Onset of Cooperative Dynamics in an Equilibrium Glass-Forming

Jan 22, 2016 - Liquidmetal Technologies Inc., Santa Margarita, California 92688, United States. ¶ Quantum Condensed Matter Division, Oak Ridge Nation...
3 downloads 4 Views 2MB Size
Download PDF
Article pubs.acs.org/JPCB

Onset of Cooperative Dynamics in an Equilibrium Glass-Forming Metallic Liquid Abhishek Jaiswal,† Stephanie O’Keeffe,‡ Rebecca Mills,¶ Andrey Podlesynak,¶ Georg Ehlers,¶ Wojciech Dmowski,§ Konstantin Lokshin,§ Joseph Stevick,‡ Takeshi Egami,§ and Yang Zhang*,†,∥ †

Department of Nuclear, Plasma and Radiological Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ‡ Liquidmetal Technologies Inc., Santa Margarita, California 92688, United States ¶ Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States § Department of Materials Science and Engineering, Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, United States ∥ Department of Materials Science and Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ABSTRACT: Onset of cooperative dynamics has been observed in many molecular liquids, colloids, and granular materials in the metastable regime on approaching their respective glass or jamming transition points, and is considered to play a significant role in the emergence of the slow dynamics. However, the nature of such dynamical cooperativity remains elusive in multicomponent metallic liquids characterized by complex many-body interactions and high mixing entropy. Herein, we report evidence of onset of cooperative dynamics in an equilibrium glass-forming metallic liquid (LM601: Zr51Cu36Ni4Al9). This is revealed by deviation of the mean effective diffusion coefficient from its high-temperature Arrhenius behavior below TA ≈ 1300 K, i.e., a crossover from uncorrelated dynamics above TA to landscape-influenced correlated dynamics below TA. Furthermore, the onset/ crossover temperature TA in such a multicomponent bulk metallic glass-forming liquid is observed at approximately twice of its calorimetric glass transition temperature (Tg ≈ 697 K) and in its stable liquid phase, unlike many molecular liquids.

■

INTRODUCTION Increasingly cooperative motions of particles at the microscopic level are universally observed across molecular liquids,1−3 colloids,4,5 granular materials,6−8 etc. when temperature is lowered or packing fraction is increased. At high temperatures or low packing fractions, particles move rather independently without the need of exchanging information on their respective local environment due to the large energetics or associated “free volume”. However, at low temperatures or high-packing fractions, collective reorganization of particles over large length scales is required to facilitate motions such as local topological excitations,9 hopping,10 etc. for the system to overcome the associated large energy barriers and relax, resulting in highly activated dynamics.11−15 Besides, the temperature dependence of transport properties such as self-diffusion coefficient D, viscosity η, and relaxation time τ has been the subject of much attention in studying liquids and glasses.1−3,9,16−20 At high temperatures, the transport in fragile liquids follows Arrhenius-like weak temperature dependence, however, below certain crossover temperature TA, typically observed in the metastable supercooled liquid state, the transport properties increase dramatically as the temperature is lowered toward the calorimetric glass transition temperature Tg while the structure changes of the liquids are © 2016 American Chemical Society

almost unappreciable. Such a crossover temperature TA has been interpreted as the onset point of cooperative motions of particles in the system to undergo structural relaxations upon cooling.21,22 Below TA, the non-Arrhenius behavior of liquids have stimulated many intriguing theoretical ideas such as cooperatively rearranging regions,23 mode coupling,24 random first order transition,25 dynamical facilitation,26 intrinsic microscopic disorder based on shear transformation zones,27,28 etc. However, glass-forming metallic liquids are usually composed of multiple elements with distinct atomic sizes. Thus, they possess intrinsic high mixing entropy and chemical disorder.29−31 In addition, metallic liquids are mediated by the complex nonclassical many-body interactions. Therefore, how the dynamical cooperativity manifests in glass-forming metallic liquids remains largely under-explored. Herein, we study the diffusive dynamics of a multicomponent bulk metallic glass-forming liquid to characterize its nature of dynamical onset of cooperativity. Multicomponent CuZr-based bulk metallic glasses (BMGs) have attracted much scientific and technological interests because of their high glass-forming Received: November 23, 2015 Revised: January 20, 2016 Published: January 22, 2016 1142

DOI: 10.1021/acs.jpcb.5b11452 J. Phys. Chem. B 2016, 120, 1142−1148

Article

The Journal of Physical Chemistry B ability evidenced by the low critical cooling rates.32 Whether a liquid forms a crystal or glass upon quenching ultimately depends on the competition between nucleation and relaxation rates.33 Thus, quantifying the relaxational behavior of such liquids is essential to better understand the mechanism for high glass-forming ability of this material. To this end, we report the temperature dependence of mean effective diffusion coefficient of a model glass-forming metallic liquid measured by quasielastic neutron scattering (QENS) and supported by molecular dynamics (MD) simulations of the relevant system. We found that the dynamical cooperativity onset point TA in this metallic liquid occurs roughly twice of Tg and even far above its melting point in the stable liquid phase, and that it could be typical in many such metallic liquids.

from 900 to 2500 K.36 Further details on MD simulations can be found in ref 37.

