The presented work reports on the solidification studies in two alloy systems: the niobium bearing γ-TiAl, relevant for the automotive and aero-engine applications, and aluminium rich Raney-Ni, precursor alloys for catalyses used in the chemical industry. The time-resolved observations of equilibrium liquid-solid phase transformations, as well as non-equilibrium solidification from the undercooled melt, are performed by combination of in situ structural studies using high-energy X-rays at a synchrotron source and the electromagnetic levitation technique. Containerless processing assured the contamination-free environment leading to high undercooling levels even at moderate cooling rates. For the critical part of the Ti-Al-Nb phase diagram an equilibrium involving the liquid phase is deduced from the phase transformations gathered on heating periods of levitation experiment. New experimental data on the partial liquidus and solidus surfaces are delivered as well as the information on the nature of the reactions along the univariant lines. These data provide a valuable contribution to the reassessment of the thermodynamic description. The primary phase selection as function of undercooling is studied in ternary Ti-Al-Nb alloys. The metastable formation of the cubic β phase within the primary solidification region of the hexagonal α phase is observed with increasing melt undercooling. Furthermore, the microstructure evolution of the β solidifying Ti-46Al-8Nb alloy discloses the transition to the thermal growth mode for ∆T>200−250 K, accompanied by complete solute trapping. Supplemented with the data on the solidification velocity determined as function of melt undercooling, this results are discussed within the local non-equilibrium model of the free dendrite growth. The in situ observations of the non-equilibrium solidification of the binary Al-Ni system give insight into multiple phase transformation sequence. The achieved undercooling levels up to 320 K for the aluminium alloys containing 18–31.5 at.% Ni did not alter the primary phase selection. However, during further cooling of L+Al3Ni2 semisolid samples the peritectic formation of a metastable decagonal quasicrystalline phase is observed providing a critical undercooling below the peritectic temperature of Al3Ni phase is reached. On further cooling the metastable phase subsequently transforms into the equilibrium Al3Ni. A similar solidification pathways are expected for the Raney-Ni alloys produced by gas atomisation, where the associated high cooling rates allowed to retain the metastable phase at room temperature.

Magnetische Formgedächtnsilegierungen haben die besondere Fähigkeit, sich im äußeren Magnetfeld zu verformen. Dies geschieht aufgrund von Zwillingsgrenzenbewegung in der martensitischen Tieftemperaturphase. Da der Effekt bislang an Einkristallen untersucht wurde, ist es das Ziel dieser Arbeit, den Effekt an polykristallinen Proben nachzuweisen. Dafür wurden Proben nach dem Prinzip der gerichteten Erstarrung präpariert. Deren Kristallstruktur wurde durch geeignete Zusammensetzung und Wärmebehandlung einphasig eingestellt. Mechanisches Training und weitere Wärmebehandlungen ermöglichten schließlich die Demonstration der magnetischen Dehnung von ca. 1 % an polykristallinen Proben. Durch zusätzliche Einkopplung akustischer Wellen konnte die Dehnung auf 2,2 % gesteigert werden.

The presented work reports on the solidification studies in two alloy systems: the niobium bearing γ-TiAl, relevant for the automotive and aero-engine applications, and aluminium rich Raney-Ni, precursor alloys for catalyses used in the chemical industry. The time-resolved observations of equilibrium liquid-solid phase transformations, as well as non-equilibrium solidification from the undercooled melt, are performed by combination of in situ structural studies using high-energy X-rays at a synchrotron source and the electromagnetic levitation technique. Containerless processing assured the contamination-free environment leading to high undercooling levels even at moderate cooling rates. For the critical part of the Ti-Al-Nb phase diagram an equilibrium involving the liquid phase is deduced from the phase transformations gathered on heating periods of levitation experiment. New experimental data on the partial liquidus and solidus surfaces are delivered as well as the information on the nature of the reactions along the univariant lines. These data provide a valuable contribution to the reassessment of the thermodynamic description. The primary phase selection as function of undercooling is studied in ternary Ti-Al-Nb alloys. The metastable formation of the cubic β phase within the primary solidification region of the hexagonal α phase is observed with increasing melt undercooling. Furthermore, the microstructure evolution of the β solidifying Ti-46Al-8Nb alloy discloses the transition to the thermal growth mode for ∆T>200−250 K, accompanied by complete solute trapping. Supplemented with the data on the solidification velocity determined as function of melt undercooling, this results are discussed within the local non-equilibrium model of the free dendrite growth. The in situ observations of the non-equilibrium solidification of the binary Al-Ni system give insight into multiple phase transformation sequence. The achieved undercooling levels up to 320 K for the aluminium alloys containing 18–31.5 at.% Ni did not alter the primary phase selection. However, during further cooling of L+Al3Ni2 semisolid samples the peritectic formation of a metastable decagonal quasicrystalline phase is observed providing a critical undercooling below the peritectic temperature of Al3Ni phase is reached. On further cooling the metastable phase subsequently transforms into the equilibrium Al3Ni. A similar solidification pathways are expected for the Raney-Ni alloys produced by gas atomisation, where the associated high cooling rates allowed to retain the metastable phase at room temperature.

