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This paper deals with the one-phase, undercooled Stefan problem, in space dimension N = 2. We show herein that planar, one-dimensional blow-up behaviours corresponding to the undercooling parameter Delta = 1 are unstable with respect to small, transversal perturbations, The solutions thus produced are shown to generically generate crisps in finite time, when they exhibit an undercooling Delta = 1 - O(c) < 1, where 0 < c << 1, and epsilon is a parameter that measures the strength of the perturbation. The asymptotic behaviour of solutions and interfaces near their cusps is also obtained. All results are derived by means of matched asymptotic expansions techniques., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

Phase relations of a tephritic lava erupted at La Palma, Canary Islands, the 2nd of October 2021, during the eruption of Cumbre Vieja volcano were determined experimentally in the temperature/water content space, T (°C)/H2O (wt%). The crystallisation experiments were carried out at a fixed pressure of 275 MPa for temperatures varying from 1000 to 1200 °C and with H2O added contents ranging from 0 to 5 wt%. Results from the synthetic products are compared with those obtained from thermodynamic simulations and with the natural phases to constrain the pre-eruptive conditions of the tephritic magma stored in the shallow reservoir. The major phases (clinopyroxene + olivine + oxides) occurring in the natural products were reproduced. The experimental results combined with thermodynamic modelling allow us to constrain the pre-eruptive temperature to ∼1100 °C considering H2O to 3 wt% and to restrict the crystallisation of plagioclase at low pressures (< 20 MPa). The results indicate that, under the presence of a pure H2O fluid, amphibole is stable at pressures higher than 300 MPa and temperatures ∼1000 °C. Our results on pre-eruptive conditions of the 2021 Tajogaite eruption provide important constraints on mechanisms of storage and transport in primitive alkaline magmas.

A theory of stable dendrite growth in an undercooled binary melt is developed for the case of intense convection. Conductive heat and mass transfer boundary conditions are replaced by convective conditions, where the flux of heat (or solute) is proportional to the temperature or concentration difference between the surface of the dendrite and far from it. The marginal mode of perturbation wavelengths is calculated using the linear morphological stability analysis. Combining this analysis with the solvability theory, we have derived a selection criterion that represents the first condition to define a combination of dendrite tip velocity and tip diameter. The second condition—the undercooling balance—is derived for intense convection. The theory under consideration determines the dendrite tip velocity and tip diameter for low undercooling. This convective theory is combined with the classical theory of dendritic growth (conductive boundary conditions), which is valid for moderate and high undercooling. Thus, the entire range of melt undercooling is covered. Our results are in good agreement with experiments on Al–Ge crystallization. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.

This article proposes an analytical model to understand the rod growth of eutectic in the bulk undercooled melt. Based on the previous derivations of the lamellar eutectic growth models, relaxing the assumptions of small Péclet numbers, the model is derived by considering melt kinetic and thermal undercoolings. The intent of this model is to predict the transitions in eutectic pattern for conditions of the low and high growth velocities. In addition to investigation of the transition between lamellar and rod eutectic patterns, mathematical simplifications of solving Bessel function are presented as well, which is the most important priority to model calculation. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.

Time- and temperature-resolved phase formation in the equiatomic NbTiVZr refractory high-entropy alloy has been studied in situ using high-energy synchrotron X-ray diffraction and high-speed video imaging during non-equilibrium solidification. Phase formation is shown to be dependent on the solidification conditions. When the melt is undercooled over 80 K it crystallizes as a bcc single-phase solid solution despite solute partitioning between dendrites and interdendritic regions. When the sample is for some time kept in the semisolid state, two additional bcc phases form in the interdendritic regions. The crystal growth velocity for the NbTiVZr alloy, as estimated from the high-speed videos, shows pronounced sluggish kinetics.

Motivated by an important application of dendritic crystals in the form of an elliptical paraboloid, which widely spread in nature (ice crystals), we develop here the selection theory of their stable growth mode. This theory enables us to separately define the tip velocity of dendrites and their tip diameter as functions of the melt undercooling. This, in turn, makes it possible to judge the microstructure of the material obtained as a result of the crystallization process. So, in the first instance, the steady-state analytical solution that describes the growth of such dendrites in undercooled one-component liquids is found. Then a system of equations consisting of the selection criterion and the undercooling balance that describes a stable growth mode of elliptical dendrites is formulated and analyzed. Three parametric solutions of this system are deduced in an explicit form. Our calculations based on these solutions demonstrate that the theoretical predictions are in good agreement with experimental data for ice dendrites growing at small undercoolings in pure water. © 2021 IOP Publishing Ltd.

The paper deals with the analysis of stable thermo-solutal dendritic growth in the presence of intense convection. The n-fold symmetry of crystalline anisotropy as well as the two- and three-dimensional growth geometries are considered. The steady-state analytical solutions are found with allowance for the convective-type heat and mass exchange boundary conditions at the dendritic surface. A linear morphological stability analysis determining the marginal wavenumber is carried out. The new stability criterion is derived from the solvability theory and stability analysis. This selection criterion takes place in the regions of small undercooling. To describe a broader undercooling diapason, the obtained selection criterion, which describes the case of intense convection, is stitched together with the previously known selection criterion for the conductive-type boundary conditions. It is demonstrated that the stitched selection criterion well describes a broad diapason of experimental undercoolings. © 2020 John Wiley & Sons, Ltd.