■

RESULTS AND DISCUSSION We study the quaternary BMG LM601 with atomic compositions Zr51Cu36Ni4Al9. Contribution to the measured neutron scattering spectrum in the Q range of 0.5−1.6 Å−1 arises roughly equally from incoherent and coherent scattering processes. Zr, Cu, and Al are primarily coherent scatterers, resulting in a significant contribution of coherent scattering to the measured signal. The incoherent contributions are mainly from Ni and Cu. In many simple liquids, the coherent scattering in the small Q and small QENS energy transfer range appears as a broad background in the measured spectrum because the thermal diffusivity is usually much larger than the self-diffusion for metallic liquids differing by roughly 2 orders of magnitude.38−41 However, the relaxation time scales for selfdiffusion and collective thermal diffusion in the ternary Cu40Zr51Al9 system were found to be very similar. In fact, both types of scattering weighted by their respective scattering lengths reveal roughly equal contribution to the measured signal in the studied Q range.42 The measured static structure factor S(Q) is Q-independent, as it is well below its first peak at 2.7 Å−1 (Figure 1). The static structure factor S(Q) is obtained

■

METHODS Materials. High quality lab-grade BMG samples of LM601 with atomic compositions Zr51Cu36Ni4Al9 were prepared by Liquidmetal Technologies Inc. using counter gravity cast. The samples were cast into rectangular slabs with dimensions of 30 mm ×30 mm ×2.5 mm and bulk density of 6.8 g/cm3. The material undergoes a glass transition at 697 K and extends up to 730 K, with complete melting observed at 1170 K as revealed by the Differential Scanning Calorimetric (DSC) measurements reported elsewhere.34 Quasi-Elastic Neutron Scattering (QENS). QENS measurements were carried out at the Cold Neutron Chopper Spectrometer (CNCS) at the Spallation Neutron Source at Oak Ridge National Laboratory. The samples were cut into rectangular sticks with average size 1.5 mm × 1.5 mm × 30 mm and stacked in a cylindrical MgO container with an MgO rod insert. MgO crucible was a suitable choice as it showed no significant reactions with the melted sample. The thickness of the sample was thus controlled as 1.75 mm (×2 layers) in order to avoid multiple scattering. The crucible was suspended to the thermocouples using thin niobium wires inside a high temperature furnace. A high-purity inert helium gas in a high vacuum (∼10−5 Torr) was maintained during measurements. Two thermocouples were used at various locations to verify the uniformity of temperature inside the furnace. The measurements were carried out in the temperature range of 900−1100 °C, in steps of 25 °C. A low energy incident neutron beam of 1.55 meV was used in the “High Flux” operational mode of the choppers. At these operating conditions, the energy resolution of the instrument (fwhm) was ∼45 μeV; the wave vector transfer Q range was 0.1−1.7 Å−1; and the useful energy transfer E range is −4.7−0.8 meV. At a specific temperature, data was collected for approximately 4 h to obtain good counting statistics. The total scattered neutron intensity spectrum was corrected for the time-independent background and normalized by the white-beam vanadium run. An empty MgO crucible was measured at both room and high temperature and used for the background subtraction. Crucible scattering near the elastic line was also used as the instrument resolution and fitted with one Gaussian. Molecular Dynamics (MD). Molecular dynamics (MD) simulations were performed using the open-source atomistic simulator LAMMPS35 on a relevant ternary Cu40Zr51Al9 system. The low concentration of Ni in LM601 was replaced with Cu because of their similarity in atomic sizes. Hence, we were able to use the reliable ternary embedded atom method (EAM) potential to simulate the system in the equilibrium liquid state

Figure 1. Static structure factor S(Q) of melted bulk metallic glass LM601 in the Q range of 0.1−1.6 Å−1 at various temperatures. Other than the very low- and high-Q, and a spike at Q ≈ 0.8 Å−1 and peak at at Q ∼ 1.5 Å−1, S(Q) is a constant, indicating the predominately incoherent scattering nature.

by integrating the elastic intensity of the measured quasi-elastic spectra in the energy transfer range of [−0.25, 0.25] meV. Hence, the Q resolution is not as good as in a dedicated diffraction instrument. The data collected at the very low- and high-angle detectors are affected by various backgrounds. The spike at Q ≈ 0.8 Å−1 and variations at Q ∼ 1.5 Å−1 arise from imperfect crucible scattering subtraction. The upturn at very small Q < 0.3 Å−1 comes from the beam stop. Investigating the microscopic dynamics of such liquids is possible through QENS measurements because liquid convection occurs at a much larger time scale than that of neutron energy transfers and thus does not impact measurements of 1143

