Metallic Glass-forming Liquids Research Articles

Measured and ideal glass transition temperatures of glass-forming liquids

Herein, measured and ideal glass transition temperatures of glass-forming liquids have been investigated. The value of T0/Tg increases with increasing fragility parameter m or decreasing strength parameter D (where Tg and T0 are the measured and ideal glass transition temperatures, respectively). We utilize T0/Tg values to classify various glass-forming liquids into three broad categories, which are strong, metallic glass-forming (intermediate) and fragile liquids. The result reveals that strong liquids with 15.25 < m ≤ 30 (or 37.3 ≤ D) have 0 < T0/Tg ≤ 0.49. By contrast, fragile liquids obtain 0.82 ≤ T0/Tg ≤ 0.94 when m values lie in 100 ≤ m ≤ 214 (or 1.8 ≤ D ≤ 9.1). Metallic glass-forming liquids have 0.52 ≤ T0/Tg ≤ 0.77 when m values have 32 ≤ m ≤ 66 (or 10.8 ≤ D ≤ 32.8).

Revisiting the fragile-to-strong crossover in metallic glass-forming liquids: Application to CuxZrxAl100−2x alloy

The fragile-to-strong crossover seems to be a general feature of metallic glass-forming liquids. Here, we study the behavior of shear viscosity, diffusion coefficient and vibrational density of states for Cu$_\text{x}$Zr$_\text{x}$Al$_{\text{100-2x}}$ alloy through molecular dynamics simulations. The results reveal that the fragile-to-strong temperature (T$_\text{fs}$) and the glass transition temperature (T$_\text{g}$) increase as the aluminum content becomes larger. The inverse of the diffusion coefficient as a function of temperature exhibits a dynamical crossover in the vicinity of T$_\text{g}$, at a much lower temperature than that predicted by nearly all previous studies. At the temperature in which the dynamical crossover occurs determined by the inverse of the diffusion coefficient, we found an excess of vibrational states at low frequencies, resembling a pronounced peak in the reduced vibrational density of states characteristic of a strong liquid. Finally, the behavior of the shear viscosity as a function of reduced temperature (T$_\text{g}$/T) also shows that, besides the fragile-to-strong crossover nearby T$_\text{g}$, another dynamical crossover is present near the onset of the supercooled regime.

Description of the unusual non-Arrhenius viscosity pattern of metallic glass-forming liquids

Metallic glass-forming liquids (MGFLs) exhibit a quite unusual pattern in the temperature dependence of the viscosity when plotted in a wide range of temperature. Among the fragile liquids, the MGFLs have the propensity that at high temperature the viscosity exhibits a very low activation energy, while at low temperature a straight-line viscosity behavior appears in the Arrhenius representation. This unusual pattern hinders a theoretical description over a wide temperature range and the understanding of its microscopic mechanism. In the present study, we show that the modified BSCNF model describes well the temperature dependence of the viscosity of MGFLs. The relevance of the result to the fragile-to-strong transition that can occur in the supercooled regime is discussed briefly.

Evaluation of a Characteristic Temperature in the Relaxation of Metallic Glass Forming Liquids

The high-temperature viscosity of metallic glass-forming liquids is investigated by using the Bond Strength-Coordination Number Fluctuation (BSCNF) model developed by the authors. For many glass-forming liquids, a salient change in the structural relaxation is observed above the melting point. The temperature dependence of the structural relaxation exhibits a deviation from an Arrhenius-like behavior, and upon cooling it transforms to a non-Arrhenius-like one. In the present study, we show that the BSCNF model describes well the high-temperature viscosity behaviors of metallic liquids. The analysis based on the BSCNF model also enables to extract a characteristic temperature at high temperature. The results of the present study show that such characteristic temperature can be a good indicator for the evaluation of the range of the transition from the Arrhenius-like to the non-Arrhenius-like relaxation behavior.

Highly collective atomic transport mechanism in high-entropy glass-forming metallic liquids

Quasielastic neutron scattering (QENS) has been used to study the atomic relaxation process and microscopic transport mechanism in high-entropy glass-forming metallic (HE-GFM) liquids. Self-intermediate scattering functions obtained from the QENS data show unusually large stretching, which indicates highly heterogeneous atomic dynamics in HE-GFM liquids. In these liquids, a group of atoms over a length scale of about 21 Å diffuses collectively even well above the melting temperature. However, the temperature dependence of diffusion process in one of the HE-GFM liquid is Arrhenius, but in the other HE-GFM liquid it is non-Arrhenius. Although the glass-forming ability of these HE-GFM liquids is very poor, the diffusion coefficients obtained from the QENS data indicate the long range atomic transport process is much slower than that of the best metallic glass-forming liquids at their melting temperatures.