In dieser Arbeit wurde der Einfluss der Schmelzkonvektion auf das erstarrende Gefüge von peritektischen Nd-Fe-B – und TiAl-Legierungen mit Hilfe neuartiger Methoden untersucht. Da die magnetischen und mechanischen Eigenschaften dieser technisch relevanten Legierungen stark vom Gefüge und insbesondere vom Volumenanteil der properitektischen Phase abhängen, sind diese Untersuchungen von großem Interesse. Auf der Basis der numerischen Simulationen der Schmelzkonvektionsmoden und des elektromagnetischen Problems in einer induktiv beheizten Schmelze, die am Forschungszentrum Dresden-Rossendorf durchgeführt wurden, wurden am IFW Dresden neuartige Versuchsaufbauten entwickelt, die die Modifizierung der Konvektion in einer Metallschmelze ermöglichen. Dies sind ein Aufbau zur erzwungenen Schmelzrotation in einem Tiegel und eine modifizierte Floating-Zone-Anlage. Die erzwungene Schmelzrotation, bei der der Schmelztiegel mit einer definierten Frequenz rotiert, führt in Übereinstimmung mit der Simulation zu einer starken Reduzierung der Konvektion in Abhängigkeit von der Frequenz. Diese Methode wurde auf Nd-Fe-B-Legierungen angewendet mit dem Ziel, die Bildung der unerwünschten weichmagnetischen Eisenphase zu unterdrücken bzw. deren Volumenanteil zu reduzieren. Im Ergebnis konnte der Volumenanteil der properitektischen Phase mit diesem Verfahren um 38.5 % reduziert werden. Das dendritische Gefüge wurde einer ausführlichen statistischen Analyse unterzogen, bei der die Abstände der sekundären Dendritenarme (SDAS) gemessen wurden. Es konnte gezeigt werden, dass die SDAS sich mit steigender Frequenz der Tiegelrotation, was einer reduzierten Schmelzkonvektion entspricht, verringern. Die Verringerung des Volumenanteils der properitektischen Eisenphase und der SDAS wird mit dem reduzierten konvektiven Massentransport unter reduzierter Schmelzkonvektion erklärt. Starke interdendritische Strömung reduziert die Dicke der Diffusionsgrenzschicht um die properitektische Phase. Dadurch wird der Stofftransport durch die Grenzschicht erleichtert. Kleinere Dendritenarme werden in die Schmelze zurückgeschmolzen, wodurch sich der Abstand zwischen den verbleibenden Dendritenarmen vergrößert. Eine Floating-Zone-Anlage, die das tiegelfreie Prozessieren von Metallschmelzen erlaubt wurde so modifiziert, dass mit Hilfe eines Doppelspulensystems eine zusätzliche wohl definierte elektromagnetische Kraft eingebracht wird, über die eine sehr intensive (Zweiphasenrührer in Parallelschaltung) bzw. stark verringerte Strömung (Doppelspule in Reihenschaltung) in der Schmelze eingestellt werden kann. Die experimentellen Ergebnisse der Untersuchungen am Nd-Fe-B-System mit der Doppelspule in Reihenschaltung zeigten, dass sich bei einem optimalen Spulenabstand von 5,1 mm die geringste Schmelzkonvektion ergab, wobei der Anteil des a-Eisen-Volumenanteils weiter verringert werden konnte. Im Gegensatz dazu wurde mit dem Zweiphasenrührer in Parallelschaltung eine sehr starke Schmelzkonvektion mit einem maximalen Volumenanteil der a-Eisen-Phase eingestellt, wobei durch die starke Rührung ein Wechsel der Morphologie von dendritisch zu globular zu beobachten war. Die Untersuchungen zum Einfluss der starken Schmelzkonvektion wurden auf ein weiteres peritektisch erstarrendes System ausgedehnt, um eine generalisierte Aussage zum Einfluss der Konvektion auf Gefüge und Eigenschaften peritektisch erstarrender Legierungen zu erhalten. Die ausgewählte Ti45Al55 - Legierung erstarrte unter starker Schmelzkonvektion ebenfalls globulitisch, wobei Reste dendritisch erstarrter properitektischer Phase gefunden wurden. Der Volumenanteil der properitektischen Phase steigt dabei mit zunehmender Rührwirkung an. Der Wechsel der Morphologie von dendritisch zu globular/dendritisch kann mit sphärischem Wachstum oder Fragmentierung der Dendritenarme erklärt werden. Die mechanischen Eigenschaften unter unterschiedlicher Schmelzkonvektion erstarrter Ti45Al55 – Legierung wurden bei Druckversuchen untersucht. Es wurde eine signifikant höhere plastische Verformbarkeit an der unter starker Schmelzkonvektion erstarrten Ti45Al55 – Legierung gefunden. Dies wird der isotropen spherischen Morphologie der lamellaren a2/g-Phase zugeordnet, während die anisotrope Orientierung der dendritisch- lamellaren Phase unerwünschte plastische Eigenschaften zeigt. Die Untersuchungen