Metastable Liquid Phase Research Articles

Containerless Measurements of Thermophysical Properties of Zr54Ti8Cu20Al10Ni8

High-temperature measurement and study of reactive materials can be difficult with conventional processing methods because contamination from the measuring apparatus and container walls can adversely affect measurements. Containerless processing techniques can be employed to isolate samples from their environment, reducing contamination. Benefits of containerless processing include reduction in heterogeneous nucleation sites, which in turn delays the onset of solidification and allows the study of meta-stable undercooled phases. However, property measurements must use noncontact methods as well. Fortunately, several optical-based methods have been developed and successfully employed to measure thermophysical properties, including surface tension, viscosity, density, and thermal expansion. Combining these techniques with the electrostatic levitator (ESL) located at the NASA Marshall Space Flight Center (MSFC) has resulted in an excellent facility to perform containerless material studies which support microgravity flight projects. Currently, studies of the thermophysical properties of liquid quasi-crystal forming and related alloys ranging from superheated to deeply undercooled states are being done with this facility in support of the NASA-funded flight project Quasi-crystalline Undercooled Alloys for Space Investigation (QUASI). While the primary purpose of these measurements is to support planned flight experiments, they are also a desirable resource for future manufacturing considerations and for fundamental insight in the physics of icosahedral ordering in liquids and solids. Presented here is an overview of the contactless measuring methods for surface tension, viscosity, density, and thermal expansion applied to Zr54Ti8Cu20Al10Ni8, for the superheated and meta-stable undercooled liquid phases, in support of QUASI.

Metastable phase separation and rapid solidification of undercooled Co-Cu alloy under different conditions

The metastable liquid phase separation and rapid solidification behaviours of Co61.8Cu38.2 alloy were investigated by using differential thermal analysis (DTA) in combination with glass fluxing, electromagnetic levitation (EML) and drop tube techniques. It is found that the liquid phase separation process and the solidification microstructures intensively depend on the experimental processing parameters, such as undercooling level, cooling rate, gravity level, liquid surface tension and the wetting state of crucible. Large undercooling and surface tension difference of the two liquids tend to facilitate further separation and cause severe macrosegregation. On the other hand, rapid cooling and low gravity effectively suppress the coalescence of the minority phase. Severe macrosegregation patterns are formed in the bulk samples processed by both DTA and EML. In contrast, disperse structures with fine spherical Cu-rich spheres homogeneously distributed in the matrix of Co-rich phase have been obtained in drop tube.

Solidification of Co-Cu Alloys in the Metastable Miscibility Gap under Low Gravity Conditions

Liquid Cu-Co shows a metastable miscibility gap where the homogeneous melt separates into the Co-rich L1-liquid and the Cu-rich L2-liquid. The required undercooling of the melt of > 120 K can be achieved by containerless methods as electromagnetic levitation, laser melting or drop tube processing. Due to the large undercooling, rapid solidification of the melt is favoured and preserves microstructure features of the metastable (liquid) phases. In Co-84.0 at% Cu alloy the L1- phase nucleates in the Cu-rich majority phase L2 as a dispersion of spherical droplets. Convective flow in the liquid influences largely the time evolution and the nature of the droplet dispersion and makes a theoretical description of the droplet growth extremely difficult. In the present work droplet dispersions are compared which formed under processing methods with different levels of convection: (i) (Terrestrial) electromagnetic levitation (EML), (ii) processing in the TEMPUS facility under parabolic flight conditions and (iii) processing in an 8 m drop tube. The distributions of droplet radii of the L1-phase has been measured in the solidified samples. EML processing leads to significant convection in the melt which causes coagulation of droplets. Reduced gravity conditions in the TEMPUS facility during parabolic flight or in a drop tube can decrease convection, but effects of the convective flow on the dispersion of droplets are still present. The need for experiments under micro-gravity conditions is evident from the results.