Configuration correlation governs slow dynamics of supercooled metallic liquids

The origin of dramatic slowing down of dynamics in metallic glass-forming liquids toward their glass transition temperatures is a fundamental but unresolved issue. Through extensive molecular dynamics simulations, here we show that, contrary to the previous beliefs, it is not local geometrical orderings extracted from instantaneous configurations but the intrinsic correlation between configurations that captures the structural origin governing slow dynamics. More significantly, it is demonstrated by scaling analyses that it is the correlation length extracted from configuration correlation rather than dynamic correlation lengths that is the key to determine the drastic slowdown of supercooled metallic liquids. The key role of the configuration correlation established here sheds important light on the structural origin of the mysterious glass transition and provides an essential piece of the puzzle for the development of a universal theoretical understanding of glass transition in glasses.

Effects of pressure on structure and dynamics of metallic glass-forming liquid with miscibility gap

The metallic liquid with miscibility gap has been widely explored recently because of the increasing plastic deformation ability of phase-separated metallic glass. However, the poor glass-forming ability limits its application as the structural materials due to the positive mixing enthalpy of the two elements. Since high pressure is in favor of the formation of the glass, the effect of pressure on the structural and dynamical heterogeneity of phase-separated Cu50Ag50 liquid is investigated by molecular dynamics simulation in the pressure range of 0–16 GPa. The results clearly show that the pressure promotes the formation of metallic glass by increasing the number of fivefold symmetry cluster W and dynamical relaxation time; meanwhile, the liquid–liquid phase separation is also enhanced, and the homogenous atom pairs show stronger interaction than heterogeneous atom pairs with increasing pressure. The dynamical heterogeneity is related to the formation of fivefold symmetry clusters. The lower growing rate of W at higher pressure with decreasing temperature corresponds to the slow increase in dynamical heterogeneity. The pressured glass with miscibility gap may act as a candidate glass with improved plastic formation ability. The results explore the structural and dynamical heterogeneity of phase-separated liquid at atomic level.

Dynamical, structural and chemical heterogeneities in a binary metallic glass-forming liquid

As it approaches the glass transition, particle motion in liquids becomes highly heterogeneous and regions with virtually no mobility coexist with liquid-like domains. This complex dynamic is believed to be responsible for different phenomena including non-exponential relaxation and the breakdown of the Stokes–Einstein relation. Understanding the relationships between dynamical heterogeneities and local structure in metallic liquids and glasses is a major scientific challenge. Here we use classical molecular dynamics simulations to study the atomic dynamics and microscopic structure of alloy in the supercooling regime. Dynamical heterogeneities are identified via an isoconfigurational analysis. We demonstrate the transition from isolated to clustering low mobility with decreasing temperature. These slow clusters, whose sizes grow upon cooling, are also associated with concentration fluctuations, characterized by a Zr-enriched phase, with a composition . In addition, a structural analysis of slow clusters based on Voronoi tessellation evidences an increase with respect of the bulk system of the fraction of Cu atoms having a local icosahedral order. These results are in agreement with the consolidated scenario of the relevant role played by icosahedral order in the dynamic slowing-down in supercooled metal alloys.

The role of local-geometrical-orders on the growth of dynamic-length-scales in glass-forming liquids

The precise nature of complex structural relaxation as well as an explanation for the precipitous growth of relaxation time in cooling glass-forming liquids are essential to the understanding of vitrification of liquids. The dramatic increase of relaxation time is believed to be caused by the growth of one or more correlation lengths, which has received much attention recently. Here, we report a direct link between the growth of a specific local-geometrical-order and an increase of dynamic-length-scale as the atomic dynamics in metallic glass-forming liquids slow down. Although several types of local geometrical-orders are present in these metallic liquids, the growth of icosahedral ordering is found to be directly related to the increase of the dynamic-length-scale. This finding suggests an intriguing scenario that the transient icosahedral connectivity could be the origin of the dynamic-length-scale in metallic glass-forming liquids.

Indications for a fragile-to-strong transition in the high- and low-temperature viscosity of the Fe43Cr16Mo16C15B10 bulk metallic glass-forming alloy

Viscosity of the Fe-based bulk metallic glass-forming liquid Fe43Cr16Mo16C15B10 is measured around the glass transition and in the stable liquid. Low-temperature measurements are conducted using three-point beam bending in a thermomechanical analyzer, and high-temperature data are obtained from the damping behavior of an oscillating droplet which is electromagnetically levitated in microgravity on a reduced-gravity aircraft. The alloy displays an intermediately strong liquid behavior (D* = 15.1) at low temperatures and a fragile behavior (D* = 7.9) at high temperatures. Hence, the temperature dependence of viscosity changes drastically between the high- and the low-temperature regime, which suggests the existence of a fragile-to-strong liquid-liquid transition in the supercooled liquid. Furthermore, viscosity and fragility data are discussed with respect to the glass-forming ability of the alloy.

