<p>This master’s thesis work is a study of oxidation and degradation of nickel-base alloys at high temperatures. The materials studied are designed for use in critical gas turbine components such as turbine blades and vanes. Some of the alloys are used today, whereas others have not yet entered commercial application. In order to maximize the efficiency of gas turbines, there is an ambition to maximize the operating temperatures. There is therefore a demand for materials which can withstand the damage mechanisms active at high temperatures. Among these damage mechanisms are oxidation and microstructural degradation.</p><p>To investigate the oxidation resistance of 7 different monocrystalline and polycrystalline alloys, samples have been exposed isothermally in still air at temperatures between 850 and 1000°C, for exposure times of up to 20000h. Two of the alloys were also exposed cyclically at 950°C. Oxidation during the heat treatment resulted in significant weight changes, which were measured after each cycle for cyclically exposed samples and after completed heat treatment for isothermally exposed samples. The weight change data was used to evaluate the relative oxidation resistance of the alloys. The ranking of the alloys with respect to oxidation resistance was generally in agreement with the oxidation resistance predicted by a simple consideration of the Cr and Al contents of the alloys. However, the single-crystal alloy PWA1483 displayed better oxidation resistance than predicted from its chemical composition.</p><p>Metallographic analysis of the samples indicated that the oxide scales formed consisted of several different types of oxides. The oxide scales were mainly composed of Cr2O3 and Al2O3. Fragments of the oxide scales spalled off, primarily during cooling but also in some cases during the long-term heat treatments. Spalling of the oxide scale accelerated the oxidation process, since the ability of the oxide scale to impede diffusion decreased with its decrease in thickness. Oxidation caused depletion of Al and thereby local dissolution of the aluminum-rich γ′ particles, which are of vital importance to the mechanical properties of the material. A γ′ depleted zone thereby formed underneath the oxide scale. In this zone nitrides and needle-like particles, believed to be topologically close packed μ phase, precipitated during heat treatment. Recrystallization in the depletion zone was observed in some of the monocrystalline materials. MC carbides (M=metal) present in the virgin material decomposed during heat treatment and M23C6 carbides were formed. The γ′ particles coarsened during heat treatment, which resulted in decreased hardness. The hardness decreased with exposure temperature up to 950°C, as expected due to the increased coarsening rate. At 1000°C an unexpected increase in hardness was observed for all sample materials except one. A possible explanation for this hardness increase is redistribution of γ′, by dissolution of γ′ during heat treatment and reprecipitation during cooling as much finer particles. A fine dispersion of γ′ is expected to contribute more to the hardness than a corresponding volume of γ′ in the form of larger particles. For some of the sample series, clear correlations between hardness and γ′ particle size or exposition time were found. These relationships could potentially be used to estimate the exposure temperature of service-exposed material.</p><p>A numerical model was implemented in Matlab to describe the process of oxide growth and spalling, cycle by cycle. The model was successfully adapted to experimental data from the cyclic oxidation measurements. The general applicability of the model to cyclic oxidation data at different temperatures and cycle frequencies was not investigated. At long times of cyclic exposure, the net weight loss of the samples could be well approximated as a linear function of the number of cycles. However, during the last few cycles the amount of oxide spalled in each cycle suddenly decreased. This change in spallation behavior was mainly observed for the samples cooled in air between every cycle and to a much smaller extent for the samples cooled in water. The proposed explanation is that spalling occurred preferentially at a weak subscale interface and that the spalling propensity decreased with decreasing area of this weak interface. The deviating results of the last few cycles were not included in the modeling of the cyclic oxidation process.</p>

Ce travail présente les résultats d'un modèle théorique de précipitation de particules Al$_2$Cu dans un alliage d'aluminium de fonderie de type 319 traité thermiquement T7, prenant en compte les équations de la théorie de la coalescence. L'utilisation d'une distribution de taille de particules expérimentale discrétisée comme point de départ du modèle rend possible l'utilisation d'une équation de flux afin de modéliser l'évolution du rayon moyen des particules dans un élément de volume représentatif de l'alliage. L'utilisation d'un schéma numérique implicite permet de ramener la résolution du problème physique à l'inversion d'une matrice tridiagonale. Ainsi, l'évolution du rayon critique de coalescence, du nombre total et de la fraction volumique de précipités sont obtenus pour plusieurs vieillissements. Les résultats du modèle a été confrontés aux résultats des mesures expérimentales qui ont été réalisées à l'aide d'observations en microscopie électronique à transmission et qui ont