DOI: 10.1021/acs.jpcb.5b11452 J. Phys. Chem. B 2016, 120, 1142−1148

Article

The Journal of Physical Chemistry B relaxation times. For liquids, particles undergoing stochastic diffusive motions at long time, interaction with neutrons leads to unquantized energy gain or loss of the neutrons and thus a broadening of the elastic scattering peak, as observed in Figure 2. In such multicomponent systems, the mixing of elements in

Figure 2. Illustration of model fitting with KWW stretched exponential function. Dynamic structure factor S(Q = 0.5 Å−1, E) of LM601 at 1000 °C was normalized by the peak intensity. Solid line denotes the model fitting described in eq 1 and 2 in main text. The broadening near the elastic peak of the room temperature measurement of empty crucible is taken as the instrumental resolution (ENS, dotted line). Dashed line denotes the Fourier transform of KWW stretched relaxation component (QENS) and the dash-dotted line represents the constant background (Bkg).

Figure 3. (a and b) Measured spectra of glass-forming metallic liquid LM601 at two wave-vector transfer values (Q = 0.6, 1.3 Å−1). The measured dynamic structure factor S(Q,E) is normalized by the peak height to illustrate the quasi-elastic broadening of the liquid. Solid lines denote the fittings using Fourier transform of KWW model convoluted with the instrumental resolution function eq 1 and 2. (c and d) Qdependence of S(Q,E) at 900 and 1100 °C with KWW fits. The kinematically accessible energy transfer E range is largest at the highest Q.

disparate sizes leads to both density and concentration fluctuations. Furthermore, the phonons scattering is weak and consequently, in LM601, the time scale for thermal diffusion is effectively the same as that for self-diffusion. In addition, due to similar relaxation times of thermal and self-diffusion, the width of the measured S(Q,E) peak can be taken as an approximate measure of the self-diffusion. The measured spectrum shows enhanced broadening at higher temperatures and a reduction in scattering intensity due to escalating atomic mobility in the liquid (Figure 3, parts a and b). The generalized hydrodynamic regime (Q: 0.5−1.6 Å−1)41 is marked by frequency and wave-vector transfer dependence of transport properties. Hence, the spectral shape of S(Q,E) shows non-Debye relaxation behavior. The kinematically accessible energy transfer E range at the energy loss side is limited by the incident neutron energy, while it is Q-dependent in the energy gain side with a much larger dynamic range (Figure 3, parts c and d) and provides, in theory, the same information. At high temperatures, the detailed balance factor is negligible in the measured dynamic range. Fourier transform of the Kohlrausch−Williams−Watts (KWW) stretched exponential function convoluted with the instrumental energy resolution function eq 1 provides excellent fit to the QENS spectrum.34,43

intermediate scattering function that quantifies both the selfand collective density correlations because of their similar time scale in the studied Q range; and R(Q,E) is the Q-dependent instrumental energy resolution function. The density correlator F(Q,t) is modeled as F(Q , t ) = AQ exp[−(t /τ )β ]

where AQ is the effective Debye−Waller factor in a liquid, τ is the relaxation time, and β is the stretching exponent. In our analysis, AQ is fixed to unity as it is coupled to the normalization factor N and thus cannot be extracted reliably at the same time. Illustration of the various components of the fitted curve is provided in Figure 2. In the fitting, the usable dynamic range varies for each Q-value. The background was treated as an energy independent constant. Data for Q < 0.5 Å−1 were discarded as the dynamic range is very narrow due to kinetic constraint of neutrons and affected by the proximity to the direct neutron beam. The relaxation times obtained from model-fittings are in the range of 1−100 ps (Figure 4, parts a and b) across the various Q values. Such a time scale corresponds to the slow, αrelaxation in the system. The stretching exponent β shows a gradual increase at higher temperatures (Figure 4c). This is expected as it suggests that the relaxations are more stretched at lower temperatures. β is nearly Q-independent for a given temperature and lies in the range of 0.5−0.9 for the measured temperatures except at the lowest Q. At Q = 0.5 and 1.4 Å−1, f(Q) was adjusted to obtain reasonable value for τ while still maintaining a sensible fit. This lead to an artificial drop in the stretching exponent β. In many metallic glass-forming liquids β

S(Q , E) = N[f (Q )δ(E) + (1 − f (Q ))-{F(Q , t )}] ⊗ R (Q , E )

(2)

(1)

where N is the normalization prefactor; f(Q) is the fraction of elastic scattering component that takes into account any contribution from immobile particles with very low mobility such that they appear immobile in the measured QENS time window, and remnant elastic background; F(Q,t) is the 1144

