Spinodal decomposition is a phenomenon which hinders the usage of ferrite containing steels under certain conditions. With a better understanding and knowledge of spinodal decomposition new ferritic and duplex stainless steels could be designed. The project is divided into two parts, an experimental part and a theoretical part. The aim of the theoretical part was to compare simulated values of the amplitude and wavelength of spinodal decomposition, obtained from solving the Cahn-Hilliard equation with other experimental values. The experimental part is performed as to determine the chemical diffusion coefficient and the mobility of Fe and Cr in the binary Fe-Cr system for lower temperatures using the Boltzmann-Matano method from chemical profiles of different samples. Another purpose with the project is to determine if the methods and the approach which are taken is viable and useful for calculating diffusion coefficients and if it can be used in studies to come. The simulations were in good agreement with other data at higher time intervals, but deviates at lower times. The calculated interdiffusion coefficients were in all cases lower than the expected values and as such the conclusion that is drawn is that the methods which are used could need further development. / Spinodalt sönderfall är ett fenomen som hindrar användningen av stål som innehåller ferrit under vissa förutsättningar. Med en större förståelse och mer kunskap om spinodalt sönderfall så kan nya ferritiska och duplexa rostfria stål utformas. Projektet är uppdelat i två delar, en experimentell del och en teoretisk del. Syftet med den teoretiska delen var att jämföra simulerade värden av amplituden och våglängden för spinodalt sönderfall, vilka erhölls från att lösa Cahn-Hilliard ekvationen med andra experimentella värden. Den experimentella delen utförs för att bestämma kemiska diffusionskoefficienter för Fe och Cr i det binära Fe-Cr system för lägre temperaturer med hjälp av Boltzmann-Matano metod från kemiska profiler av olika prover. Ett annat syfte med projektet är att ta reda på om de metoder och tillvägagångssätt som tas är livskraftiga och användbara för beräkning av diffusionskoefficienter och om den kan användas i studier framöver. Simuleringarna var i god överensstämmelse med annan experimentel data vid högre tidsintervall, men avviker vid lägre tider. De beräknade Interdiffusion koefficienterna var i samtliga fall lägre än de förväntade värdena och som sådan, dras slutsatsen att de metoder som används kan förbättras.

Surface energy plays a major role in many phenomena that are important in technological and industrial processes, for example in wetting, grain growth and sintering. In this thesis, such surface-energy driven processes are studied by means of the phase-field method. The phase-field method is often used to model mesoscale microstructural evolution in materials. It is a diffuse interface method, i.e., it considers the surface or phase boundary between two bulk phases to have a non-zero width with a gradual variation in physical properties such as energy density, composition and crystalline structure. Neck formation and coarsening are two important diffusion-controlled features in solid-state sintering and are studied using our multiphase phase-field method. Inclusion of Navier-Stokes equation with surface-tension forces and convective phase-field equations into the model, enables simulation of reactive wetting and liquid-phase sintering. Analysis of a spreading liquid on a surface is investigated and is shown to follow the dynamics of a known hydrodynamic theory. Analysis of important capillary phenomena with wetting and motion of two particles connected by a liquid bridge are studied in view of important parameters such as contact angles and volume ratios between the liquid and solid particles. The interaction between solute atoms and migrating grain boundaries affects the rate of recrystallization and grain growth. The phenomena is studied using a phase-field method with a concentration dependent double-well potential over the phase boundary. We will show that with a simple phase-field model it is possible to model the dynamics of grain-boundary segregation to a stationary boundary as well as solute drag on a moving boundary. Another important issue in phase-field modeling has been to develop an effective coupling of the phase-field and CALPHAD methods. Such coulping makes use of CALPHAD's thermodynamic information with Gibbs energy function in the phase-field method. With the appropriate thermodynamic and kinetic information from CALPHAD databases, the phase-field method can predict mictrostructural evolution in multicomponent multiphase alloys. A phase-field model coupled with a TQ-interface available from Thermo-Calc is developed to study spinodal decomposition in FeCr, FeCrNi and TiC-ZrC alloys. / QC 20100622

