa. Argon was used as gas species under an operation pressure of 2.4×10 -2 Pa. The as-received films were detached from the PC substrates by dissolving the in-between Aluminum layer in 1 mol L -1 NaOH solution, and then the films were cleaned by deionized water. The nanoindentation samples (2 μm thick) were directly deposited on Si(001) substrates. Ordinary MG ribbons (20 μm thick) were produced by melt-spinning technique for comparison.

Calorimetric characterization

DSC measurements for the vapor-deposited MGs were performed on a Perkin-Elmer DSC 8000 at a heating rate of 20 K min -1 with 20 mL min -1 flowing pure argon gas to prevent surface oxidation. The mass of the DSC samples is 15~20 mg to achieve good data accuracy. Prior to measurements, the DSC was calibrated with standard samples In and Zn.

X-ray diffraction

The amorphous structure of the as-deposited films was firstly checked with a Bruker D8 Advance XRD using a Cu Kα source in the Bragg-Brentano geometry. Highenergy synchrotron XRD measurements were carried out with an incoming beam energy of 79.5 keV on the ID15A beamline at ESRF, Grenoble (France). At 79.5 keV, the calculated X-ray attenuation for the 2 μm thick glass films varies from 0.17% at q  0 Å -1 to 0.24% at qmax  30 Å -1 (q is the wavevector transfer). The calculated value for the 20 μm thick ribbon varies instead from 1.7% at q  0 Å -1 to 2.4% at qmax  30 Å -1 . The attenuation is therefore linearly proportional to the sample thickness, weakly dependent on q, very small, and consequently negligible. The diffraction signal is also linearly proportional to the sample thickness. For such reasons, it is not necessary to use samples of similar thickness.

The incident flux normalization is done with a diode placed in front of the sample. Diffraction patterns were collected in transmission geometry by using a Pilatus3 X CdTe 2M hybrid photon counting detector. The detector was off-centered with respect to the incident beam and located close to the sample to access up to q ≈ 30 Å -1 and to be able to calculate with a good resolution the G(r) functions. The intensity profiles were corrected for the background contribution, polarization of the X-rays and detector geometrical correction. The G(r) functions were calculated using routines from the Diffpy-CMI library [START_REF] Juhás | Complex Modeling: A Strategy and Software Program for Combining Multiple Information Sources to Solve Ill Posed Structure and Nanostructure Inverse Problems[END_REF] with some local modifications for outlier rejection and treatment of background effects.

Transmission electron microscopy and energy dispersive spectroscopy

Specimens for the TEM characterizations were prepared by gentle ion milling with 3 keV Argon ions at the liquid nitrogen temperature. HRTEM and HAADF-STEM observations were conducted using a cold field emission TEM (JEM-ARM200F, JEOL) equipped with a spherical aberration (Cs) corrector for the probe-forming objective lens.

Preparation of TEM specimens sometimes leads to inhomogeneous thinning, making possible artifacts confused with the intrinsic microstructures. [START_REF] Sun | Artifacts Induced in Metallic Glasses during TEM Sample Preparation[END_REF] According to Refs., [START_REF] Zhu | Correlation between Local Structure Order and Spatial Heterogeneity in a Metallic Glass[END_REF][START_REF] Sun | Artifacts Induced in Metallic Glasses during TEM Sample Preparation[END_REF] our preparation of the TEM specimens for the studied MG system is not expected to induce any artifacts. EDS mappings were recorded at STEM mode to characterize the compositional distribution. For the 0.8 nm min -1 deposited MG, the EDS mapping was performed on the JEM-ARM200F Cs-STEM. The STEM image shown in Fig. 3(a) was taken at the same region of the EDS mapping. For the 5.7 nm min -1 deposited MG, another Cs-STEM instrument (JEM-2100F, JEOL, 200 kV) was employed at the same operation conditions. The STEM image shown in Fig. 3(e) was the morphology trace during the EDS mapping, therefore, it has lower resolution than Fig. 3(a).

Nanoindentation

The hardness and elastic modulus were characterized by nanoindentation with a diamond Berkovich indenter on a Nanoindenter G200 XP system (Skysight, USA). The force resolution and vertical displacement resolution are 50 nN and < 0.01 nm, respectively. The MGs for nanoindentation tests were deposited on Si(001) substrates to a thickness of 2 µm. Prior to the beginning of tests, the contact area function was calibrated using a standard fused silica material. The indentations were performed under a load-control mode with a maximum load of 5 mN and at a loading-unloading rate of 1 mN s -1 . The load was held for a period of 5 s at the peak load before unloading.