DOI: 10.1021/acs.jpcb.5b11452 J. Phys. Chem. B 2016, 120, 1142−1148

Article

The Journal of Physical Chemistry B

time of all elements at this level, and thus should not be confused with an average of the relaxation times of each element weighted by their atomic concentrations. However, it is still a good approximation of the true self-diffusion coefficient because of the similar time scale of self-and collective relaxations. While our measured Q range is not strictly in the hydrodynamic regime, the Q2 dependence of 1/τ is still observed, therefore it is justifiable to extract the slope as the mean effective diffusion coefficient. The intercept was unfixed during the fittings, however, it is very small. Similarly, we can also use ⟨τ⟩ = τ/β Γ(1/β) to estimate the mean effective diffusion coefficient, but the difference in results is minor. The large and almost temperature-independent nature of β means that ⟨τ⟩ is slightly larger than τ by a constant scaling factor. Figure 5a shows the temperature dependence of the mean effective diffusion coefficient compared to the scaled self-

Figure 4. (a) Temperature dependence of relaxation time τ in melted LM601 at available Q values in the generalized hydrodynamic range 0.5−1.6 Å−1 and steps of 0.1 Å−1. (b) Inverse of relaxation time plotted against Q2 to demonstrate the linearity at small Q values. As Q increases, relaxation time decreases. Solid lines denote linear fits applied to extract the effective diffusion coefficient of the metallic liquid in the temperature range. Error bars are smaller than the symbol size for many data points in parts a and b. (c) Temperature dependence of stretching exponent β reveals values in the range 0.5− 1.0. At lower temperatures structural relaxation is more stretched, which is expected due to increasing heterogeneous dynamics and influence from energy landscape. (d) f(Q) follows the shape of S(Q) of the crucible. Hence a peak at Q ∼ 1.5 Å−1 is observed.

Figure 5. Temperature dependence of mean effective diffusion coefficient obtained from QENS measurements in the generalized hydrodynamic regime of melted LM601 in the temperature range 900−1100 °C (red circles) and the unweighted mean self-diffusion coefficient obtained from MD simulations (blue triangles). Solid line is Arrhenius fit at high temperatures. Deviations from the fit is observed at low temperatures which marks the dynamical onset temperature TA, shown for the experimental data in the inset. The fitting parameters are diffusion constant D0 = 13.0 ± 3.1 Å2/ps, and activation energy EA = 55.8 ± 2.7 kJ/mol.

is found to vary from 0.5−1.0 for alpha relaxations.44−46 Usually, the α-relaxation occurs at a time scale corresponding to the start of diffusive motion in the equilibrium liquid with an exponential behavior of Fs(Q,t). However, τ and β are coupled in the stretched exponential model. Hence to extract these two parameters unambiguously usually requires excellent data quality, a suitable dynamic range, and energy dependent background. Also, in the generalized hydrodynamic regime (Q: 0.5−1.6 Å−1), the Q dependence of transport properties can give rise to nonexponential relaxation. Furthermore, in such multicomponent liquids with chemical disorder there is an added possibility of deviations from exponential behavior due to distributions of elemental relaxations times.37 The elastic fraction fitting parameter f(Q) lies in the range of 0−0.2 and follows the shape of S(Q) of the crucible (Figure 4(d)). As temperature increases, the mobility of the system increases and this fraction becomes smaller. Figure 4b shows the inverse of the experimentally obtained relaxation time τ plotted against Q2. In the hydrodynamic limit, the “mean” effective diffusion coefficient of the liquid can be related to the relaxation time as follows: 1 Deff = lim 2 Q → 0 τQ (3)

diffusion coefficient computed (with a scaling factor = 2.1) from MD simulations (Figure: 6a). High-temperature dependence of D is admirably fitted by Arrhenius behavior, only revealing a deviation at TA ≈ 1300 ± 50 K. Interestingly, the activation barrier EA is ∼10 kBTg, which is surprisingly similar to that of many van der Waals molecular liquids.20,47 In our recent computational study,37 we characterized this behavior as the onset of cooperativity, which is accompanied by enhanced dynamical clustering and decoupling of elemental transport coefficients. The identified onset/crossover temperature TA is approximately twice larger than the glass transition temperature Tg ≈ 697 K for this BMG. Note that the dynamical facilitation onset temperature TA is typically 1.4 ± 0.2 Tg in many molecular liquids, despite some outliers with directional bonds;2,48 while the mode coupling crossover temperature Tc is typically 1.3 ± 0.2 Tg in many molecular liquids and in the metastable supercooled regime.18,33 However, TA in the studied metallic liquid is much higher and even above the material’s melting point Tm ≈ 1170 K. Therefore, the dynamical onset/ crossover phenomenon occurs in the stable liquid state, in contrast to metastable supercooled states in many molecular liquids. The complex many-body interactions and the chemical

