Ve všeobecnosti, poznatky o design slitin, jejich výrobě a výběru legujúcich prvků sú omezené na slitiny s jedním základním prvkem. Tento fakt ale výrazně limituje možnosti a volnost výběru prvků pro dosáhnuti speciálních vlastností a mikrostruktur. V poslední dekádě se ukázalo, že materiálová věda a inženýrství nejsou ještě zdaleka prozkoumané v důsledku objevu nové třídy materiálů nazvané vysoko entropické slitiny (HEA high entropy alloys). Jejich objev upoutal pozornost vědecké komunity. Základní koncept pro jejich design je, že namísto jednoho, nebo dvou základních prvků obsahují minimálně 5 prvků v podobných atomových koncentracích. V posledních letech se objevila skupina materiálů odvozená od HEA, nazvaná slitiny so střednou entropii (MEA medium entropy alloys). Na rozdíl od HEA ale obsahují 3, nebo 4 prvky. Táto práce je věnovaná studiu přípravy a charakterizaci HEA, MEA a jejich kompozitů s pomocí metod práškové metalurgie. V této práci byli dohromady zkoumány tři kompozice: AlCoCrFeNiTi0.5, Co1.5Ni1.5CrFeTi0.5 a CoCrNi, kompozity s kovovou matricí (MMC metal matrix composites) vyztužené částicemi B4C s CoCrNi jako matricí. Hloubková mikrostrukturní a mechanická analýza těchto materiálů byla provedena pomoví metod rastrovací a transmisní elektronové mikroskopie spojené s tahovými a ohybovými zkouškami. V průběhu celé studie se objevovaly problémy s kontaminací kyslíkem, co se projevilo vznikem značného množství oxidů v připravených materiálech. U Slitiny AlCoCrFeNiTi0.5 byla naměřena tvrdost přesahující 800 HV. Její houževnatost ale byla velice omezena. V její mikrostruktuře byly identifikovány částice in-situ TiC v důsledku přítomnosti organického, anti-aglomeračního činidla (metanolu) v mlecí misce. Tato reakce může být použita v budoucnu k přípravě MMC se záměrnou disperzí TiC. Na druhé straně, slitina CoCrNi ukázala vysoké hodnoty tažnosti (26%) a meze pevnosti přes 1000 MPa. Mikrostruktura obsahovala majoritní FCC fázi s BCC precipitáty. Tahle slitina byla z důvodu vysoké tažnosti zvolena pro přípravu kompozitu s výztuží B4C. V průběhu slinování ale došlo k reakci mezi přítomným Cr a B4C, které výsledkem byl Cr5B3 borid. Tento kompozit mel pevnost v tahu 1400 MP a extrémne jemnozrnnou strukturu. Celková tažnost ale klesla na 1.9 %. Slitina AlCoCrFeNiTi0.5, která mela strukturu složenou jen z FCC tuhého roztoku dosáhla nejlepší kombinaci mechanických vlastností s pevností přesahující 1300 MPa a dostatečnou tažností 4%. Prášková metalurgie se ukázala jako vhodná metoda pro přípravu HEA a MEA slitin a jejich kompozitů, s dobrou kombinací pevnosti a tažnosti. Tato metoda dovoluje měnit mikrostrukturní parametry připravených materiálů jednoduchou úpravou parametrů procesu.

This Master’s thesis is focused on theoretical study of the high entropy alloy CoCrNi using ab initio calculations. The focus was on the effect of short range order on the relative stability of FCC and HCP structures and the value of stacking fault energy.The results show increase of stability in both types of structures wtih decreasing number of Cr-Cr nearest neighbours. The effect of the number of Cr-Cr nearest neighbours on the stacking fault energy previously shown in literature was not observed. However the strong dependency was found on the change of short range order caused by the shift of (1 1 1) planes after the transformation from the FCC to HCP structure. The effect of interstitial atoms C a N was also studied. Both these interstitials stabilise FCC structure and thus cause the increase of stacking fault energy. Both interstitials prefer octahedral positions with higher amount of Cr in their nearest neighbour shell.