The solid-phase pattern in the form of a dendrite is one of the frequently met structures produced from undercooled liquids. In the last decades, an analytical approach describing the steady-state crystal growth in the presence of conductive heat and mass transport has been constructed. However, experimental works show that crystal patterns frequently grow in the presence of convection. In this paper, a theoretical description based on convective heat and solute concentration transport near the solid/liquid phase interface is developed. The stable regime of crystallization in the presence of vigorous convection near the steady-state crystal vertex is studied. The stability analysis, determining the stable growth mode, and the undercooling balance law have been applied to deduce the stable values for the growth rate and tip diameter. Our analytical predictions (with convective transport) well describe experimental data for a small melt undercooling. Moreover, we compare both convective and conductive mechanisms in the vicinity of the crystal vertex. Our theory shows that convective fluxes substantially change the steady-state growth of crystals. © 2021 Institute of Physics Publishing. All rights reserved.

The theory of stable dendritic growth within a forced convective flow field is tested against the enthalpy method for a single-component nickel melt. The growth rate of dendritic tips and their tip diameter are plotted as functions of the melt undercooling using the theoretical model (stability criterion and undercooling balance condition) and computer simulations. The theory and computations are in good agreement for a broad range of fluid velocities. In addition, the dendrite tip diameter decreases, and its tip velocity increases with increasing fluid velocity. © 2020, The Author(s).

Kinetics of crystal growth in undercooled melts is analyzed by methods of theoretical modeling. Special attention is paid to rapid growth regimes occurring at deep undercoolings at which non-linearity in crystal velocity appears. A traveling wave solution of the phase field model (PFM) derived from the fast transitions theory is used for a quantitative description of the crystal growth kinetics. The "velocity - undercooling" relationship predicted by the traveling wave solution is compared with the data of molecular dynamics simulation (MDS) which were obtained for the crystal-liquid interfaces growing in the 100-direction in the Ni50Al50 alloy melt. © Published under licence by IOP Publishing Ltd.

Boundary conditions for the solid–liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases are taken at the interface and the quantities characterizing interfacial surface such as the surface temperature and the surface heat flux. Introduction of the surface temperature as an independent variable allows us to describe the scattering energy at the interface. For the steady-state motion of the planar interface the expression for the temperature discontinuity across the phase boundary has been obtained. Effect of Kapitza resistance on the interface velocity is considered. It is shown that heat resistance leads to non-linearity in solidification kinetics, namely, in “velocity-undercooling” relationship. The conditions of the steady-state motion of the planar interface have been found. © 2017 Elsevier B.V.

Melt flow is often quoted as the reason for a discrepancy between experiment and theory on dendritic growth kinetics at low undercoolings. But this flow effect is not justified for glass-fluxed melts where the flow field is weaker. In the present work, we modeled the thermal history, flow pattern and dendritic structure of a glass-fluxed nickel sample by magnetohydrodynamics calculations. First, the temperature distribution and flow structure in the molten and undercooled melt were simulated by reproducing the observed thermal history of the sample prior to solidification. Then the dendritic structure and surface temperature of the recalescing sample were simulated. These simulations revealed a large thermal gradient crossing the sample, which led to an underestimation of the real undercooling for dendritic growth in the bulk volume of the sample. By accounting for this underestimation, we recalculated the dendritic tip velocities in the glass-fluxed nickel melt using a theory of three-dimensional dendritic growth with convection and concluded an improved agreement between experiment and theory. © 2016 Elsevier B.V.

Accepted: 2006-10-16

Dendritic growth velocities in an undercooled melt of pure nickel under static magnetic fields up to 6 T were measured using a high-speed camera. The growth velocities for undercoolings below 120 K are depressed under low magnetic fields, but are recovered progressively under high magnetic fields. This retrograde behavior arises from two competing kinds of magnetohydrodynamics in the melt and becomes indistinguishable for higher undercoolings. The measured data is used for testing of a recent theory of dendritic growth with convection. A reasonable agreement is attained by assuming magnetic field-dependent flow velocities. As is shown, the theory can also account for previous data of dendritic growth kinetics in pure succinonitrile under normal gravity and microgravity conditions. These tests demonstrate the efficiency of the theory which provides a realistic description of dendritic growth kinetics of pure substances with convection. © 2015 Acta Materialia Inc.

The experiment of melt and solidification of glass using HTF (High Temperature Furnace) under microgravity environment is planned by NASDA as a part of TR-1A (Test Rocket-1A) sounding rocket missions. This experiment using MU-300 aircraft in October 1991 was carried out as the preliminary study of HTF mission. The purpose of this experiment is to understand melting condition of glass materials under microgravity environment and to establish how to support a glass material on the cylinder and how to measure the temperature using photodiode. This paper describes the result of melting and solidifying condition of glass materials, as well as observing undercooling phenomena using CCD camera and measuring the temperature and luminosity using thermocouple and photodiode., NASDAではTR-1A(宇宙実験用小型ロケット)ミッションの一環として、微小重力下での高温加熱炉(HTF)を用いたガラスの溶融・凝固実験を計画している。HTFミッションの予備研究として、1991年10月、MU-300型航空機による実験を行った。本実験は、微小重力環境下におけるガラス材料の溶融状態把握、ガラス材料のシリンダへの支持方法、およびフォトダイオードを用いる温度計測技術の確立を目的として実施した。ここでは、ガラス材料の溶融・凝固の状態、CCD(電荷結合素子)カメラによる過冷却現象観測、熱電対とフォトダイオードによる温度および光度計測の実験結果について述べた。

The mechanism and kinetics of the peritectic phase transition in steel were studied by using a concentric solidification technique in a high-temperature laser-scanning confocal microscope. Strong solute diffusion fields are established during solidification of the primary delta phase, which leads to suppression of nucleation of the austenite phase, and hence the extent to which a steel can be cooled to a temperature below the equilibrium peritectic temperature before the peritectic reaction will occur. The magnitude of these diffusion fields was also determined as a function of carbon content, alloying additions, cooling rate and the fraction of primary delta phase that solidified before the peritectic reaction occurred. Depending on the extent of undercooling required to nucleate the first austenite platelet on the liquid/delta-ferrite interface, three different modes of the solid-state peritectic transformation of delta to austenite have been observed: a diffusion-controlled phase transformation that occurred by the progression of a planar interface; a diffusion-controlled transformation with cellular/dendritic morphology; and a massive-type of transformation. Under certain circumstances, a changeover between these modes has also been observed. The underpinning thermodynamic considerations that lead to these different modes of transformation are discussed and a new explanation is provided for the occurrence of a massive transformation of delta-ferrite to austenite. The relevance to and implications of these new findings to the continuous casting of steel of near-peritectic steel composition are also discussed.