Note that τ is extracted from the measured double differential cross section, which naturally contains weighting of the respective coherent and incoherent bound scattering lengths of each element. It represents a measure of a “mean” relaxation 1145

DOI: 10.1021/acs.jpcb.5b11452 J. Phys. Chem. B 2016, 120, 1142−1148

Article

The Journal of Physical Chemistry B

value when self-intermediate scattering function Fs(Q,t) decay to 1/e of its initial value (Figure 6(b)). The MD α-relaxation time τ plotted against inverse temperature scale at various Qvalues and temperature range measured in the experiments lies in the same range of (1−100) ps (Figure 6(c)). Uncertainties in τ could arise from minor variations in temperature thermostat for every 20 K. Inverse of τ plotted against Q2 illustrates the linear behavior close to the hydrodynamic regime (Figure 6d), as in experiments. Diffusion coefficient extracted by this method agrees well with those computed from mean squared displacement. The proximity of relaxation times at 1290 and 1310 K in Figure 6d accompanied by a clear separation in Qdependent τ observed between 1270 and 1290 K, could arise from fluctuations in temperature of the simulated liquid; however, these observations also coincides with the onset of correlated dynamics in the system. In order to understand the mechanism involved in the observation of dynamical onset in the stable liquid phase in such metallic glass melts, we further computed the nonGaussian parameter α2(t) and four-point correlation function χ4(t)22 that can quantify spatially heterogeneous dynamics in a liquid.12,52 Both quantities are computed for the entire system. Hence, there is an additional heterogeneity induced by composition, i.e., the differences in the mobility of Cu, Zr, and Al. This additional heterogeneity is presumably temperature independent and thus does not alter the temperature dependence of the maxima values α*2 and χ*4 . Parts a and b of Figure 7 show the temperature dependence of α2(t) and χ4(t) respectively, marked by an enhanced increase below the onset temperature TA (Figure 7, parts c and d). Although the

Figure 6. MD Simulation of a ternary metallic liquid, Cu40Zr51Al9: (a) Temperature dependence of mean squared displacement of all atoms (unweighted). The long-time diffusive behavior of ⟨r2(t)⟩ is fitted with a linear form to extract the mean self-diffusion coefficient as the slope. (b) Temperature dependence of the self-intermediate scattering function Fs(Q = 2.7 Å−1,t) of all atoms (unweighted). At high temperatures the relaxation is almost exponential but becomes more stretched at low temperatures with a pronounced shoulder following the fast relaxations. (c) Temperature dependence of τ shown in an Arrhenius plot for the same Q range measured in experiments. (d) Q2dependence of 1/τ can also be fitted to obtain the diffusion coefficient D.

disorder in this quaternary system may be partially responsible for the high shift of TA to the equilibrium liquid phase. Consequently, the dynamics of such metallic liquid turns sluggish even above the melting point, leading to excellent glass-forming ability. This comparison agrees with recent encouraging studies of viscosity in several metallic liquids that identified the cooperative temperature Tcoop from deviations of Arrhenius behavior of bulk viscosity at high temperatures.49,50 Tcoop was also presented to be twice of Tg. This crossover observed in viscosity does not imply similar behavior in diffusion coefficient as metallic liquids are found to not obey the Stokes−Einstein relation even in the liquid state.51 In several other studies, temperature dependence of D(T) has been fitted by the mode coupling theory (MCT) scaling laws extrapolated to a critical temperature that marks the dynamic singularity temperature Tc.44−46 Here, our results portray another picture that dynamical onset in metallic melts is found in the liquid state and it can be understood in terms of deviations from Arrhenius behavior of diffusion coefficients, consistent with reported results on viscosity. The detailed MD simulation comparison is shown in Figure 6. All quantities presented here are computed for all atom types without using their respective scattering lengths as weights. The detailed elemental studies can be found in ref 37. Mean squared displacement is used to compute the self-diffusion coefficient in Figure 5a of the simulated ternary system by applying linear fits to its long-time behavior (Figure 6a). Additionally, the Qdependent relaxation time τ is estimated by taking the time

Figure 7. (a) Non-Gaussian parameter α2(t) for all atoms in the MD simulated ternary liquid. A nonzero value arises at short time corresponding to ballistic motions due to difference in mobility of Cu, Zr, and Al. (b) Four-point correlation function χ4(t) for all the atoms in the liquid. (c) Maximum of the non-Gaussian parameter denoted as α*2 over the temperature range simulated shows an enhanced increase below TA ≈ 1300 K. (d) Similar increasing trend is observed in the maximum of χ4(t) denoted as χ*4 . The time scale corresponding to the maxima is close to the α-relaxation time of the liquid. These observations are consistent with results of elemental α2(t) and χ4(t).37 1146