Nuclear spinodal instabilities are investigated in non-relativistic and relativistic stochastic mean-field approaches for charge asymmetric and charge symmetric nuclear matter. Quantum statistical effect on the growth of instabilities are calculated in non-relativistic approach. Due to quantal effects, in both symmetric and asymmetric matter, dominant unstable modes shift towards longer wavelengths and modes with wave numbers larger than the Fermi momentum are strongly suppressed. As a result of quantum statistical effects, in particular at lower temperatures, amplitude of density fluctuations grows larger than those calculated in semi-classical approximation. Relativistic calculations in the semi-classical limit are compared with the results of non-relativistic calculations based on Skyrme-type effective interactions under similar conditions. A qualitative difference appears in the unstable response of the system: the system exhibits most unstable behavior at higher baryon densities around $rho_{B}=0.4 rho_{0}$ in the relativistic approach while most unstable behavior occurs at lower baryon densities around $rho_{B}=0.2 rho_{0}$ in the non-relativistic calculations.

The nuclear matter liquid-gas phase transition is expected to be a signal of nuclear spinodal instabilities as a result of density fluctuations. Nuclear spinodal instabilities in symmetric nuclear matter are studied within a stochastic relativistic density-dependent model in semi-classical approximation. We use two parameterization for the Lagrange density, DDME1 and TW sets. The early growth of density fluctuations is investigated by employing relativistic Vlasov equation based on QHD and discussed the cluster size of the condensations from the early growth of density correlation functions. Expectations are that hot nuclear matter behaves unstable around &rho / b &asymp / &rho / 0/4 (below the saturation density) and at low temperatures. We therefore present our results at low temperature T=1 MeV and at higher temperature T=5 MeV, and also at a lower initial baryon density &rho / b = 0.2 &rho / 0 and a higher value &rho / b = 0.4 &rho / 0 where unstable behavior is within them. Calculations in density-dependent model are compared with the other calculations obtained in a relativistic non-linear model and in a Skyrme type nonivrelativistic model. Our results are consistent with them. Qualitatively similar results show that the physics of the quantities are model-independent. The size of clusterization is estimated in two ways, by using half-wavelength of the most unstable mode and from the width of correlation function at half maximum. Furthermore, the average speed of condensing fragments during the initial phase of spinodal decomposition are determined by using the current density correlation functions.

Le mélanome est un cancer dont la mortalité augmente rapidement avec le temps. Afin d'assurer une détection précoce, des campagnes de sensibilisation ont été menées donnant des critères morphologiques pour le distinguer des grains de beauté. Mais, l'origine des différences d'aspects entre lésions bénignes et malignes reste inconnue. L'objectif est ici de relier les effets des modifications génétiques à l'aspect des tumeurs, en utilisant des outils venus de la physique macroscopique. Les mélanomes ont l'avantage d'être facilement observables et fins, ce qui en font un système idéal. Ce travail commence par rappeler les aspects physiologiques des cancers de la peau. On explique le fonctionnement de la peau saine, puis nous décrivons les différents types de lésions cutanées, et enfin nous donnons un bref aperçu des différents chemins génétiques connus menant au mélanome. Ensuite, nous faisons un rappel des différents modèles mathématiques du cancer. Nous nous attardons sur l'utilisation de la théorie des mélanges comme base théorique de mise en équation des tumeurs. Nous l'appliquons ensuite dans un modèle simplifié à deux phases en deux dimensions. Puis, nous analysons ces équations. Une étude des composantes spatiales montre la possibilité d'un processus de séparation de phases : la décomposition spinodale. L'étude temporelle permet de montrer que ces équations contiennent les ingrédients nécessaires à décrire plusieurs types de mélanomes observés in vivo. Nous terminons par l'étude des effets de la troisième dimension jusqu'alors mis de côté dans le modèle. Nous mettons en équation des mélanomes évoluant sur un épiderme ondulé, au niveau des mains et des pieds. / Melanoma is a cancer whose mortality grows rapidly with time. In order to insure an early diagnosis, advertising campaigns have emphasized the importance of morphological criteria in order to distinguish moles from melanoma. But, the origins of those criteria are still poorly understood. Our goal is to understand the link between genetic modifications and melanoma patterns using physical tools. As melanoma is easily observable and thin, this makes it an ideal system. This work begins by recalling the physiological aspect of skin cancer. Healthy skin is thoroughly described, then cancerous lesions are depictesd, and melanoma genetic pathways are briefly discussed. Then, continuous mathematical models of cancer are reviewed. We show how mixture theory is used to put cancer into equations. Then, this framework is simplified in a two phases 2D model.Those equations are analysed. The spatial study shows the possibility of a phase separation process: the spinodal decomposition. And, the time study shows thet this model contains the ingredients necessary to describe several melanoma types seen in vivo.Focussing finally on the third dimension. Melanoma evolving on a wavy epidermis (hands and feet skin) are studied. We explain how melanoma patterns should follow the skin ridges (fingerprints).