The mechanism and kinetics of the peritectic phase transition in steel were studied by using a concentric solidification technique in a high-temperature laser-scanning confocal microscope. Strong solute diffusion fields are established during solidification of the primary delta phase, which leads to suppression of nucleation of the austenite phase, and hence the extent to which a steel can be cooled to a temperature below the equilibrium peritectic temperature before the peritectic reaction will occur. The magnitude of these diffusion fields was also determined as a function of carbon content, alloying additions, cooling rate and the fraction of primary delta phase that solidified before the peritectic reaction occurred. Depending on the extent of undercooling required to nucleate the first austenite platelet on the liquid/delta-ferrite interface, three different modes of the solid-state peritectic transformation of delta to austenite have been observed: a diffusion-controlled phase transformation that occurred by the progression of a planar interface; a diffusion-controlled transformation with cellular/dendritic morphology; and a massive-type of transformation. Under certain circumstances, a changeover between these modes has also been observed. The underpinning thermodynamic considerations that lead to these different modes of transformation are discussed and a new explanation is provided for the occurrence of a massive transformation of delta-ferrite to austenite. The relevance to and implications of these new findings to the continuous casting of steel of near-peritectic steel composition are also discussed.

The mechanism and kinetics of the peritectic phase transition in steel were studied by using a concentric solidification technique in a high-temperature laser-scanning confocal microscope. Strong solute diffusion fields are established during solidification of the primary delta phase, which leads to suppression of nucleation of the austenite phase, and hence the extent to which a steel can be cooled to a temperature below the equilibrium peritectic temperature before the peritectic reaction will occur. The magnitude of these diffusion fields was also determined as a function of carbon content, alloying additions, cooling rate and the fraction of primary delta phase that solidified before the peritectic reaction occurred. Depending on the extent of undercooling required to nucleate the first austenite platelet on the liquid/delta-ferrite interface, three different modes of the solid-state peritectic transformation of delta to austenite have been observed: a diffusion-controlled phase transformation that occurred by the progression of a planar interface; a diffusion-controlled transformation with cellular/dendritic morphology; and a massive-type of transformation. Under certain circumstances, a changeover between these modes has also been observed. The underpinning thermodynamic considerations that lead to these different modes of transformation are discussed and a new explanation is provided for the occurrence of a massive transformation of delta-ferrite to austenite. The relevance to and implications of these new findings to the continuous casting of steel of near-peritectic steel composition are also discussed.

The mechanism and kinetics of the peritectic phase transition in steel were studied by using a concentric solidification technique in a high-temperature laser-scanning confocal microscope. Strong solute diffusion fields are established during solidification of the primary delta phase, which leads to suppression of nucleation of the austenite phase, and hence the extent to which a steel can be cooled to a temperature below the equilibrium peritectic temperature before the peritectic reaction will occur. The magnitude of these diffusion fields was also determined as a function of carbon content, alloying additions, cooling rate and the fraction of primary delta phase that solidified before the peritectic reaction occurred. Depending on the extent of undercooling required to nucleate the first austenite platelet on the liquid/delta-ferrite interface, three different modes of the solid-state peritectic transformation of delta to austenite have been observed: a diffusion-controlled phase transformation that occurred by the progression of a planar interface; a diffusion-controlled transformation with cellular/dendritic morphology; and a massive-type of transformation. Under certain circumstances, a changeover between these modes has also been observed. The underpinning thermodynamic considerations that lead to these different modes of transformation are discussed and a new explanation is provided for the occurrence of a massive transformation of delta-ferrite to austenite. The relevance to and implications of these new findings to the continuous casting of steel of near-peritectic steel composition are also discussed.

Tato bakalářská práce se zabývá studiem krystalizace vody v podchlazených roztocích cukrů (30 hmot.% sacharózy a 30 hmot.% glukózy). V teoretické části jsou popsány vznik, růst a rekrystalizace krystalů ledu, vliv sacharidů a podchlazení na krystalizaci, morfologie krystalů ledu a některé experimentální metody používané při výzkumu krystalizace ledu v podchlazených vodných roztocích sacharidů. Experimentální část práce je zaměřena na studium růstu krystalů ledu ve vodných roztocích sacharózy a glukózy a teploty tání v těchto roztocích., This bachelor's thesis is focused on crystallization of water in undercooled sugar solutions (30 % w/w sucrose and 30 % w/w glucose). The theoretical part describes a genesis, growth and recrystallization of ice crystals, an influence of saccharides and undercooling on crystallization, a morphology of ice crystals and some experimental methods using in research of ice crystallization in undercooled sugar solutions. The experimental part is aimed at the study of growth ice crystals and their melting points in water solutions of sucrose and glucose., Katedra analytické chemie, Studentka přednesla obhajobu své bakalářské práce a zodpověděla dotazy zkušební komise.

