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Monotectic solidification
Abstract
The solidification mechanism of melts of monotectic composition is considered. It is shown that important microstructural differences can arise as a result of changes in the relative magnitudes of the interfacial energies between the two liquids and the solid substrate. Conflicting results from previous publications are rationalized by the present theory.
... The results show that, contrary to what some authors have assumed [4,14,17,24,51] the growth of a monotectic alloy is not like eutectic, because although two phases grow side by side simultaneously, the thermocapillary effect acts in some cases, making the law proposed by [23] not valid. In their studies, [14] had already shown this fact when they developed their model for monotectic behavior, as well as [52], also in the development of their model. ...
Monotectic alloys show promising applications in wear-resistant automotive components, once these systems have remarkable self-lubricating properties that are of great interest for using in bearings. Much research has been devoted to better comprehend monotectic reactions. Some studies assume that the interphase spacing evolution in monotectic alloys follows the classical relationship used for eutectics or the dendritic growth relationship; however, some studies reported that the growth laws seem not to be valid for some cases. Because of that, obtaining single mathematical expressions that allow describing the development of solidification structures as a function of thermal parameters is very important. Based on the above, this chapter proposes a systematic analysis of the monotectic growth laws proposed in the literature and suggests exclusive growth laws as a function of solidification parameter for monotectic alloys solidified under different heat extracting configurations.
... In our case, the density of the drop substance ρ 2 is more than that of the liquid matrix phase ρ 1 , so the resultant of gravity and buoyancy forces will push it to the front. The second liquid wets the crystal, if the condition [26] is satisfied: σ are the coefficients of surface tension at the interface "solid phase 1 -liquid phase 2", "solid phase 1 -liquid phase 1", and "liquid phase 1 -liquid phase 2", respectively. In this case, the approaching front captures a drop. ...
Solidification of liquating silicate magmatic melts may lead to formation of rare earth mineral deposits. By the example of quasi-binary system SiO2–Sc2O3, the processes of cooling and directional solidification of the melt in an intrusive chamber have been studied, and velocities of the phase fronts and the width of the phase separation field have been calculated. Using the fluctuation approach, the physical and mathematical model of the formation and growth of dispersed phase in the continuous cooling of liquating melt was developed, and the conditions of incorporating the dispersed inclusions by solidified matrix phase were determined. The proposed model allows obtaining quantitative estimates of the size and number of inclusions per unit of hardened rock, depending on the solidification conditions and the initial chemical composition of the melt.
... After that, one of the immiscible liquid phases will float or sedimentate due to the action of large density difference between the two phases. This is known as Stokes sedimentation [3,4]. If this occurs, the obtained immiscible alloy will be useless. ...
... The correlation between eutectic spacing and growth rate is presented inFig. 12 for different experiments extracted from the literature43444546. In this figure, the gray and white points correspond to the results obtained by other authors in Al–Cu alloys and the red points correspond to the results obtained in the present research. ...
Providing benchmark data of the thermal and metallographic parameters during the columnar-to-equiaxed transition (CET) in a wide range of alloy concentrations is of fundamental importance for understanding this phenomenon as well as for metallurgical and modeling purposes. The aim of this study was to investigate the columnar-to-equiaxed transition (CET) in aluminum–copper alloys of different compositions covering a wide range from 2 to 33.2 wt%Cu (eutectic composition), which were directionally solidified from a chill face. The thermal parameters studied included recalescence, cooling rates, temperature gradients and interphase velocities. We found that the temperature gradient and velocity of the liquidus interphase reached critical values at the CET; these critical values were between −0.44 and 0.09 K/mm and between 0.67 and 2.16 mm/s, respectively. The metallographic parameters analyzed were grain size, primary and secondary dendritic arm spacing and also eutectic spacing. The results obtained were compared with previous experimental studies, published predictions and models of the CET for similar alloys.
Directional solidification of Zn-0.63 at.% Bi monotectic alloys at different growth rates with and without a 5-T high static magnetic field (HSMF) was studied. Regardless of whether an HSMF was applied, the solid–liquid (S–L) interface changed in a consistent manner with increasing growth rate. The HSMF affected the S–L interface morphology and solidified microstructure by suppressing melt convection above the S–L interface. Two mechanisms led to the formation of strings of droplets. One was the Rayleigh instability of fibres caused by the bulk diffusion process as a result of the minimisation of the total interfacial energy of the system. The HSMF improved the stability of the fibre phase by reducing the interfacial energy, thereby helping to process material with a complete fibre-coupled growth structure, which has a greater specific surface area. The other was that constitutional instability at the S–L interface only existed when the growth rate was 3 μm/s under a 5-T HSMF. A revised stability-limit-diagram model was mapped to reveal solidification mechanism in monotectic systems. This work offers a new approach for processing functional monotectic alloy materials in the future.