permis une mesure de la taille des précipités. Ces derniers ont été assimilés à des sphères de volume équivalent aux plaquettes réelles et ont été analysés numériquement. Les résultats fournis par le modèle théorique sont en bon accord avec les mesures expérimentales et ont permis le couplage du modèle de coalescence avec un modèle micromécanique fondé sur la théorie des dislocations et calibré à l'aide d'essais de traction en température. Il permet de déterminer la limite d'élasticité de l'alliage pour un vieillissement jusqu'à 1000h compris entre 23°C et 300°C. La limite d'élasticité est alors assimilée à une somme de trois contraintes~: une contrainte liée à la friction de réseau (contrainte de Peierls), une contrainte liée au contournement des précipités par les dislocations (contrainte d'Orowan) et une contrainte liée à la présence de solution solide. Enfin, des essais de fatigue oligocyclique à différentes températures ont permis de déterminer les variables internes de la loi de comportement macroscopique. Il s'agit d'une loi élasto-viscoplastique de type Lemaitre et Chaboche, à laquelle la limite d'élasticité calculée par le modèle micromécanique est couplée. Ainsi, le comportement physique macroscopique de l'alliage est fonction de la coalescence des précipités. Des calculs 1D ou 3D, par éléments finis, permettent alors de déterminer le comportement général d'une culasse soumise à de la fatigue thermomécanique / This work highlights the results of a theoretical Al$_2$Cu particles coarsening model in a T7 thermal treated 319 aluminum alloy. As an input of the model, the experimental and discretised size distribution of the precipitates, in a 1$mu$m$^3$ representative volume element of the alloy, is used and coupled to a flux equation. The use of a numerical implicit scheme allows us to solve the problem by the inversion of a tridiagonal matrix. Thus, the evolution of the critical radius of coarsening, of the total number and of the volumical fraction of particles are modeled in a range of temperature going from 23°C to 300°C up to 1000h ageing time. Results were then compared to transmission electron microscope observations and are in good agreement with experimental measurements. Hence, the model was then coupled to a micro-mechanical model which is based on the theory of dislocations. It determines the real yield stress of the alloy generated by the interaction of the dislocations with the lattice (Peierls stress), with the precipitates (Orowan stress) and with the atoms in solid solution. Both models were then combined into a mechanical macro-scale model in order to represent the LCF behavior of the material. An elasto-viscoplastic law has been used and all the internal variables were experimentally determined using LCF stress/strain loops for the mechanical steady state. The simulation results are in good agreement with the experiments. Finally, 1D and 3D finite element computations could be run, taking into account the evolution of the microstructure during ageing and its impact on the evolution of the mechanical properties, to determine the head cylinder behavior under thermomechanical fatigue

Recozimentos realizados nos aços elétricos semiprocessados pelos fabricantes de motores sem um controle adequado da descarbonetação pode resultar em regiões das läminas com pequeno tamanho de grão e consequentemente aumento das perdas magnéticas com queda no rendimento dos motores elétricos. A maioria dos fabricantes de motores nacionais utilizam este tipo de aço e fazem internamente o recozimento final em fornos contínuos com atmosfera à base de nitrogênio com cerca de 5 a 10% de H2 e uma pequena fração de vapor dágua suficiente para gerar uma atmosfera que reaja com o carbono do aço, removendo-o. Caso esta descarbonetação não seja realizada com êxito há uma perda significativa no rendimento do motor pela aumento das perdas magnéticas. Amostras comerciais de diferentes aços com variados teores de carbono foram selecionadas para avaliar a influência do teor de carbono, do grau de redução, do tempo e da atmosfera do forno no aumento do tamanho de grão e nas perdas magnéticas. Foram realizados recozimentos a vácuo e em atmosfera descarbonetante. Medições de perdas magnéticas e do tamanho de grão além da avaliação da microestrutura foram efetuados para determinar esta influência. Foi verificado que no recozimento a vácuo, mesmo em variados graus de deformação, amostras com o teor de carbono inicial maior que 300 ppm, tiveram um significativo atraso no aumento do tamanho de grão. Nas situações em que não ocorreu significativo aumento do TG as perdas magnéticas apresentaram valores altos e 9 indesejáveis. Por outro lado amostras isentas de deformação não apresentaram aumento significativo do tamanho de grão mesmo com descarbonetação durante o recozimento. Foi verificado ainda que a formação de grãos colunares ocorre em faixas de deformação específicas, em recozimentos com descarbonetação para aços com mais de 300 ppm de carbono e onde haja um rápido aquecimento da amostra até a temperatura de recozimento. / Annealing applied by the motors plants that are made on the semi processed electrical steels without an exact and precisious control of the decarburization on the lamination can brings undesirable results on the grain size coarsening and as a result an increasing on the core losses with a significant depreciation on the efficiency of the electrical motors. Most of the domestic motors fabrics make use of