The allowable drift rate is 0.05 nm s -1 . Six indents were made for each sample to verify the accuracy and scatter of the indentation data.

  surface residence time]

Figure 2

 2 Figure 2 shows the high-resolution transmission electron microscopy (HRTEM) and high-angle annular dark-field STEM (HAADF-STEM) images of the MGs deposited at different rates, and the liquid-quenched MG for comparison. The homogeneous maze-like patterns in the HRTEM micrographs and the diffuse halo of the selected area electron diffraction (SAED) patterns reveal typical amorphous structure [Fig. 2(a-d)]. While no discernible difference between these samples is observed with HRTEM and electron diffraction [Fig. 2(a-d)], HAADF-STEM which is sensitive to the local chemistry and density (atomic configuration) reveals an intriguing microstructure which is strongly dependent on R [Fig. 2(e-g)]. The MG film deposited at 5.7 nm min -1 shows a highly heterogeneous morphology [Fig. 2(e)], consisting of mixed equiaxed and columnar domains about 4-10 nm separated by ≈1~2 nm thick boundaries with distinct contrast. As R is lowered to 2.8 nm min -1 , the darker boundaries expand outward and become more fuzzy while the brighter domains become, accordingly, smaller in size and less in amount. At the same time the contrast difference between these two structures decreases [Fig. 2(f)]. Eventually, at R = 0.8 nm min -1 this dual-phase nanostructure disappears, and a homogeneous, featureless morphology is observed [Fig. 2(g)].

  ), STEM energydispersive X-ray spectroscopy (EDS) mapping for the 0.8 nm min -1 deposited MG indicates the absence of chemical fluctuation for all three elements, consistent with the uniform STEM morphology [Fig. 2(g)]. In contrast, the 5.7 nm min -1 deposited MG shows remarkable chemical fluctuations. While the distribution of Al atoms is uniform [Fig. 3(h)], those of Zr and Cu atoms are heterogeneous [Fig. 3(f,g)]. The brighter regions in the STEM image are enriched in Cu with, accordingly, less Zr, and the darker regions are enriched in Zr with less Cu. These results indicate that the heterogeneous structure observed in the faster deposited MGs is related to compositional fluctuations, which diminish with decreasing R and eventually disappear at the slowest deposition at 0.8 nm min -1 . The liquid-quenched MG should not have decomposition, hence, the heterogeneous structure at much smaller length scales (≈2 nm) [Fig. 2(h)] indicates the presence of local atomic configuration variations as usually observed in liquidquenched MGs. 31 The visibly more homogenous structure of the 0.8 nm min -1 deposited ultrastable MG [Fig. 2(g)], suggests the absence of both compositional fluctuation and obvious structural heterogeneity. Nanoscale phase separation in ZrCu MGs has been reported first in MGs

Figure 4 (

 4 Figure 4(a) displays the pair distribution functions (PDF), G(r), derived from the synchrotron XRD patterns [the inset in Fig. 4(a)]. Due to the different thickness of the vapor-deposited MG films and the liquid-quenched MG ribbon, their scattering signal and the calculated G(r) have different intensity, hence, for better comparison the G(r) functions were normalized by their first peak maximum. Figure 4(b) shows the zoomedin first peaks together with the interatomic distance and weight factor of the atomic pairs (TableS1). The first peaks split into a sub-peak located at r = 2.82 Å and a

Figure 4 (

 4 Figure 4(c) and (d) indicate that the G(r) oscillations beyond the nearest-neighbor are smaller in the vapor-deposited MGs than in the liquid-quenched MG. In particular,

Figure 1 .

 1 Figure 1. (a) DSC scans measured at 20 K min -1 for Zr46Cu46Al8 MGs deposited at different rates (R). (b) Hardness (H), modulus (E) and Tg as a function of R, the line is guide to the eye. Inset: Representative nanoindentation load-depth (P-h) curves.

20 Figure 2 .

 202 Figure 2. (a-d) HRTEM and (e-h) HAADF-STEM images of the MGs deposited at 5.7 nm min -1 (a,e), 2.8 nm min -1 (b,f) and 0.8 nm min -1 (c,g), and the liquid-quenched MG (d,h) for comparison. Insets in (a-d): SAED patterns.

Figure 3 .

 3 Figure 3. EDS mapping of the MGs deposited at 0.8 nm min -1 (a-d) and at 5.7 nm min - 1 (e-h). Two different Cs-STEM instruments were used for the EDS mapping of the two samples (see detailed explanation in Experimental Methods).

Figure 4 .

 4 Figure 4. (a) Pair distribution functions G(r) for MGs deposited at 4.4 nm min -1 and 0.8 nm min -1 , and liquid-quenched MG ribbon for comparison. Inset: Synchrotron XRD patterns, the vertical lines denote the peak position of liquid-quenched MGs. (b-d) Close-up views of the first (b), the second to the fifth (c), the sixth and later peaks of G(r) (d). The vertical bars in (b) indicate the weight factors of atomic pairs Wij.

Acknowledgements

This research was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB30000000), National Key Research and Development Plan (No. 2018YFA0703603), National Natural Science Foundation of China (Nos.

61888102 and 11790291), and Natural Science Foundation of Guangdong Province (No. 2019B030302010). Y.T.S was supported by National Natural Science Foundation of China (Grant No.51801230).

Supporting Information

The Supporting Information is available free of charge at