In the present study, we employ a multiphase-field model based on the grand chemical potential formulation to simulate the microstructural transition in a binary FeSn monotectic alloy. In a directional solidification environment, we systematically investigate the formation of monotectic microstructures. At equilibrium monotectic composition, we observe that depending on the imposed temperature gradient and the solidification velocity, the liquid L2 phase transforms into an array of droplets embedded in the solid phase matrix. Initiated at the solidification front, the minor liquid phase undergoes detachment and spherodization to form L2 droplets as a result of post-solidification ripening behind the growth front. We show that the wavelength of the oscillating phase is critical to observe a lamellar to droplet transition. A microstructural selection map at various growth conditions is delineated to illustrate the different monotectic microstructures. The present phase-field simulations, while providing significant insights into the formation of microstructures closes the gap with the in-situ observations reported earlier. In addition, the influence of lamellar spacing is investigated in detail through the Jackson and Hunt analytical relationship for the present material system.
Immiscible alloys gained a considerable interest in last decades due to their valuable properties and potential applications. Many experimental and theoretical researches were carried out worldwide to investigate the solidification of immiscible alloys under the normal gravity and microgravity condition. The objective of this article is to review the research work in this field during the last few decades.
High temperature gradient is employed under the directional condition to examine the influence of the ratio of gradient to solidification rate, G/R, on the microstructure of Al-17.5%In (mass fraction) alloys. The experimental results show that the microstructure evolution of monotectic alloy under the directional solidification is similar to the one of eutectic alloy. When steady growth is formed, there exists an In-rich zone in the front of α phase and vice versa. The diffusion process plays a dominate role in the steady growth due to the small lamella distance. Unidirectional solidification microstructure of the alloys changes from fibrous structure to regular droplet-like array and finally random dispersion of In droplets in the aluminum matrix with increasing growth rate or decreasing temperature gradient. The change suggests that the transition of monotectic solidification structure has a closed relation to the morphological transition of solid-liquid interface.
Some of the first reported directional solidification experiments in immiscible alloy systems were carried out in the 1960s. Questions about the results of these experiments arose almost immediately due to conflicting findings between investigators. Later work revealed that several factors that were usually not considered critically important, especially the interfacial energy relationships between phases, could have a dramatic influence on the type of microstructure produced in immiscible alloy systems. During the 1980s, much effort was put into studying the influence of the interfacial energy relationships between phases on the types of microstructures produced. However, some of the findings raised new questions. In the mid 1990s and continuing through today, most efforts have focused on modeling the monotectic growth process and on obtaining steady state coupled growth conditions in hypermonotectic alloys. This paper focuses on some of the advances that have been made to date in understanding solidification in immiscible alloy systems and some of the questions that still need to be answered today. © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
A review of alloy solidification is given that spans the range of physical processes from atomic to macroscopic phenomena. Particular emphasis is given to the formation of alloy microstructure on the scale that is relevant to control, manipulate and/or improve the properties of cast materials. Topics include: heat transfer and chemical diffusion, thermodynamics, nucleation, liquid-solid interface kinetics, growth with planar/cellular/dendritic liquid-sold interface shapes, dendritic microsegregation and eutectic solidification. Where possible, solidification of ternary and higher order systems is included. The description of cast structure includes factors the affect grain size, macrosegregation, porosity and inclusion formation. Developing and emerging manufacturing methods that involve solidification are briefly described.
Unidirectional solidification experiments with monotectic and near monotectic Cu-Pb alloys have been performed with the growth direction both parallel and antiparallel to the gravity vector. It was found that a more regular composite structure was possible to achieve in the samples solidified parallel to the gravity vector. It was also found that the amount of lead rich phase, regularily incorporated in the structure, was less than one would expect theoretically. It is proposed that monotectic alloys can solidify to two different kinds of composite structures. One, which can be described by the theory of coupled growth of a rod eutecticum, and the other similar to the growth of primary rods.
Studies have been made of the microstructures developed in directionally solidified monotectic Al-In, Al-Bi and Zn-Bi alloys, as a function of growth velocity and temperature gradient. With increasing growth velocity and decreasing gradient the microstructures show transitions from regular rod-like arrangements of the lower melting point phase, through arrays of aligned droplets to coarse irregular droplet dispersions. Intermediate stages show rods with longitudinal shape perturbations of a classic Rayleigh-type instability. The changes are discussed in terms of oscillatory instabilities at the solid-liquid interface (enhanced by increasing growth velocity and decreasing temperature gradient) coupled with ripening effects in the solid + liquid region behind the interface.