this kind of electrical steel and they do on their process the final annealing on continuous furnaces with atmospheres based on nitrogenium with around 5 until 10% of hidrogeniun and a little fraction of water vapor enough to generate an atmosphere that reacts to the carbon from the steel, eliminating it. If this decarburization is not been made sucessfully there will be an effective loss on the motor efficiency due the incresing on the core losses. Commercial samples from different steels with several carbon contents were choosen to evaluate the influence of carbon content, strain grade, time and furnace atmosphere on the grain size coarsening and core losses. It was effetived vacumn and decarburizing annealing. Core losses and grain size measurements were made in addition to the evaluation of the microstructure to determine this influence. It was verified that on the vacumn annealing, even on differents strain reductions grades, the samples with initial carbon content bigger than 300 ppm, had a meaninfull late on the grain size increase. On the situation that do not occurred a significative increase on the grain size the core losses presented undesirable high values. On the other hand samples without strain did not presented a significative increase on the grain size even with decarburization during the annealing. It was still verified that the columnar grain formation occur on specific strain grades, on decarburizing annealing and to more than 300 ppm carbon content steels. In addition where there is a fast heating rate until the annealing temperature.

Recozimentos realizados nos aços elétricos semiprocessados pelos fabricantes de motores sem um controle adequado da descarbonetação pode resultar em regiões das läminas com pequeno tamanho de grão e consequentemente aumento das perdas magnéticas com queda no rendimento dos motores elétricos. A maioria dos fabricantes de motores nacionais utilizam este tipo de aço e fazem internamente o recozimento final em fornos contínuos com atmosfera à base de nitrogênio com cerca de 5 a 10% de H2 e uma pequena fração de vapor dágua suficiente para gerar uma atmosfera que reaja com o carbono do aço, removendo-o. Caso esta descarbonetação não seja realizada com êxito há uma perda significativa no rendimento do motor pela aumento das perdas magnéticas. Amostras comerciais de diferentes aços com variados teores de carbono foram selecionadas para avaliar a influência do teor de carbono, do grau de redução, do tempo e da atmosfera do forno no aumento do tamanho de grão e nas perdas magnéticas. Foram realizados recozimentos a vácuo e em atmosfera descarbonetante. Medições de perdas magnéticas e do tamanho de grão além da avaliação da microestrutura foram efetuados para determinar esta influência. Foi verificado que no recozimento a vácuo, mesmo em variados graus de deformação, amostras com o teor de carbono inicial maior que 300 ppm, tiveram um significativo atraso no aumento do tamanho de grão. Nas situações em que não ocorreu significativo aumento do TG as perdas magnéticas apresentaram valores altos e 9 indesejáveis. Por outro lado amostras isentas de deformação não apresentaram aumento significativo do tamanho de grão mesmo com descarbonetação durante o recozimento. Foi verificado ainda que a formação de grãos colunares ocorre em faixas de deformação específicas, em recozimentos com descarbonetação para aços com mais de 300 ppm de carbono e onde haja um rápido aquecimento da amostra até a temperatura de recozimento. / Annealing applied by the motors plants that are made on the semi processed electrical steels without an exact and precisious control of the decarburization on the lamination can brings undesirable results on the grain size coarsening and as a result an increasing on the core losses with a significant depreciation on the efficiency of the electrical motors. Most of the domestic motors fabrics make use of this kind of electrical steel and they do on their process the final annealing on continuous furnaces with atmospheres based on nitrogenium with around 5 until 10% of hidrogeniun and a little fraction of water vapor enough to generate an atmosphere that reacts to the carbon from the steel, eliminating it. If this decarburization is not been made sucessfully there will be an effective loss on the motor efficiency due the incresing on the core losses. Commercial samples from different steels with several carbon contents were choosen to evaluate the influence of carbon content, strain grade, time and furnace atmosphere on the grain size coarsening and core losses. It was effetived vacumn and decarburizing annealing. Core losses and grain size measurements were made in addition to the evaluation of the microstructure to determine this influence. It was verified that on the vacumn annealing, even on differents strain reductions grades, the samples with initial carbon content bigger than 300 ppm, had a meaninfull late on the grain size increase. On the situation that do not occurred a significative increase on the grain size the core losses presented undesirable high values. On the other hand samples without strain did not presented a significative increase on the grain size even with decarburization during the annealing. It was still verified that the columnar grain formation occur on specific strain grades, on decarburizing annealing and to more than 300 ppm carbon content steels. In addition where there is a fast heating rate until the annealing temperature.