This work identifies alloy terminal freezing range, columnar growth, grain coarsening, liquid availability towards the terminal stage of solidification, and segregation towards boundaries as primary factors affecting the hot-cracking susceptibility of fusion-based additive manufacturing (F-BAM) processed alloys. Additionally, an integrated computational materials engineering (ICME)-based approach has been formulated to design novel Al alloys, and high entropy alloys for F-BAM processing. The ICME-based approach has led to heterogeneous nucleation-induced grain refinement, terminal eutectic solidification-enabled liquid availability, and segregation-induced coalescence of solidification boundaries during laser-powder bed fusion (L-PBF) processing. In addition to exhibiting a wide crack-free L-PBF processing window, the designed alloys exhibited microstructural heterogeneity and hierarchy (MHH), and thus could leverage the unique process dynamics of L-PBF to produce a fine-tunable MHH and mechanical behavior. Furthermore, alloy chemistry-based fine tuning of the stacking fault energy has led to transformative damage tolerant alloys. Such alloys can shield defects stemming from the stochastic powder bed in L-PBF, and consequently can prevent catastrophic failure despite the solidification defects. A modified materials systems approach that explicitly includes alloy chemistry as a means to modify the printability, properties and performance with F-BAM is also presented. Overall, this work is expected to facilitate application specific manufacture with F-BAM and eventually facilitate widespread adoption of F-BAM in structural application.

The novel alloying concept of high-entropy alloys (HEAs) has been the focus of many recent investigations revealing an interesting combination of properties. Alloying with aluminium and titanium showed strong influence on microstructure and phase composition. However, detailed investigations on the influence of titanium are lacking. In this study, the influence of titanium in the alloy system AlCoCrFeNiTix was studied in a wide range (molar ratios x = 0.0; 0.2; 0.5; 0.8; 1.0; 1.5). Detailed studies investigating the microstructure, chemical composition, phase composition, solidification behaviour, and wear behaviour were carried out. Alloying with titanium showed strong influence on the resulting microstructure and lead to an increase of microstructural heterogeneity. Phase analyses revealed the formation of one body-centred cubic (bcc) phase for the alloy without titanium, whereas alloying with titanium caused the formation of two different bcc phases as main phases. Additional phases were detected for alloys with increased titanium content. For x ≥ 0.5, a minor phase with face-centred cubic (fcc) structure was formed. Further addition of titanium led to the formation of complex phases. Investigation of wear behaviour revealed a superior wear resistance of the alloy AlCoCrFeNiTi0.5 as compared to a bearing steel sample.

The high entropy alloys (HEAs) have been developed based on the concept of entropic stabilization associated with a large number of constituent elements. The high configurational entropy in HEAs is expected to cause promising characteristic properties, i.e. high microstructural stability and high mechanical properties. In this study, the equiatomic fcc-structured FeNiCoCrMn and the bcc-structured TiNbHfTaZr single phase high entropy alloys (HEAs) were investigated regarding the effect of multiple atom species on microstructure, intrinsic lattice strain and mechanical properties. In a comparison with the HEAs, the sub-alloys having less chemical complexity were studied. The selected sub-alloys of the FeNiCoCrMn HEA were FeNiCoCr, FeNiCo, FeNi alloys and pure Ni, while equiatomic TiNbHfTa, TiNbHf, TiNb alloys and pure Nb were studied to compare with the TiNbHfTaZr HEA. The samples in this study were prepared by arc-melting, cold-crucible casting and thermomechanical treatment. The thermal phase stability