Miscibility Gap Systems Research Articles

Phase Field Study of Discontinuous Precipitation in a Miscibility Gap System

AbstractA phase field model is developed to study the discontinuous (cellular) precipitation (DP) reaction in a hypothetical A-B miscibility gap system. Unlike previous treatments, the model employs an interaction energy term which couples the composition and the phase field variable to enable the necessary grain boundary movement. The influence of factors such as interaction energy, interfacial mobility and grain boundary diffusivity on the transformation rate and overall microstructure evolution are discussed.

A transmission electron microscopy study of discontinuous precipitation in the high misfit system (Ti,Zr)C

(Ti,Zr)C synthesized and aged in the immiscibility temperature range was investigated to improve understanding of the mechanism of phase separation, particularly the nucleation and early growth stages. The phase separation was observed to occur through discontinuous precipitation at grain boundaries. The nuclei were found enriched in titanium and associated with dislocations intersecting grain boundaries. During growth, zirconium enriched regions form subsequently and the semi-coherent interfaces of the Ti- and Zr-rich phases contain misfit dislocations. These observations suggest that dislocations play an important role for the nucleation and growth during discontinuous precipitation in the (Ti,Zr)C high misfit miscibility gap system.

First-principles calculation of sulfur–selenium segregation in ZnSe1−xSx: The role of lattice vibration

First-principles phase diagram calculations based on density functional theory within the generalized gradient approximation in combination with Monte Carlo (MC) techniques and cluster expansion were performed for the ZnSe1−xSx alloys. Formation energies were used as a basis for fitting cluster expansion Hamiltonians. All formation energies of ZnSe1−xSx alloys are positive, showing that ZnSe1−xSx alloys is a miscibility gap system and has a tendency to phase separation. For ZnSe1−xSx alloys the phase diagram computed with conventional cluster expansion shows a miscibility gap with consolute temperature Tc=327K. The contributions of lattice vibration reduce Tc to 281K (about 15%). We presented a MC study of the spatial distribution of S and Se in ZnSe0.5S0.5 alloys. We found that, the system becomes more homogeneous including lattice vibration at lower temperature. It is consistence with the calculation of phase diagram of ZnSe1−xSx alloys.

Phase equilibrium of a CuInSe2–CuInS2 pseudobinary system studied by combined first-principles calculations and cluster expansion Monte Carlo simulations

We report the phase diagram of a CuInSe2–CuInS2 pseudobinary system calculated by a combination of first-principles calculations based on density functional theory, cluster expansion, and Monte Carlo simulations. All formation energies of CuIn(Se1−xSx)2 (CISS) alloys are positive, indicating that CISS alloy is a miscibility gap system and has a tendency to phase separation. The phase diagram computed with conventional cluster expansion shows a miscibility gap with consolute temperature TC=170K. The contribution of lattice vibrations lowers TC to 130K. The miscibility gaps for the CuInSe2–CuInS2 system are predicted to be asymmetric. The effect of lattice vibrations on the miscibility gap is found to be large, and the size mismatch mechanism can be used to explain the large vibrational effect in the CuInSe2–CuInS2 system.

Effect of the ordering potential on the structure of liquid alloys

The concept of “ordering or alloying potential” (J. Hafneri: from Hamiltonians to phase diagrams: Springer Berlin 1987 and R. N. Singh and F. Sommerii Rep. Prog. Phys. 60 (1997) 57–150) enables the understanding of the different kind of alloys: hetero-coordinated one’s leading to compounds, homocoordinated ones leading to miscibility gap systems and substitutional alloys. The ordering potential is based on the comparison of identical atom interionic potentials (V11 and V22) and different atom interionic potential (V12) It allows the description of the demixing properties of some alloys. In order to understand the concepts, we developed our calculations by using a Lennard-Jones potential, the atomic structure being calculated by molecular dynamics simulation. We obtained surprising and unexpected results putting in evidence the time of simulation and the strength of the ordering potential.

Resistivity of the liquid gallium-lead miscibility gap system

We present our electrical resistivity measurements of the gallium-lead system which shows a very large miscibility gap between 2.4 and 94.5 at. % lead with a critical temperature of $606\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ and composition of 40 at. % lead. A small negative deviation of the experimental temperature coefficient of the resistivity (TCR) appears near the critical composition of the alloy. The resistivity of the alloys is interpreted and discussed in terms of the extended Faber-Ziman formula using the $t$-matrix formalism with hard-sphere and experimental (for pure metals only) structure factors. An approach is proposed, taking into account the information given by the experimental density of states which allowed us to explain the resistivity of pure lead and that of the liquid gallium-lead alloys. As a conclusion it was shown that two electrons in the conduction band of liquid lead better explain the experimental resistivity than four electrons.