Ce travail de thèse s’est focalisé sur l’étude des alliages Fe-14%Cr nanorenforcés par dispersion d’oxydes obtenus par broyage à haute énergie à partir de poudres pré-alliées de la matrice et d’Y2O3. L’objectif était double : (i) étudier la cinétique de précipitation, en particulier la phase de coalescence, des oxydes en fonction de la teneur en élément d’addition (Ti, Y, O) lors de traitements thermiques à haute température et postérieurs à l’étape de consolidation, et (ii) d’analyser les hétérogénéités de déformations élastiques et élastoplastiques dans ces aciers en fonction de l’avancement de la précipitation. La microstructure et la nanostructure ont été étudiées par microscopie électronique en transmission (MET) et diffusion de neutrons aux petits angles (DNPA). L’ensemble de ces techniques a permis de mettre en évidence des comportements différents selon les teneurs en éléments d’addition. En particulier, l’ajout de titane induit un ralentissement très net de la coalescence des particules contrairement aux ajouts d’oxygène et d’yttrium. Ces variations de teneurs initiales influent sur la forme, la structure cristallographique des particules, sur les relations d’orientations avec la matrice et en voie de conséquence, sur les cinétiques de précipitation. Par conséquent, assurer un rapport Ti /Y supérieur à 1 et limiter l’apport en oxygène sont des garants de la stabilité des nanoparticules à hautes températures dans les aciers ODS. Le phénomène de recristallisation a également été observé à haute température dans les matériaux dans lesquels la coalescence des oxydes est largement avancée. Afin de corréler l’évolution des microstructures avec celle des propriétés mécaniques, une modélisation macroscopique du durcissement a ensuite été réalisée, en distinguant les différentes contributions (nanoparticules, taille de grains et dislocations). Le durcissement calculé à partir des observations expérimentales est en très bon accord avec les valeurs mesurées. Ces calculs rendent bien compte des variations entre alliages et mettent en évidence l’influence prépondérante de la taille des particules sur la dureté des matériaux. Enfin une étude fine des hétérogénéités de déformation des grains en fonction de leur orientation cristallographique a été menée par diffraction de neutrons. Ces résultats ont été confrontés à un calcul micromécanique en champ moyen. Cette dernière partie a montré l’existence de comportements locaux différents dans des matériaux présentant des comportements macroscopiques similaires. / This PhD work focused on the study of Fe-14%Cr alloys nanoreinforced by oxide dispersion obtained by high energy milling from pre-alloyed powders of the matrix and Y2O3.The main objectives were: (i) the study of the precipitation kinetics of oxides, in particular the coarsening, according to the content of added elements (Ti, Y, O) after consolidation and after heat treatments at high temperature. (ii) The elastoplastic and elastic deformations heterogeneities analyze in these alloys, depending on the progress of the precipitation. Microstructure and nanostructure were studied by Transmission Electron Microscopy (TEM) and Small angles neutron scattering (SANS).All of these techniques allowed identifying different behaviors depending on the added element contents. In particular, the addition of titanium induced a marked deceleration of oxide coarsening in contrast to those samples added oxygen and yttrium. These variations of initial contents have an influence on the form, the crystallographic structure of the particles, the orientation relationships with the matrix and consequently, the precipitation kinetics. Therefore, ensuring the ratio Ti/Y greater than 1 and, limiting the oxygen can guarantee the stability of the nanoparticles at high temperatures in the ODS alloys. The recrystallization phenomenon was also observed at high temperature in the materials of which the oxides coarsening is fast. In order to correlate the evolution of microstructure with the mechanical properties, a macroscopic model of hardening was then carried out by distinguishing the different contributions (nanoparticles, grain size and dislocations). The hardening calculated from experimental observations, is in good agreement with measured values. These calculations demonstrate the high influence of particle size on the hardness of materials. Finally, a detailed study of deformation heterogeneities of the grains according to their crystallographic orientation was carried out by neutron diffraction. These results were compared to a mean field micromechanics calculation. This last part has shown the existence of different local behaviors for materials presenting similar macroscopic behavior.

