Spinodal decomposition is a phase separation mechanism within the miscibility gap. Its importance in case of Fe-Cr system, the basis of the whole stainless steel family, stems from a phenomenon known as the “475oC embrittlement” which results in a ruin of mechanical properties of ferritic, martensitic and duplex stainless steels. This work is aimed at a better understanding of the phase separation process in   the Fe-Cr system. Alloys of 10 to 55 wt.% Cr , each five percent, were homogenized to achieve fully ferritic microstructure and then isothermally aged at 400, 500 and 600oC for different periods of time ranging from 30min to 1500 hours. Hardness of both homogenized and aged samples were measured by the Vickers micro-hardness method and then selected samples were studied by means of Transmission Electron Microscopy (TEM).  It was observed that hardness of homogenized samples increased monotonically with increasing Cr content up to 55 wt.% which can be attributed to solution hardening as well as higher hardness of pure chromium compared to pure iron.  At 400oC no significant change in hardness was detected for aging up to 1500h, therefore we believe that phase separation effects at 400oC are very small up to this time. Sluggish kinetics is imputed to lower diffusion rate at lower temperatures. At 500oC even after 10h a noticeable change in hardness, for alloys containing 25 wt.% Cr and higher, was observed which indicates occurrence of phase separation. The alloy with 10 wt.% Cr did not show change in hardness up to 200h which suggests that this composition falls outside the miscibility gap at 500oC. For compositions of 15 and 20 wt.% Cr only a small increase in hardness was detected even after 200h of aging at 500oC, which could be due to the small amounts of α´ formed. However, it means that alloys of 15 wt.% Cr and higher are suffering phase separation. For compositions inside the miscibility gap, hardening effect is a result of phase separation either by nucleation and growth or spinodal decomposition. To distinguish between these two mechanisms, TEM studies were performed and we found evidence that at 500oC the Fe-25 wt.% Cr sample decomposes by nucleation  and growth  while that of 35 wt.% Cr  shows characteristics of the spinodal mechanism. For compositions inside the miscibility gap, with increasing Cr content up to 40% the change in hardness generally increased and for 45% and higher it always decreased. This suggests that the composition range corresponding to the spinodal region at 500oC is biased towards the Fe-rich side of the phase diagram. At 600oC only samples of 25, 30 and 35 wt.% Cr were studied because according to the previous studies, the spinodal boundary is most probably located in this composition range. However, no change in hardness was observed even up to 24h. We believe that this means the miscibility line lies below 600oC for alloys containing 35 wt.% Cr and lower. Further investigations are needed to confirm and explain this result.

Duplex stainless steels (DSSs) are important engineering materials due to their combination of good mechanical properties and corrosion resistance. However, as a consequence of their ferrite content, DSSs are sensitive to the so-called ‘475°C embrittlement’, which is induced by phase separation, namely, the ferrite decomposed into Fe-rich ferrite (α) and Cr-rich ferrite (α'), respectively. The phase separation is accompanied with a severe loss of toughness. Thus, the ‘475°C embrittlement’ phenomenon limits DSSs’ upper service temperature to around 250°C. In the present work, Fe-Cr binary model alloys and commercial DSSs from weldments were investigated for the study of phase separation in ferrite. Different techniques were employed to study the phase separation in model alloys and commercial DSSs, including atom probe tomography, transmission electron microscopy and micro-hardness test. Three different model alloys, Fe-25Cr, Fe-30Cr and Fe-35Cr (wt. %) were analyzed by atom probe tomography after different aging times. A new method based on radial distribution function was developed to evaluate the wavelength and amplitude of phase separation in these Fe-Cr binary alloys. The results were compared with the wavelengths obtained from 1D auto-correlation function and amplitudes from Langer-Bar-On-Miller method. It was found that the wavelengths from 1D auto-correlation function cannot reflect the 3D nano-scaled structures as accurate as those obtained by radial distribution function. Furthermore, the Langer-Bar-On-Miller method underestimates the amplitudes of phase separation. Commercial DSSs of SAF2205, 2304, 2507 and 25.10.4L were employed to investigate the connections between phase separation and mechanical properties from different microstructures (base metal, heat-affected-zone and welding bead) in welding. Moreover, the effect of external tensile stress during aging on phase separation of ferrite was also investigated. It was found that atom probe tomography is very useful for the analysis of phase separation in ferrite and the radial distribution function (RDF) is an effective method to compare the extent of phase separation at the very early stages. RDF is even more sensitive than frequency diagrams. In addition, the results indicate that the mechanical properties are highly connected with the phase separation in ferrite and other phenomena, such as Ni-Mn-Si-Cu clusters, that can also deteriorate the mechanical properties. / <p>QC 20130308</p>