des Einflusses der Schmelzkonvektion auf das Gefüge peritektisch erstarrender Legierungen zeigten, dass ein maßgeschneidertes Gefüge durch optimale Wahl der Schmelzkonvektion möglich ist und damit magnetische bzw. mechanische Eigenschaften verbessert werden können. Die Kontrolle der Schmelzkonvektion ist daher ein geeignetes Mittel gewünschte Gefüge und Eigenschaften in Abhängigkeit von den Prozessabläufen einzustellen. / In this work, the effect of melt convection on the microstructure evolution of peritectic Nd-Fe-B and Ti-Al alloy systems was studied using novel techniques. The microstructural formation including the change in volume fraction and morphology of the properitectic phase influences the magnetic and mechanical properties for the Nd-Fe-B and Ti-Al alloy systems, respectively. On the basis of numerical simulations by the research group of Dr. Gunter Gerbeth from Department of Magnetohydrodynamics, Forschungszentrum Dresden-Rossendorf, two types of specially designed facilities were developed where melt convection can be altered by changing a number of parameters. These are: forced rotation facility and modified floating zone facility. According to the numerical simulation, an additional crucible rotation suppresses the internal melt motion significantly during forced rotation experiments, where the molten alloy is rotated at a well-defined frequency. This method was applied during the solidification of Nd-Fe-B alloys with the aim to suppress the volume fraction of undesired soft magnetic a-Fe phase. As a result, the volume fraction of properitectic phase with this method can be reduced up to 38 %. A detailed statistical analysis of secondary dendritic arm spacing (SDAS) measurements of a-Fe showed that the SDAS decreases as the rotational frequency increases and melt convection decreases. The reduction in the phase fraction and SDAS of properitectic phase is attributed to the reduced convective mass transfer under reduced melt motion. At high fluid velocity and low rotational frequency, the stronger interdendritic flow reduces the solute boundary layer and increases the transfer of solute through the interface. The smaller dendrite arms dissolve into the melt and thus the SDAS becomes higher than that of the samples solidified at higher rotational frequencies with reduced melt convection. Floating zone facility, which allows contactless heating without any contamination for highly reactive melts, was modified with a double coil system so that an additional electromagnetic force is introduced inside the melt. This induces either very intensive (two-phase stirrer in parallel connection coil system) or very reduced flow (series connection coil system) inside the melt The experimental results of series connection coil system showed that a reduced melt convection state is achieved near 5.1 mm coil distance where a-Fe volume fraction becomes minimum. On the contrary, the parallel coil system experiments showed that a-Fe volume fraction becomes maximum when the phase shift between the coils is close to 90°. The morphology of the a-Fe becomes globular due to spherical growth under strong convection. The study on the effect of strong stirring was extended to another alloy to get a generalized idea about the influence of melt convection on the microstructure development and resulting properties of peritectic alloys. Peritectic Ti45Al55 alloys were investigated by the two-phase stirrer using the coils connected in parallel to study the effect of enhanced melt convection. The increase in the properitectic phase fraction together with a strong change in the morphology from dendritic to spherical were observed in the stirred samples. The increase in the properitectic phase fraction occurs due to the enhanced effective mass transfer under strong melt convection. The change in morphology of the properitectic phase is attributed to spherical growth or fragmentation of dendrite arms under strong convection. The mechanical properties of Ti45Al55 alloys, which are solidified at different convection states, were studied. There was a significantly higher plastic deformability of stirred samples compared to unstirred samples. The coarse anisotropic orientation of the dendritic lamellar phase is detrimental for the plastic deformability, which is absent in the stirred samples due to the spherical and discrete morphology of the properitectic phase. This study indicates that tailored microstructure can be obtained either by decreasing (e.g. for Nd-Fe-B alloy) or increasing (e.g. for Ti-Al alloy) the convection state using effective techniques inside the melt to improve the magnetic and mechanical properties, respectively. Thus, controlling convection is a useful way to get favorable microstructure according to the process need.