Fe-Cr based steels, i.e. stainless steels, possessing a combination of excellent corrosion resistance and good mechanical properties, have indispensable applications ranging from low-end cooking utensils, to sophisticated components for nuclear power plants. However, the bcc/bct phase containing stainless steels which have a miscibility gap (MG) suffer from the so-called “475 oC embrittlement” leading to hardness increase and toughness deterioration. It occurs due to demixing of Fe and Cr leading to the formation of Fe-rich (α) and Cr-rich (α′) regions in bcc/bct phases. The demixing is referred to as phase separation (PS). The goal of this work was to study PS in ferrite containing stainless steels mainly by small-angle neutron scattering (SANS). Firstly, the application of different experimental techniques for the study of phase separation in Fe-Cr based steels was reviewed and supplemented by new measurements. SANS was shown to be very sensitive to the nanostructure change caused by PS and capable of characterizing the early stages of PS in Fe-Cr alloys. However, atom probe tomography and transmission electron microscopy are complementary to SANS. Therefore, in order to have a more complete view of the microstructure, the combination of these techniques should be pursued. Secondly, the factors affecting the initial microstructure prior to aging treatment and the effect of the resulted initial microstructure on PS were systematically investigated using binary Fe-Cr model alloys. The critical temperature of the MG was determined to be located between 560 and 580 oC in binary Fe-Cr. The results indicate that the solution treatment temperature above the MG and the cooling rate after solution treatment have significant effects on the initial microstructure and thus on PS during subsequent aging. The mechanisms responsible for the changed aging behavior are Cr clustering, quenched-in vacancy and decomposition during cooling. Therefore, computational simulations should take into account these factors and the initial microstructure to make predictions that are more accurate. Thirdly, the study was extended to PS in commercial duplex stainless steels (DSSs) which are of practical importance in various industries, e.g., nuclear power. It is found that alloying elements have an important effect on PS in DSSs. The grade 2507 (25 %Cr, 7 %Ni) experiences stronger PS than grade 2205 (22 %Cr, 5 % Ni) for the same heat treatment. Moreover, the fracture mechanisms as well as the mechanical properties depend on the extent of PS.  Finally, the fundamental aspects regarding the neutron scattering behavior for Fe-Cr alloys were examined. The results show that the nuclear and magnetic scattering of neutrons depend on the evolution of the nanoscale compositional fluctuation in Fe-Cr alloys. The ratio of the magnitude of nuclear scattering versus magnetic scattering varies with the extent of PS. / Stål baserade på Fe-Cr systemet, det vill säga rostfria stål, som har en kombination av utmärkta korrosionsegenskaper och bra mekaniska egenskaper, har många tillämpningar; allt från köksredskap, till sofistikerade komponenter för kärnkraftverk. Rostfria stål som innehåller Bcc / bct-fasen och som således har en blandningslucka, är känsliga för den så kallade "475 °C försprödningen" som leder till en hårdhetsökning men kraftigt försämrad slagseghet. Detta uppstår på grund av en uppdelning av Fe och Cr som leder till bildandet av Fe-rika (a) och Cr-rika (a’) regioner i bcc / bct-fasen. Denna uppdelning brukar kallas fasseparation. Målet med detta arbete var att studera fasseparationen i ferrit-innehållande rostfria stål främst genom lågvinkel-spridning av neutroner (SANS). Till att börja med studerades och jämfördes olika experimentella tekniker för undersökning av fasseparation i Fe-Cr-baserade stål med nya SANS- mätningar. SANS visade sig vara mycket känslig för förändringar på nano-skala orsakad av fasseparation och tekniken visade sig även kapabel att karakterisera de tidiga stadierna av fasseparation i Fe-Cr-legeringar. För att få en mer fullständig bild av mikrostrukturen efter fasseparation, bör emellertid en kombination av SANS och komplementära tekniker, såsom atomsond och transmissions-elektronmikroskopi, användas. Vidare undersöktes de faktorer som påverkar den ursprungliga mikrostrukturen före åldringsbehandling, och effekten av den initiala mikrostrukturen på fasseparation studerades systematiskt med användning av binära modell-legeringar av Fe-Cr. Den kritiska temperaturen för blandningsluckan i Fe-Cr bestämdes vara belägen mellan 560 och 580 °C. Resultaten indikerar att temperaturen för upplösningsbehandling ovanför blandningsluckan och kylhastigheten har en signifikant inverkan på den initiala mikrostrukturen och därmed på fasseparationen under efterföljande åldring. Mekanismerna som är ansvariga för det förändrade åldringsbeteendet är: Cr-klustring, insläckta vakanser och fasseparation under kylning. Simuleringar av fasseparationen bör därför ta hänsyn till dessa faktorer och den ursprungliga mikrostrukturen för att göra mer exakta förutsägelser av hur mikrostrukturen utvecklar sig med åldringstiden. Fasseparationen i kommersiella duplexa rostfria stål (DSS), som är av stor praktisk betydelse i olika branscher, t ex kärnkraft, studerades också med SANS. Det visade sig att mängden av olika legeringselement har en viktig effekt på graden av fasseparation i DSS. Legeringen 2507 uppvisade en tydligare fasseparation jämfört med legering 2205 för samma värmebehandling. Brottmekanismerna såväl som de mekaniska egenskaperna visade sig bero på omfattningen av fasseparationen. Slutligen undersöktes de grundläggande aspekterna hos neutronspridnings-beteendet för binära Fe-Cr-legeringar. Resultaten visade att kärn- och magnetisk spridning av neutroner beror på utvecklingen av sammansättningsfluktuationerna på en nanoskala i Fe-Cr-legeringar. Förhållandet mellan magnetisk- och kärnspridning varierar med omfattningen av fasseparationen. / <p>QC 20171117</p>