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This thesis is a theoretical study of configurational and magnetic interactions in multicomponent solids. These interactions are the projections onto the configurational and magnetic degrees of freedom of the underlying electronic quantum mechanical system, and can be used to model, explain and predict the properties of materials. For example, the interactions govern temperature induced configurational and magnetic order-disorder transitions in Heusler alloys and ternary nitrides. In particular three perspectives are studied. The first is how the interactions can be derived from first-principles calculations at relevant physical conditions. The second is their consequences, like the critical temperatures for disordering, obtained with e.g. Monte Carlo simulations. The third is their origin in terms of the underlying electronic structure of the materials. Intrinsic defects in the half-Heusler system NiMnSb are studied and it is found that low-energy defects do not destroy the important half-metallic property at low concentrations. Deliberate doping of NiMnSb with 3d-metals is considered and it is found that replacing some Ni with extra Mn or Cr creates new strong magnetic interactions which could be beneficial for applications at elevated temperature. A self-consistent scheme to include the effects of thermal expansion and one-electron excitations in the calculation of the magnetic critical temperature is introduced and applied to a study of Ni1−xCuxMnSb. A supercell implementation of the disordered local moments approach is suggested and benchmarked for the treatment of paramagnetic CrN as a disordered magnetic phase. It is found that the orthorhombic-to-cubic phase transition in this nitride can be understood as a first-order magnetic order-disorder transition. The ferromagnetism in Ti1−xCrxN solid solutions, an unusual property in nitrides, is explained in terms of a charge transfer induced change in the Cr-Cr magnetic interactions. Cubic Ti1−xAlxN solid solutions displays a complex and concentration dependent phase separation tendency. A unified cluster expansion method is presented that can be used to simulate the configurational thermodynamics of this system. It is shown that short range clustering do influence the free energy of mixing but only slightly change the isostructural phase diagram as compared to mean-field estimates.

Este é o primeiro trabalho que apresenta simulações tridimensionais completamente adaptativas de um modelo de campo de fase para um fluido incompressível com densidade de massa constante e viscosidade variável, conhecido como Modelo H. Solucionando numericamente as equações desse modelo em malhas refinadas localmente com a técnica AMR, simulamos computacionalmente escoamentos bifásicos tridimensionais. Os modelos de campo de fase oferecem uma aproximação física sistemática para investigar fenômenos que envolvem sistemas multifásicos complexos, tais como fluidos com camadas de mistura, a separação de fases sob forças de cisalhamento e a evolução de micro-estruturas durante processos de solidificação. Como as interfaces são substituídas por delgadas regiões de transição (interfaces difusivas), as simulações de campo de fase requerem muita resolução nessas regiões para capturar corretamente a física do problema em estudo. Porém essa não é uma tarefa fácil de ser executada numericamente. As equações que caracterizam o modelo de campo de fase contêm derivadas de ordem elevada e intrincados termos não lineares, o que exige uma estratégia numérica eficiente capaz de fornecer precisão tanto no tempo quanto no espaço, especialmente em três dimensões. Para obter a resolução exigida no tempo, usamos uma discretização semi-implícita de segunda ordem para solucionar as equações acopladas de Cahn-Hilliard e Navier-Stokes (Modelo H). Para resolver adequadamente as escalas físicas relevantes no espaço, utilizamos malhas refinadas localmente que se adaptam dinamicamente para recobrir as regiões de interesse do escoamento, como por exemplo, as vizinhanças das interfaces do fluido. Demonstramos a eficiência e a robustez de nossa metodologia com simulações que incluem a separação dos componentes de uma mistura bifásica, a deformação de gotas sob cisalhamento e as instabilidades de Kelvin-Helmholtz. / This is the first work that introduces 3D fully adaptive simulations for a phase field model of an incompressible fluid with matched densities and variable viscosity, known as Model H. Solving numerically the equations of this model in meshes locally refined with AMR technique, we simulate computationally tridimensional