The present work reports on flow boiling visualization of refrigerant R-134a in a vertical circular channel with an internal diameter of 1.33 mm and 235 mm in heated length. A quartz tube with a homogeneous Indium Tin Oxide coating is used to allow heating and simultaneous visualization. Flow patterns have been observed along the heated length with the aid of high-speed complementary metal oxide semiconductor (CMOS) digital camera. From the flow boiling visualization, seven distinct two-phase flow patterns have been observed: isolated bubbly flow, confined bubbly flow, slug flow, churn flow, slug-annular flow, annular flow, and mist flow. Two-phase flow pattern observations are presented in the form of flow pattern maps. The effects of the saturation temperature and the inlet subcooling degree on the two-phase flow pattern transitions are elucidated. Finally, the experimental flow pattern map is compared with models developed for conventional sizes as well as to a microscale map for air-water mixtures available in literature, showing a large discrepancy., QC 20110125

Solid or molten oxides are considered to act as nucleation sites during continuous steel casting. The influence of the kind of oxide crystal and atmospheric oxygen partial pressure on the degree of undercooling and contact angle of pure molten iron on oxide substrates was measured by the sessile drop method. On Al2O3 and MgAl2O4 substrates, we found that the change in the degree of undercooling was dependent on the existence of a reaction layer and its thickness. On an MgO substrate, since no reaction layer formed, the degree of undercooling was small and was governed by the lattice misfit parameter. The equilibrium contact angle of a molten iron drop on the FeAl2O4 layer formed between the Al2O3 substrate and drop was about 100 degrees; a similar contact angle was obtained on MgAl2O4. The contact angle on MgO changed during observation due to the evaporation of Mg., QC 20110304 Conference on Cutting Edge of Studies in Inclusions and Precipitates Behavior Related to Microstructure Control, Kumamoto, JAPAN, SEP, 2008

The European legislation prohibits the use of lead containing solders in Europe. However, lead free solders have a higher melting point (typical 20%) and their mechanical characteristics are worse. Additional problems are aging and adhesion of the solder on the electronic circuits. Thus, research activities must focus on the optimization of the properties of Sn-Ag-Cu based lead free solders chosen by the industry. Two main objectives are treated in this work. In the center of the first one is the study of curious hysteresis effects of metallic cadmium-antimony alloys after thermal cycles by measuring electronic transport phenomena (thermoelectric power and electrical resistivity). The second objective, within the framework of “cotutelle” between the universities of Metz and of Chemnitz and supported by COST531, is to study more specifically lead free solders. A welding must well conduct electricity and well conduct and dissipate heat. In Metz, we determined the electrical conductivity, the thermoelectric power and the thermal conductivity of various lead free solders (Sn-Ag-Cu, Sn-Cu, Sn-Ag, Sn-Sb) as well in the liquid as well in the solid state. The results have been compared to classical lead-tin (Pb-Sn) solders. In Chemnitz we measured the surface tension, the interfacial tension and the density of lead free solders. We also measured the viscosity of these solders without and with additives, in particular nickel. These properties were related to the industrial problems of wettability and spreadability. Lastly, we solidified alloys under various conditions. We observed undercooling. We developed a technique of mixture of nanocristalline powder with lead free solders "to sow" the liquid bath in order to obtain "different" solids which were examined using optical and electron microscopy., Die europäische Gesetzgebung verbietet die Benutzung von Lötmitteln, die Blei enthalten. Bleilose Lote haben aber einen höheren Schmelzpunkt (typisch 20%) und ihre mechanischen Eigenschaften sind schlechter. Zusätzliche Probleme sind das Alterungsverhalten und das Haftvermögen des Lots an den Leiterbahnen. Daher müssen sich Forschungsaktivitäten auf die Optimierung der Eigenschaften von bleifreien Sn-Ag-Cu (SAC) Loten konzentrieren, die von der Industrie gewählt wurden. Zwei Hauptgebiete werden in dieser Arbeit bearbeitet. Im Zentrum des Ersten stehen seltsame Hysterese-Effekte von metallischen Kadmium- Antimon Legierungen bei thermischen Zyklen, wobei Transporteigenschaften wie die thermoelektrische Kraft und der elektrische Widerstand untersucht werden. Die zweite Aktivität, die in einer Kooperation der Universitäten Metz und Chemnitz (cotutelle) bearbeitet und die durch COST531 unterstützt wird, besteht in der detaillierten Erforschung des Lötprozesses ohne Blei. Eine Lötverbindung muß den Strom gut führen und die Wärme gut ableiten. In Metz haben wir die elektrische Leitfähigkeit, die thermoelektrische Kraft und das Wärmeleitvermögen bestimmt für verschiedene bleilose Lote (Sn-Ag-Cu, Sn-Cu, Sn-Ag, Sn-Sb), sowohl im flüssigen als auch festen Zustand. Die Ergebnisse wurden mit dem klassischen bleihaltigen Lötzinn (Sn-Pb) verglichen. In Chemnitz haben wir die Oberflächen- und Grenzflächenspannung und die Dichte bleifreier Lote gemessen. Ebenfalls wurde die Viskosität dieser Lote ohne und mit Zusätzen (insbesondere Nickel) gemessen. Diese Eigenschaften wurden in Beziehung gesetzt zu den industriellen Problemen der Benetzbarkeit und des Fließverhaltens. Schließlich haben wir Legierungen unter verschiedenen Bedingungen verfestigt. Wir haben Unterkühlung beobachtet. Wir haben eine Technik entwickelt, basierend auf einer Mischung von Lot mit Pulver. Durch "Einsäen" von Nanokristallen in das flüssige Bad erhielten wir "verschiedene" Festkörper, die mit optischer und Elek

