Glass-forming Systems Research Articles

Classification of solid and liquid structures using a deep neural network unveils origin of dynamical heterogeneities in supercooled liquids

As the temperature decreases, the dynamics of supercooled liquids significantly slow down and become increasingly heterogeneous in space. Many previous studies have found that static structures also become heterogeneous and are spatially correlated with the dynamical heterogeneity. However, there are still debates on whether the dynamical heterogeneity is controlled by the structures, and which structural order parameters should be used to describe the structural heterogeneities (if exist) in amorphous systems. The appropriate order parameter depends on the specific details of the system and needs to be determined for each system. To address this difficulty, here, we use a machine-learning-based method that was trained solely by the static structures. This method combines convolutional neural networks and gradient-weighted class activation mapping, providing interpretable characteristic structures, which can quantify the degrees of liquid-like and solid-like structures in every local part of the system. We apply this method to a canonical glass-forming system and demonstrate that particles in the liquid-like structures are mobile, while those in the solid-like structures are immobile. The present work develops a novel approach to accurately characterize amorphous structures, which will be particularly useful for systems where appropriate structural order parameters have not yet been identified.

General Relations between Stress Fluctuations and Viscoelasticity in Amorphous Polymer and Glass-Forming Systems.

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, moreover, exhibit long-range correlations contributing to the dynamically heterogeneous nature of such systems. Recent studies show that stress correlations and relaxation elastic moduli are intimately related in isotropic viscoelastic systems. However, the origin of these relations (involving spatially resolved material relaxation functions) is non-trivial: some relations are based on the fluctuation-dissipation theorem (FDT), while others involve approximations. Generalizing our recent results on 2D systems, we here rigorously derive three exact FDT relations (already established in our recent investigations and, partially, in classical studies) between spatio-temporal stress correlations and generalized relaxation moduli, and a couple of new exact relations. We also derive several new approximate relations valid in the hydrodynamic regime, taking into account the effects of thermal conductivity and composition fluctuations for arbitrary space dimension. One approximate relation was heuristically obtained in our previous studies and verified using our extended simulation data on two-dimensional (2D) glass-forming systems. As a result, we provide the means to obtain, in any spatial dimension, all stress-correlation functions in terms of relaxation moduli and vice versa. The new approximate relations are tested using simulation data on 2D systems of polydisperse Lennard-Jones particles.

Stress-tunable abilities of glass forming and mechanical amorphization

Mechanical amorphization, a widely observed phenomenon, has been utilized to synthesize novel phases by inducing disorder through external loading, thereby expanding the realm of glass-forming systems. Empirically, it has been plausible that mechanical amorphization ability consistently correlates with glass-forming ability. However, through a comprehensive investigation in binary, ternary, and quaternary systems combining neutron diffraction, calorimetric experimental approaches and molecular dynamics simulation, we demonstrate that this impression is only partly true and we reveal that the mechanical amorphization ability can be inversely correlated with the glass forming ability in certain cases To provide insights into these intriguing findings, we present a stress-dependent nucleation theory that offers a coherent explanation for both experimental and simulation results. Our study identifies the intensity of mechanical work, contributed by external stress, as the key control parameter for mechanical amorphization, rendering the ability to tune this process. This discovery not only unravels the underlying correlation between mechanical amorphization and glass-forming ability but also provides a pathway for the design and discovery of new amorphous phases with tailored properties.

Sulphuric precipitates in novel titanium-based, sulphur-bearing bulk metallic glass – a BMG composite?

ABSTRACT New titanium-based metallic glasses containing sulphur as a key element have recently been developed and are the subject of ongoing research related to the effects of sulphur introduction into glass-forming alloy systems. Here we report on the formation of sulphuric precipitates during solidification of a Ti40Zr35Cu17S8 alloy and on the occurrence of secondary intermetallic compound crystallization starting in sulphur-depleted zones around the precipitates. The alloy is a promising metallic glass for use as a structural and biomedical material as it shows a high yield strength and good corrosion resistance paired with a low density. The role of sulphur for the glass formation in the Ti-Zr-Cu-S system is discussed and specimens quenched into different structural states are investigated by means of high-energy synchrotron diffraction and electron microscopy. The electron microscopic findings reveal that sulphuric precipitates precede the crystallization of an intermetallic (Ti, Zr)2Cu phase, which is the primary phase when sulphur is not present in the system and thus lead to a higher glass-forming ability. The sulphuric precipitates are found in specimens of various casting thickness and differ in their volume percentages depending on the size of the cast sample, while the secondary phase (Ti, Zr)2Cu crystallizes heterogeneously in the interfaces between the sulphuric precipitates and the local matrix.

