Gas-liquid nucleation at large metastability: unusual features and a new formalism

Nucleation at large metastability is still largely an unsolved problem, even though it is a problem of tremendous current interest, with wide-ranging practical value, from atmospheric research to materials science. It is now well accepted that the classical nucleation theory (CNT) fails to provide a qualitative picture and gives incorrect quantitative values for such quantities as activation-free energy barrier and supersaturation dependence of nucleation rate, especially at large metastability. In this paper, we present an alternative formalism to treat nucleation at large supersaturation by introducing an extended set of order parameters in terms of the kth largest liquid-like clusters, where k = 1 is the largest cluster in the system, k = 2 is the second largest cluster and so on. At low supersaturation, the size of the largest liquid-like cluster acts as a suitable order parameter. At large supersaturation, the free energy barrier for the largest liquid-like cluster disappears. We identify this supersaturation as the one at the onset of kinetic spinodal. The kinetic spinodal is system-size-dependent. Beyond kinetic spinodal many clusters grow simultaneously and competitively and hence the nucleation and growth become collective. In order to describe collective growth, we need to consider the full set of order parameters. We derive an analytic expression for the free energy of formation of the kth largest cluster. The expression predicts that, at large metastability (beyond kinetic spinodal), the barrier of growth for several largest liquid-like clusters disappears, and all these clusters grow simultaneously. The approach to the critical size occurs by barrierless diffusion in the cluster size space. The expression for the rate of barrier crossing predicts weaker supersaturation dependence than what is predicted by CNT at large metastability. Such a crossover behavior has indeed been observed in recent experiments (but eluded an explanation till now). In order to understand the large numerical discrepancy between simulation predictions and experimental results, we carried out a study of the dependence on the range of intermolecular interactions of both the surface tension of an equilibrium planar gas-liquid interface and the free energy barrier of nucleation. Both are found to depend significantly on the range of interaction for the Lennard-Jones potential, both in two and three dimensions. The value of surface tension and also the free energy difference between the gas and the liquid phase increase significantly and converge only when the range of interaction is extended beyond 6-7 molecular diameters. We find, with the full range of interaction potential, that the surface tension shows only a weak dependence on supersaturation, so the reason for the breakdown of CNT (with simulated values of surface tension and free energy gap) cannot be attributed to the supersaturation dependence of surface tension. This remains an unsettled issue at present because of the use of the value of surface tension obtained at coexistence.

Solubility and activity of oxygen in liquid gallium and gallium copper alloys

The solubility of oxygen in liquid gallium in the temperature range 775 –1125 °C and in liquid gallium-copper alloys at 1100 °C, in equilibrium with β-Ga2O3, has been measured by an isopiestic equilibrium technique. The solubility of oxygen in pure gallium is given by the equation log (at.% O) = −7380/T + 4.264 (±0.03) Using recently measured values for the standard free energy of formation of β-Ga2O3 and assuming that oxygen obeys Sievert's law up to the saturation limit, the standard free energy of solution of oxygen in liquid gallium may be calculated : View the MathML sourceΔ°298 = −52 680 + 6.53T (±200) cal where the standard state for dissolved oxygen is an infinitely dilute solution in which the activity is equal to atomic per cent. The effect of copper on the activity of oxygen dissolved in liquid gallium is found to be in good agreement with that predicted by a recent quasichemical model in which it was assumed that each oxygen is interstitially coordinated to four metal atoms and that the nearest neighbour metal atoms lose approximately half their metallic cohesive energies.

Solubility and activity of oxygen in liquid indium and copper indium alloys

The solubility of oxygen in liquid indium in the temperature range 650–820 °C and in liquid copper-indium alloys at 1100 °C in equilibrium with indium sesquioxide has been measured by a phase equilibration technique. The solubility of oxygen in pure indium is given by the relation log(at.% O) = −4726/T + 3.73 (±0.08) Using the recently measured values for the standard free energy of formation of In2O3 and assuming that oxygen obeys Sievert's law up to saturation, the standard free energy of solution of molecular oxygen in liquid indium is calculated as View the MathML sourceΔG°= −51 440 + 8.07 T (±500) cal where the standard state for dissolved oxygen is an infinitely dilute solution in which activity is equal to atomic per cent. The effect of indium additions on the activity coefficient of oxygen dissolved in liquid copper was measured by a solid oxide galvanic cell. The interaction parameter ϵ0In is given by View the MathML source The experimentally determined variation of the activity coefficient of oxygen in dilute solution in Cu-In alloys is in fair agreement with that predicted by a quasichemical model in which each oxygen atom is assumed to be interstitially coordinated to four metal atoms and the nearest neighbour metal atoms are assumed to lose approximately half their metallic cohesive energies.