of the FeNiCoCrMn HEA, TiNbHfTaZr HEA and their sub-alloys were observed and no second phase was formed between 300 - 1500 K. In high entropy alloys, the random arrangement of multiple atom species is assumed to cause large atomic displacements at lattice sites, which give rise to a severe lattice distortion. The evidences of lattice distortion in HEAs have been limitedly reported due to a difficulty of experimental investigation. In this work, the pair distribution function (PDF) method was used to assess local strain with analysis of diffuse intensities on total synchrotron X-ray scattering data. The current study found that the level of local lattice strain associated with atomic displacement was a function of atomic size misfit. The local lattice strain of the FeNiCoCrMn HEA was small and comparable to that of the sub-alloys which obtain similar values of the atomic size misfit. In contrast to the FeNiCoCrMn system, the magnitude of the local lattice strain increased with the value of atomic size misfit from the unary Nb sample to the quinary TiNbHfTaZr HEA. The lattice distortion was evident in the TiNbHfTaZr HEA due to large local lattice strain, but the local lattice strain of the FeNiCoCrMn HEA was not anomalously large. The level of lattice strain determines the solid solution hardening as a consequence of the elastic interaction between dislocations and atoms. The comparable level of the lattice strain in the FeNiCoCrMn HEA, its sub-alloys and Ni sample led to narrow range of hardness (64 – 132 HV) and tensile yield strength (60 – 192 MPa). For the bcc-structured samples, the hardness and the yield strength significantly varied depending on the level of local lattice strain, between 80 – 327 HV of hardness and 207 – 985 MPa of tensile yield strength. It is clear from the result that the atomic size misfit influences the level of the local lattice strain and the solid solution hardening. Cold rotary swaging was used to study the work hardening in the HEAs because it can delay fracture by large hydrostatic stresses. The large plastic deformability was observed in the FeNiCoCrMn and TiNbHfTaZr HEAs. The TiNbHfTaZr HEA was cold-swaged by 90% reduction of the cross-sectional area without intermediate annealing. The FeNiCoCrMn HEA was swaged until 85% reduction of the cross-sectional area; however, it was observed that it could be further deformed. The dislocation densities of the HEAs and its sub-alloys after the cold deformation were calculated as in the range between 1014 - 1015 m-2, in a good agreement with reported values of conventional metals after severe plastic deformation. This finding suggested that the level of dislocation density storage was correlated with the number of the constituent elements, the level of lattice distortion associated with atomic size misfit and the intrinsic properties (i.e. the stacking fault energy and the melting point). Whereas the intrinsic lattice strains of the FeNiCoCrMn HEA and its sub-alloys were comparable, the levels of dislocation storage were different possibly due to a difference of stacking fault energy. For the bcc-structured samples, the dislocation densities of the TiNbHfTaZr HEA, TiNbHfTa and TiNbHf alloys were large due to the large atomic size misfits. The high dislocation density leads to strong interactions between dislocations, which results in high resistance to dislocation motions. The high mechanical properties (hardness and yield strength) in the as-deformed FeNiCoCrMn and TiNbHfTaZr HEA were presented with the evidence of high dislocation densities. Moreover, the hardness and yield strength of the FeNiCoCrMn HEA significantly increased by the deformation, while those of the TiNbHfTaZr HEA after the deformation were slightly changed from the undeformed HEA. The large work hardenability of the FeNiCoCrMn HEA is possibly caused by small solid solution hardening and ease of twin formation. The research results suggest a further step towards designing an alloy composition for a development