The role of gravity during solidification processing in systems exhibiting a liquid-liquid miscibility gap

Liquid miscibility gap systems are characterized by a region in which two liquids, often with very different compositions and densities, are in thermodynamic equilibrium. Upon passing through such a region during solidification processing, the density difference between the two liquids promotes rapid separation, coalescence, and, subsequently, severe macrosegregation. With the intent of minimizing this density driven segregation, the microgravity environment of space has long been envisioned as an ideal processing arena. This paper briefly considers results from previous and new studies, both Earth (unit-gravity) and microgravity based. In view of the conclusions drawn, novel methods recently developed for processing hypermonotectic alloys, on Earth, are presented and the role of the microgravity environment is reexamined.

Composite growth in hypermonotectic alloys

The feasibility of solidifying uniformly aligned composites from alloys of hypermonotectic composition was investigated through the use of organic analogues and a directional solidification temperature gradient stage. Previously demonstrated macrostructurally detrimental effects due to coalescence and/or preferential wetting (or lack of) by the excess LII phase have been taken advantage of by the inclusion of constrained fibers aligned parallel to the growth direction. Upon passing through the miscibility gap,L II droplets are shown to attach and grow along the fibers prior to the monotectic reaction, resulting in a uniform composite. The results of different fiber materials in combination with “wetting” and “nonwetting” miscibility gap systems are presented and discussed in reference to processing in a microgravity environment.

Solidification behavior of impurity-doped succinonitrile solutions in high-surface area, low-bulk volume containers

Differential scanning calorimetry (DSC) of fast-quenched succinonitrile-water solutions has shown interesting undercooling characteristics. Degree of undercooling during fast-quenches of solutions that are near monotectic is partly a function of equilibration temperature in cells having high surface: bulk volume ratios. These experiments were performed in hydrophilic cells where the dopant, water, preferentially wets the wall. The explanation of these phenomena is consistent with preferred homogeneous solution aggregates at various temperatures, and temperature dependent relative adsorption in miscibility-gap systems. Additionally, directional solidification of succinonitrile-based solutions in narrow path-length cells shows evidence of bulk morphology dependence on cell surface properties. To supplement the DSC data, Fourier transform infrared (FTIR) spectra were taken using a zinc selenide attenuated total reflectance (ATR) cell. Spectra were taken at various temperatures and concentrations in succinonitrile-rich and water-rich homogeneous solutions.

Modeling of collision and coalescence of droplets during microgravity processing of Zn-Bi immiscible alloys

A population balance model is presented for the coarsening of the dispersed phase of liquid-liquid two-phase mixtures in microgravity due to gravity sedimentation and Marangoni migration, which lead to the collision and coalescence of droplets. The model is used to predict the evolution of the size distribution of the dispersed phase in a liquid-phase miscibility gap system, Zn-Bi, which has been used in a number of experimental microgravity processing studies in which significant phase segregation has been observed. The analysis shows that increasing the temperature gradient, gravity level, volume fraction of the dispersed phase, initial average drop radius, initial standard deviation of droplet radii, or the temperature coefficient of the interfacial tension leads to an increase in the rate of droplet growth due to collision and coalescence. Comparison of the distribution evolutions for unimodal and bimodal initial distributions shows that the latter yield significantly more rapid droplet growth. Finally, it is shown that droplet growth can be dramatically reduced with antiparallel orientation of the gravity vector and the temperature gradient, provided that the relative magnitude of these two vectors is properly chosen.

Crystallization microstructure in transparent monotectic alloys

Transparent binary metallic alloy models are important in material and metallurgical science, as phase transformations and processes can be observed during solidification. The best transparent models for metallic growth and solidification morphology studies are members of the ‘plastic’ crystals group. These compounds have low entropies of fusion and cubic crystal structures, resulting in nonfaceted solid/liquid interfaces1,2. We describe here the surprising morphology which occurs at the Hquid1/liquid2/solid (L1/L2/S) triple junction in directionally solidifying miscibility gap systems at the monotectic temperature. The monotectic temperature in a binary mixture is the temperature at which two immiscible solutions of the same two components form phases in equilibrium with the solid phase of one of the components. These observations were made on succinonitrile (sn)-based systems (C4H4N2, the ‘plastic’ crystal component, with a second component) on a thermal gradient microscope apparatus3–5. Figure 1 shows two succinonitrile-based monotectic phase diagrams used in this study. The specimen cells contained sample gaps ranging from 50 to 150 μm, temperature gradients from 5 to 70° Ccm−1, and growth rates from 0.75 to 10.0 μm s−1.

Optical studies of a binary miscibility gap system

Model transparent fluids are being studied to develop a better understanding of phase separation processes in binary miscibility gap metal alloys. The model selected for the reported work is diethylene glycol-ethyl salicylate. This system is well characterized with respect to its phase diagram, density, surface and interfacial tensions, viscosity, and other pertinent physical properties. Minority phase growth, coalescence, and droplet motions are observed using holographic microscopy which is capable of recording particle densities up to 10 7 particles/cm 3 and is able to resolve particles as small as 2 to 3 μm in diameter throughout the entire volume of the test cell. Sequential holograms allow determination of droplet size distribution changes throughout the total volume with respect to time and temperature. This allows a direct method for testing various theories of droplet growth and ripening phenomena.