The European legislation prohibits the use of lead containing solders in Europe. However, lead free solders have a higher melting point (typical 20%) and their mechanical characteristics are worse. Additional problems are aging and adhesion of the solder on the electronic circuits. Thus, research activities must focus on the optimization of the properties of Sn-Ag-Cu based lead free solders chosen by the industry. Two main objectives are treated in this work. In the center of the first one is the study of curious hysteresis effects of metallic cadmium-antimony alloys after thermal cycles by measuring electronic transport phenomena (thermoelectric power and electrical resistivity). The second objective, within the framework of “cotutelle” between the universities of Metz and of Chemnitz and supported by COST531, is to study more specifically lead free solders. A welding must well conduct electricity and well conduct and dissipate heat. In Metz, we determined the electrical conductivity, the thermoelectric power and the thermal conductivity of various lead free solders (Sn-Ag-Cu, Sn-Cu, Sn-Ag, Sn-Sb) as well in the liquid as well in the solid state. The results have been compared to classical lead-tin (Pb-Sn) solders. In Chemnitz we measured the surface tension, the interfacial tension and the density of lead free solders. We also measured the viscosity of these solders without and with additives, in particular nickel. These properties were related to the industrial problems of wettability and spreadability. Lastly, we solidified alloys under various conditions. We observed undercooling. We developed a technique of mixture of nanocristalline powder with lead free solders "to sow" the liquid bath in order to obtain "different" solids which were examined using optical and electron microscopy., Die europäische Gesetzgebung verbietet die Benutzung von Lötmitteln, die Blei enthalten. Bleilose Lote haben aber einen höheren Schmelzpunkt (typisch 20%) und ihre mechanischen Eigenschaften sind schlechter. Zusätzliche Probleme sind das Alterungsverhalten und das Haftvermögen des Lots an den Leiterbahnen. Daher müssen sich Forschungsaktivitäten auf die Optimierung der Eigenschaften von bleifreien Sn-Ag-Cu (SAC) Loten konzentrieren, die von der Industrie gewählt wurden. Zwei Hauptgebiete werden in dieser Arbeit bearbeitet. Im Zentrum des Ersten stehen seltsame Hysterese-Effekte von metallischen Kadmium- Antimon Legierungen bei thermischen Zyklen, wobei Transporteigenschaften wie die thermoelektrische Kraft und der elektrische Widerstand untersucht werden. Die zweite Aktivität, die in einer Kooperation der Universitäten Metz und Chemnitz (cotutelle) bearbeitet und die durch COST531 unterstützt wird, besteht in der detaillierten Erforschung des Lötprozesses ohne Blei. Eine Lötverbindung muß den Strom gut führen und die Wärme gut ableiten. In Metz haben wir die elektrische Leitfähigkeit, die thermoelektrische Kraft und das Wärmeleitvermögen bestimmt für verschiedene bleilose Lote (Sn-Ag-Cu, Sn-Cu, Sn-Ag, Sn-Sb), sowohl im flüssigen als auch festen Zustand. Die Ergebnisse wurden mit dem klassischen bleihaltigen Lötzinn (Sn-Pb) verglichen. In Chemnitz haben wir die Oberflächen- und Grenzflächenspannung und die Dichte bleifreier Lote gemessen. Ebenfalls wurde die Viskosität dieser Lote ohne und mit Zusätzen (insbesondere Nickel) gemessen. Diese Eigenschaften wurden in Beziehung gesetzt zu den industriellen Problemen der Benetzbarkeit und des Fließverhaltens. Schließlich haben wir Legierungen unter verschiedenen Bedingungen verfestigt. Wir haben Unterkühlung beobachtet. Wir haben eine Technik entwickelt, basierend auf einer Mischung von Lot mit Pulver. Durch "Einsäen" von Nanokristallen in das flüssige Bad erhielten wir "verschiedene" Festkörper, die mit optischer und Elek

The European legislation prohibits the use of lead containing solders in Europe. However, lead free solders have a higher melting point (typical 20%) and their mechanical characteristics are worse. Additional problems are aging and adhesion of the solder on the electronic circuits. Thus, research activities must focus on the optimization of the properties of Sn-Ag-Cu based lead free solders chosen by the industry. Two main objectives are treated in this work. In the center of the first one is the study of curious hysteresis effects of metallic cadmium-antimony alloys after thermal cycles by measuring electronic transport phenomena (thermoelectric power and electrical resistivity). The second objective, within the framework of “cotutelle” between the universities of Metz and of Chemnitz and supported by COST531, is to study more specifically lead free solders. A welding must well conduct electricity and well conduct and dissipate heat. In Metz, we determined the electrical conductivity, the thermoelectric power and the thermal conductivity of various lead free solders (Sn-Ag-Cu, Sn-Cu, Sn-Ag, Sn-Sb) as well in the liquid as well in the solid state. The results have been compared to classical lead-tin (Pb-Sn) solders. In Chemnitz we measured the surface tension, the interfacial tension and the density of lead free solders. We also measured the viscosity of these solders without and with additives, in particular nickel. These properties were related to the industrial problems of wettability and spreadability. Lastly, we solidified alloys under various conditions. We observed undercooling. We developed a technique of mixture of nanocristalline powder with lead free solders "to sow" the liquid bath in order to obtain "different" solids which were examined using optical and electron microscopy., Die europäische Gesetzgebung verbietet die Benutzung von Lötmitteln, die Blei enthalten. Bleilose Lote haben aber einen höheren Schmelzpunkt (typisch 20%) und ihre mechanischen Eigenschaften sind schlechter. Zusätzliche Probleme sind das Alterungsverhalten und das Haftvermögen des Lots an den Leiterbahnen. Daher müssen sich Forschungsaktivitäten auf die Optimierung der Eigenschaften von bleifreien Sn-Ag-Cu (SAC) Loten konzentrieren, die von der Industrie gewählt wurden. Zwei Hauptgebiete werden in dieser Arbeit bearbeitet. Im Zentrum des Ersten stehen seltsame Hysterese-Effekte von metallischen Kadmium- Antimon Legierungen bei thermischen Zyklen, wobei Transporteigenschaften wie die thermoelektrische Kraft und der elektrische Widerstand untersucht werden. Die zweite Aktivität, die in einer Kooperation der Universitäten Metz und Chemnitz (cotutelle) bearbeitet und die durch COST531 unterstützt wird, besteht in der detaillierten Erforschung des Lötprozesses ohne Blei. Eine Lötverbindung muß den Strom gut führen und die Wärme gut ableiten. In Metz haben wir die elektrische Leitfähigkeit, die thermoelektrische Kraft und das Wärmeleitvermögen bestimmt für verschiedene bleilose Lote (Sn-Ag-Cu, Sn-Cu, Sn-Ag, Sn-Sb), sowohl im flüssigen als auch festen Zustand. Die Ergebnisse wurden mit dem klassischen bleihaltigen Lötzinn (Sn-Pb) verglichen. In Chemnitz haben wir die Oberflächen- und Grenzflächenspannung und die Dichte bleifreier Lote gemessen. Ebenfalls wurde die Viskosität dieser Lote ohne und mit Zusätzen (insbesondere Nickel) gemessen. Diese Eigenschaften wurden in Beziehung gesetzt zu den industriellen Problemen der Benetzbarkeit und des Fließverhaltens. Schließlich haben wir Legierungen unter verschiedenen Bedingungen verfestigt. Wir haben Unterkühlung beobachtet. Wir haben eine Technik entwickelt, basierend auf einer Mischung von Lot mit Pulver. Durch "Einsäen" von Nanokristallen in das flüssige Bad erhielten wir "verschiedene" Festkörper, die mit optischer und Elek