Many phenomena determining the microstructure of a tool steel and consequently the properties of the material, are governed by multicomponent diffusion. The diffusion driven reactions that take place during, for example, tempering of a hot-work tool steel or when the microstructure develops during hot isostatic pressing of cold-work tool steel, are dependent on the types and amounts of alloying elements. In order for computational methods to be usable, these alloying effects need to be understood and incorporated in the models. In this work the influence of some typical tool steel alloying elements on the coarsening behavior of precipitates is investigated. Experimental coarsening studies are performed and the impact of the diffusion mobility descriptions and the thermodynamic descriptions are investigated by means of DICTRA coarsening calculations. The kinetic descriptions for diffusion in the body centered-cubic phase in the case of the chromium-iron-vanadium system and the chromium-iron-molybdenum system are improved by assessments of diffusion mobility parameters, and are shown to have a large impact on the calculated coarsening rate for vanadium-rich and molybdenum-rich precipitates. The effect of cobalt is examined by a coarsening experiment for vanandiumrich carbides and by a diffusion couple experiment for the investigation of the vanadium interdiffusion. The presence of cobalt is experimentally shown to have retarding effect on the coarsening rate of the carbides, but not on the vanadium diffusion. The coarsening rate of nitrogen-rich precipitates is compared to the coarsening rate of carbon-rich precipitates, and a lower coarsening rate for nitrides compared to carbides can be confirmed. Correlation between coarsening calculations and experiments is obtained suggesting that the thermodynamic description of the two systems is the underlaying reason for the different coarsening rates. Further, calculations utilizing the DICTRA software are combined with experimental investigations in order to study the possibility to apply computational methods for compound material development and explore application areas for high nitrogen alloyed tool steels produced by powder metallurgy. / <p>QC 20121011</p>

In this thesis 9-12 % Cr steels, used for high-temperaturecomponents in fossil-fired power plants are considered. Thecreep strength of thees steels depend on their microstructurethat consists of a matrix of tempered lath martensite withdensely distributed precipitates. The mechanical properties arestrongly influenced by precipitates present in the matrix andthe more densely distributed they are the higher is thehardening effect. These particles nucleate, grow and coarsenduring use in power plants, leading to a degradation ofmechanical properties. In this thesis the nucleation andcoarsening behaviour of the precipitates in the Cr steels aresimulated by new models and the results are compared withtransmission electron microscopy (TEM) observations of testedmaterials. A model of the nucleation of MX, which mainly isvanadium-nitrides, is presented. MX precipitates are assumed tonucleate on dislocations during annealing. The model takes intoaccount the full multicomponent thermodynamical behaviour ofthe system as well as the strain energy caused by a puredilatoric strain and the shape of the nucleus. The calculationsyield a critical size and shape represented by an oblatespheroid with a radius of a few nanometers and a thickness ofan atomic layer. This is in agreement with TEM observations ofsupercritical particles. A new coarsening model, which takes into account themulticomponent effects, is presented and it has been tested ondifferent systems to validate the model.     Four different carbides, Cr7C3, Mo6C, VC and NbC, in austenitic matrix as well asγ ' in ternary Ni-base super-alloy systems (Ni-Al-Mo)were compared with measurements from literature.     TiC-particles in austenitic stainless steel, ASTM 316Ti,were considered. The simulations were performed taking intoaccount iron and 7 alloying elements. The measurements wereperformed with TEM on samples that had been heat-treated at900° C.     