Das Hochtemperaturverhalten beeinflusst viele verschiedene Prozesse von der Materialherstellung bis hin zur technologischen Anwendung. In-situ Transmissionselektronenmikroskopie (TEM) bietet die Möglichkeit, die atomaren Prozesse während struktureller Phasenübergänge direkt und in Realzeit zu beobachten. In dieser Arbeit wurde in-situ TEM angewendet, um die Reversibilität des Schmelz- und Kristallisationsprozesses, sowie das anisotropen Sublimationsverhaltens von Ge-Sb-Te (GST) Dünnschichten zu untersuchen. Die gezielte Probenpräparation für die erfolgreiche Beobachtung der Hochtemperatur-Phasenübergänge wird hervorgehoben. Die notwendige Einkapselung für die Beobachtung der Flüssigphase unter Vakuumbedingungen und die erforderliche sauberer Oberfläche für den Sublimationsprozess werden detailliert beschrieben. Außerdem wird die Elektronenenergieverlustspektroskopie eingesetzt um die lokale chemische Zusammensetzung vor und nach den Übergängen zu bestimmen. Die Untersuchung der Grenzflächenstruktur und Dynamik sowohl beim Phasenübergang fest-flüssig als auch flüssig-fest zeigt Unterschiede zwischen den beiden Vorgängen. Die trigonale Phase von GST weist beim Schmelzen eine teilweise geordnete Übergangszone an der fest-flüssig-Grenzfläche auf, während ein solcher Zwischenzustand bei der Erstarrung nicht entsteht. Außerdem läuft der Schmelzvorgang zeitlich linear ab, während die Kristallisation durch eine Wurzelabhängigkeit von der Zeit mit überlagerter Start-Stopp-Bewegung beschrieben werden kann. Der Einfluss der Substrat-Grenzfläche wird diskutiert und die Oberflächenenergie von GST bestimmt. Die anisotrope Dynamik führt beim Phasenübergang fest-gasförmig der kubischen Phase von GST zur Ausbildung stabiler {111} Facetten. Dies erfolgt über die Bildung von Kinken und Stufen auf stabilen Terrassen. Die Keimbildungsrate und die bevorzugten Keimbildungsorte der Kinken wurden identifiziert und stimmen mit den Voraussagen des Terrassen-Stufen-Kinken Modells überein. / High-temperature behavior influence many different processes ranging from material processing to device applications. In-situ transmission electron microscopy (TEM) provides the means for direct observation of atomic processes during structural phase transitions in real time. In this thesis, in-situ TEM is applied to investigate the reversibility of the melting and solidification processes as well as the anisotropic sublimation behavior of Ge-Sb-Te (GST) thin films. The purposeful sample preparation for the successful observation of the high-temperature phase transitions is emphasized. The required encapsulation for the observation of the liquid phase inside the vacuum conditions and the necessary clean surface for sublimation process are discussed in detail. Additionally electron energy-loss spectroscopy in the TEM is used to determine the local chemical composition before and after the phase transitions. The analysis of the interface structure and dynamic during the solid-to-liquid as well as the liquid-to-solid phase transition shows differences between both processes. The trigonal phase of GST exhibits a partially ordered transition zone at the solid-liquid interface during melting while such an intermediate state does not form during solidification. Additionally the melting process proceeds with linear dependence on time, whereas crystallization can be described as having a square-root time-dependency featuring a superimposed start-stop motion. The influence of the interface is addressed and the surface energies of GST are determined. The anisotropic dynamic of the solid-to-gas phase transition of the cubic GST phase leads to the formation of stable {111} facets. This happens via kink and step nucleation on stable terraces. The nucleation rates and the preferred kink nucleation sites are identified and are in accordance with the predictions of terrace-step-kink model.