Solubility and activity of oxygen in liquid germanium and germanium copper alloys

The solubility of oxygen in liquid germanium in the temperature range 1233 to 1397 K, and in liquid germanium-copper alloys at 1373 K, in equilibrium with GeO2 has been measured by the phase equilibration technique. The solubility of oxygen in pure germanium is given by the relation R470 log(at. pct 0)=-6470/T+4.24 (±0.07). The standard free energy of solution of oxygen in liquid germanium is calculated from the saturation solubility, and recently measured values for the free energy of formation of GeO2, assuming that oxygen obeys Sievert’s law up to the saturation limit. For the reaction, 1/2 O2(g)→ OGe ΔG° =-39,000 + 3.21T (±500) cal = -163,200 + 13.43T (±2100) J. where the standard state for dissolved oxygen is that which makes the value of activity equal to the concentration (in at. pct), in the limit, as concentration approaches zero. The effect of copper on the activity of oxygen dissolved in liquid germanium is found to be in good agreement with that predicted by a quasichemical model in which each oxygen was assumed to be bonded to four metal atoms and the nearest neighbor metal atoms to an oxygen atom are assumed to lose approximately half of their metallic bonds.

Vapor pressure of liquid metals and alloys

The Gibbs-Bogoliubov formalism in conjunction with the pseudopotential theory is applied to the calculation of the vapour pressure of eight liquid metals from Groups I to IV of the periodic table and of alloys (Na-K). The calculated vapour pressure of the elements and their temperature dependencies, the partial pressures, activities and boiling points of the alloys are all found to be in reasonable agreement with measured data.

Solubility and activity of oxygen in liquid antimony

The solubility limit of oxygen in liquid antimony has been measured by a novel isopiestic technique in the temperature range 995--1175 deg K. The results can be expressed by the equation log c = --5500/T + 3.754 ( plus/minus 0.04) with c in at.% O and T in deg K. The oxygen potential over Sb + O alloys equilibrium with Sb2O3 has been measured by a solid state cell using a fully stabilized CaO.ZrO2 electrolyte. The cell was designed to contain the Sb + Sb2O3 mixture in a closed volume, that the vaporization of the oxide can be minimized and true equilibrium attained. The Gibbs free energy of the reaction 2 Sb(s) + 3/2 O2 = Sb2O3(s) is Delta G deg = --719560 + 274.51 T( plus/minus 500) and Sb(l) + 3/2 O2 = Sb2O3(l), Delta G deg = --704711 + ( plus/minus 500) ( Delta G deg in J/mole, T in deg K). The combination of these results with Sieverts' law yields the standard free energy of solution of oxygen in liquid antimony according to the reaction 1/2 O2 = \O\Sb,at.% as Delta G deg = --129620 + 14.23 T ( plus/minus 950). The standard enthalopy and entropy of the solution of oxygen in Sb are compared with values for other metal- oyxgen systems, and with the standard enthalpies of formation of corresponding oxides. The resulting correlations permit the estimation of the standard free energy of solution of oxygen in pure metals for which experimental information is lacking. 24 ref.--AA

Solubility and activity of oxygen in liquid manganese

The oxygen concentration of liquid manganese in equilibrium with MnAl2+2xO4+3x and α−Al2O3 has been determined in the temperature range 1520 to 1875 K. The oxygen content of quenched samples, wrapped in oxygen-free nickel foil, was determined by an inert gas fusion technique. The results are combined with accurate data now available on the Gibbs energies of formation of MnO and Al2O3−saturated MnAl2+2xO4+3x to derive the oxygen content of liquid manganese in equilibrium with MnO and the Gibbs energy of solution of diatomic oxygen gas in liquid manganese. The enthalpy and entropy of solution of oxygen in manganese are compared with similar data on other metal-oxygen systems.