Proof of concept for a nonadditive stochastic model of supercooled liquids.

The recently proposed nonadditive stochastic model (NSM) offers a coherent physical interpretation for diffusive phenomena in glass-forming systems. This model presents nonexponential relationships between viscosity, activation energy, and temperature, characterizing the non-Arrhenius behavior observed in supercooled liquids. In this work, we fit the NSM viscosity equation to experimental temperature-dependent viscosity data corresponding to 25 glass-forming liquids and compare the fit parameters with those obtained using the Vogel-Fulcher-Tammann (VFT), Avramov-Milchev (AM), and Mauro-Yue-Ellison-Gupta-Allan (MYEGA) models. The results demonstrate that the NSM provides an effective fitting equation for modeling viscosity experimental data in comparison with other established models (VFT, AM, and MYEGA), characterizing the activation energy in fragile liquids, presenting a reliable indicator of the degree of fragility of the glass-forming liquids.

Normal-to-Supercooled Liquid Transition in Molecular Glass-Formers: A Hidden Structural Transformation Fuelled by Conformational Interconversion.

Molecular dynamics and transport coefficients change significantly around the so-called Arrhenius crossover in glass-forming systems. In this article, we revisit the dynamic processes occurring in a glass-forming macrocyclic crown thiaether MeBzS2O above its glass transition, revealing two crossover temperatures: TB at 309 and TA at 333 K. We identify the second one as the Arrhenius crossover that is closely related to the normal-to-supercooled liquid transition in this compound. We show that the transformation occurring at this point goes far beyond molecular dynamics (where the temperature dependence of structural relaxation times changes its character from activation-like to super-Arrhenius), being reflected also in the internal structure and diffraction pattern. In this respect, we found a twofold local organization of the nearest-neighbor molecules via weak van der Waals forces, without the formation of any medium-range order or mesophases. The nearest surrounding of each molecule evolves structurally in time due to the ongoing fast conformational changes. We identify several conformers of MeBzS2O, demonstrating that its lowest-energy conformation is preferred mainly at lower temperatures, i.e., in the supercooled liquid state. Its increased prevalence modifies locally the short-range intermolecular order and promotes vitrification. Consequently, we indicate that the Arrhenius transition is fuelled rather by conformational changes in this glass-forming macrocyclic crown thiaether, which is a different scenario from the so-far existing concepts. Our studies combine broadband dielectric spectroscopy (BDS), X-ray diffraction, Fourier transform infrared (FTIR) spectroscopy, molecular dynamics (MD) simulations, and density functional theory (DFT) calculations.

Design and characterization of novel Zr-Al-Fe-Y metallic glasses with nanoscale phase separation

We present a new phase-separated Zr-based metallic glass (MG) composition, free of toxic elements (Ni and Cu) prepared in a glass-forming system by alloying addition. The substitution of Y in Zr70-xAl12.5Fe17.5Yx (x = 0–15 at.%) results in phase separation, giving rise to nano-amorphous domains in a glassy matrix. A homogeneous MG feature is observed for low concentrations of Y up to x = 5. Microstructure and thermal property analysis indicate that the glasses with x = 10 and 15 at.% Y exhibit a typical liquid phase separation-induced two-glassy phase (Zr-rich and Y-rich) with droplet-like microstructures (nano-amorphous domains). With increasing Y addition, the domain size increases. The microstructural evolution arising due to phase separation in these alloys is confirmed by a combination of transmission electron microscopy (TEM) and atom probe tomography (APT) analysis. The formation of nanometer-size Y-enriched clusters is confirmed by APT for x = 15.

Revisiting Dynamic Processes and Relaxation Mechanisms in a Heterocyclic Glass-Former: Direct Observation of a Transient State.