Melt flow plays an important role in directional solidification of multicrystalline silicon influencing the temperature field and the crystallization interface as well as the transport of impurities. This work investigates the potential of a traveling magnetic field (TMF) for an active control of the melt flow. A system of 3D numerical models was developed and adapted based on open-source software for calculations of Lorentz force, melt flow, and related phenomena. Isothermal and non-isothermal model experiments with a square GaInSn melt were used to validate the numerical models by direct velocity measurements. Several new 3D flow structures of turbulent TMF flows were observed for different melt heights. Further numerical parameter studies carried out for silicon melts showed that already a weak TMF-induced Lorentz force can stir impurities near to the complete mixing limit. Simultaneously, the deformed temperature field leads to an increase of the deflection of crystallization interface, which may exhibit a distinct asymmetry. The numerical results of this work were implemented in a research-scale silicon crystallization furnace. Scaling laws for various phenomena were derived allowing a limited transfer of the results to the industrial scale.

Techn. Universiẗat, Diss., 2002--Darmstadt.

Röntgenradioskopische Bildgebungsverfahren ermöglichen es, ein besseres Verständnis der zweiphasigen Strömungsphänomene und der Prozesse der Mikrostrukturentstehung während der Erstarrung in Metallschmelzen intuitiv zu gewinnen, da diese Verfahren die innere Gestalt der sonst undurchsichtigen Flüssigkeiten abbilden. In der vorliegenden Arbeit wurden dazu Untersuchungen zu zwei unterschiedlichen Teilaufgaben durchgeführt. Zum einen wurde die Dichteverteilung in dünnen Erstarrungsproben in Echtzeit und in-situ mit räumlichen Auflösungen von wenigen Mikrometern untersucht, um den Einfluss natürlicher und erzwungener Schmelzenströmungen auf die Erstarrung einer binären Gallium-Indium-Metalllegierung experimentell nachzuweisen. Zum anderen wurden Gasblasenströmungen in nichttransparenten Metallschmelzen nicht-invasiv und in-situ visualisiert und charakterisiert, um Kenntnis der Eigenschaften und der Bewegung von Argon-Einzelblasen und Blasenketten in flüssigem Gallium-Indium-Zinn ohne und unter dem Einfluss eines externen magnetischen Feldes zu erlangen. Diese experimentellen Untersuchungen wurden mit einem Mikrofokus-Röntgenbildgebungssystem durchgeführt. Die Implementation angepasster Bildverarbeitungs-algorithmen ermöglichte die präzise quantitative Vermessung der dendritischen Strukturparameter und der Wachstumsgeschwindigkeiten. Die Strömungsgeschwindigkeiten in der Schmelze vor der Erstarrungsfront wurden durch Berechnung des optischen Flusses in den Röntgenbildsequenzen vermessen. Thermosolutale Konvektionsbewegungen und der Einfluss magnetisch angetriebener erzwungener Schmelzenströmung auf die Gefügeentstehung konnten durch die Röntgenvisualisierung nachgewiesen werden. Die lokale Akkumulation angereicherter Schmelze, das Aufschmelzen von Dendritenarmen und das Entstehen von Entmischungskanälen im Zweiphasengebiet hinter der Erstarrungsfront wurden unmittelbar beobachtet. Für die Untersuchung des Verhaltens von Gasblasen in einer schmalen Flüssigmetall-Blasensäule wurde das Röntgenbildgebungssystem modifiziert. Das ermöglichte die Vermessung der Gasblasengrößen, der Trajektorien und der Geschwindigkeiten zur Charakterisierung der Blasenströmungen. Die Abhängigkeit der Gasblasengrößen von der Benetzung der Mündungsöffnung wurde gezeigt. Vergleichsexperimente im Gas-Wasser-System verdeutlichten die signifikanten Unterschiede der zweiphasigen Gas-Flüssigmetall-Strömungen. / X-ray radioscopic imaging methods enables one to intuitively gain a better understanding of the two-phase flow phenomena and the processes of microstructure formation during solidification in molten metals, as these methods depict the internal shape of the otherwise opaque liquids. In the present work, investigations were carried out on two different subtasks. On one hand, the density distribution in thin solidification samples was investigated in real time and in-situ with a spatial resolution of a few micrometers in order to demonstrate experimentally the influence of natural and forced melt flow on the solidification of a binary gallium-indium (GaIn) metal alloy. On the other hand, gas bubble flows in non-transparent metal melts were visualized and characterized non-invasively and in-situ in order to gain knowledge of the properties and the movement of individual argon bubbles and bubble chains in liquid gallium-indium-tin (GaInSn) without and under the influence of an external magnetic field. These experimental studies were performed with a microfocus X-ray imaging system. The implementation of adapted image processing algorithms enabled the precise quantitative measurement of the dendritic structure parameters and the growth rates. The flow velocities in the melt in front of the solidification front were measured by calculating the optical flow in the X-ray image sequences. Thermosolutal convection and the influence of magnetically driven forced melt flow on the formation of the structure could be demonstrated by the X-ray visualization. The local accumulation of enriched melt, the melting of dendrite arms and the emergence of segregation channels in the two-phase area behind the solidification front were observed directly. The X-ray imaging system was modified to study the behavior of gas bubbles in a narrow column of liquid metal bubbles. This made it possible to measure the gas bubble sizes, the trajectories and the velocities to characterize the bubble flows. The dependence of the gas bubble sizes on the wetting of the nozzle opening was shown. Comparative experiments in the gas-water system clearly revealed the significant differences in two-phase gas-liquid metal flows.