The European legislation prohibits the use of lead containing solders in Europe. However, lead free solders have a higher melting point (typical 20%) and their mechanical characteristics are worse. Additional problems are aging and adhesion of the solder on the electronic circuits. Thus, research activities must focus on the optimization of the properties of Sn-Ag-Cu based lead free solders chosen by the industry. Two main objectives are treated in this work. In the center of the first one is the study of curious hysteresis effects of metallic cadmium-antimony alloys after thermal cycles by measuring electronic transport phenomena (thermoelectric power and electrical resistivity). The second objective, within the framework of “cotutelle” between the universities of Metz and of Chemnitz and supported by COST531, is to study more specifically lead free solders. A welding must well conduct electricity and well conduct and dissipate heat. In Metz, we determined the electrical conductivity, the thermoelectric power and the thermal conductivity of various lead free solders (Sn-Ag-Cu, Sn-Cu, Sn-Ag, Sn-Sb) as well in the liquid as well in the solid state. The results have been compared to classical lead-tin (Pb-Sn) solders. In Chemnitz we measured the surface tension, the interfacial tension and the density of lead free solders. We also measured the viscosity of these solders without and with additives, in particular nickel. These properties were related to the industrial problems of wettability and spreadability. Lastly, we solidified alloys under various conditions. We observed undercooling. We developed a technique of mixture of nanocristalline powder with lead free solders "to sow" the liquid bath in order to obtain "different" solids which were examined using optical and electron microscopy., Die europäische Gesetzgebung verbietet die Benutzung von Lötmitteln, die Blei enthalten. Bleilose Lote haben aber einen höheren Schmelzpunkt (typisch 20%) und ihre mechanischen Eigenschaften sind schlechter. Zusätzliche Probleme sind das Alterungsverhalten und das Haftvermögen des Lots an den Leiterbahnen. Daher müssen sich Forschungsaktivitäten auf die Optimierung der Eigenschaften von bleifreien Sn-Ag-Cu (SAC) Loten konzentrieren, die von der Industrie gewählt wurden. Zwei Hauptgebiete werden in dieser Arbeit bearbeitet. Im Zentrum des Ersten stehen seltsame Hysterese-Effekte von metallischen Kadmium- Antimon Legierungen bei thermischen Zyklen, wobei Transporteigenschaften wie die thermoelektrische Kraft und der elektrische Widerstand untersucht werden. Die zweite Aktivität, die in einer Kooperation der Universitäten Metz und Chemnitz (cotutelle) bearbeitet und die durch COST531 unterstützt wird, besteht in der detaillierten Erforschung des Lötprozesses ohne Blei. Eine Lötverbindung muß den Strom gut führen und die Wärme gut ableiten. In Metz haben wir die elektrische Leitfähigkeit, die thermoelektrische Kraft und das Wärmeleitvermögen bestimmt für verschiedene bleilose Lote (Sn-Ag-Cu, Sn-Cu, Sn-Ag, Sn-Sb), sowohl im flüssigen als auch festen Zustand. Die Ergebnisse wurden mit dem klassischen bleihaltigen Lötzinn (Sn-Pb) verglichen. In Chemnitz haben wir die Oberflächen- und Grenzflächenspannung und die Dichte bleifreier Lote gemessen. Ebenfalls wurde die Viskosität dieser Lote ohne und mit Zusätzen (insbesondere Nickel) gemessen. Diese Eigenschaften wurden in Beziehung gesetzt zu den industriellen Problemen der Benetzbarkeit und des Fließverhaltens. Schließlich haben wir Legierungen unter verschiedenen Bedingungen verfestigt. Wir haben Unterkühlung beobachtet. Wir haben eine Technik entwickelt, basierend auf einer Mischung von Lot mit Pulver. Durch "Einsäen" von Nanokristallen in das flüssige Bad erhielten wir "verschiedene" Festkörper, die mit optischer und Elek