Including Nonequilibrium Relaxation in Models for Rapid Multiphase Flow in Wells

Summary The modeling of rapid flow of multiphase reservoir fluids in wells involving nonequilibrium partial separation of dissolved gases from the metastable oil and water phases is reviewed and formulated. The multiphase-fluid flow is described by means of the differential mass, momentum, and energy-balance equations along the well. The rate of gas transfer from the metastable liquid phases to the gas phase is expressed in terms of the relaxation time determined by the prevailing gas-phase volume fraction and the pressure and temperature conditions. The differential equations are solved numerically under a typical scenario involving the constant gas-, oil-, and water-production rates at the wellhead. It is demonstrated that the nonequilibrium saturation and pressure distributions in wells deviate from the equilibrium results, depending on the variation of the local relaxation time along the well. It is concluded that inclusion of nonequilibrium relaxation effects in models for rapid multiphase flow in wells is required.

Critical behavior of the specific heat in glass formers

We show numeric evidence that, at low enough temperatures, the potential energy density of a glass-forming liquid fluctuates over length scales much larger than the interaction range. We focus on the behavior of translationally invariant quantities. The growing correlation length is unveiled by studying the finite-size effects. In the thermodynamic limit, the specific heat and the relaxation time diverge as a power law. Both features point towards the existence of a critical point in the metastable supercooled liquid phase.

Vitrification in the BaO–B 2O 3–Al 2O 3–TiO 2 system containing small admixtures of PbO

The fields of vitrification in different diagrams were identified for the system BaO–Al 2O 3–B 2O 3–TiO 2 containing 2.4–3.4 mol% admixtures of PbO and varied contents of other components. The glasses obtained were stable from spontaneous crystallization and had relatively low (1450 °C) melting temperature. Liquid phase immiscibility took place in all compositions investigated: TiO 2-rich and B 2O 3-rich glassy phases were formed. The contents of B 2O 3 and Al 2O 3 determined the structure of glasses synthesized, glasses with [B 2O 3] in the range of 7–20 mol% and [Al 2O 3] < 22 mol% showed metastable liquid phase separation. Higher contents of Al 2O 3 and/or B 2O 3 (i.e. [R 2O 3] > 37 mol%) promoted spinodal decomposition. The structure of the main vitreous phase in the glasses with metastable liquid formation is formed by polyanions containing TiO 6/2 and AlO 6/2 octahedra altogether with (B 3O 6) 3− rings, whereas the second vitreous phase includes BO 3/2, BO 4/2, TiO 4/2 and AlO 4/2 structural units.

Liquid‐phase nucleation and evolution as a cause of superplasticity in alloys of the Al–Ge system

AbstractThe kinetics of phase transformations taking place under conditions of superplastic flow in the matrix alloys of the Al–Ge system was studied. It has been found that these alloys manifest superplasticity in the nonequilibrium state that is characterized by the presence of the metastable liquid phase in their structure. It is shown that the liquid‐phase formation in the Al–Ge alloys is due to the effect of contact melting. The time of existence of the liquid phase in these alloys correlates with the time of superplastic deformation. The liquid‐phase formation is considered as a cause of superplasticity in the alloys under study. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

In situ formation of two amorphous phases by liquid phase separation in Y–Ti–Al–Co alloy

The Y28Ti28Al24Co20 alloy undergoes metastable liquid phase separation in the under-cooled liquid state and subsequently solidifies into two different Y-rich and Ti-rich amorphous phases. Secondary phase separation occurs due to the supersaturation of the primary separated liquids as the temperature decreases. Depending on the degree of local undercooling, a wide range of length scale of the microstructure is observed. The characteristic length scale of the two amorphous phases is ∼250nm near the air side of the ribbon, and ∼25nm near the wheel side of the ribbon.

Coexistence of two Bose–Einstein condensates of two-dimensional magnetoexcitons. Exciton-plasmon collective elementary excitations

Possibility of the Bose–Einstein condensation of magnetic excitons in an ideal two-dimensional system in a strong perpendicular magnetic field is investigated theoretically taking into account the influence of virtual transitions to the excited Landau levels and Anderson-type coherent excited states. It was understood, that the Bose–Einstein condensed (BEC-ed) magnetoexcitons with considerable wave vector K and motional dipole moment Kl 2, where l is the magnetic length, can form the droplets of the metastable dielectric liquid phase, whereas the BEC-ed magnetoexcitons with K =0 can form a stable degenerate Bose-gas surrounding the droplet. We have shown that collective elementary excitations of the BEC of excitons are mixed with plasma oscillations of the electron–hole system in the presence of strong perpendicular magnetic field. Their mutual influence is determined by the coherence factor and essentially depends on the condensate wave vector K.