High-entropy alloys (HEAs) have attracted significant interest in the materials science community over the last 15 years. At the first moment, what caught the attention was the fact that these alloys tend to form solid solutions at room temperature, despite being composed of multiple elements in equiatomic or near-equiatomic concentrations. It was initially concluded that the configurational entropy plays a key role in the stabilization of the solid solutions. Later studies revealed the importance of lattice strain enthalpies, enthalpies of mixing, structural mismatch of constituents, and kinetics in phase formation/stability. The study presented in this thesis was branched into three major parts, all related to understanding phase formation, stability, or metastability in this class of alloys. The first part deals with developing an empirical method to predict single-phase solid solution formation in multi-principal element alloys. The second, which makes the core of this thesis, are non-equilibrium solidification studies of CrFeNi and CoCrNi medium-entropy alloys, and CoCrFeNi, Al0.3CoCrFeNi, and NbTiVZr high-entropy alloys. The last part is devoted to understanding the thermophysical properties of CrFeNi, CoCrNi, and CoCrFeNi medium- and high-entropy alloys. An empirical approach, based on the theoretical elastic-strain energy, has been developed to predict the phase formation and its stability for complex concentrated alloys. The conclusiveness of this approach is compared with the traditional empirical rules based on the atomic-size mismatch, enthalpy of mixing, and valence-electron concentration for a database of 235 alloys. The proposed “elastic-strain energy vs. valence-electron concentration” criterion shows an improved ability to distinguish between single-phase solid solutions, mixtures of solid solutions, and intermetallic phases when compared to the available empirical rules used to date. The criterion is especially strong for alloys that precipitate the μ phase. The elastic-strain-energy parameter can be combined with other known parameters, such as those noted above, to establish new criteria which can help in designing novel complex concentrated alloys with the on-demand combination of mechanical properties. The solidification behavior of the CoCrFeNi high-entropy alloy and the ternary CrFeNi and CoCrNi medium-entropy suballoys has been studied in situ using high-speed video-camera and synchrotron X-ray diffraction (XRD) on electromagnetically levitated samples at Leibniz Institute for Solid State and Materials Research Dresden (IFW Dresden) and German Synchrotron DESY, Hamburg. In all alloys, the formation of a primary metastable body-centered cubic bcc phase was observed if the melt was sufficiently undercooled. The delay time for the onset of the nucleation of the stable face-centered cubic fcc phase, occurring within bcc crystals, is inversely proportional to the melt undercooling. The experimental findings agree with the stable and metastable phase equilibria for the (CoCrNi)-Fe section. Crystal-growth velocities for the CrFeNi, CoCrNi, and CoCrFeNi medium- and high-entropy alloys, extracted from the high-speed video sequences in the present study, are comparable to the literature data for Fe-rich Fe-Ni and Fe-Cr-Ni alloys, evidencing the same crystallization kinetics. The effect of melt undercooling on the microstructure of solidified samples is analyzed and discussed in the thesis. To understand the effect of Al addition on the non-equilibrium solidification behavior of the equiatomic CoCrFeNi alloy, the Al0.3CoCrFeNi HEA has been studied. While the quaternary alloy melt could be significantly undercooled, this was not possible in the five-component alloy. Therefore, the investigations on phase formation, crystal growth, and microstructural evolution were confined to the low undercooling regime. In situ XRD measurements revealed that the liquid crystallized into a fcc single-phase solid solution at this undercooling level. However, ex situ XRD revealed the precipitation of the ordered L12 phase for a sample solidified with ΔT = 30 K. Crystal growth velocities are shown to be smaller than in the CoCrFeNi, CrFeNi, and CoCrNi alloys; nonetheless, they are in the same order of magnitude. Spontaneous grain refinement, without the formation of crystal twins, is observed at low undercooling of ΔT = 70 K, which could be explained by the dendrite tip radius dependence on melt undercooling. In situ studies of the equiatomic NbTiVZr refractory high-entropy alloys revealed the effect of processing conditions on the high-temperature phase formation. When the melt was undercooled over 80 K, it crystallized as a bcc single-phase solid solution despite solute partitioning between the dendritic and interdendritic regions. When the sample was solidified