Local environments of atomic clusters and the effect on dynamics in CuZr metallic glass-forming liquids

The effect of local environments of various atomic clusters on the dynamics in CuZr metallic glass-forming liquids was investigated via classical molecular dynamics simulations. It is found that atomic clusters exhibit different local connectivity, leading to different local environments, even for the same type of clusters. Moreover, local environments of atomic clusters are found to have a different impact on dynamics in supercooled liquids. For pentagon-rich clusters such as ⟨0,0,12,0⟩ and ⟨0,1,10,2⟩, the dynamics becomes slower with increasing connectivity in both α and β relaxation time scales. In contrast, as local connectivity increases, atomic mobility of connected ⟨0,3,6,4⟩ clusters is enhanced. The evolution of atomic symmetries in clusters with local connectivity is found to be the underlying structural basis for the correlation between local environments and dynamics of atomic clusters. These findings indicate that local environments of atomic clusters are more critical in the relaxation dynamics and the dynamical heterogeneity in metallic glass-forming liquids.

Role of fivefold symmetry in the dynamical slowing down of metallic glass-forming liquids

Fivefold symmetry is supposed to have an important role in suppressing crystallization and promoting glass transition due to its structural incompatibility with crystal. In this paper, we study the correlation between the fivefold symmetry and the dynamical slowing down in glass-forming Cu-Zr liquids using the single-particle dynamics method based on molecular dynamics simulations. The dynamics of the glass-forming liquids is microscopically characterized by the jump cage motion for individual atoms; moreover, the cooperative jumps become more pronounced upon approaching the glass transition temperature. We find that the role of fivefold symmetry in the dynamical slowing down does not lie in caging atomic motion but, more importantly, in suppressing cooperative jumps. The atoms with a high degree of fivefold symmetry and involved in jump motions appear more sluggish compared to other jumps. This behavior significantly suppresses the cooperative jumps around them, leading to the slowing down of fast dynamics. The degree of suppression has a close relation to the glass-forming ability and contributes to the ``strong'' character of liquids.

Pressure effects on structure and dynamics of metallic glass-forming liquid.

Although the structure and dynamics of metallic glass-forming liquids have been extensively investigated, studies of the pressure effects are rare. In the present study, the structural and dynamical properties of a ternary metallic liquid are systematically studied via extensive molecular dynamics simulations. Our results clearly show that, like isobaric cooling, isothermal compression could also slow down the dynamics of metallic liquid, leading to glass formation. However, the temperature- and pressure-induced glass transitions differ in the formation of local coordination structures and the variation of fragility. The increase of the kinetic fragility with increasing pressure is also accompanied by a monotonic structural fragility change. These findings may suggest a link between dynamics and structure. In addition, with increasing pressure, the dynamics becomes more heterogeneous, as revealed by the non-Gaussian parameter and dynamic correlation length. Here the length scales of both slow and fast domains are examined and discussed by analyzing the four-point dynamic structure factor associated with spatial correlations of atomic mobility. These correlation lengths coexist in the metallic liquids and grow comparatively in the considered temperature and pressure ranges. Finally, the scaling relation between the relaxation times and correlation lengths is discussed, which is found to be consistent with the spirit of Adam-Gibbs and random first-order transition theories.

Structural origin of fractional Stokes-Einstein relation in glass-forming liquids

In many glass-forming liquids, fractional Stokes-Einstein relation (SER) is observed above the glass transition temperature. However, the origin of such phenomenon remains elusive. Using molecular dynamics simulations, we investigate the break- down of SER and the onset of fractional SER in a model of metallic glass-forming liquid. We find that SER breaks down when the size of the largest cluster consisting of trapped atoms starts to increase sharply at which the largest cluster spans half of the simulations box along one direction, and the fractional SER starts to follows when the largest cluster percolates the entire system and forms 3-dimentional network structures. Further analysis based on the percolation theory also confirms that percolation occurs at the onset of the fractional SER. Our results directly link the breakdown of the SER with structure inhomogeneity and onset of the fraction SER with percolation of largest clusters, thus provide a possible picture for the break- down of SER and onset of fractional SER in glass-forming liquids, which is is important for the understanding of the dynamic properties in glass-forming liquids.