two-phase flows. Phase field models offer a systematic physical approach to investigate complex multiphase systems phenomena such as fluid mixing layers, phase separation under shear and microstructure evolution during solidification processes. As interfaces are replaced by thin transition regions (diffuse interfaces), phase field simulations need great resolution in these regions to capture correctly the physics of the studied problem. However, this is not an easy task to do numerically. Phase field model equations have high order derivatives and intricate nonlinear terms, which require an efficient numerical strategy that can achieve accuracy both in time and in space, especially in three dimensions. To obtain the required resolution in time, we employ a semi-implicit second order discretization scheme to solve the coupled Cahn-Hilliard/Navier-Stokes equations (Model H). To resolve adequatly the relevant physical scales in space, we use locally refined meshes which adapt dynamically to cover special flow regions, e.g., the vicinity of the fluid interfaces. We demonstrate the efficiency and robustness of our methodology with simulations that include spinodal decomposition, the deformation of drops under shear and Kelvin-Helmholtz instabilities.

Dans ce manuscrit, un travail multidisciplinaire, de la synthèse de précurseurs métalliques à la caractérisation des matériaux est présenté. La première porte sur l’élaboration de poudres d’oxyde TiO2 dopé Nb5+ et d’oxydes mixtes SnO2-TiO2 dopé Nb5+ par une approche Sol-Gel. Leur mise en forme sous forme de pastille par une méthode moderne de frittage flash (SPS) a permis d’étudier leurs propriétés physiques vibrationnelles et thermoélectriques. La deuxième partie de cette étude présente l’élaboration de nouveaux précurseurs d’étain et de tantale adaptés au procédé de dépôt de couches minces par DLI-MOCVD. Afin de répondre aux exigences de ce procédé, des dérivés moléculaires à base de ligand beta-aminoalcool fluoré ou pas ont été élaborées. Les complexes métalliques ont ensuite été entièrement caractérisés à l’état solide et en solution. Le bon comportement thermique (stabilité et volatilité) de certains de ces composés ont conduit à l’élaboration et à la caractérisation de couches minces de SnO2 et SnO2:F / In this manuscript, a multidisciplinary work, from the synthesis of metal precursors to the characterization of materials, is presented. The first concerns the development of Nb5+ doped TiO2 oxide powders and Nb5+ doped SnO2-TiO2 mixed oxides by a Sol-Gel approach. Their shaping into a pellet form by a modern flash sintering method (SPS) made it possible to study their physical, vibrational and thermoelectric properties. The second part of this study presents the development of new tin and tantalum precursors adapted to the DLI-MOCVD thin film deposition process. In order to meet the requirements of this process, molecular derivatives based on fluorinated or non-fluorinated beta-aminoalcohol ligand have been developed. The metal complexes were then fully characterized in solid state and in solution. The good thermal behaviour (stability and volatility) of some of these compounds has led to the development and characterization of thin layers of SnO2 and SnO2:F

We propose a hypothesis and a numerical model for the formation of branching plagioclase textures visible at both macroscopic (∼cm to ∼m) and microscopic scale within melagabbro of the Isle of Rum, Scotland, based on macroscopic, microscopic observations and relevant geological history. The plagioclase crystals are typically linked as twins and form meshes of planar stellate structures (m-scale) with a large range in geometrical organization from patchy to radiating. Evidence of macroscopic crystal aggregation and alignment is attributed to interfacial free energy minimization at the microscopic scale during growth. Accordingly, a binary immiscible Lattice Boltzmann model was developed to simulate diffusion of simplified plagioclase in the melt phase. Isothermal phase transitions modelled via first order chemical reactions are subsequently coupled with stochastic dynamics at the crystal growth front to simulate energy minimization processes including twinning during crystallization in an igneous environment. The solid phase and the liquid phase are coupled with a temporal flexibility that sets the overall ratio between the rate of diffusion and chemical enrichment in the liquid state and the rate of crystallization. The parameter space of the model is explored extensively, followed by a reasonable transcription of physical parameters and an estimation of other parameters to construct realistic simulation scenarios yielding synthetic plagioclase stellates. The results are presented, analyzed and discussed. They appear to be in reasonable qualitative agreement with observations, and several aspects of the natural stellates such as the stellate spacing and long continuous stretches of plagioclase with epitaxial junctions seem to be in reasonable quantitative agreement with observations.