Outgoing

Casting experiments have been performed with eutectic and hypereutectic castings with plate thicknesses from 2 to 8 mm involving both temperature measurements during solidification and microstructural examination afterwards. The nodule count was the same for the eutectic and hypereutectic castings in the thin plates (≤4.3 mm) while in the 8 mm plate the nodule count was higher in the hypereutectic than in the eutectic castings. The minimum temperature before the eutectic recalescence (Tmin) was 15 to 20ºC lower for the eutectic than for the hypereutectic castings. This is due to nucleation of graphite nodules which begins at a lower temperature in the eutectic than in the hypereutectic castings. The recalescence ∆Trec was however also larger for the eutectic casting and in the thin plates the maximum temperature after recalescence (Tmax) was the same in the eutectic and hypereutectic plates. This is because higher undercooling gives a larger driving force for the solidification process and the equal nodule counts therefore give the same Tmax. However, the higher undercooling before recalescence increases the risk for formation of carbides during the solidification. In the 8 mm plates, the lower nodule count in the eutectic plates also gave a lower Tmax than in the hypereutectic castings.

Casting experiments have been performed with eutectic and hypereutectic castings with plate thicknesses from 2 to 8 mm involving both temperature measurements during solidification and microstructural examination afterwards. The nodule count was the same for the eutectic and hypereutectic castings in the thin plates (≤4.3 mm) while in the 8 mm plate the nodule count was higher in the hypereutectic than in the eutectic castings. The minimum temperature before the eutectic recalescence (Tmin) was 15 to 20ºC lower for the eutectic than for the hypereutectic castings. This is due to nucleation of graphite nodules which begins at a lower temperature in the eutectic than in the hypereutectic castings. The recalescence ∆Trec was however also larger for the eutectic casting and in the thin plates the maximum temperature after recalescence (Tmax) was the same in the eutectic and hypereutectic plates. This is because higher undercooling gives a larger driving force for the solidification process and the equal nodule counts therefore give the same Tmax. However, the higher undercooling before recalescence increases the risk for formation of carbides during the solidification. In the 8 mm plates, the lower nodule count in the eutectic plates also gave a lower Tmax than in the hypereutectic castings.

Casting experiments have been performed with eutectic and hypereutectic castings with plate thicknesses from 2 to 8 mm involving both temperature measurements during solidification and microstructural examination afterwards. The nodule count was the same for the eutectic and hypereutectic castings in the thin plates (≤4.3 mm) while in the 8 mm plate the nodule count was higher in the hypereutectic than in the eutectic castings. The minimum temperature before the eutectic recalescence (Tmin) was 15 to 20ºC lower for the eutectic than for the hypereutectic castings. This is due to nucleation of graphite nodules which begins at a lower temperature in the eutectic than in the hypereutectic castings. The recalescence ∆Trec was however also larger for the eutectic casting and in the thin plates the maximum temperature after recalescence (Tmax) was the same in the eutectic and hypereutectic plates. This is because higher undercooling gives a larger driving force for the solidification process and the equal nodule counts therefore give the same Tmax. However, the higher undercooling before recalescence increases the risk for formation of carbides during the solidification. In the 8 mm plates, the lower nodule count in the eutectic plates also gave a lower Tmax than in the hypereutectic castings.

Latent heat during recalesence and nucleation and post-recalesence temperature was analysed for refractory metals. An effect on latent heat was found by alloying the pure elements with other refractories. Latent heat was found to be 15-65% of tabulated values. Interface energy was evaluated from undercooling experiments. It was found that the dimensionless numbers β (σLs/ σLv) and α can be used to classify elements into distinctive groups and crystallographic structure. The phase diagrams for Al-Ti, Al-Ti-B and Al-Ti-C as well as inoculation were analysed. It was found that Al nucleates on Al3Ti which nucleates on TiB2. TiC was found to decompose into Al4C3 and Al3Ti. The inoculation of nodular cast iron with Mg, Ce; Ca and the formation of sulphides and oxides was analysed. The formation of new inclusions during the solidification as well as the formation of graphite is discussed., QC 20100602

Latent heat during recalesence and nucleation and post-recalesence temperature was analysed for refractory metals. An effect on latent heat was found by alloying the pure elements with other refractories. Latent heat was found to be 15-65% of tabulated values. Interface energy was evaluated from undercooling experiments. It was found that the dimensionless numbers β (σLs/ σLv) and α can be used to classify elements into distinctive groups and crystallographic structure. The phase diagrams for Al-Ti, Al-Ti-B and Al-Ti-C as well as inoculation were analysed. It was found that Al nucleates on Al3Ti which nucleates on TiB2. TiC was found to decompose into Al4C3 and Al3Ti. The inoculation of nodular cast iron with Mg, Ce; Ca and the formation of sulphides and oxides was analysed. The formation of new inclusions during the solidification as well as the formation of graphite is discussed., QC 20100602

Latent heat during recalesence and nucleation and post-recalesence temperature was analysed for refractory metals. An effect on latent heat was found by alloying the pure elements with other refractories. Latent heat was found to be 15-65% of tabulated values. Interface energy was evaluated from undercooling experiments. It was found that the dimensionless numbers β (σLs/ σLv) and α can be used to classify elements into distinctive groups and crystallographic structure. The phase diagrams for Al-Ti, Al-Ti-B and Al-Ti-C as well as inoculation were analysed. It was found that Al nucleates on Al3Ti which nucleates on TiB2. TiC was found to decompose into Al4C3 and Al3Ti. The inoculation of nodular cast iron with Mg, Ce; Ca and the formation of sulphides and oxides was analysed. The formation of new inclusions during the solidification as well as the formation of graphite is discussed., QC 20100602