Fragile-to-strong transition in metallic glass-forming liquids

It has been observed that many glass-forming liquids are transformed from fragile to strong liquids in a supercooled region upon cooling. This is the so-called fragile-to-strong (F-S) transition. Since its discovery in water, the F-S transition, as a frontier problem, as well as a hot issue, in condensed matter physics and material science, has aroused the considerable interest of researchers. It has been generally accepted that the F-S transition might be a universal dynamic behavior of metallic glass-forming liquid (MGFL). Studying the F-S transition is important not only for better understanding the nature of glass transition, uncovering the microstructural inheritance during the liquid-solid transformation, clarifying the structural competition during crystallization, improving the stability of MGs, but also for promoting the standardization during the production and treatment technology of MGs. In this paper, the general and special features of the F-S transition for bulk and marginal MGFLs are studied and described in terms of a physical model. A characteristic parameter f is introduced to quantify the F-S transition. With two relaxation regimes, on the basis of Mauro-Yuanzheng-Ellison-Gupta-Allan model, we propose a generalized viscosity model for capturing the liquids with the F-S transition. Using this model, we calculate the F-S transition temperature for metallic glass. From the calculation results, the F-S transition might occur around (1.36±0.03) Tg. By using the hyperquenching annealing-calorimetric approach, we find that the anomalous crystallization behavior occurs in both LaAlNi and CuZrAl glass ribbons. This phenomenon implies the existence of a thermodynamic F-S transition, which could be used as an alternative method of detecting the F-S transition in MGFLs. To date, the origin of the F-S transition is far from understanding. We find that the F-S transition in CuZr(Al) GFLs is attributed to the competition among the MRO clusters composed of different locally ordering configurations. By comparing the parameter f with the parameter r that characterizes the competition between the α and the slow β relaxations in 19 MGFLs, we find that the slow β relaxation plays a dominant role in the F-S transition and the extent of the F-S transition is mainly determined by the degree of the comparability in structure units between the α and the slow β relaxations. The existence of the liquid-liquid phase transition might also be the root of the F-S transition. The tendency of investigation of the F-S transition is also evaluated.

Inherited structure of amorphous matter

The inherent atomic packing mode of glassy solid is still one of the most interesting and fundamental problems in condensed-matter physics and material science. Although significant progress has been made and provided insights into the atomic-level structure and short-to-medium-range order in glass, the way of leading to the medium-range order is still unclear. Does a universal rule exist in nature to construct a glass structure as what has been discovered for crystals? Is there any connection between glassy and crystalline structures? If so, what does the connection look like and how is the connection related to the properties of the glassy solids? A glassy state is usually obtained through supercooling a liquid fast enough to avoid crystallization. The amorphous nature of glassy solid is experimentally ascertained by X-ray diffraction (XRD), transmission electron microscopy or selected area electron diffraction (SAED). Almost all kinds of glassy solids exhibit similar maze-like SAED patterns without any local lattice fringes and broad diffraction maximum characteristics in XRD data. However, the glassy solids are inherently different in atomic-level structure, demonstrated by their different response behaviors under certain conditions, for example, the diverse annealing-precipitated crystallinephases, the distinct mechanical strengths and ductilities, and the different thermal stabilities against crystallization. Unfortunately, such a difference in inherent structure among glassy solids cannot be easily differentiated from a trivial analysis of the experimental diffraction data. However, the diffraction data such as structure factors or pair correlation functions (PCFs) are not as trivial as they look like. On the contrary, some studies have demonstrated that plenty of structural information is hidden behind the data of structure factors or PCFs, for example, global packing containing both spherical-periodic order and local translational symmetry has been revealed by analyzing PCFs of many metallic glasses. A fractal nature of medium-range order in metallic glassis also found by examining the relationships between the first peak positions in structure factors and atomic molar volumes in many metallic glasses. In fact, the oscillation in the structure factor or PCF is an indication that a certain order does exist in amorphous solid. Therefore, a more careful scrutiny of the diffraction data is desired to gain a more in-depth insight into the glassy structure features and find a clue to unveil the natures of the inherent structures in different glasses. In this paper, we briefly review the recent molecular dynamics simulation results that the distinct hidden orders of atomic packing formula in medium range in these pure glassy solids are unveiled to be inherited from bcc order in glassy Fe and fcc order in glassy Ni, respectively, reflecting nontrivial structural homology between glassy and crystalline solids. By analyzing the partial PCFs of three two-component metallic glasses of CuZr, NiAl, and NiCu which are similar but have distinct glass-forming ability via MD simulations, very different hidden orders are observed in each individual system, indicating that the hidden orders are more complex in multicomponent metallic glasses. The different hidden orders in a multicomponent metallic glass may be entangled topologically. More different hidden orders lead to more complex topological entanglement. Further analysis indicates that the formation of the hidden orders during cooling and their topological entanglement produces the geometrical frustration against crystallization and is closely correlated with the glass-forming ability of metallic alloys. A “genetic map” of hidden orders in metallic glass is finally constructed, which provides new insights into the structural properties and structure-property relationships in metallic glass-forming liquids and glasses.

