Structural evolution in Au- and Pd-based metallic glass forming liquids and the case for improved molecular dynamics force fields.

The results of a combined experimental and computational investigation of the structural evolution of Au81Si19, Pd82Si18, and Pd77Cu6Si17 metallic glass forming liquids are presented. Electrostatically levitated metallic liquids are prepared, and synchrotron x-ray scattering studies are combined with embedded atom method molecular dynamics simulations to probe the distribution of relevant structural units. Metal-metalloid based metallic glass forming systems are an extremely important class of materials with varied glass forming ability and mechanical processibility. High quality experimental x-ray scattering data are in poor agreement with the data from the molecular dynamics simulations, demonstrating the need for improved interatomic potentials. The first peak in the x-ray static structure factor in Pd77Cu6Si17 displays evidence for a Curie-Weiss type behavior but also a peak in the effective Curie temperature. A proposed order parameter distinguishing glass forming ability, 1/ST,q1-1, shows a peak in the effective Curie temperature near a crossover temperature established by the behavior of the viscosity, TA.

Breakdown of the Stokes-Einstein relationship and rapid structural ordering in CuZrAl metallic glass-forming liquids.

The results of a combined structural and dynamical study of Cu-Zr-Al metallic glass forming liquids are presented. Containerless high-energy x-ray scattering experiments made using electrostatic levitation are combined with molecular dynamics simulations to probe the onset of rapid structural ordering as well as the temperature-dependent diffusivity and viscosity in three liquids: Cu49Zr45Al6, Cu47Zr45Al8, and Cu43Zr45Al12. These compositions were chosen because they are reported to have dramatically different glass forming-ability. Experimental data show that the first peak in the x-ray static structure factor displays evidence for a Curie-Weiss type behavior, but also a peak in the effective Curie temperature. The evidence provided here for the onset of cooperativity, marked by a crossover temperature, TA (which is usually above the liquidus temperature), is accompanied by the onset of development of more spatially extended structural order in the liquids. Based on the molecular dynamics simulations, each of the liquids exhibits a clear breakdown of the Stokes-Einstein relation at a temperature near, but below, the crossover temperature, TA. The breakdown is manifest as a rapid reduction in the relative diffusion coefficients between Cu, Zr, and Al.

X-ray and neutron scattering measurements of ordering in a Cu46Zr54 liquid.

The structural evolution of the equilibrium and supercooled Cu46Zr54 liquids was investigated with a combination of elastic neutron scattering (with isotopic substitution) and synchrotron x-ray scattering studies. The partial pair correlation functions were determined over a wide temperature range (∼270 °C). These show that the Cu-Cu and Zr-Zr ordering increases as the temperature decreases, while the Cu-Zr ordering decreases. This surprising result is in contradiction with the results from molecular dynamics studies.

Experimental determination of the temperature-dependent Van Hove function in a Zr80Pt20 liquid.

Even though the viscosity is one of the most fundamental properties of liquids, the connection with the atomic structure of the liquid has proven elusive. By combining inelastic neutron scattering with the electrostatic levitation technique, the time-dependent pair-distribution function (i.e., the Van Hove function) has been determined for liquid Zr80Pt20. We show that the decay time of the first peak of the Van Hove function is directly related to the Maxwell relaxation time of the liquid, which is proportional to the shear viscosity. This result demonstrates that the local dynamics for increasing or decreasing the coordination number of local clusters by one determines the viscosity at high temperature, supporting earlier predictions from molecular dynamics simulations.

Resistivity Saturation in Metallic Liquids Above a Dynamical Crossover Temperature Observed in Measurements Aboard the International Space Station.

Although a resistivity saturation (minimum conductivity) is often observed in disordered metallic solids, such phenomena in the corresponding liquids are not known. Here we report a saturation of the electrical resistivity in Zr_{64}Ni_{36} and Cu_{50}Zr_{50} liquids above a dynamical crossover temperature for the viscosity (T_{A}). The measurements were made for the levitated liquids under the microgravity conditions of the International Space Station. Based on recent molecular dynamics simulations, the saturation is likely due to the ineffectiveness of electron-phonon scattering above T_{A} when the phonon lifetime becomes too short compared to the electron relaxation time. This is different from the conventional resistivity saturation mechanisms in solids.