DOI: 10.1021/acs.jpcb.5b11452 J. Phys. Chem. B 2016, 120, 1142−1148

Article

The Journal of Physical Chemistry B magnitudes of both maxima α*2 and χ*4 are not substantial compared to deeply supercooled liquids, their sharp increases below TA are evident. The concepts of increasing cooperativity in metallic liquids can also be qualitatively understood in terms of the underlying potential energy landscape. Below the dynamical onset temperature TA, the system enters the landscape-influenced regime and is able to sample deeper potential energy minima.53,54 Hence, to overcome these deeper energy barriers requires structural rearrangement of several particles within a cluster simultaneously and thus gives rise to cooperative dynamics. Furthermore, the role of atomic arrangement in connection to the landscape-influenced regime has been discussed in terms of local configurational excitations (LCE). Bond formation or breaking events between neighboring atoms,9,55 LCEs, change atomic connectivity network and subsequently control structural relaxations in the system. Thus, below the dynamical onset temperature TA, LCEs are believed to interact via the dynamic long-range stress fields they create. Such dynamic communications among LCEs’ are thus involved in the flow mechanism and may give rise to spatially heterogeneous dynamics in the system.56 The elastically cooperative activated barrier hopping theory also predicts a dynamical crossover when collective elastic effects begin to dominate local cage scale activated process.47 Above the dynamic onset temperature, correlation between atoms is not required for atomic mobility thus giving rise to nearly nonactivated transport.2

Part of the research conducted at ORNL’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. We thank Prof. Kenneth Schweizer for insightful discussions and the Program of Computational Science and Engineering at UIUC for providing us with the computing resources.

■

■

CONCLUSIONS We conclude that dynamical onset/crossover in a glass-forming metallic liquid, which marks the emergence of atomic dynamical cooperativity, can be identified by a deviation from high-temperature Arrhenius behavior of the mean diffusion coefficient. This crossover temperature TA is roughly twice of Tg and in the stable liquid phase. The onset of correlated dynamics may be interpreted in terms of increasing heterogeneous dynamics or development of intermittent correlated rearranging regions mediated by the dynamic communication among local configurational or topological excitations. This work raises interesting questions beyond just extending the idea of dynamic crossover to metallic liquids. It remains an open question whether such a crossover happening at twice of Tg in metallic liquids, unlike many molecular systems, has a thermodynamic origin.34 A fundamental link between the kinetic fragility and the onset temperature in glass-forming liquids remains unexplored. Furthermore, the observation of dynamic crossover in both diffusion coefficient and the viscosity of metallic liquids tied with the breakdown of Stokes−Einstein relation in metallic liquids is an intriguing question that we are exploring.

■

REFERENCES

(1) Angell, C. A.; Ngai, K. L.; McKenna, G. B.; McMillan, P. F.; Martin, S. W. Relaxation in Glassforming Liquids and Amorphous Solids. J. Appl. Phys. 2000, 88, 3113−3157. (2) Elmatad, Y. S.; Chandler, D.; Garrahan, J. P. Corresponding States of Structural Glass Formers. J. Phys. Chem. B 2009, 113, 5563− 5567. (3) Mallamace, F.; Branca, C.; Corsaro, C.; Leone, N.; Spooren, J.; Chen, S.-H.; Stanley, H. E. Transport Properties of Glass-Forming Liquids Suggest That Dynamic Crossover Temperature is as Important as the Glass Transition Temperature. Proc. Natl. Acad. Sci. U. S. A. 2010, 107, 22457−22462. (4) Weeks, E. R.; Crocker, J. C.; Levitt, A. C.; Schofield, A.; Weitz, D. A. Three-Dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition. Science 2000, 287, 627−631. (5) Kegel, W. K.; van Blaaderen, A. Direct Observation of Dynamical Heterogeneities in Colloidal Hard-Sphere Suspensions. Science 2000, 287, 290−293. (6) Keys, A. S.; Abate, A. R.; Glotzer, S. C.; Durian, D. J. Measurement of Growing Dynamical Length Scales and Prediction of the Jamming Transition in a Granular Material. Nat. Phys. 2007, 3, 260−264. (7) Silbert, L. E.; Liu, A. J.; Nagel, S. R. Vibrations and Diverging Length Scales Near the Unjamming Transition. Phys. Rev. Lett. 2005, 95, 098301. (8) Angelini, T. E.; Hannezo, E.; Trepat, X.; Marquez, M.; Fredberg, J. J.; Weitz, D. A. Glass-like Dynamics of Collective Cell Migration. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 4714−4719. (9) Iwashita, T.; Nicholson, D. M.; Egami, T. Elementary Excitations and Crossover Phenomenon in Liquids. Phys. Rev. Lett. 2013, 110, 205504. (10) Kob, W.; Andersen, H. C. Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The Van Hove Correlation Function. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1995, 51, 4626−4641. (11) Debenedetti, P. G.; Stillinger, F. H. Supercooled Liquids and the Glass Transition. Nature 2001, 410, 259−267. (12) Berthier, L.; Biroli, G. Theoretical Perspective on the Glass Transition and Amorphous Materials. Rev. Mod. Phys. 2011, 83, 587− 645. (13) Ediger, M. D.; Harrowell, P. Perspective: Supercooled Liquids and Glasses. J. Chem. Phys. 2012, 137, 080901. (14) Stevenson, J. D.; Schmalian, J.; Wolynes, P. G. The Shapes of Cooperatively Rearranging Regions in Glass-Forming Liquids. Nat. Phys. 2006, 2, 268−274. (15) Donati, C.; Franz, S.; Glotzer, S. C.; Parisi, G. Theory of NonLinear Susceptibility and Correlation Length in Glasses and Liquids. J. Non-Cryst. Solids 2002, 307−310, 215−224. (16) Angell, C. Glass-Formers and Viscous Liquid Slowdown Since David Turnbull: Enduring Puzzles and New Twists. MRS Bull. 2008, 33, 544−555. (17) Bö hmer, R.; Ngai, K. L.; Angell, C. A.; Plazek, D. J. Nonexponential Relaxations in Strong and Fragile Glass Formers. J. Chem. Phys. 1993, 99, 4201−4209. (18) Novikov, V. N.; Sokolov, A. P. Universality of the Dynamic Crossover in Glass-Forming Liquids: A “Magic” Relaxation Time. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 67, 031507. (19) Tarjus, G.; Kivelson, D.; Viot, P. The Viscous Slowing down of Supercooled Liquids as a Temperature-Controlled Super-Arrhenius