L’acier inoxydable martensitique durci par précipitation 15-5PH est utilisé dans le domaine del’aéronautique comme matériau constitutif des pièces liant les réacteurs aux ailes, il est ainsi soumisen utilisation à des températures de l’ordre de 300°C, ce qui entraine sa fragilisation. Cettefragilisation des aciers inoxydables dans ce domaine de températures est causée par la démixtion dufer et du chrome, principaux constituants de la matrice, par décomposition spinodale. De plus, lamicrostructure complexe du 15-5PH contient également des précipités de cuivre assurant ledurcissement initial de l’alliage, de l’austénite de réversion, connue dans ce type d’aciers pourapporter un regain de ductilité, apparaissant lors du traitement de précipitation du cuivre et de laphase G apparaissant au cours du vieillissement. L’évolution de ces phases pourrait égalemententrainer une modification des propriétés mécaniques de l’alliage. Pour observer les différentesévolutions de la microstructure nous avons utilisé une combinaison de techniques apportant desinformations complémentaires afin d’en obtenir une caractérisation la plus complète possible. Nousavons ainsi pu montrer que les modifications de propriétés sont causées par la décompositionspinodale de la matrice. L’évolution de ses caractéristiques microstructurales a pu être décrite pardes lois phénoménologiques, fonctions de la durée et de la température de vieillissement. Nousavons également pu fournir une méthode permettant la mesure indirecte de l’avancée duvieillissement du 15-5PH, validée par les observations microstructurales, ainsi qu’un modèlephénoménologique permettant de prévoir la dureté de l’alliage.Mots clés : acier martensitique, décomposition spinodale, vieillissement, diffusion aux petits angles,sonde atomique tomographique, calorimétrie différentielle à balayage. / The precipitation hardened martensitic stainless steel grade 15-5PH is used in the airplane industryas constitutive material of parts joining reactors to wings. Due to its application it is subjected totemperatures around 300°C leading to its embrittlement. Stainless steels embrittlement in thistemperature range is due to iron-chromium unmixing by spinodal decomposition. In addition, the 15-5PH grade has a complex microstructure comprising copper precipitates responsible for the initialhardening of the alloy, reversed austenite, known in this kind of steels to improve the toughness,which appears during the precipitation thermal treatment and G phase that precipitates duringaging. The evolutions of these microstructure components could also lead to some modifications ofthe material mechanical properties. In order to study the microstructure evolutions we use acombination of characterization techniques aiming at their most complete description. We show thatthe mechanical properties evolution is controlled by the spinodal decomposition of the matrix whoseevolution we are able to depict by simple phenomenological laws. We propose an indirect methodfor the measurement of aging kinetics of the 15-5PH steel, which we have correlated to directmeasurements, and a phenomenological law allowing the prediction of the alloy hardness based onits thermal history.