Maximum supercooling studies in Ti39.5Zr39.5Ni21, Ti40Zr30Ni30, and Zr80Pt20 liquids-Connecting liquid structure and the nucleation barrier.

Almost three quarters of a century ago, Charles Frank proposed that the deep supercooling observed in metallic liquids is due to icosahedral short-range order (ISRO), which is incompatible with the long-range order of crystal phases. Some evidence in support of this hypothesis had been published previously. However, those studies were based on a small population of maximum supercooling measurements before the onset of crystallization. Here, the results of a systematic statistical study of several hundred maximum supercooling measurements on Ti39.5Zr39.5Ni21, Ti40Zr30Ni30, and Zr80Pt20 liquids are presented. Previous X-Ray and neutron scattering studies have shown that the structures of these liquid alloys contain significant amounts of ISRO. The results presented here show a small work of critical cluster formation (W* = 31-40 kBT) from the analysis of the supercooling data for the Ti39.5Zr39.5Ni21 liquid, which crystallizes to a metastable icosahedral quasicrystal. A much larger value (W* = 54-79 kBT and W* = 60-99 kBT) was obtained for the Ti40Zr30Ni30 and Zr80Pt20 liquids, respectively, which do not crystallize to an icosahedral quasicrystal. Taken together, these results significantly strengthen the validity of Frank's hypothesis.

Strength of the repulsive part of the interatomic potential determines fragility in metallic liquids.

The dynamical behaviour of liquids is frequently characterized by the fragility, which can be defined from the temperature dependence of the shear viscosity, η (ref. ). For a strong liquid, the activation energy for η changes little with cooling towards the glass transition temperature, Tg. The change is much greater in fragile liquids, with the activation energy becoming very large near Tg. While fragility is widely recognized as an important concept-believed, for example, to play an important role in glass formation-the microscopic origin of fragility is poorly understood. Here, we present new experimental evidence showing that fragility reflects the strength of the repulsive part of the interatomic potential, which can be determined from the steepness of the pair distribution function near the hard-sphere cutoff. On the basis of an analysis of scattering data from ten different metallic alloy liquids, we show that stronger liquids have steeper repulsive potentials.

A re-evaluation of thermal expansion measurements of metallic liquids and glasses from x-ray scattering experiments.

Previous studies reported a number of anomalies when estimates of linear thermal expansion coefficients of metallic liquids and glasses from x-ray scattering experiments were compared with direct measurements of volume/length changes with temperature. In most cases, the first peak of the pair correlation function showed a contraction, while the structure factor showed an expansion, but both at rates much different from those expected from the direct volume measurements. In addition, the relationship between atomic volume and the characteristic lengths obtained from the structure factor from scattering experiments was found to have a fractional exponent instead of one equal to three, as expected from the Ehrenfest relation. This has led to the speculation that the atomic packing in liquids and glasses follow a fractal behavior. These issues are revisited in this study using more in-depth analysis of recent higher resolution data and some new ideas suggested in the literature. The main conclusion is that for metallic alloys, at least to a large extent, most of these anomalies arise from complicated interplays of the temperature dependences of the various partial structure factors, which contribute to the total intensities of the scattering peaks.

A possible structural signature of the onset of cooperativity in metallic liquids.

It is widely, although not universally, believed that there must be a connection between liquid dynamics and the structure. Previous supporting studies, for example, have demonstrated a link between the structural evolution in the liquid and kinetic fragility. Here, new results are presented that strengthen the evidence for a connection. By combining the results from high-energy synchrotron X-ray scattering studies of containerlessly processed supercooled liquids with viscosity measurements, an accelerated rate of structural ordering beyond the nearest neighbors in the liquid is demonstrated to correlate with the temperature at which the viscosity transitions from Arrhenius to super-Arrhenius behavior. This is the first confirmation of predictions from several recent molecular dynamics studies.

Correlation of the fragility of metallic liquids with the high temperature structure, volume, and cohesive energy.