Low-temperature phase diagram of condensedpara-hydrogen in two dimensions

Extensive Path Integral Monte Carlo simulations of condensed para-Hydrogen in two dimensions at low temperature have been carried out. In the zero temperature limit, the system is a crystal at equilibrium, with a triangular lattice structure. No metastable liquid phase is observed, as the system remains a solid down to the spinodal density, and breaks down into solid clusters at lower densities. The equilibrium crystal is found to melt at a temperature close to 7 K.

In situ study of the ZnO–NaCl system during the growth of ZnO nanorods

Synchrotron x-ray diffraction and high temperature SEM examinationswere used to study the crystallochemical and morphological evolution of aZnO–NaCl system during thermal processing. Decomposition of ZnO precursor(Zn2(OH)2CO3*xH2O)at T<400 °C is accompanied by shrinkage and destruction of its fibre-like particlesinto nanosized isotropic ZnO crystallites. Intensive intergrowth of ZnOnanoparticles and its interaction with coarse NaCl crystallites leads atT = 650–700 °C to the formation of a continuous sponge-like framework with an elementary unit size whichis far below the initial size of NaCl crystallites. The higher temperature processing at is accompanied by the appearance of nanorods. The role ofthe metastable liquid phase in the formation of ZnO nanorods atT<800 °C is discussed. Luminescence properties of ZnO nanorods synthesized at 500 and700 °C were demonstrated.

Entropy crisis, ideal glass transition, and polymer melting: exact solution on a Husimi cactus.

We investigate an extension of the lattice model of melting of semiflexible polymers originally proposed by Flory. Along with a bending penalty epsilon, present in the original model and involving three sites of the lattice, we introduce an interaction energy epsilon (p), corresponding to the presence of a pair of parallel bonds and an interaction energy epsilon (h), associated with a hairpin turn. Both these new terms represent four-site interactions. The model is solved exactly on a Husimi cactus, which approximates a square lattice. We study the phase diagram of the system as a function of the energies. For a proper choice of the interaction energies, the model exhibits a first-order melting transition between a liquid and a crystalline phase at a temperature T(M). The continuation of the liquid phase below T(M) gives rise to a supercooled liquid, which turns continuously into a new low-temperature phase, called metastable liquid, at T(MC)<T(M). This liquid-liquid transition seems to have some features that are characteristic of the critical transition predicted by the mode-coupling theory. The exact calculation provides a thermodynamic justification for the entropy crisis (entropy becoming negative), generally known as the Kauzmann paradox, caused by the rapid drop of the entropy near the Kauzmann temperature. It occurs not in the supercooled liquid, but in the metastable liquid phase since its Helmholtz free energy equals the absolute zero equilibrium free energy at a positive temperature. A continuous ideal glass transition occurs to avoid the crisis when the metastable liquid entropy, and not the excess entropy, goes to zero. The melting transition in the original Flory model, corresponding to the vanishing of the four-site interactions, appears as a tricritical point of the model.

Thermodynamic instability in supersaturated lysozyme solutions: effect of salt and role of concentration fluctuations.

Experimental and theoretical work has suggested that protein crystal nucleation can be affected by the separation of two metastable liquid phases with different local concentrations, or more specifically by critical density fluctuations. We measure the amplitude and correlation length of local concentration fluctuations by light scattering for supersaturated solutions of hen egg-white lysozyme (at pH 4.5 and at different NaCl concentrations, up to 7% w/v). By extrapolating the critical divergent behavior of concentration fluctuation amplitude versus temperature, we determine the spinodal line, that is the limit of stability. Cloud-point measurements are used to determine liquid-liquid coexistence, consistent with previous work. In the present work, which is an extensive study of off-critical fluctuations in supersaturated protein solution, we observe a nonclassical scaling divergent behavior of the correlation length of concentration fluctuations, thus suggesting that off-critical fluctuations may have a role in crystallization kinetics. To appropriately fit the spinodal data, an entropic term must be added to the van der Waals or to the adhesive hard-sphere model. We interpret this contribution as due to the salt-induced modulation of protein hydration.