Este é o primeiro trabalho que apresenta simulações tridimensionais completamente adaptativas de um modelo de campo de fase para um fluido incompressível com densidade de massa constante e viscosidade variável, conhecido como Modelo H. Solucionando numericamente as equações desse modelo em malhas refinadas localmente com a técnica AMR, simulamos computacionalmente escoamentos bifásicos tridimensionais. Os modelos de campo de fase oferecem uma aproximação física sistemática para investigar fenômenos que envolvem sistemas multifásicos complexos, tais como fluidos com camadas de mistura, a separação de fases sob forças de cisalhamento e a evolução de micro-estruturas durante processos de solidificação. Como as interfaces são substituídas por delgadas regiões de transição (interfaces difusivas), as simulações de campo de fase requerem muita resolução nessas regiões para capturar corretamente a física do problema em estudo. Porém essa não é uma tarefa fácil de ser executada numericamente. As equações que caracterizam o modelo de campo de fase contêm derivadas de ordem elevada e intrincados termos não lineares, o que exige uma estratégia numérica eficiente capaz de fornecer precisão tanto no tempo quanto no espaço, especialmente em três dimensões. Para obter a resolução exigida no tempo, usamos uma discretização semi-implícita de segunda ordem para solucionar as equações acopladas de Cahn-Hilliard e Navier-Stokes (Modelo H). Para resolver adequadamente as escalas físicas relevantes no espaço, utilizamos malhas refinadas localmente que se adaptam dinamicamente para recobrir as regiões de interesse do escoamento, como por exemplo, as vizinhanças das interfaces do fluido. Demonstramos a eficiência e a robustez de nossa metodologia com simulações que incluem a separação dos componentes de uma mistura bifásica, a deformação de gotas sob cisalhamento e as instabilidades de Kelvin-Helmholtz. / This is the first work that introduces 3D fully adaptive simulations for a phase field model of an incompressible fluid with matched densities and variable viscosity, known as Model H. Solving numerically the equations of this model in meshes locally refined with AMR technique, we simulate computationally tridimensional two-phase flows. Phase field models offer a systematic physical approach to investigate complex multiphase systems phenomena such as fluid mixing layers, phase separation under shear and microstructure evolution during solidification processes. As interfaces are replaced by thin transition regions (diffuse interfaces), phase field simulations need great resolution in these regions to capture correctly the physics of the studied problem. However, this is not an easy task to do numerically. Phase field model equations have high order derivatives and intricate nonlinear terms, which require an efficient numerical strategy that can achieve accuracy both in time and in space, especially in three dimensions. To obtain the required resolution in time, we employ a semi-implicit second order discretization scheme to solve the coupled Cahn-Hilliard/Navier-Stokes equations (Model H). To resolve adequatly the relevant physical scales in space, we use locally refined meshes which adapt dynamically to cover special flow regions, e.g., the vicinity of the fluid interfaces. We demonstrate the efficiency and robustness of our methodology with simulations that include spinodal decomposition, the deformation of drops under shear and Kelvin-Helmholtz instabilities.

We propose a hypothesis and a numerical model for the formation of branching plagioclase textures visible at both macroscopic (∼cm to ∼m) and microscopic scale within melagabbro of the Isle of Rum, Scotland, based on macroscopic, microscopic observations and relevant geological history. The plagioclase crystals are typically linked as twins and form meshes of planar stellate structures (m-scale) with a large range in geometrical organization from patchy to radiating. Evidence of macroscopic crystal aggregation and alignment is attributed to interfacial free energy minimization at the microscopic scale during growth. Accordingly, a binary immiscible Lattice Boltzmann model was developed to simulate diffusion of simplified plagioclase in the melt phase. Isothermal phase transitions modelled via first order chemical reactions are subsequently coupled with stochastic dynamics at the crystal growth front to simulate energy minimization processes including twinning during crystallization in an igneous environment. The solid phase and the liquid phase are coupled with a temporal flexibility that sets the overall ratio between the rate of diffusion and chemical enrichment in the liquid state and the rate of crystallization. The parameter space of the model is explored extensively, followed by a reasonable transcription of physical parameters and an estimation of other parameters to construct realistic simulation scenarios yielding synthetic plagioclase stellates. The results are presented, analyzed and discussed. They appear to be in reasonable qualitative agreement with observations, and several aspects of the natural stellates such as the stellate spacing and long continuous stretches of plagioclase with epitaxial junctions seem to be in reasonable quantitative agreement with observations.