from the semisolid state, it resulted in the formation of two additional bcc phases at the interdendritic regions. The crystal growth velocity, as estimated from the high-speed videos, showed pronounced sluggish kinetics: it is 1 to 2 orders of magnitude smaller compared to literature data of other medium and high-entropy alloys. The study of the linear expansion coefficient α and heat capacity at constant pressure 𝐶𝑝 of the equiatomic CoCrFeNi and the medium-entropy CrFeNi and CoCrNi alloys revealed an anomalous behavior with S-shaped curves in the temperature range of 700 – 950 K. The anomalous behavior is shown to be reversible as it occurred during the first and second heating. However, a minimum is only observed on the first heating, while in the second heating a sudden increase of both the α and 𝐶𝑝 occurs at the temperature of the onset of the minima in the first heating. Magnetic moment measurements as a function of temperature showed that the observed anomaly is not associated with the Curie temperature. Consideration of the structural and microstructural evaluation discards a first-order phase transformation or recrystallization as probable causes, at least for the CoCrFeNi and CoCrNi alloys. Based on literature evidence, the anomalies in the temperature dependences of the linear expansion coefficient and heat capacity are believed to be caused by a chemical short-range order transition known as the K-state effect. However, to reveal the exact nature of this phenomenon, further experimental and theoretical studies are required, which is outside the frame of the present work.:Abstract ....................................................................................................................... I Kurzfassung .............................................................................................................. IV Chapter 1: Motivation and Fundamentals .................................................................. 1 1.1 Introduction .......................................................................................................... 1 1.2 The high-entropy alloy (HEA) design concept ...................................................... 4 1.3 Empirical rules of phase formation for HEAs ....................................................... 6 1.4 Calculation of phase diagrams of HEAs ............................................................. 18 1.5 The core effects of HEAs ................................................................................... 20 1.5.1 Lattice distortion .............................................................................................. 20 1.5.2 Sluggish diffusion ............................................................................................ 22 1.5.3 Cocktail effect................................................................................................... 23 1.6 Mechanical properties ........................................................................................ 24 1.6.1 Lightweight high-entropy alloys ....................................................................... 24 1.6.2 Overcoming the strength-ductility tradeoff ...................................................... 26 1.6.3 Cryogenic high-entropy alloys ......................................................................... 28 1.6.4 Refractory high-entropy alloys ........................................................................ 30 1.7 Functional properties .......................................................................................... 33 1.7.1 Soft magnetic properties ................................................................................. 33 1.7.2 Magnetocaloric properties ............................................................................... 35 1.7.3 Hydrogen storage ............................................................................................ 36 Chapter 2: Experimental .......................................................................................... 38 2.1 Sample preparation ............................................................................................ 38 2.2 Electromagnetic levitation .................................................................................. 40 2.3 In situ X-ray diffraction ........................................................................................ 43 2.4 Microstructural and structural analysis ............................................................... 44 2.5 Thermal analysis ................................................................................................ 45 2.6 Dilatometry ......................................................................................................... 45 2.7 Magnetic moment ............................................................................................... 46 2.8 Heat treatment ................................................................................................... 46 Chapter 3: In situ study of non-equilibrium solidification of CoCrFeNi high-entropy alloy and CrFeNi and CoCrNi ternary suballoys ...................................................... 47 3.1 Introduction ........................................................................................................ 47 3.2 Results ............................................................................................................... 