Glass and polycrystal states in a lattice spin model

We numerically study a nondisordered lattice spin system with a first order liquid–crystal transition, as a model for supercooled liquids and glasses. Below the melting temperature the system can be kept in the metastable liquid phase, and it displays a dynamic phenomenology analogous to fragile supercooled liquids, with stretched exponential relaxation, power law increase of the relaxation time, and high fragility index. At an effective spinodal temperature Tsp the relaxation time exceeds the crystal nucleation time, and the supercooled liquid loses stability. Below Tsp liquid properties cannot be extrapolated, in line with Kauzmann’s scenario of a lower metastability limit of supercooled liquids as a solution of Kauzmann’s paradox. The off-equilibrium dynamics below Tsp corresponds to fast nucleation of small, but stable, crystal droplets, followed by extremely slow growth, due to the presence of pinning energy barriers. In the early time region, which is longer the lower the temperature, this crystal-growth phase is indistinguishable from an off-equilibrium glass, both from a structural and a dynamical point of view: crystal growth has not advanced enough to be structurally detectable, and a violation of the fluctuation–dissipation theorem (FDT) typical of structural glasses is observed. On the other hand, for longer times crystallization reaches a threshold beyond which crystal domains are easily identified, and FDT violation becomes compatible with ordinary domain growth.

Thermodynamique des melanges binaires LiPO3-Pb(PO3)2 diagramme de phases et étude thermodynamique du liquide

Study of solid-liquid phase diagram of LiPO3-Pb(PO3)2 binary system, in certain calcination conditions, shows the existence of several metastable phasis. When heated at a temperature of 723 K the binary mixtures lead uncompletely to a defined compound Pb2Li(PO3). On heating these ternary solid mixtures, three eutectic reactions have been observed: LiPO3+Pb(PO3)2→Liquid at a temperature of 793 K(1) LiPO3+Pb2Li(PO3)5→Liquid at a temperature of 843 K (2) Pb2Li(PO3)5+Pb(PO3)2→Liquid at a temperature of 891 K (3) The metastable liquid phase appears in the system at temperature of 793 K. DTA experiments performed on the binary LiPO3-Pb(PO3)2 mixtures, show a superposition of two diagrams. The first one is metastable and the second represents the stable equilibrium phase diagram. Measurements of liquid enthalpy of binary LiPO3-Pb(PO3)2 system at temperature of 979.65 K were reported. The corresponding values were very small and so the binary system can be considered as athermal. Assuming an ideal behaviour, the liquidus curves in the metastable diagram were calculated and the eutectic reaction (LiPO3-Pb(PO3)2→Liquid) was confirmed at 793 K.

Investigation of laser surface alloying of copper on high nickel austenitic ductile iron

Laser surface alloying (LSA) of pure copper on high nickel austenitic ductile iron was carried out using a 2 kW continuous wave (CW) CO 2 laser with two processing conditions: laser beam spot size D=5 mm, scanning speed V=2 mm s −1, power density E=1.02×10 4 W cm −2 (condition 1) and D=2 mm, V=9 mm s −1, 6.37×10 4 W cm −2 (condition 2). Microstructure in the alloyed zone was found to consist mainly of primary γ-austenite dendrites and an interdendritic eutectic of γ-austenite and M 7C 3 carbides with copper wetting the dendritic boundaries. Distribution of the copper in the alloyed zone is fairly uniform across the depth of the pool and the concentration of copper in the alloyed zone highly depends on the power density. Copper spheroidal particles can be observed at the interdendritic boundaries under condition 1, indicating that the melt could be near the metastable miscibility gap and liquid phase separation (LPS) takes place due to rapid solidification. After LSA, hardness of the alloyed zone is considerably higher than before, which is attributed to both precipitation hardening and work hardening caused by the thermal stress.