of microstructure and mechanical properties of high entropy alloys. It is evidently clear from the findings that the large number of constituent elements (in a term of high configurational entropy) is not only a factor in the determination of lattice distortion, microstructure and mechanical properties, but the type and the combination of constituent elements including the atomic interactions (i.e. atomic size misfit) have also an effect.:Abstract v Zusammenfassung ix Contents xiii 1. Motivation and objectives 1 2. Fundamentals 5 2.1 Concept of high entropy alloys 5 2.1.1 Phase formation and thermodynamic 5 2.1.2 Four core effects 10 2.2 Alloy classification of high entropy alloys 13 2.3 Mechanical properties of high entropy alloys 14 3. Experiments 19 3.1 Alloy preparation 19 3.1.1 Alloy selection 19 3.1.2 Melting and casting 21 3.1.3 Thermomechanical treatment 23 3.2 Sample characterization 27 3.2.1 Chemical analyses 27 3.2.2 Differential scanning calorimetry (DSC) 27 3.2.3 Scanning electron microscopy and microstructural analyses 28 3.2.4 X-ray diffraction (XRD) 29 3.2.5 High energy synchrotron X-ray diffraction 29 3.2.6 Mechanical Properties 33 4. Thermal phase stability of single phase high entropy alloys 35 5. An assessment of lattice strain in single phase high entropy alloys 49 5.1 Analysis of micro lattice strain on fcc- and bcc-structured high entropy alloys 50 5.2 Analysis of local lattice strain on fcc- and bcc-structured high entropy alloys 56 6. Solid solution hardening in single phase high entropy alloys 65 6.1 Hardness of fcc- and bcc-structured high entropy alloys 65 6.2 Tensile strength of fcc- and bcc-structured high entropy alloys 70 6.3 Correlation between atomic size misfit and solid solution hardening in Ti-Nb-Hf-Ta-Zr system 82 7. Work hardening in single phase high entropy alloys 91 7.1 Work hardenability of fcc- and bcc-structured high entropy alloys 91 7.2 Dislocation density of fcc- and bcc-structured high entropy alloys after cold swaging 93 8. Summary and outlook 109 8.1 Summary 109 8.2 Outlook 112 References 113 Acknowledgements 131 Erklärung 133 / Die Hochentropielegierungen (HELen) wurden auf der Grundlage des Konzepts der entropischen Stabilisierung entwickelt, was eine große Anzahl von Legierungselementen beinhaltet. Es wird erwartet, dass die hohe Konfigurationsentropie in HELen vielversprechende charakteristische Eigenschaften hervorruft, d.h. hohe mikrostrukturelle Stabilität und hohe mechanische Eigenschaften. In dieser Studie wurden die äquiatomare kfz-strukturierte FeNiCoCrMn und die krz-strukturierte TiNbHfTaZr Einphasen-Hochentropielegierung hinsichtlich der Wirkung mehrerer Atomarten auf das Gefüge, die intrinsische Gitterdehnung und die mechanischen Eigenschaften untersucht. Im Vergleich zu den HELen wurden die Sublegierungen mit geringerer chemischer Komplexität untersucht. Die ausgewählten Sublegierungen der FeNiCoCrMn HEL waren FeNiCoCr, FeNiCo, FeNi-Legierungen und reines Ni, während äquiatomare TiNbHfTa, TiNbHf, TiNbHf, TiNb-Legierungen und reines Nb im Vergleich zur TiNbHfTaZr HEL untersucht wurden. Die Proben in dieser Studie wurden durch Lichtbogenschmelzen, Kalttiegelguss und thermomechanische Behandlung hergestellt. Die thermische Phasenstabilität der FeNiCoCrMn HEL, der TiNbHfTaZr HEL und ihrer Sublegierungen wurde untersucht und es wurde keine zweite Phase zwischen 300 - 1500 K gebildet. Bei Hochentropielegierungen wird angenommen, dass die zufällige Anordnung mehrerer Atomarten zu großen Atomverschiebungen an den Gitterplätzen führt, die eine starke Gitterverzerrung hervorrufen. Aufgrund der Schwierigkeit der experimentellen Untersuchung wurden Beweise für Gitterverzerrungen bei HELen nur begrenzt berichtet. In dieser Studie wurde die Methode der Paarverteilungsfunktion (PDF) verwendet, um die lokale Dehnung mit Analyse der diffusen Intensitäten der gesamten Synchrotron-Röntgenstreuungsdaten zu beurteilen. Die aktuelle Studie ergab, dass die Höhe der lokalen Gitterdehnung, die mit der atomaren