The objective of the research is to show that ceramic particles can be melted in flight, undercooled in flight, and impacted on a substrate to form a thick film. It is further hypothesized that with adequate process control, deposits of high temperature ceramics can be created on heat sensitive substrates, e.g., hybrid electronic structures. The approach is to flow powders in a gas stream through a region of high photon flux to melt the powders, cool the molten particles by radiation, convection and conduction during free flight, and control phase selection and droplet spreading on a substrate by modeling, in-process diagnostics, and metallographic examination of the deposits. The primary application of this process is for the sealing of hybrid ceramic bio-implantable devices, such as pacemakers. Ceramic pacemakers have communication capabilities, integrated feedthroughs, and are MRI and biologically compatible. There is presently no known biocompatible method for sealing these hybrid devices. Other applications include the formation of thick films at high rates for ceramic superconducting tapes and wires, ceramic superconducting coatings for electromagnetic shielding, thermal barrier coatings on heat sensitive substrates, micro coatings for MEMS components, and ceramic joining., Briefing charts.

20100528

At high undercooling, the solidification of alloys can result in the suppression of the usual crystallization reactions and in the formation of nonequilibrium phases with distinct and novel microstructures. When a liquid is subdivided into a fine droplet dispersion in order to isolate nucleation catalysis, substantial undercooling may he observed before the onset of solidification, as demonstrated by the current work, An improved droplet technique has been applied to investigate the phase selection kinetics, nucleation catalysis reactions and thermal history that control microstructural evolution during solidification of highly undercooled melts. New developments involving droplet population and single droplet experiments in the application of nucleation catalysis to control undercooling have been used to Identify specific active nucleants. In studies on Al-base alloys, an enhanced control and reproducibility of fine scale microstructure formation processes has been achieved in elevated temperature alloys and the new class of amorphous Al alloys. A continuing development of droplet methods to treat copper alloys and cast iron has been pursued along with the application of particle incorporated droplets to examine composite solidification processing. Throughout the experimental work, attention will is given to the evaluation of the relevant metastable phase equilibria and reaction kinetics which are quite useful for the interpretation of solidification microstructure and in the identification of alloy design strategies. In addition, processing models have been developed further with the aim to formulate microstructure maps for high undercooling solidification in order to guide the control of microstructure synthesis. An assessment of the undercooling and thermal history of the solidification products is provided by calorimetric measurements, controlled upquenching

A study of the bulk formation of YBa2Cu3O7-x from the Y2BaCuO5 plus liquid regime reveals that phase formation occurs at appreciable rates below 950°C in air. This result has been observed for phase-pure YBa2Cu3O7-x starting material given two types of heat treatment: held at 1100°C and slow-cooled from 1030°C at 6°C/h or heat-treated isothermally. Differential thermal analysis, with a cooling rate of 10°C/min indicates that the degree of undercooling for the peritectic formation of YBa2Cu3O7-x is greater than 100°C. © 1994.

In solidification, when the process is limited by diffusion of released latent heat or solute, often the two-phase interface forms finger-like shapes called dendrites, whose tips are nearly paraboloidal in form. For a pure material solidifying into an undercooled melt, if surface energy and gravity are negligible, a well-known solution due to Ivantsov (1947) describes the steady growth with a paraboloidal interface. We construct a regular perturbation to this solution for a downward growing axisymmetric dendrite, based on the smallness of a buoyancy parameter G, to examine the effects of buoyant flow on the solidification. The analytic solution predicts that generally the buoyancy enhances growth and changes the shape of the interface, giving a sharper tip and wider base. These effects depend strongly on the Prandtl number, and also on the Stefan number (undercooling). The results compare will with the experiments of Huang and Glicksman (1981) up to G 5000, but over predict convective effects for higher G.

In spray deposition via the Osprey process a stream of molten metal is atomized by an inert gas to form a spray of liquid droplets. The droplets are cooled by the deposit. Current research at Drexel Univ. is directed towards a fundamental science-based understanding of the spray deposition process and involves both theoretical and experimental studies. A computer model of the spray deposition process has been developed to predict velocity and temperature profiles of the metal droplets in flight. This model takes into account the undercooling and solidification of the droplets. Another computer model has been developed to predict how the droplets spread and consolidate upon impingement with the substrate. Experiments were designed to verify the predictions made by the two models and also to determine the most influential spray depostion process parameters. Short-exposure still photography has been used to estimate droplet velocities. To study the extent of solidification of individual droplets, glass slides have been traversed through the metal spray.

The rapid solidification of highly undercooled liquid alloys in fine droplet form has been studied under controlled conditions by thermal analysis, x-ray diffraction and metallographic examination. Droplet undercooling is affected by processing variables such as particle size, melt superheat and cooling rate, but the undercooling limit is often set by a catalysis at the droplet surface. By varying the droplet coating and nucleation site the development of solidification microstructure and the effect of recalescence thermal history has been examined at controlled undercooling levels including the hypercooling range.

Prepared in cooperation with General Electric Co. Evendale, OH Aircraft Engine Group.

The undercooling and solidification of liquid alloys in fine droplet form has been examined by thermal analysis, X-ray diffraction and metallography. New maximum undercooling limits have been established for several metals and hypercooling has been demonstrated for the first time in a metallic system. In alloys some aspects of the phase selection kinetics for formation of metastable phases have been identified in eutectic, peritectic and monotectic reactions. The use of droplet samples allows the measurement of thermodynamic properties of undercooled liquids and the study of microstructure development with changing undercooling. In some alloys, the effective isolation of nucleants that is possible with micron size droplets results in a continuous solidification to the amorphous state. The observations are presented in terms of the potential of undercooling for structure modification and rapid solidification technology. (Author)

Sponsored in part by Grant NSF-DMR77-13932.