A galvanic sensor for SO3/SO2 based on CaF2/CaSO4 couple

Measurements on the solid state cell, View the MathML source using single crystal CaF2 as the solid electrolyte and CaSO4 as an auxiliary electrode, indicate that the EMF is in agreement with that predicted by the Nernst equation when equilibrium is assumed in the gas phase near the electrodes. The cell can be used to measure the View the MathML source content of gases at temperatures near 1200 K, where approximately 2 h ate required to obtain a steady EMF, without the use of catalysts to improve the kinetics of exchange reaction in the auxiliary electrode. For most applications, the cell EMF will be affected by the presence of water vapour in the gas phase. The cell is well suited for thermodynamic measurements on sulfates, pyrosulfates and their solid and liquid solutions.

Measurement and modeling of Alloy-Spinel-Corundum equilibrium in the Ni-Mn-Al-0 system at 1873 K

The oxygen content of liquid Ni-Mn alloy equilibrated with spinel solid solution, (Ni,Mn)O. (1 +x)A12O3, and α-Al2O3 has been measured by suction sampling and inert gas fusion analysis. The corresponding oxygen potential of the three-phase system has been determined with a solid state cell incorporating (Y2O3)ThO2 as the solid electrolyte and Cr + Cr2O3 as the reference electrode. The equilibrium composition of the spinel phase formed at the interface of the alloy and alumina crucible was obtained using EPMA. The experimental data are compared with a thermodynamic model based on the free energies of formation of end-member spinels, free energy of solution of oxygen in liquid nickel, interaction parameters, and the activities in liquid Ni-Mn alloy and spinel solid solution. Mixing properties of the spinel solid solution are derived from a cation distribution model. The computational results agree with the experimental data on oxygen concentration, potential, and composition of the spinel phase.

Relation between Local Structure and Glass Forming Ability of Liquid Alloys

An attempt has been made to describe the glass forming ability (GFA) of liquid alloys, using the concepts of the short range order (SRO) and middle range order (MRO) characterizing the liquid structure.A new approach to obtain good GFA of liquid alloys is based on the following four main factors: (1) formation of new SRO and competitive correlation with two or more kinds of SROs for crystallization, (2) stabilization of dense random packing by interaction between different types of SRO, (3) formation of stable cluster (SC) or middle range order (MRO) by harmonious coupling of SROs, and (4) difference between SRO characterizing the liquid structure and the near-neighbor environment in the corresponding equilibrium crystalline phases. The atomic volume mismatch estimated from the cube of the atomic radius was found to be a close relation with the minimum solute concentration for glass formation. This empirical guideline enables us to provide the optimum solute concentration for good GFA in some ternary alloys. Model structures, denoted by Bernal type and the Chemical Order type, were again tested in the novel description for the glass structure as a function of solute concentration. We illustrated the related energetics of the completion between crystal embryo and different types of SRO. Recent systematic measurements also provide that thermal diffusivity of alloys in the liquid state may be a good indicator of their GFA.

Microstructure evolution and metastable phase formation in laser-ablation-deposited films of Ti5Si3 intermetallic compound

Thin films of Ti62.5Si37.5 composition were deposited by the pulsed-laser ablation technique on single-crystal Nad substrates at room temperature and on ′single-crystal′ superalloy substrates at elevated temperatures. Both vapour and liquid droplets generated by pulsed-laser ablation of the target become quenched on the substrate. Amorphization had taken place in the process of quenching of vapour-plasma as well as small liquid droplets on NaCl substrates at room temperature. In addition to the formation of Ti5Si3, a metastable fcc phase (a 0 = 0.433 nm) also forms in micron-sized large droplets as well as in the medium-sized submicron droplets. The same metastable fcc phase nucleates during deposition from the vapour state at 500°C and at 600°C on a superalloy substrate as well as during crystallization of the amorphous phase. The evolution of the metastable fcc phase in the Ti-Si system during non-equilibrium processing is reported for the first time.

Effect of liquid precursor pyrolysis on phase selection in the MgO-MgAl2O4 system

Aqueous solutions of Al and Mg nitrates have been spray pyrolysed at 673 K to synthesize powders with compositions varying between MgO and MgAl2O4. This has been carried out with the aim of studying phase selection and phase evolution in this system. The powders have been subsequently heat treated and the sequence of phases characterised by X-ray diffraction and transmission electron microscopy. Metastable extensions of the different phase fields have been calculated based on functions which predict the equilibrium phase diagram accurately. The appearance of phases is closely related to the temperature and to the non-stoichiometry in different compositional ranges of the system. The sequence of phase evolution has been correlated to the thermodynamics of nucleation in the system.