Verschiebung einhergeht, eine Funktion der Differenz der Atomgröße ist. Die lokale Gitterdehnung der FeNiCoCrMn HEL war klein und vergleichbar mit der der Sublegierungen, für die ähnliche Werte für die Atomgrößen-Unterschiede ermittelt wurden. Im Gegensatz zum FeNiCoCrMn-System stieg die Größe der lokalen Gitterdehnung mit dem Wert der Atomgrößendifferenz von der unären Nb-Probe bis zur quinären TiNbHfTaZr HEL. Die Gitterverzerrung war in der TiNbHfTaZr HEL aufgrund der großen lokalen Gitterdehnung offensichtlich, wohingegen die lokale Gitterdehnung der FeNiCoCrMn HEL nicht ungewöhnlich groß war. Die Höhe der Gitterdehnung bestimmt die Mischkristallverfestigung als Folge der elastischen Wechselwirkung zwischen Versetzungen und Atomen. Der vergleichbare Wert der Gitterdehnung in der FeNiCoCrMn HEL, seinen Sublegierungen und den Ni-Proben führte zu einem engen Härte- (64 - 132 HV) und Streckgrenzenbereich (60 - 192 MPa). Für die krz-strukturierten Proben variierten die Härte und die Streckgrenze dagegen je nach Höhe der lokalen Gitterdehnung signifikant, d.h zwischen 80 - 327 HV hinsichtlich der Härte und zwischen 207 - 985 MPa hinsichtlich der Streckgrenze. Aus dem Ergebnis ist ersichtlich, dass die Differenz der Atomgröße einen Einfluss auf die Höhe der lokalen Gitterdehnung und die Mischkristallverfestigung hat. Das Kalthämmen wurde für die Untersuchung der Kaltverfestigung in den HELen genutzt, da es den Bruch durch die großen hydrostatischen Spannungen verzögern kann. Die große plastische Verformbarkeit wurde bei den FeNiCoCrMn und TiNbHfTaZr HELen beobachtet. Die TiNbHfTaZr HEL wurde ohne Zwischenglühen um 90% der Querschnittsfläche kaltgehämmert. Die FeNiCoCrMn HEL wurde bis zu einer Verkleinerung der Querschnittsfläche von 85% gehämmert, wobei jedoch eine weitere Verformung möglich gewesen wäre. Die Versetzungsdichten der HELen und ihrer Sublegierungen wurden nach dem Verformung in einem Bereich zwischen 1014 - 1015 m-2 berechnet, was in guter Übereinstimmung mit den berichteten Werten konventioneller Metalle nach starker plastischer Verformung ist. Dieses Ergebnis deutete darauf hin, dass die Höhe der gespeicherten Versetzungsdichte mit der Anzahl der beinhaltenden Elemente, dem Grad der Gitterverzerrung im Zusammenhang mit der Differenz der Atomgröße und den intrinsischen Eigenschaften (d.h. der Stapelfehlerenergie und dem Schmelzpunkt) korreliert. Obwohl die intrinsischen Gitterdehnungen der FeNiCoCrMn HEL und seiner Sublegierungen vergleichbar waren, waren die Werte der gespeicherten Versetzungen unterschiedlich, was möglicherweise an einer Differenz der Stapelfehlerenergie lag. Für die krz-strukturierten Proben waren die Versetzungsdichten der TiNbHfTaZr HEL, der TiNbHfTa- und der TiNbHf-Legierungen aufgrund der großen Atomgrößenunterschiede hoch. Die hohe Versetzungsdichte bewirkt starke Wechselwirkungen zwischen den Versetzungen, was zu einem hohen Widerstand gegen Versetzungsbewegungen führt. Die hohen mechanischen Eigenschaften (Härte und Streckgrenze) in den verformten FeNiCoCrMn und TiNbHfTaZr HELen wurden mit dem Nachweis hoher Versetzungsdichten belegt. Darüber hinaus wurden die Härte und die Streckgrenze des FeNiCoCrMn HEL durch das Kalthämmern deutlich erhöht, während die der TiNbHfTaZr HEL nach dem Hämmerprozess nur leicht gegenüber der unverformten HEL verändert wurden. Die große Kaltverfestigung der FeNiCoCrMn HEL ist möglicherweise auf eine geringe Mischkristallhärtung und eine geringfügige Zwillingsbildung zurückzuführen. Die Forschungsergebnisse empfehlen für die Entwicklung des Gefüges und der mechanischen Eigenschaften von Hochentropielegierungen weitere Schritte hinsichtlich eines zielführenden Legierungsdesigns durchzuführenhin. Aus den Ergebnissen geht eindeutig hervor, dass die große Anzahl an Legierungselementen ( hinsichtlich einer hochkonfigurativen Entropie) nicht die einzige Einflussgrößebei der Bestimmung von Gitterverzerrungen, dem Gefüge und der mechanischen Eigenschaften darstellt, sondern auch die Art und die