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.

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.

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.

Demonstration of the effect of stirring on nucleation from experiments on the International Space Station using the ISS-EML facility.

The effect of fluid flow on crystal nucleation in supercooled liquids is not well understood. The variable density and temperature gradients in the liquid make it difficult to study this under terrestrial gravity conditions. Nucleation experiments were therefore made in a microgravity environment using the Electromagnetic Levitation Facility on the International Space Station on a bulk glass-forming Zr57Cu15.4Ni12.6Al10Nb5 (Vit106), as well as Cu50Zr50 and the quasicrystal-forming Ti39.5Zr39.5Ni21 liquids. The maximum supercooling temperatures for each alloy were measured as a function of controlled stirring by applying various combinations of radio-frequency positioner and heater voltages to the water-cooled copper coils. The flow patterns were simulated from the known parameters for the coil and the levitated samples. The maximum nucleation temperatures increased systematically with increased fluid flow in the liquids for Vit106, but stayed nearly unchanged for the other two. These results are consistent with the predictions from the Coupled-Flux model for nucleation.

Low-temperature nucleation anomaly in silicate glasses shown to be artifact in a 5BaO·8SiO2 glass.

For over 40 years, measurements of the nucleation rates in a large number of silicate glasses have indicated a breakdown in the Classical Nucleation Theory at temperatures below that of the peak nucleation rate. The data show that instead of steadily decreasing with decreasing temperature, the work of critical cluster formation enters a plateau and even starts to increase. Many explanations have been offered to explain this anomaly, but none have provided a satisfactory answer. We present an experimental approach to demonstrate explicitly for the example of a 5BaO ∙ 8SiO2 glass that the anomaly is not a real phenomenon, but instead an artifact arising from an insufficient heating time at low temperatures. Heating times much longer than previously used at a temperature 50 K below the peak nucleation rate temperature give results that are consistent with the predictions of the Classical Nucleation Theory. These results raise the question of whether the claimed anomaly is also an artifact in other glasses.

Nucleation pathways in barium silicate glasses.

Nucleation is generally viewed as a structural fluctuation that passes a critical size to eventually become a stable emerging new phase. However, this concept leaves out many details, such as changes in cluster composition and competing pathways to the new phase. In this work, both experimental and computer modeling studies are used to understand the cluster composition and pathways. Monte Carlo and molecular dynamics approaches are used to analyze the thermodynamic and kinetic contributions to the nucleation landscape in barium silicate glasses. Experimental techniques examine the resulting polycrystals that form. Both the modeling and experimental data indicate that a silica rich core plays a dominant role in the nucleation process.

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.

Curie-Weiss behavior of liquid structure and ideal glass state.

We present the results of a structural study of metallic alloy liquids from high temperature through the glass transition. We use high energy X-ray scattering and electro-static levitation in combination with molecular dynamics simulation and show that the height of the first peak of the structure function, S(Q) - 1, follows the Curie-Weiss law. The structural coherence length is proportional to the height of the first peak, and we suggest that its increase with cooling may be related to the rapid increase in viscosity. The Curie temperature is negative, implying an analogy with spin-glass. The Curie-Weiss behavior provides a pathway to an ideal glass state, a state with long-range correlation without lattice periodicity, which is characterized by highly diverse local structures, reminiscent of spin-glass.

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.

Calculation of absorption and secondary scattering of X-rays by spherical amorphous materials in an asymmetric transmission geometry. Corrigendum.

A revised version of Table 2 of Bendert et al. [Acta Cryst. (2013). A69, 131-139] is provided.

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.

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.

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.

Kinetic and structural fragility-a correlation between structures and dynamics in metallic liquids and glasses.

The liquid phase remains poorly understood. In many cases, the densities of liquids and their crystallized solid phases are similar, but since they are amorphous they lack the spatial order of the solid. Their dynamical properties change remarkably over a very small temperature range. At high temperatures, near their melting temperature, liquids flow easily under shear. However, only a few hundred degrees lower flow effectively ceases, as the liquid transforms into a solid-like glass. This temperature-dependent dynamical behavior is frequently characterized by the concept of kinetic fragility (or, generally, simply fragility). Fragility is believed to be an important quantity in glass formation, making it of significant practical interest. The microscopic origin of fragility remains unclear, however, making it also of fundamental interest. It is widely (although not uniformly) believed that the dynamical behavior is linked to the atomic structure of the liquid, yet experimental studies show that although the viscosity changes by orders of magnitude with temperature, the structural change is barely perceptible. In this article the concept of fragility is discussed, building to a discussion of recent results in metallic glass-forming liquids that demonstrate the presumed connection between structural and dynamical changes. In particular, it becomes possible to define a structural fragility parameter that can be linked with the kinetic fragility.

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.

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}).