TiAlN and TiAlN-based coatings that are used of relevance as protection of cutting tool inserts used in metal machining have been studied. All coatings were deposited by reactive cathodic arc evaporation using industrial scale deposition systems. The metal content of the coatings was varied by using different combinations of compound cathodes. The as-deposited coatings were temperature annealed at ambient pressure and in some cases also at high pressure. The resulting microstructure was first evaluated through a combination of x-ray diffraction and transmission electron microscopy. In addition, mechanical properties such as hardness by nanoindentation were also reported. TiAlN coatings with two different compositions were deposited on polycrystalline boron nitride substrates and then high pressure high temperature treated in a BELT press at constant 5.35 GPa and at 1050 and 1300 °C for different times. For high pressure high temperature treated TiAlN it has been shown that the decomposition is slower at higher pressure compared to ambeint pressure and that no chemical interaction takes place between TiAlN and polycrystalline cubic boron nitride during the experiments. It is concluded that this film has the potential to protect a polycrystalline cubic boron nitride substrate during metal machining due to a high chemical integrity. TiZrAlN coatings with different predicted driving forces for spinodal decomposition were furthermore annealed at different temperatures. For this material system it has been shown that for Zr-poor compositions the tendency for phase separation between ZrN and AlN is strong at elevated temperatures and that after spinodal decomposition stable TiZrN is formed.

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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