The formation of aligned spheres in miscibility gap systems

During directional solidification of monotectic systems, two types of aligned structures are obtained. The second constituent appears as rods when the temperature gradient ( G) to growth rate ( R) ratio is large. It appears as rows of spheres when the G R ratio is small. The occurrence of these structures can be explained in terms of interface breakdown and capillary instability mechanisms between two liquid phases.

The gibbs surface excess in binary miscibility gap systems

The Gibbs surface excess in the homogeneous region of the phase diagram was measured in the ethyl salicylate-diethylene glycol system and the hexane-aniline system. Both systems contain a liquid miscibility gap in their phase diagram. Surface excess was determined by measurements of surface tensions and activity coefficients for a number of solutions and by application of Gibbs' adsorption equation. It was found that the component of lower surface tension is always the surface-active species, and that its surface excess increases as solutions approach the conditions of the consolute point. The maximum surface excess does not occur directly above the consolute point, but is slightly shifted toward the component of higher surface tension. The surface excess in these systems was found to be qualitatively predicted by the two-surface-layer regular solution model. It is proposed that the degree of adsorption and micelle formation can be estimated from the position of the eutectic point on the phase diagram.

Experimental test of classical nucleation theory in a liquid-liquid miscibility gap system

The classical formulation of homogeneous nucleation theory has been tested in the methylcyclohexane-perfluoromethylcyclohexane liquid-liquid gap miscibility system. The theory was found to be invalid for temperatures above 35°C. The discrepancy between theory and experiment (critical undercoolings are predicted which are less than those observed) can not be explained by simple modifications of the theory. These results confirm the discrepancy found by Sundquist and Oriani.

Mass spectrometric study of the thermodynamic properties of solid Au−Pt alloys

The ratios of vapor pressures of gold in equilibrium with liquid gold and with each of eleven Au−Pt alloys have been measured over the approximate temperature range of 1340° to 1520°K by means of a dual-chamber effusion cell and a mass-spectrometric detection system. From these ratios, thermodynamic activities and related integral and partial molar thermodynamic quantities have been evaluated at 1423°K. When the thermodynamic quantities are referred to a hypothetical standard state of superheated gold at 1423°K, the results indicate both substantial positive deviations from ideal behavior and positive molar heats of mixing as is expected for miscibility-gap systems. The integral moalr quantities are adequately predicted by either the subregular or the Lumsden model. Observed integral entropies are discussed in terms of thermal, electronic, and configurational contributions, whereas the positive integral molar free energies are tentatively attributed to strain effects arising from ion-core repulsions.

Thermodynamics of a miscibility gap system and a test of nucleation theory

In an earlier paper an attempt was made to perform a critical test of nucleation theory for condensed systems using the miscibility gap system methylcyclohexane + perfluoromethylcyclohexane (C7H14+C7F14) and the equation for the thermodynamic free energy of mixing derived by Dyke, Rowlinson and Thacker from their vapour pressure measurements. Because these equations are not fully consistent with the phase diagram it was necessary to modify them in an arbitrary manner for application to the nucleation problem. A more complete analysis of the vapour pressure data of Dyke et al. has now been performed. The newly-derived free energies of mixing are sufficiently consistent with the phase diagram that no correction need be applied. Using these new free-energy-of mixing functions in the test of nucleation theory leads to the same conclusion as reached earlier, i.e., verification of the corrected nucleation theory.

Homogeneous Nucleation in a Miscibility Gap System. A Critical Test of Nucleation Theory

A critical test of the classical nucleation theory applied to condensed phases has been carried out for the liquid miscibility gap system, methylcyclohexane-perfluoromethylcyclohexane (C7H14–C7F14). The densities of, and the interfacial free energies between the coexisting liquid phases have been measured as a function of temperature. The interfacial free energy is found to vary as the 32 power of the critical temperature Tc, less the experimental temperature, and these data are used to calculate the gradient energy parameter κ in the Cahn-Hilliard theory of nucleation. The magnitudes of the relevant parameters are such that the Cahn-Hilliard theory reduces to the classical theory for the present system. These data, together with literature data on the thermodynamic properties of the bulk solutions, enable the degree of undercooling for a sensible nucleation rate to be calculated from classical theory. The experimentally determined undercoolings necessary to nucleate the C7H14-rich phase from the solution are found to be much greater than those predicted by the classical theory by factors ranging from 8.5 at 10 deg below Tc to 340 at 0.3 deg below Tc. These very large discrepancies are attributable to the breakdown of the traditional approximation in the classical nucleation theory that the number of molecules involved in the embryo population is a negligible fraction of the number of molecules in the system. When this approximation is avoided, the very complicated expression that results can be evaluated for the present case, leading to reasonable agreement between the predicted and the observed undercoolings. This is believed to constitute a satisfactory verification of the ``corrected'' classical theory of nucleation for condensed systems. The ``embryo population'' factor can be neglected in homogeneous nucleation in solidification and condensation (except near the critical temperature) and in most of the corresponding cases of heterogeneous nucleation. However, it is extremely important for nucleation in miscibility gap systems, or in any system in which the properties of the parent and daughter phases become identical at a critical temperature.