Kombination der Legierungselementen einschließlich der atomaren Wechselwirkungen (d.h. Atomgrößenunterschiede) einen Effekt haben.:Abstract v Zusammenfassung ix Contents xiii 1. Motivation and objectives 1 2. Fundamentals 5 2.1 Concept of high entropy alloys 5 2.1.1 Phase formation and thermodynamic 5 2.1.2 Four core effects 10 2.2 Alloy classification of high entropy alloys 13 2.3 Mechanical properties of high entropy alloys 14 3. Experiments 19 3.1 Alloy preparation 19 3.1.1 Alloy selection 19 3.1.2 Melting and casting 21 3.1.3 Thermomechanical treatment 23 3.2 Sample characterization 27 3.2.1 Chemical analyses 27 3.2.2 Differential scanning calorimetry (DSC) 27 3.2.3 Scanning electron microscopy and microstructural analyses 28 3.2.4 X-ray diffraction (XRD) 29 3.2.5 High energy synchrotron X-ray diffraction 29 3.2.6 Mechanical Properties 33 4. Thermal phase stability of single phase high entropy alloys 35 5. An assessment of lattice strain in single phase high entropy alloys 49 5.1 Analysis of micro lattice strain on fcc- and bcc-structured high entropy alloys 50 5.2 Analysis of local lattice strain on fcc- and bcc-structured high entropy alloys 56 6. Solid solution hardening in single phase high entropy alloys 65 6.1 Hardness of fcc- and bcc-structured high entropy alloys 65 6.2 Tensile strength of fcc- and bcc-structured high entropy alloys 70 6.3 Correlation between atomic size misfit and solid solution hardening in Ti-Nb-Hf-Ta-Zr system 82 7. Work hardening in single phase high entropy alloys 91 7.1 Work hardenability of fcc- and bcc-structured high entropy alloys 91 7.2 Dislocation density of fcc- and bcc-structured high entropy alloys after cold swaging 93 8. Summary and outlook 109 8.1 Summary 109 8.2 Outlook 112 References 113 Acknowledgements 131 Erklärung 133

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Fundamental understanding of high strain rate deformation behavior of materials is critical in designing new alloys for wide-ranging applications including military, automobile, spacecraft, and industrial applications. High entropy alloys, consisting of multiple elements in (near) equimolar proportions, represent a new paradigm in structural alloy design providing ample opportunity for achieving excellent performance in high strain rate applications by proper selection of constituent elements and/or thermomechanical processing. This dissertation is focused on fundamental understanding of high strain-rate deformation behavior of several high entropy alloy systems with widely varying microstructures. Ballistic impact testing of face centered cubic Al0.1CoCrFeNi high entropy alloy showed failure by ductile hole growth. The deformed microstructure showed extensive micro-banding and micro-twinning at low velocities while adiabatic shear bands and dynamic recrystallization were seen at higher velocities. The Al0.7CoCrFeNi and AlCoCrFeNi2.1 eutectic high entropy alloys, with BCC and FCC phases in lamellar morphology, showed failure by discing. A network of cracks coupled with small and inhomogeneous plastic deformation led to the brittle mode of failure in these eutectic alloys. Phase-specific mechanical behavior using small-scale techniques revealed higher strength and strain rate sensitivity for the B2 phase compared to the L12 phase. The interphase boundary demonstrated good stability without any cracks at high compressive strain rates. The Al0.3CoCrFeNi high entropy alloy with bimodal microstructure demonstrated an excellent combination of strength and ductility. Ballistic impact testing of Al0.3CoCrFeNi alloy showed failure by ductile hole growth and demonstrated superior performance compared to all the other high entropy alloy systems studied. The failure mechanism was dominated by micro-banding, micro-twining, and adiabatic shear localization. Comparison of all the high entropy alloy systems with currently used state-of-the-art rolled homogenous armor (RHA) steel showed a strong dependence of failure modes on microstructural features.