AUTHOR INFORMATION

Corresponding Author

*(Y.Z.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Y.Z. is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under Award Number DE-SC-0014804. 1147

DOI: 10.1021/acs.jpcb.5b11452 J. Phys. Chem. B 2016, 120, 1142−1148

Article

The Journal of Physical Chemistry B Activated Process: A Description in Terms of Frustration-Limited Domains. J. Phys.: Condens. Matter 2000, 12, 6497. (20) Schmidtke, B.; Petzold, N.; Kahlau, R.; Hofmann, M.; Rössler, E. A. From Boiling Point to Glass Transition Temperature: Transport Coefficients in Molecular Liquids Follow Three-Parameter Scaling. Phys. Rev. E 2012, 86, 041507. (21) Kob, W.; Donati, C.; Plimpton, S.; Poole, P.; Glotzer, S. Dynamical Heterogeneities in a Supercooled Lennard-Jones Liquid. Phys. Rev. Lett. 1997, 79, 2827−2830. (22) Lačević, N.; Starr, F. W.; Schroder, T. B.; Glotzer, S. C. Spatially Heterogeneous Dynamics Investigated via a Time-Dependent FourPoint Density Correlation Function. J. Chem. Phys. 2003, 119, 7372− 7387. (23) Adam, G.; Gibbs, J. H. On the Temperature Dependence of Cooperative Relaxation Properties in Glass-Forming Liquids. J. Chem. Phys. 1965, 43, 139−146. (24) Reichman, D. R.; Charbonneau, P. Mode-Coupling Theory. J. Stat. Mech.: Theory Exp. 2005, 2005, P05013. (25) Kirkpatrick, T.; Thirumalai, D. Colloquium: Random First Order Transition Theory Concepts in Biology and Physics. Rev. Mod. Phys. 2015, 87, 183−209. (26) Chandler, D.; Garrahan, J. P. Dynamics on the Way to Forming Glass: Bubbles in Space-Time. Annu. Rev. Phys. Chem. 2010, 61, 191− 217. (27) Langer, J. S.; Lemaître, A. Dynamic Model of Super-Arrhenius Relaxation Rates in Glassy Materials. Phys. Rev. Lett. 2005, 94, 175701. (28) Langer, J. S. Dynamics and Thermodynamics of the Glass Transition. Phys. Rev. E 2006, 73, 041504. (29) Inoue, A. Stabilization of Metallic Supercooled Liquid and Bulk Amorphous Alloys. Acta Mater. 2000, 48, 279−306. (30) Johnson, W. L. Bulk Glass-Forming Metallic Alloys: Science and Technology. MRS Bull. 1999, 24, 42−56. (31) Wang, W. H.; Dong, C.; Shek, C. H. Bulk Metallic Glasses. Mater. Sci. Eng., R 2004, 44, 45−89. (32) Chen, M. A Brief Overview of Bulk Metallic Glasses. NPG Asia Mater. 2011, 3, 82−90. (33) Cavagna, A. Supercooled Liquids for Pedestrians. Phys. Rep. 2009, 476, 51−124. (34) Jaiswal, A.; Podlesynak, A.; Ehlers, G.; Mills, R.; O’Keeffe, S.; Stevick, J.; Kempton, J.; Jelbert, G.; Dmowski, W.; Lokshin, K.; et al. Coincidence of Collective Relaxation Anomaly and Specific Heat Peak in a Bulk Metallic Glass-Forming Liquid. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 24202. (35) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. (36) Cheng, Y. Q.; Ma, E.; Sheng, H. W. Atomic Level Structure in Multicomponent Bulk Metallic Glass. Phys. Rev. Lett. 2009, 102, 245501. (37) Jaiswal, A.; Egami, T.; Zhang, Y. Atomic-Scale Dynamics of a Model Glass-Forming Metallic Liquid: Dynamical Crossover, Dynamical Decoupling, and Dynamical Clustering. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 134204. (38) Meyer, A. The Measurement of Self-Diffusion Coefficients in Liquid Metals with Quasielastic Neutron Scattering. EPJ Web Conf. 2015, 83, 01002. (39) Copley, J. R. D.; Lovesey, S. W. The Dynamic Properties of Monatomic Liquids. Rep. Prog. Phys. 1975, 38, 461−563. (40) Verkerk, P. Dynamics in Liquids. J. Phys.: Condens. Matter 2001, 13, 7775−7799. (41) Scopigno, T.; Ruocco, G.; Sette, F. Microscopic Dynamics in Liquid Metals: The Experimental Point of View. Rev. Mod. Phys. 2005, 77, 881−933. (42) Jaiswal, A.; Zhang, Y. To be published, 2016,. (43) Bée, M. Quasielastic Neutron Scattering: Principles and Applications in Solid State Chemistry, Biology, and Materials Science; Adam Hilger: Bristol, England, 1988. (44) Meyer, A.; Petry, W.; Koza, M.; Macht, M. P. Fast Diffusion in ZrTiCuNiBe Melts. Appl. Phys. Lett. 2003, 83, 3894−3896.