Glass, Gel, and Liquid Crystals: Arrested States of Graphene Oxide Aqueous Dispersions

Colloidal systems with competing interactions are known to exhibit a range of dynamically arrested states because of the systems' inability to reach its underlying equilibrium state due to intrinsic frustration. Graphene oxide (GO) aqueous dispersions constitute a class of 2D-anisotropic colloids with competing interactions long-range electrostatic repulsion, originating from ionized groups located on the rim of the sheets, and weak dispersive attractive interactions originating from the unoxidized graphitic domains. We show here that aqueous dispersions of GO exhibit a range of arrested states, encompassing fluid, glass, and gels that coexist with liquid-crystalline order with increasing volume fraction. These states can be accessed by varying the relative magnitudes of the repulsive and attractive forces. This can be realized by changing the ionic strength of the medium. We observe at low salt concentrations, where long-range electrostatic repulsion dominates, the formation of a repulsive Wigner glass, while at high salt concentrations, when attractive forces dominate, the formation of gels exhibits a nematic to columnar liquid-crystalline transition. The present work highlights how the chemical structure of GO hydrophilic ionizable groups and hydrophobic graphitic domains coexisting on a single sheet gives rise to a rich and complex array of arrested states.

Modeling of the non-isothermal liquid droplet impact on a heated solid substrate with heterogeneous wettability

A comprehensive numerical investigation on the impingement and spreading of a non-isothermal liquid droplet on a solid substrate with heterogeneous wettability is presented in this work. The time-dependent incompressible Navier-Stokes equations are used to describe the fluid flow in the liquid droplet, whereas the heat transfer in the moving droplet and in the solid substrate is described by the energy equation. The arbitrary Lagrangian-Eulerian (ALE) formulation with finite elements is used to solve the time-dependent incompressible Navier-Stokes equation and the energy equation in the time-dependent moving domain. Moreover, the Marangoni convection is included in the variational form of the Navier-Stokes equations without calculating the partial derivatives of the temperature on the free surface. The heterogeneous wettability is incorporated into the numerical model by defining a space-dependent contact angle. An array of simulations for droplet impingement on a heated solid substrate with circular patterned heterogeneous wettability are presented. The numerical study includes the influence of wettability contrast, pattern diameter, Reynolds number and Weber number on the confinement of the spreading droplet within the inner region, which is more wettable than the outer region. Also, the influence of these parameters on the total heat transfer from the solid substrate to the liquid droplet is examined. We observe that the equilibrium position depends on the wettability contrast and the diameter of the inner surface. Consequently. the heat transfer is more when the wettability contrast is small and/or the diameter of inner region is large. The influence of the Weber number on the total heat transfer is more compared to the Reynolds number, and the total heat transfer increases when the Weber number increases. (C) 2015 Elsevier Ltd. All rights reserved.

Oscillatory instability of Rayleigh-Marangoni-Bénard convection in two-layer liquid systems

The oscillatory behaviour of the Rayleigh-Marangoni-Bénard convective instability (R-M-B instability) regarding two combinations of two-layer fluid systems has been investigated theoretically and numerically. For the two-layer system of Silicone oil (10cSt) over Fluorinert (FC70), both linear instability analysis and 2D numerical simulation show that the instability of the system depends strongly on the depth ratio Hr = H1/H2 of the two-layer liquid. The oscillatory regime at the onset of R-M-B convection enlarges with reducing Γ = Ra/Ma values. In the two-layer system of Silicone oil (2cSt) over water, it loses its stability and onsets to steady convection at first, then the steady convection bifurcates to oscillatory convection with increasing Rayleigh number Ra. This behaviour was found through numerical simulation above the onset of steady convection in the case of r = 2.9, ε=(Ra-Ruc)/Rac = 1.0, and Hr = 0.5. Our findings are different from the previous study of the Rayleigh-Benard instability and show the strong effects of the thermocapillary force at the interface on the time-dependent oscillations at or after the onset of convection. We propose a secondary oscillatory instability mechanism to explain the experimental observation of Degen et al. [Phys. Rev. E, 57 (1998), 6647-6659].