The thermal expansion coefficients, structure factors, and viscosities of twenty-five equilibrium and supercooled metallic liquids have been measured using an electrostatic levitation (ESL) facility. The structure factor was measured at the Advanced Photon Source, Argonne, using the ESL. A clear connection between liquid fragility and structural and volumetric changes at high temperatures is established; the observed changes are larger for the more fragile liquids. It is also demonstrated that the fragility of metallic liquids is determined to a large extent by the cohesive energy and is, therefore, predictable. These results are expected to provide useful guidance in the future design of metallic glasses.

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}).

Preface: Special Topic on Nucleation: New Concepts and Discoveries.

Many phenomena in the world around us depend on infrequent, yet short-lived, events that completely alter how a system subsequently develops in time. In the physical sciences, there are many examples of such crucial "rare events." Among the most important of these are nucleation processes, in which, due to a rare fluctuation, a new phase forms spontaneously within a meta-stable parent phase. Because nucleation processes are both rare and rapid and happen on a microscopic spatial scale, their experimental study is challenging. In recent years, there have been major developments both in the experimental study of nucleation phenomena and in the numerical simulation of such processes. As the articles in this special issue demonstrate, these recent advances in the ability to probe nucleation phenomena have transformed our understanding of the field.

Experimental and molecular dynamics simulation study of structure of liquid and amorphous Ni62Nb38 alloy.

The state-of-the-art experimental and atomistic simulation techniques were utilized to study the structure of the liquid and amorphous Ni62Nb38 alloy. First, the ab initio molecular dynamics (AIMD) simulation was performed at rather high temperature where the time limitations of the AIMD do not prevent to reach the equilibrium liquid structure. A semi-empirical potential of the Finnis-Sinclair (FS) type was developed to almost exactly reproduce the AIMD partial pair correlation functions (PPCFs) in a classical molecular dynamics simulation. This simulation also showed that the FS potential well reproduces the bond angle distributions. The FS potential was then employed to elongate the AIMD PPCFs and determine the total structure factor (TSF) which was found to be in excellent agreement with X-ray TSF obtained within the present study demonstrating the reliability of the AIMD for the simulation of the structure of the liquid Ni-Nb alloys as well as the reliability of the developed FS potential. The glass structure obtained with the developed potential was also found to be in excellent agreement with the X-ray data. The analysis of the structure revealed that a network of the icosahedra clusters centered on Ni atoms is forming during cooling the liquid alloy down to Tg and the Nb Z14, Z15, and Z16 clusters are attached to this network. This network is the main feature of the Ni62Nb38 alloy and further investigations of the properties of this alloy should be based on study of the behavior of this network.

Anomalous thermal contraction of the first coordination shell in metallic alloy liquids.

Except for a few anomalous solids and liquids, materials expand upon heating. For liquids, this should be reflected as a shift in the peak positions in the pair correlation function, g(r), to higher r. Here, we present the results of a detailed study of the volume thermal expansion coefficients and the temperature dependences of g(r) for a large number of binary, ternary, and quaternary liquids in the equilibrium and supercooled (metastable liquid below the liquidus temperature) states. The data were obtained from x-ray scattering and volume measurements on levitated liquids using the electrostatic levitation technique. Although the volumes of all liquids expand with increasing temperature, the peak positions in g(r) for the first coordination shells contract for the majority of alloy liquids studied. The second and third peaks in g(r) expand, but at rates different from those expected from the volume expansion. This behavior is explained qualitatively in terms of changes in the coordination numbers and bond-lengths as clusters in liquids break up with increasing temperature.

Electromagnetic levitation containerless processing of metallic materials in microgravity: rapid solidification.

Space levitation processing allows researchers to conduct benchmark tests in an effort to understand the physical phenomena involved in rapid solidification processing, including alloy thermodynamics, nucleation and growth, heat and mass transfer, solid/liquid interface dynamics, macro- and microstructural evolution, and defect formation. Supported by ground-based investigations, a major thrust is to develop and refine robust computational tools based on theoretical and applied approaches. This work is accomplished in conjunction with experiments designed for precise model validation with application to a broad range of industrial processes.

Volume expansion measurements in metallic liquids and their relation to fragility and glass forming ability: an energy landscape interpretation.