(45) Chathoth, S. M.; Damaschke, B.; Koza, M. M.; Samwer, K. Dynamic Singularity in Multicomponent Glass-Forming Metallic Liquids. Phys. Rev. Lett. 2008, 101, 037801. (46) Chathoth, S. M.; Damaschke, B.; Embs, J. P.; Samwer, K. Dynamics in Cu46Zr42Al7Y5Melts: Interplay Between Packing Density and Viscosity. Appl. Phys. Lett. 2009, 94, 201906. (47) Mirigian, S.; Schweizer, K. S. Elastically Cooperative Activated Barrier Hopping Theory of Relaxation in Viscous Fluids. I. General Formulation and Application to Hard Sphere Fluids. J. Chem. Phys. 2014, 140, 194506. (48) Mirigian, S.; Schweizer, K. S. Elastically Cooperative Activated Barrier Hopping Theory of Relaxation in Viscous Fluids. II. Thermal Liquids. J. Chem. Phys. 2014, 140, 194507. (49) Blodgett, M. E.; Egami, T.; Nussinov, Z.; Kelton, K. F. Proposal for Universality in the Viscosity of Metallic Liquids. Sci. Rep. 2015, 5, 13837. (50) Mauro, N. A.; Blodgett, M.; Johnson, M. L.; Vogt, A. J.; Kelton, K. F. A Structural Signature of Liquid Fragility. Nat. Commun. 2014, 5, 4616. (51) Brillo, J.; Pommrich, A. I.; Meyer, A. Relation Between SelfDiffusion and Viscosity in Dense Liquids: New Experimental Results from Electrostatic Levitation. Phys. Rev. Lett. 2011, 107, 165902. (52) Ediger, M. D. Spatially Heterogeneous Dynamics in Supercooled Liquids. Annu. Rev. Phys. Chem. 2000, 51, 99−128. (53) Sastry, S.; Debenedetti, P. G.; Stillinger, F. H. Signatures of Distinct Dynamical Regimes in the Energy Landscape of a GlassForming Liquid. Nature 1998, 393, 554−557. (54) Stevenson, J. D.; Wolynes, P. G. A Universal Origin for Secondary Relaxations in Supercooled Liquids and Structural Glasses. Nat. Phys. 2010, 6, 62−68. (55) Angell, C. A. Configurational Excitations in Condensed Matter, and the “Bond Lattice” Model for the Liquid-Glass Transition. J. Chem. Phys. 1972, 57, 470−481. (56) Egami, T. Elementary Excitation and Energy Landscape in Simple Liquids. Mod. Phys. Lett. B 2014, 28, 1430006.

1148

DOI: 10.1021/acs.jpcb.5b11452 J. Phys. Chem. B 2016, 120, 1142−1148