MX and M23C6in a 9 % Cr steel were investigated with energyfiltering transmission electron microscopy (EFTEM) andcompared with simulations. The used samples had been heattreated for various periods of time at 600 and 650° Cfor up to 26 000 h. The agreement of the simulations with the experiments wasgood in all cases when reasonable values of the interfacialenergy, the only adjustable parameter, were chosen. Coarsening simulations were also performed to investigatethe influence of changes in composition on the coarsening rate.For MX, in a 9 % Cr steel, the coarsening rate is almostindependent of the V/Nb ratio but highly dependent on theN-content. Also the effect on the coarsening rate for M23C6by adding Co to a Cr steel was investigated bysimulation. Co is known to increase the resistance totempering. The results show that a final average radius of thecarbides after 30 000 h at 600° C decreases with 30 % witha Co addition of 10 mass %. <b>Keywords:</b>Cr steels, nucleation, coarsening, model,DICTRA, precipitates, carbides, carbo-nitrides, MX, VN, M23C6, TiC, TEM, EFTEM, Curie-temperature

In this research, controlled Waspaloy microstructures were produced with the objective of studying microstructural evolution in this alloy via electrically-based ac/dc non-destructive techniques. Correlations were developed between electrical measurements and alternate characterization techniques such as Ultra Small Angle X-ray Scattering (USAXS), Scanning Electron Microscopy (SEM) and X-ray Diffraction (XRD) to gain a complete understanding of the microstructural transformations and the associated mechanisms. Three different sets of controlled microstructures were produced in this research. In Set I microstructures, matrix (gamma) grain sizes of 13, 52 and 89 micrometers were obtained after solution-treatments at 1045 and 176;C, 1090 and 176;C and 1145 and 176;C respectively. A vacancy stabilization treatment at 1045 and 176;C followed after which, the specimens were aged at 800 and 176;C for times ranging from 0.1 hrs to 100 hrs to vary the gamma prime precipitate size distribution. In Sets II and III, the solution-treatment was only conducted at 1145 and 176;C, with the stabilization treatment conducted only in Set II. Subsequently, aging experiments were conducted at 725 and 176;C (or 700 and 176;C in Set II), 800 and 176;C and 875 and 176;C for times up to 100 hrs. DC four-point probe resistivity of specimens increased to a maximum upon initial aging from the solution-treated condition and showed a decreasing trend thereafter with successive aging. This, in addition to complementary evidence from SEM and USAXS, led to the conclusion that gamma prime nucleation-growth was complete by the time the resistivity maximum was observed. Resistivity variations that ensued upon successive aging after the maximum were attributed to microstructural/compositional changes due to gamma prime coarsening. The height of the maximum decreased drastically with increase in aging temperature from 725 and 176;C to 800 and 176;C, while the resistivity did not increase from the solution-treated condition upon aging at 875 and 176; C. Coarsening studies based on USAXS analysis indicated an LSW type volume diffusion mechanism of coarsening in Waspaloy, with an average coarsening rate constant of 3.25x10-29 [m3/sec] for Set I specimens aged at 800 and 176;C. Analytical and Finite Element (FE) models of two-probe impedance and dc four-point probe resistivity methods were developed to gain insight into the measured response and the accurate determination of material properties. AFM-based localized electrical examination of sub-grain Waspaloy microstructures was successfully conducted using electrostatic force microscopy (EFM), scanning Kelvin probe microscopy (SKPM) and current-AFM (I-AFM) electrical modes. I-AFM experiments revealed that the conductivity of the gamma prime phase was lower than that of the gamma phase.