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

<p>  </p> <p>This work explored the dynamic behavior and failure mechanisms of an additively manufactured high-entropy alloy (HEA) when subjected to high-strain rate shock impacts. A laser-induced projectile impact testing (LIPIT) setup was used to study the dynamic behavior of the Cantor alloy CoCrFeMnNi samples manufactured using a directed-energy deposition technique. HEA flyers were accelerated by a pulse laser to velocities up to 1 km/s prior to impact with lithium fluoride glass windows. A photon Doppler velocimetry (PDV) system recorded the velocity of the flyer during the acceleration and subsequent impact. From this velocity profile, the Hugoniot coefficient and sound speed of the HEA samples were determined.</p> <p><br></p> <p>Upon determination of key shock parameters, spallation occurring due to shock was analyzed. Using the same LIPIT and PDV systems as the earlier testing, aluminum flyers of various thicknesses were accelerated into HEA samples. The back-surface velocity profiles of the HEA samples showed a characteristic “pullback” caused by the interaction of the tensile stress waves indicative of spall occurrence in the material. The magnitude of this pullback and the material properties determined in the first experiments allow for the measurement of spall strength at various strain-rates. This data is compared to previous data looking at similar HEAs manufactured using traditional methods. A comparison of this data showed that the spall strength of the HEA samples was equivalent to that of similar alloys but at significantly higher strain rates. As an increased strain-rate tends to result in increased spall strengths, further examination was needed to determine the reasons for this decreased spall strength in the AM samples.</p> <p><br></p> <p>Post-shock specimen recovery allowed for the failure mechanisms behind the spallation to be observed. Scanning electron microscope (SEM) images of the cross-section of the samples showed ductile fracture and void growth outside of the predicted spall region. Further imaging using energy dispersive spectroscopy (EDS) showed the presence of potentially chromium-oxide deposits in regions outside of the predicted spall plane. It is hypothesized that these regions created nucleation points about which spallation occurred. Thus, to achieve spall strength in AM HEAs equivalent to strengths in traditionally-casted alloys, the AM sample must be refined to reduce the occurrence of these deposits and voids.  </p>

The irradiation of crystalline materials in environments such as nuclear reactors leads to the accumulation of micro and nano-scale defects with a negative impact on material properties such as strength, corrosion resistance, and dimensional stability. Point defects in the crystal lattice, the vacancy and self-interstitial, form the basis of this damage and are capable of migrating through the lattice to become part of defect clusters and sinks, or to annihilate themselves. Recently, attention has been given to HEAs for fusion and fission components, as some materials of this class have shown resilience to irradiation-induced damage. The ability to predict defect diffusion and accelerate simulations of defect behaviour in HEAs using ML techniques is consequently a subject that has gathered significant interest. The goal of this work was to produce an unsupervised neural network capable of learning the interatomic dynamics within a specific HEA system from MD data in order to create a KMC type predictor of defect diffusion paths for common point defects in crystal systems such as the vacancy and self-interstitial. Self-interstitial defect states were identified and purified from MD datasets using graph-isomorphism, and a proof-of-concept model for the HEA environment was used with several interaction setups to demonstrate the feasibility of training a GCN to predict vacancy defect transition rates in the HEA crystalline environment.