Despite decades of studies, a clear understanding of near-Tg phenomena remains challenging for glass-forming systems. This review delves into the intricate molecular dynamics of the small, heterocyclic thioether, 6-methyl-2,3-dihydro-1,4-benzodithiine (MeBzS2), with a particular focus on its near-Tg cold crystallization and relaxation mechanisms. Investigating isothermal crystallization kinetics at various temperatures reveals a significant interplay between its molecular dynamics and recrystallization from a supercooled liquid. We also identify two independent interconversion paths between energetically privileged conformers, characterized by strained transition states. We demonstrate that these spatial transformations induce substantial alterations in the dipole moment orientation and magnitude. Our investigation also extends to the complex salt PdCl2(MeBzS2), where we observe the transient conformers directly, revealing a direct relationship between their abundance and the local or macroscopic electric field. The initially energetically privileged isomers in an undisturbed system become less favored in the presence of an external electric field or ions, resulting even in an unexpected inversion of states. Consequently, we confirm the intramolecular character of secondary relaxation in MeBzS2 and its mechanism related to conformational changes within the heterocyclic ring. The research is based on the combination of broadband dielectric spectroscopy, X-ray diffraction, and quantum density functional theory calculations.

Effect of the nature of the solid substrate on spatially heterogeneous activated dynamics in glass forming supported films.

We extend the force-level elastically collective nonlinear Langevin equation theory to treat the spatial gradients of the alpha relaxation time and glass transition temperature, and the corresponding film-averaged quantities, to the geometrically asymmetric case of finite thickness supported films with variable fluid-substrate coupling. The latter typically nonuniversally slows down motion near the solid-liquid interface as modeled via modification of the surface dynamic free energy caging constraints that are spatially transferred into the film and which compete with the accelerated relaxation gradient induced by the vapor interface. Quantitative applications to the foundational hard sphere fluid and a polymer melt are presented. The strength of the effective fluid-substrate coupling has very large consequences for the dynamical gradients and film-averaged quantities in a film thickness and thermodynamic state dependent manner. The interference of the dynamical gradients of opposite nature emanating from the vapor and solid interfaces is determined, including the conditions for the disappearance of a bulk-like region in the film center. The relative importance of surface-induced modification of local caging vs the generic truncation of the long range collective elastic component of the activation barrier is studied. The conditions for the accuracy and failure of a simple superposition approximation for dynamical gradients in thin films are also determined. The emergence of near substrate dead layers, large gradient effects on film-averaged response functions, and a weak non-monotonic evolution of dynamic gradients in thick and cold films are briefly discussed. The connection of our theoretical results to simulations and experiments is briefly discussed, as is the extension to treat more complex glass-forming systems under nanoconfinement.

Dynamics-Entropy Relationship in Metallic Glasses.

Establishing a robust quantitative correlation between thermodynamics and dynamics in amorphous matter remains a significant challenge in condensed matter physics. Although the classical Adam-Gibbs relationship represents a pivotal step in this direction and the correlation between relaxation time and configurational entropy has been partially verified in simple liquids, this quantitative link has yet to be tested in realistic glass-forming systems where complex many-body interactions are present. Here we conduct free energy samplings and lattice dynamics analysis to distinguish vibrational entropy from configurational entropy in a realistic Cu-Zr model of a metallic glass. Our calculations unveil a power-law relationship (with a substantial exponent of ∼3) between the logarithmic relaxation time and configurational entropy, surpassing the linear prediction of the original Adam-Gibbs relationship. This nonlinear entropy driven relaxation time variation likely originates from anisotropic nature of atomic many-body interactions, suggesting that factors beyond thermodynamics contribute to the glass transition phenomenon.

Active-parameter polydispersity in the 2d ABP Yukawa model

In experiments and simulations of passive as well as active matter the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional active Brownian particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocity v 0. Uniform and binary parameter distributions are considered in the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case of v 0 polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e. a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.

Rapidly screening out refractory metallic alloys with high glass-forming ability by laser surface remelting

Compared with conventional metallic glasses, refractory metallic glasses (RMGs) with a mass of refractory element(s), high glass-transition temperature (Tg) and outstanding mechanical properties (like ultrahigh strength, high hardness and good wear resistance) exhibit fascinating potential applications in high temperature field. However, the development of RMGs is painfully slow, and one of the key problems is the lack of rapid and convenient way to screen out high glass-forming refractory alloys. In this study, a method for rapid evaluation of glass forming ability (GFA) based on laser surface remelting was provided. The high-efficiency screening-out method was validated in a classical glass-forming model system of Ni–Nb binary refractory alloys. The effects of different laser parameters on the glass formation and phase evolution were investigated by experimental analysis and finite element simulation. By correlating thermal history of the laser treatment with glass formation, the alloys with high GFA in Ni–Nb system was screened out rapidly. The screening-out efficiency of the novel method can be improved one order of magnitude, compared with that of the conventional techniques, and the materials cost can be reduced, especially for RMGs. The revealed formation mechanism of glassy and crystalline phases in time and spatial distributions influenced by thermal history under multi-scanning laser treatment can provide a significant insight in the construction of the bulk-metallic-glass materials and the related composite ones by laser additive manufactory.