<p>In this thesis 9-12 % Cr steels, used for high-temperaturecomponents in fossil-fired power plants are considered. Thecreep strength of thees steels depend on their microstructurethat consists of a matrix of tempered lath martensite withdensely distributed precipitates. The mechanical properties arestrongly influenced by precipitates present in the matrix andthe more densely distributed they are the higher is thehardening effect. These particles nucleate, grow and coarsenduring use in power plants, leading to a degradation ofmechanical properties. In this thesis the nucleation andcoarsening behaviour of the precipitates in the Cr steels aresimulated by new models and the results are compared withtransmission electron microscopy (TEM) observations of testedmaterials.</p><p>A model of the nucleation of MX, which mainly isvanadium-nitrides, is presented. MX precipitates are assumed tonucleate on dislocations during annealing. The model takes intoaccount the full multicomponent thermodynamical behaviour ofthe system as well as the strain energy caused by a puredilatoric strain and the shape of the nucleus. The calculationsyield a critical size and shape represented by an oblatespheroid with a radius of a few nanometers and a thickness ofan atomic layer. This is in agreement with TEM observations ofsupercritical particles.</p><p>A new coarsening model, which takes into account themulticomponent effects, is presented and it has been tested ondifferent systems to validate the model.</p><p>    Four different carbides, Cr₇C₃, Mo₆C, VC and NbC, in austenitic matrix as well asγ ' in ternary Ni-base super-alloy systems (Ni-Al-Mo)were compared with measurements from literature.</p><p>    TiC-particles in austenitic stainless steel, ASTM 316Ti,were considered. The simulations were performed taking intoaccount iron and 7 alloying elements. The measurements wereperformed with TEM on samples that had been heat-treated at900° C.</p><p>    MX and M₂₃C₆in a 9 % Cr steel were investigated with energyfiltering transmission electron microscopy (EFTEM) andcompared with simulations. The used samples had been heattreated for various periods of time at 600 and 650° Cfor up to 26 000 h.</p><p>The agreement of the simulations with the experiments wasgood in all cases when reasonable values of the interfacialenergy, the only adjustable parameter, were chosen.</p><p>Coarsening simulations were also performed to investigatethe influence of changes in composition on the coarsening rate.For MX, in a 9 % Cr steel, the coarsening rate is almostindependent of the V/Nb ratio but highly dependent on theN-content. Also the effect on the coarsening rate for M₂₃C₆by adding Co to a Cr steel was investigated bysimulation. Co is known to increase the resistance totempering. The results show that a final average radius of thecarbides after 30 000 h at 600° C decreases with 30 % witha Co addition of 10 mass %.</p><p><b>Keywords:</b>Cr steels, nucleation, coarsening, model,DICTRA, precipitates, carbides, carbo-nitrides, MX, VN, M₂₃C₆, TiC, TEM, EFTEM, Curie-temperature</p>

In this thesis morphologies, coarsening mechanisms and kinetics are examined in a systematic way, when phase separation and subsequent microstructural coarsening is modelled using deterministic mean field and stochastic Monte Carlo methods. For the mean field approach a microscopic diffusion equation due to Khachaturyan is employed, and a variation of it with an environment dependent mobility. Monte Carlo simulations are carried out with vacancy and Kawasaki dynamics, and a residence time algorithm is applied in the vacancy case. In mean field models microstructural evolution results from a direct minimization of a free energy functional, and the mechanism of atomic diffusion does not appear explicitly. In Monte Carlo models, changes in site occupancies are effected by direct exchanges of neighbouring atoms (Kawasaki dynamics), or through vacancy motion. In this thesis the correspondence between mean field and Monte Carlo models in describing phase transformations in binary alloys is examined. Several examples of cases in which these differences between deterministic and stochastic models affect the phase transformation are given, and the underlying differences are analyzed. It is also investigated how the choice of diffusion mechanism in the Monte Carlo model affects the microstructural evolution. Most Monte Carlo studies have been carried out with Kawasaki dynamics, although in real metals such direct exchanges are very unlikely to occur. It will be shown how the vacancy diffusion mechanism produces a variety of coarsening mechanisms over a range of temperatures, which the Kawasaki dynamics fails to capture. Consequently, kinetics and resulting morphologies, especially at low temperatures, are affected. Finally, the question of physicality of time scales in mean field and Monte Carlo models is addressed. Often a linear dependence between Monte Carlo time and real physical time is assumed, although there is no rigorous justifcation for this. In mean field models, time is defined through the atomic mobility. By examining the effect of a realistic diffusion mechanism in systems undergoing phase transformation, a critical discussion of time scales in microscopic mean field models and a Monte Carlo model with Kawasaki dynamics is presented.