48 3.2.1 In situ synchrotron X-ray diffraction ................................................................. 48 3.2.2 High-speed video imaging ............................................................................... 52 3.2.3 Microstructure of the solidified samples .......................................................... 62 3.3 Discussion .......................................................................................................... 64 3.3.1 bcc-fcc nucleation and growth competition ..................................................... 64 3.3.2. Crystal growth kinetics ................................................................................... 68 3.3.3. Microstructural evolution ................................................................................ 70 Chapter 4: The effect of Al addition to the CoCrFeNi alloy on the non-equilibrium solidification behaviour.............................................................................................. 72 4.1 Introduction ........................................................................................................ 72 4.2 Results and Discussion ...................................................................................... 73 Chapter 5: Non-equilibrium solidification of the NbTiVZr refractory high-entropy alloy ................................................................................................................................. 84 5.1 Introduction ........................................................................................................ 84 5.2 Results ............................................................................................................... 85 5.2.1 In situ synchrotron X-ray diffraction ................................................................. 85 5.2.2 Room temperature synchrotron X-ray diffraction ............................................ 88 5.2.3 High-speed video imaging ............................................................................... 89 5.2.4 Microstructure and structure analysis ............................................................. 91 5.3 Discussion .......................................................................................................... 94 5.3.1 Phase formation upon solidification ................................................................ 94 5.3.2 Crystal growth kinetics .................................................................................... 98 5.3.3 Structural and microstructural features............................................................ 99 Chapter 6: Solid-state thermophysical properties of CrFeNi, CoCrNi, and CoCrFeNi medium- and high-entropy alloys ........................................................................... 101 6.1 Introduction ...................................................................................................... 101 6.2 Results ............................................................................................................. 102 6.3 Discussion ........................................................................................................ 106 6.3.1 Thermophysical properties ............................................................................ 106 6.3.2 Short-range order in medium- and high-entropy alloys ................................. 109 Chapter 7: Summary ............................................................................................... 111 7.1 Empirical rule of phase formation of complex concentrated alloys ................... 111 7.2 Non-equilibrium solidification of medium- and high-entropy alloys ................... 111 7.3 Thermophysical properties of the medium- and high-entropy alloys ................ 113 Chapter 8: Outlook ................................................................................................. 115 Appendix 1 .............................................................................................................. 117 Appendix 2 ............................................................................................................. 123 Appendix 3 ............................................................................................................. 133 Appendix 4 ............................................................................................................. 134 References.............................................................................................................. 140 Acknowledgments .................................................................................................. 164 List of publications .................................................................................................. 166 Erklärung ......................................................................................................................... 167

We present a phase-field crystal model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the microscopic density field. We showcase the model capabilities via selected numerical investigations which focus on the prototypical growth of two-dimensional crystals from the melt, resulting in faceted shapes and dendrites. This work sets the grounds for a comprehensive mesoscale model of solidification including thermal expansion.