The morphology of directionally solidified CuAl-Pb monotectic alloys has been studied. The structure consisted of a hexagonal array of Pb rods in a Cu-based matrix. In addition, elongated grain boundaries in the Cu-based matrix with lens-shaped Pb fibers on the boundary and a “denuded zone”, depleted of Pb rods, were observed. Existence of these boundaries is shown to reduce the overall surface energy of the system leading to the formation of the elongated grain boundaries.
Direct observation of the controlled melting and solidification of succinonitrile was conducted in the glovebox facility of the International Space Station (ISS). The experiment samples were prepared on ground by filling glass tubes, 1 cm ID and approximately 30 cm in length, with pure succinonitrile (SCN) in an atmosphere of nitrogen at 450 millibar pressure for eventual processing in the Pore Formation and Mobility Investigation (PFMI) apparatus in the glovebox facility (GBX) on board the ISS. Real time visualization during controlled directional melt back of the sample showed nitrogen bubbles emerging from the interface and moving through the liquid up the imposed temperature gradient. Over a period of time these bubbles disappear by dissolving into the melt. Translation is stopped after melting back of about 9 cm of the sample, with an equilibrium solid-liquid interface established. During controlled re-solidification, aligned tubes of gas were seen growing perpendicular to the planar solid/liquid interface, inferring that the nitrogen previously dissolved into the liquid SCN was now coming out at the solid/liquid interface and forming the little studied liquid = solid + gas eutectic-type reaction. The observed structure is evaluated in terms of spacing dimensions, interface undercooling, and mechanisms for spacing adjustments. Finally, the significance of processing in a microgravity environment is ascertained in view of ground-based results. Copyright © 2005 by the American Institute of Aeronautics and Astronautics. All rights reserved.
In4Se3 has been recently found to be a layered compound showing promising thermoelectric (TE) properties. In the present study, the textured In4Se3-based material grown by zone melting technique is found to be a composite with elemental indium embedded in the In4Se3 matrix. The TE properties of this composite are evaluated and a maximum figure of merit ZT of 0.9 is achieved in the direction perpendicular to the growth direction. Such result should provide a useful guidance of composition control for further ZT-enhancement in this material.
Early solidification experiments in immiscible alloy systems almost immediately led to conflicting findings between investigators. Investigations revealed that several factors usually considered unimportant, especially the interfacial energy relationships between phases, could have a dramatic influence on the types of microstructures produced in immiscible alloy systems. During the 1980s, work concentrated on the influence interfacial energy on microstructure. However, some findings raised new questions. In the mid 1990s and continuing through today, most efforts have focused on modeling the monotectic growth process and on obtaining steady state coupled growth conditions in hypermonotectic alloys. This paper focuses on some of the advances that have been made to date in understanding solidification in immiscible alloy systems and some of the questions that remain to be answered.
Planar, cellular and dendrite morphologies were observed at different concentrations in the directional solidification of Cu-Pb monotectic alloys. In Cu-Pb hypomonotectic alloys, the directional solidification microstructure changes from columnar dendrite to the irregular rod composite structure with increasing lead content and growth rate. In Cu-Pb hypermonotectic alloys, the structure changes from the band structure and elongated droplets to irregular rod composite structure with increasing growth rate. The range of composition of forming the rod composite structure around the monotectic points increases with the increasing growth rate. The transient morphology of Cu-Pb alloys in the directional solidification was obtained. The solid/liquid interface of Cu-Pb alloys presents planar and the second liquid droplets are pushed by growing front under the high temperature gradient With increasing growth rate or decreasing temperature gradient the planar interface becomes unstable and the cellular structures with L2 phase at the cell boundaries are developed.
In this article, we present two models to simulate solidification morphologies in monotectic alloys. With the first model, we investigate the morphological evolution under the influence of spinodal decomposition. The model requires that a gradient energy contribution for the concentration field should be incorporated, in order to stabilize phase separation when the liquid concentration is inside the region of miscibility gap. The free energy of the system in this model is derived from direct interpolation of the bulk energy densities. This, however, results in simulation regions in nanometer scale due to contributions from the chemical free energy of the system to the total surface excess. With the second model, our purpose is to develop a phase-field model to simulate scales that are larger than nanometer, where the departures from equilibrium are very small resulting in phase concentrations outside the spinodal region. In view of this, we exclude the concentration gradient contribution to the grand chemical potential functional, and develop a model based on [M. Plapp, Phys. Rev. E 84, 031601 (2011); A. Choudhury and B. Nestler, Phys. Rev. E 85, 021602 (2012)]. The advantage is that the free energy excess across the interface at equilibrium disappears, and hence it is easier to derive the required surface energies with higher interface widths. Due to this benefit, we employ the method to simulate the dynamic entrapment process in the monotectic reaction and study the influence of liquid(1) - liquid(2) surface energy and undercooling on the entrapment process.