Recent studies of Cu-Zr glasses have reported a rapid variation in the amorphous phase density near the optimal glass forming compositions, supporting the belief that the densest liquids are also the best glass formers. Here, we show that the measured densities of the Cu-Zr liquids at higher temperatures are not peaked sharply near these compositions, but the volume expansivities are. Theoretical studies have shown that the expansivity correlates with fragility near T(g); the experimental results presented here show that at high temperature they become anticorrelated. From energy landscape arguments, this indicates the existence of a crossover temperature for the expansivity-fragility correlation that scales inversely with the liquid fragility. These results lead to an improved understanding of the high temperature properties of liquids that form glasses and suggest a new method for identifying the best glass forming compositions within an alloy system from the properties of the equilibrium liquids.

Local atomic structure in equilibrium and supercooled liquid Zr(75.5)Pd(24.5).

Atomic structures were obtained in equilibrium and supercooled eutectic Zr(75.5)Pd(24.5) liquids by in situ high-energy synchrotron diffraction measurements using the beamline electrostatic levitation (BESL) technique, which provides a high-vacuum, containerless, environment. Reverse Monte Carlo fits to the x-ray static structure factors, constrained using partial pair correlation functions obtained from ab initio molecular dynamics simulations, indicate the presence of medium-range order (MRO) in the form of a strong tendency for Pd-Pd (solute-solute) avoidance. This order persists over the entire temperature range studied, from 170 °C above the equilibrium liquidus temperature to 263 °C below it. Further, a quantitative analysis of the atomic structures obtained indicates a modest degree of icosahedral-like local order around Pd atoms, with the clusters showing an increased tendency for face-sharing to form more extended structures with decreasing temperature.

Quantum mechanical interpretation of the minimum viscosity of metallic liquids.

Possible fundamental quantum bounds for viscosity and many other physical properties have drawn serious considerations recently from diverse communities encompassing those studying quantum gravity, high-energy physics, condensed matter physics, strongly correlated electron systems, and "strange metals," to name a few. However, little attention has been paid by materials scientists and the fluid dynamics community, perhaps because of the general belief that quantum mechanics is of little consequence for classical fluid dynamics. Here, considering the extrapolated high-temperature viscosity of 32 metallic alloy liquids as representative of minimum viscosity, experimental results are presented and evaluated in terms of a number of quantum- and statistical-mechanics-based theories. The surprising result is that the experimental data are within one order of magnitude of estimates from those theories. That quantum mechanics could be of importance at such high temperatures in conventional classical fluids is quite interesting. Another surprise is that the minimum viscosities of metallic alloy liquids are not too different from an archetypal quantum liquid, such as He.

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering.

We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via multi-scale network analysis. The method is based on "community detection" wherein interacting particles are partitioned into an "ideal gas" of optimally decoupled groups of particles. Specifically, we construct a set of network representations ("replicas") of the physical system based on interatomic potentials and apply a multiscale clustering ("multiresolution community detection") analysis using information-based correlations among the replicas. Replicas may i) be different representations of an identical static system, ii) embody dynamics by considering replicas to be time separated snapshots of the system (with a tunable time separation), or iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system in a mixture ratio of A(80)B(20) , a ternary model system with components "A", "B", and "C" in ratios of A(88)B(7)C(5) (as in Al(88)Y(7)Fe(5) , and to atomic coordinates in a Zr(80)Pt(20) system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between i) physical transitions or crossovers and ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We also briefly consider continuum approaches and discuss rigidity and the shear penetration depth in amorphous systems; this latter length scale increases as the system becomes progressively rigid.

High energy x-ray scattering studies of the local order in liquid Al.

The x-ray structure factors and densities for liquid aluminum from 1123 K to 1273 K have been measured using the beamline electrostatic levitator. Atomic structures as a function of temperature have been constructed from the diffraction data with reverse Monte Carlo simulations. An analysis of the local atomic structures in terms of the Honeycutt-Andersen indices indicates a high degree of icosahedral and distorted icosahedral order, a modest amount of body-centered cubic order, and marginal amounts of face-centered cubic and hexagonal close-packed order.