Deciphering the glass-forming ability of Al2O3-Y2O3 system from temperature susceptibility of melt structure

Despite its significance in both fundamental science and industrial applications, the glass-forming transition in the Al2O3-Y2O3 (AY) refractory system is not yet fully understood due to the elusive structure evolution upon cooling. Here, atomic-scale structural changes in AY-bearing melts with different compositions and temperatures are tracked by employing in situ high-energy synchrotron X-ray diffraction and empirical potential structure refinement simulation. We find that the glass-forming abilities (GFA) of AY-bearing melts are intriguingly correlated with the dependence of melt structure on temperature. In the case of the Al2O3 and Y3Al5O12 (YAG), the observed large structural changes from superheating to undercooling melt (i.e., higher temperature susceptibility) correspond to a low GFA. Conversely, the 74Al2O3–26Y2O3 (AY26) melt, with the smallest temperature susceptibility, exhibits the highest GFA. Simulation models illustrate that the temperature susceptibility of melt is associated with its atomic arrangement, especially the stability of cation-cation pairs. A balanced network (in AY26 melt), where the unsteady OAl3 tri-clusters are minimized and steady apex-to-apex connections between adjacent network units are abundant, contributes to stabilizing cationic interactions. This, in turn, fosters the formation of large-sized Al-O-Al rings, which topologically facilitates the subsequent glass-forming transition. Our findings provide new structural insight into the GFA of AY-bearing melts and may expand to other unconventional glass-forming systems to accelerate glassy materials design.

Diffusion in Metallic Glass-Forming Systems: A Description of the Kink Behavior Observed in the Temperature Dependence

The temperature dependence of the diffusion coefficient in metallic glass-forming systems do not follow the Arrhenius behavior over a wide temperature range. Instead, it exhibits a kink behavior at around the glass transition temperature. Some researchers associate this behavior to the difference in the diffusion mechanism operating in the glassy and the supercooled liquid state, whereas others do not support this view. In addition, usually, the temperature dependence of the diffusion coefficient is analyzed by splitting the temperature range into two regions, above and below the glass transition temperature. In the present study, we developed an analytical theory that describes the continuous variation of the diffusion coefficient across a temperature where the kink behavior is observed. According to the theory, the kink behavior arises from the freezing of free volume available for diffusion by lowering the temperature. A connection to the vacancy mechanism of diffusion has been also pointed out.

Medium-Range Order Structure Controls Thermal Stability of Pores in Zeolitic Imidazolate Frameworks.

Metal-organic framework (MOF) glasses have multiple potential applications, as they combine advantages of traditional glasses with those of MOFs. The melt-quenching process used to form MOF glasses typically leads to a significant decrease in porosity, but the structural origin of this thermally induced pore collapse remains largely unknown. Here, we study the melting process of three zeolitic imidazolate frameworks (ZIFs), namely ZIF-4, ZIF-62, and ZIF-76, using ab initio molecular dynamics (MD) simulations. By analyzing the MD data using topological data analysis, we show that while the three ZIF systems exhibit similar short-range order structural changes upon heating, they exhibit significant differences in their medium-range order structure. Specifically, ZIF-76 retains more of its medium-range order structures in the liquid state compared to the other glass-forming ZIF systems, which allows it to remain more porous than ZIF-4 and ZIF-62. As such, our results may aid in understanding the structural features that govern the ability to maintain porosity in the melt-quenched glassy state.

Real-time microscopy of the relaxation of a glass

The understanding of the dynamics of a glass above its devitrification temperature remains incomplete. Here, we build a spatio-temporal map of the relaxation dynamics of a highly stable glass into its supercooled liquid using real-time atomic force microscopy imaging. This methodology enables direct visualization of the progression of the liquid phase and clarifies and quantifies the presence of localized fast mobility regions separated by giant length scales. Our data establish a clear correlation between dynamic length and time scales in glasses. This approach may also be applicable to unveil the microscopic structure and dynamics of other glass-forming systems with much shorter length and time scales, including liquid-cooled glasses.