Models for a liquid–liquid phase transition

We use molecular dynamics simulations to study two- and three-dimensional models with the isotropic double-step potential which in addition to the hard core has a repulsive soft core of larger radius. Our results indicate that the presence of two characteristic repulsive distances (hard core and soft core) is sufficient to explain liquid anomalies and a liquid–liquid phase transition, but these two phenomena may occur independently. Thus liquid–liquid transitions may exist in systems like liquid metals, regardless of the presence of the density anomaly. For 2D, we propose a model with a specific set of hard core and soft core parameters, that qualitatively reproduces the phase diagram and anomalies of liquid water. We identify two solid phases: a square crystal (high density phase), and a triangular crystal (low density phase) and discuss the relation between the anomalies of liquid and the polymorphism of the solid. Similarly to real water, our 2D system may have the second critical point in the metastable liquid phase beyond the freezing line. In 3D, we find several sets of parameters for which two fluid–fluid phase transition lines exist: the first line between gas and liquid and the second line between high-density liquid (HDL) and low-density liquid (LDL). In all cases, the LDL phase shows no density anomaly in 3D. We relate the absence of the density anomaly with the positive slope of the LDL–HDL phase transition line.

Classification of ordering kinetics in three-phase systems.

Though equations of motion containing transport coefficients are required to quantitatively predict the phase-ordering dynamics of any given system, a great deal can be gleaned just from the shape of the free-energy landscape. We demonstrate how to extract the most information concerning phase-ordering phenomenology from a knowledge of a system's free-energy function, or phase diagram. Many putative pathways to equilibrium can be ruled out on the grounds of the second law of thermodynamics. In some parts of the phase diagram, these considerations are sufficient to completely determine the phase-ordering process without ever having to calculate a transport coefficient, even when three phases are present. The results include a large number of regions of the phase diagram with distinct phase-ordering kinetics, and some surprisingly elaborate routes to the equilibrium state. A process is found whereby a crystalline condensation nucleus becomes coated with a shell of gas, buffering it from a majority metastable liquid phase. Our results, based on thermodynamic arguments, are supported by numerical solution of model B, which describes diffusive phase-ordering kinetics. Some of our predictions are tested against experimental observations of colloid-polymer mixtures, described in more detail in the preceding paper [F. Renth, W. C. K. Poon, and R. M. L. Evans, Phys. Rev. E 64, 031402 (2001)]. A compact notation is developed to represent intricate phase-ordering pathways.

H2O below 277 K: A Novel Picture†,‡

We present a mesoscopic picture of supercooled water in which we fit the properties of water into a general scheme applicable to all so-called fragile glass-forming liquids. Water is taken as a single liquid phase above its glass transition at about 136 K. It is the only liquid known to have a Kauzmann temperature that lies above (well above) the glass transition temperature; we discuss this phenomenon and its implications. We have also associated the metastable cubic ice Ic with the defect-ordered phase predicted by the theory of frustration-limited domains, thereby developing a general physical and theoretical picture that incorporates both the metastable low-temperature liquid and solid phases at 1 atm.

Thermophysical properties of gases, liquids, and solids composed of particles interacting with a short-range attractive potential.

A short-range polynomial interaction potential is introduced which has both a repulsive core and an attractive part. It is cut off smoothly such that its first and second derivatives vanish at the cutoff distance. The potential therefore enables efficient simulation studies of a model material that exhibits similarities to a full (but computationally expensive) classical Lennard-Jones system. Thermophysical properties of the model are calculated by (nonequilibrium) molecular dynamics computer simulations and compared with analytical results. Among the quantities studied is the pressure as a function of the density for various temperatures. Equations of state for the fluid and the solid are tested. The coexistence of gaseous, (metastable) liquid, and fcc solid phases is found for a range of temperatures. Bulk and shear moduli are computed. The response of the system to a shear deformation with a constant shear rate is analyzed. The liquid shows viscoelastic behavior that can be described with a Maxwell model. The solid behaves as an elastic medium up to a finite deformation and then undergoes a transition to plastic flow, which is stick-slip-like at small shear rates and continuous at higher ones.