A Comparative Study of Molecular Motion Cooperativity in Polymeric and Metallic Glass-Forming Liquids

In order to investigate the relationship between the bonding nature and the cooperative relaxation, a comparative study of the relaxation behavior in polymeric and metallic glass forming systems has been performed based on the Bond Strength–Coordination Number Fluctuation (BSCNF) model developed by the authors. In the present work, we studied the correlations between the fragility m, the Vogel temperature T0, the degree of molecular cooperativity NB, and the Kohlrausch exponent βKWW. The results show that T0 and NB increase, whereas βKWW decreases systematically with the increase of m. Reflecting the difference of the interatomic interactions of the materials considered, the analysis by the present study reveals that the value of NB in ion-conducing polymers is about 5 times larger than that in metallic systems, and for each system, the material dependence of βKWW is clearly seen in the fragility index m and the cooperativity NB.

Correlation between Fragility and the Arrhenius Crossover Phenomenon in Metallic, Molecular, and Network Liquids.

We report the observation of a distinct correlation between the kinetic fragility index m and the reduced Arrhenius crossover temperature θ_{A}=T_{A}/T_{g} in various glass-forming liquids, identifying three distinguishable groups. In particular, for 11 glass-forming metallic liquids, we universally observe a crossover in the mean diffusion coefficient from high-temperature Arrhenius to low-temperature super-Arrhenius behavior at approximately θ_{A}≈2 which is in the stable liquid phases. In contrast, for fragile molecular liquids, this crossover occurs at much lower θ_{A}≈1.4 and usually in their supercooled states. The θ_{A} values for strong network liquids spans a wide range higher than 2. Intriguingly, the high-temperature activation barrier E_{∞} is universally found to be ∼11k_{B}T_{g} and uncorrelated with the fragility or the reduced crossover temperature θ_{A} for metallic and molecular liquids. These observations provide a way to estimate the low-temperature glassy characteristics (T_{g} and m) from the high-temperature liquid quantities (E_{∞} and θ_{A}).

Critical scaling of icosahedral medium-range order in CuZr metallic glass-forming liquids.

The temperature evolution of icosahedral medium-range order formed by interpenetrating icosahedra in CuZr metallic glassforming liquids was investigated via molecular dynamics simulations. Scaling analysis based on percolation theory was employed, and it is found that the size distribution of clusters formed by the central atoms of icosahedra at various temperatures follows a very good scaling law with the cluster number density scaled by S−τ and the cluster size S scaled by |1 − Tc/T|−1/σ, respectively. Here Tc is scaling crossover-temperature. τ and σ are scaling exponents. The critical scaling behaviour suggests that there would be a structural phase transition manifested by percolation of locally favoured structures underlying the glass transition, if the liquid could be cooled slowly enough but without crystallization intervening. Furthermore, it is revealed that when icosahedral short-range order (ISRO) extends to medium-range length scale by connection, the atomic configurations of ISROs will be optimized from distorted ones towards more regular ones gradually, which significantly lowers the energies of ISROs and introduces geometric frustration simultaneously. Both factors make key impacts on the drastic dynamic slow-down of supercooled liquids. Our findings provide direct structure-property relationship for understanding the nature of glass transition.

Thermodynamic scaling of glassy dynamics and dynamic heterogeneities in metallic glass-forming liquid.

A ternary metallic glass-forming liquid is found to be not strongly correlating thermodynamically, but its average dynamics, dynamic heterogeneities including the high order dynamic correlation length, and static structure are still well described by thermodynamic scaling with the same scaling exponent γ. This may indicate that the metallic liquid could be treated as a single-parameter liquid. As an intrinsic material constant stemming from the fundamental interatomic interactions, γ is theoretically predicted from the thermodynamic fluctuations of the potential energy and the virial. Although γ is conventionally understood merely from the repulsive part of the inter-particle potentials, the strong correlation between γ and the Grüneisen parameter up to the accuracy of the Dulong-Petit approximation demonstrates the important roles of anharmonicity and attractive force of the interatomic potential in governing glass transition of metallic glassformers. These findings may shed light on how to understand metallic glass formation from the fundamental interatomic interactions.