Solid–liquid phase equilibrium data of three binary organic systems, namely, 3-hydroxybenzaldehyde (HB)—4-bromo-2-nitroanilne (BNA), benzoin (BN)—resorcinol (RC) and urea (U)—1,3-dinitrobenzene (DNB), were studied by the thaw–melt method. While the former two systems show the formation of simple eutectic, the third system shows the formation of a monotectic and a eutectic with a large immiscibility region where two immiscible liquid phases are in equilibrium with a liquid of single phase. Growth kinetics of the pure components, the monotectic and the eutectics, studied by measuring the rate of movement (v) of solid–liquid interface in a thin U-tube at different undercoolings (ΔT) suggests the applicability of the Hillig–Turnbull’s equation: v = u (ΔT)n
, where v and n are the constants depending on the nature of the materials involved. The thermal properties of materials such as heat of mixing, entropy of fusion, roughness parameter, interfacial energy, and excess thermodynamic functions were computed from the enthalpy of fusion values, determined by differential scanning calorimeter (Mettler DSC-4000) system. The role of solid–liquid interfacial energy on morphologic change of monotectic growth has also been discussed. The microstructures of monotectic and eutectics were taken which showed lamellar and federal features.
The key physical parameters for nucleation of a second liquid phase in Al–Bi and Al–Pb monotectic liquids have been measured. The
density of coexisting liquid phases, the interfacial tension between them, and the contact angle of the liquid–liquid interface on ZrO2 and TiB2 ceramics have been determined as a function of temperature. The contact angle data suggest that Al2O3, ZrO2, and TiB2 particles can act as centres for heterogeneous nucleation of the minority liquid phase in Al–Pb and Al–Bi immiscible alloys. Casting experiments
on the alloy Al91Pb9 (wt.%) show that the maximum size of the liquid phase droplets decreases, and their population increases, upon addition of inoculants.
Fe–48.8wt.% Sn monotectic alloy was rapidly solidified both in a drop tube and with the glass fluxing method, and its phase separation characteristics and structural evolution are investigated. The regime of cooling rate of different size droplets in the drop tube is calculated from 7.0×102 to 2.8×104 K s−1 with a decrease of droplet diameter from 800 to 100 μm. The effect of Marangoni migration is more significant than that of Stokes motion with the decrease of gravitational acceleration, but it has a weak influence on the dispersion of the second liquid phase. The immiscibility gap is calculated and it shows that spinodal decomposition is difficult to occur because the necessary undercooling is quite large. Nucleation and growth show different characteristics when droplet size varies. Although the Sn-rich liquid phase separates from the undercooled melt, it cannot change significantly the composition of parent liquid phase, and the growth of terminal composition solid is suppressed, which is confirmed by the measured and calculated dendritic growth velocity by bulk undercooling experiments with the glass fluxing technique. Well-branched dendrites of the solid phase are difficult to form during monotectic transformation when droplets solidify in the drop tube owing to the very short solidification period.
It is shown that in a binary system where solid is in equilibrium with two immiscible liquids at a monotectic, crystal growth can take place without any diffusive segregation and constitutional supercooling does not occur.
A two-liquid region has been found in the Hg-Te system and the growth processes are illustrated by the results of directionally freezing HgTe melts. The growth of (Hg, Cd)Te and (Hg, Mn)Te solid solutions is also discussed, and to explain inhomogeneity it is suggested that the segregation coefficients depend on crystal orientation. Other materials might be grown by the two-liquid method, but there is insufficient evidence about the phase diagrams.
The interaction between particles and an advancing solid‐liquid interface has been investigated both experimentally and theoretically. For each particular type of particle, a ``critical velocity'' was observed, below which the particles are rejected by the interface, and above which they are trapped in the solid. The dependence of the critical velocity on various properties of matrix and particle was investigated. A theory has been developed, based on the assumption that a very short‐range repulsion exists between the particle and the solid. This repulsion occurs when the particle‐solid interfacial free energy is greater than the sum of the particle‐liquid and liquid‐solid interfacial free energies. The particle is pushed along ahead of the advancing interface and becomes incorporated into the solid if liquid cannot diffuse sufficiently rapidly to the growing solid behind the particle. Reasonable agreement was obtained between the calculated and experimentally observed critical velocities.