Synthesis and study of zirconium-containing sodium-cesium aluminoborosilicate matrix materials

During the development of new composition versions for basic systems immobilizing high-level radioactive waste, the investigation of physico-chemical peculiarities has been carried out for various glass-ceramic materials, synthesized by the quench method from melts of the Na2O – Cs2O – CaO (SrO, BaO) – Al2O3 – B2O3 – SiO2 system with high zirconium content. Factors that determine solubility and zirconium retention have been studied, as well as homogeneity of the synthesized materials. The influence of zirconium upon the phase composition of materials, formation of their structure, crystallization processes, density values, and thermal properties have been considered. The obtained data point at possibilities in application of the chosen glass-forming system with the investigated combination of components in the field of synthesis of matrix materials for immobilization of high-level radioactive waste with high zirconium content.

A deep learning approach to the measurement of long-lived memory kernels from generalized Langevin dynamics.

Memory effects are ubiquitous in a wide variety of complex physical phenomena, ranging from glassy dynamics and metamaterials to climate models. The Generalized Langevin Equation (GLE) provides a rigorous way to describe memory effects via the so-called memory kernel in an integro-differential equation. However, the memory kernel is often unknown, and accurately predicting or measuring it via, e.g., a numerical inverse Laplace transform remains a herculean task. Here, we describe a novel method using deep neural networks (DNNs) to measure memory kernels from dynamical data. As a proof-of-principle, we focus on the notoriously long-lived memory effects of glass-forming systems, which have proved a major challenge to existing methods. In particular, we learn the operator mapping dynamics to memory kernels from a training set generated with the Mode-Coupling Theory (MCT) of hard spheres. Our DNNs are remarkably robust against noise, in contrast to conventional techniques. Furthermore, we demonstrate that a network trained on data generated from analytic theory (hard-sphere MCT) generalizes well to data from simulations of a different system (Brownian Weeks-Chandler-Andersen particles). Finally, we train a network on a set of phenomenological kernels and demonstrate its effectiveness in generalizing to both unseen phenomenological examples and supercooled hard-sphere MCT data. We provide a general pipeline, KernelLearner, for training networks to extract memory kernels from any non-Markovian system described by a GLE. The success of our DNN method applied to noisy glassy systems suggests that deep learning can play an important role in the study of dynamical systems with memory.

Influence of sulfur addition on the glass formation, phase transformation and mechanical properties of Cu50Zr50 alloy

In this work, a thorough study on the effects of sulfur-addition in the Cu50Zr50 glass-forming system was conducted using laboratory-based X-ray diffraction (XRD), synchrotron-based high-energy XRD (HESXRD), differential scanning calorimetry, and uniaxial compression testing. We report that the glass-forming ability (GFA), thermal stability, phase transformation sequence during heating and cooling, as well as the mechanical properties of the Cu50Zr50 system are highly sensitive to the sulfur concentration. Proper addition of sulfur can not only stabilize the B2-CuZr phase, but also enhances the GFA of the system. This enables the formation of BMG composites that solely contain a B2 phase, which results in a combination of high strength and substantial plastic strain under compressive loading. The total strains of the newly developed BMG composites with sulfur contents of 0.5 and 1.0 at.% are as large as ∼10 at.%, exceeding the previously reported strains of the Cu50Zr50 BMG by far. These superior properties make the Cu-Zr-S BMG composites a promising candidate material for industrial applications. In addition, it is found that excessive addition of sulfur leads to the precipitation of the Cu10Zr7 phase upon cooling from the alloy melt and a sulfide phase during heating from the glassy state. HESXRD experiments suggest that the preferential bonding between Zr and S atoms could be the determining structural mechanism on the atomic scale, leading to the changing primary crystallization sequence for heating and cooling. The findings in this work further strengthen the high relevance of sulfur in alloy development and tuning of properties in BMGs, especially considering the low cost, good availability, and non-toxicity of sulfur in the relevant modifications.

Exploring the relationship between softness and excess entropy in glass-forming systems.

We explore the relationship between a machine-learned structural quantity (softness) and excess entropy in simulations of supercooled liquids. Excess entropy is known to scale well the dynamical properties of liquids, but this quasi-universal scaling is known to breakdown in supercooled and glassy regimes. Using numerical simulations, we test whether a local form of the excess entropy can lead to predictions similar to those made by softness, such as the strong correlation with particles' tendency to rearrange. In addition, we explore leveraging softness to compute excess entropy in the traditional fashion over softness groupings. Our results show that the excess entropy computed over softness-binned groupings is correlated with activation barriers to rearrangement.