Mathematical modelling using differential equations is an important tool to predict the behaviorof vanadium redox batteries, since it may contribute to improve the device performance and leadto a better understanding of the principles of its operation. Modelling can be complementedby asymptotic analysis as a mean to promote reductions or simplifications that make modelsless complex. Such simplifications are useful in this context, whereas these models usuallyaddresses one cell only – the smallest operating unit – while real applications demand tensor hundreds cells implying on larger computational requirements. In this research, severaloptions for asymptotic reductions were investigated and, applied to different models, were ableto speed up the processing time in 2.46× or reduce the memory requirements up to 11.39%. Thecomputational simulations were executed by COMSOL Multiphysics v.4.4, also by in-housecode developed in MATLAB. The validation of results was done by comparing it to experimentalresults available in literature. Additionally, correlating the results provided by COMSOL withthe ones arising from the implemented sub-routines allowed to validate the developed algorithm.Key-words: / A modelagem matemática por meio de equações diferenciais é uma importante ferramenta paraprever o comportamento de baterias redox de vanádio, pois ela pode contribuir para o aperfeiçoamentodo produto e melhor entendimento dos princípios da sua operação. Os estudos demodelagem podem ser aliados à análise assintótica no intuito de promover reduções ou simplificaçõesque tornem os modelos menos complexos, isso é feito a partir da observação da importânciaque cada termo exerce sobre as equações. Tais simplificações são úteis neste contexto, visto queos modelos geralmente abordam uma célula apenas - a menor unidade operacional da bateria- enquanto aplicações reais exigem o uso de dezenas ou centenas delas implicando em umamaximização do uso de recursos computacionais. Neste trabalho, foram investigadas múltiplasformas de reduções assintóticas que empregadas na construção dos modelos puderam acelerar otempo de processamento em até 2,46 vezes ou reduzir os requisitos de memória principal em até11,39%. As simulações computacionais foram executadas pelo software COMSOL Multiphysicsv. 4.4, e também por scripts desenvolvidos em ambiente de programação MATLAB. A validaçãodos resultados foi feita comparando-os a dados experimentais presentes na literatura. Talabordagem permitiu também validar as rotinas implementadas para a simulação dos modeloscomparando suas soluções com aquelas providas pelo COMSOL.

The aluminium alloys for electrical conductivity applications are generally not grain refinedsince the addition of grain refiners drops the electrical conductivity by introducing impuritiesinto the melt. Non-grain refined aluminium may lead to bar fracture and cracks during themetalworking process. The present study focuses to find an optimum balance between the grain refiner addition andthe electrical conductivity of commercial EC grade 1070 aluminium alloy for electricalapplication. In order to reach this goal, the electrical conductivity and the macrostructure ofcommercial EC grade 1070 aluminium (commercial pure aluminium) have been studiedunder a series of controlled lab scale trails. Specific addition levels of different grain refiners(TiBloy, Al-5Ti-1B, Al-3Ti-0.15C, and Al-3Ti-1B) were added to the metal melt and sampleswere taken at specific time intervals. The collected samples were sectioned, ground andmacro-etched. Thereafter, the macrostructure was analysed by the use of a digital camera andthe electrical conductivity was measured at temperature. The obtained result was expressed asa percentage of the International Annealed Copper Standard (IACS %). The macro-structuralanalysis showed that TiBloy, Al-5Ti-1B, and Al-3Ti-1B, with the maximum addition level of0.1%, cannot grin refine commercial pure aluminium. However, at higher grain refiner levelsthe number of columnar grains increased and their size decreased. The Al-3Ti-0.15C master alloy, with the same addition level as the once chosen for the othergrain refiners (up to 0.1%), showed significantly better grain refining. By the addition of0.1% of this grain refiner the macrostructure became very equiaxed already after 30 minutesof grain refiner addition. The fading of the Al-3Ti-0.15 master alloy was, however, observedfor samples with a long holding time. Nevertheless, by maximum addition level (0.1%) and a90 minutes holding time the macrostructure remained as equiaxed grains. The electrical conductivity results showed that none of the applied grain refiners (TiBloy, Al-5Ti-1B, Al-3Ti-0.15C, and Al-3Ti-1B), with the maximum addition level of 0.1%, decreasedthe electrical conductivity of commercial pure aluminium.

The steel quality is deteriorated at a continuous casting start. Therefore, material from the first cast slab is cut off and re-melted in the melt shop. If too little is discarded, the inferior quality in the retained length can cause defects like edge cracks during subsequent hot rolling. This means that manufacturing resources are wasted on processing inferior material which has to be re-melted anyways at a later stage. On the other hand, if an excessive length of the first slab is re-melted, good material is wasted. In either case, optimizing the length of the start-scrap material is both economically and environmentally beneficial. Edge cracks are more common in the beginning of the first slab, even though a part is cut off. It is likely that the edge cracks arise due to reduced hot ductility in the first cast material. The purpose of this project is to optimize where the cut should be made in order to achieve the best yield. The hot ductility was investigated by performing hot tensile- and bending tests. The hot tensile tests indicate high hot ductility for the investigated specimens. The area reduction, which is correlated to the hot ductility, is above 70 % for all the investigated specimens. When considering the average area reduction while neglecting possible differences between the heats, the specimens from one meter tend to have a lower hot ductility compared to the other specimens. However, the differences are small. No difference can be seen between edge and middle specimens when only looking at the tensile tests. The bending tests did not crack without notches, even though the maximum load and a test temperature of 750 °C was used. That strongly indicates high hot ductility as well. By using notches, the bending tests cracked and it was shown that edge specimens and specimens from one meter cracked the most. No edge cracks were found, after hot rolling, on the first cast slabs from the investigated heats. / Vid en stränggjutstart är kvalitén på första slaben sämre. På grund av detta så skärs en bit, av det först gjutna slabet av och smälts om i stålverket. Om för lite material kapas av kan det leda till defekter, såsom kantbrakor, under den efterföljande varmvalsningen. Detta innebär att resurser används i onödan för att tillverka material av otillräcklig kvalitet som sedan ändå måste smältas om i ett senare steg. Skärs istället för mycket material bort så smälts prima material om i onödan. Att optimera startskrotlängden är följaktligen positivt både för miljön och rent ekonomiskt. Under varmvalsningen kan defekten kantbrakor, det vill säga sprickor vid kanterna, uppstå. Trots att en bit av det första gjutna slabet skärs av, så är det första slabet fortfarande mest utsatt för kantbrakor. Detta tros bero på nedsatt varmduktilitet i det första gjutna materialet. Syftet med detta projekt är att optimera längden på startskrotet för att spara så mycket användbart material som möjligt. Varmduktiliteten undersöktes genom drag- och bockprovning. Dragproven indikerar hög varmduktilitet för de undersökta proven. Areakontraktionen, som är ett mått på varmduktiliteten, är över 70 % för alla undersökta prov. Medelareakontraktionen, när man bortser från eventuella skillnader mellan chargerna, visar att prov från en meter generellt har något lägre varmduktilitet än de övriga proven. Det är endast små skillnader som uppfattas. Ingen skillnad kan ses mellan kant- och mittenprov när man enbart tittar på dragprovsresultaten. Bockproven sprack inte trots att maximal last användes och att testtemperaturen var 750 °C. Detta tyder också på hög varmduktilitet. Genom att skapa anvisningar kunde man få bockproven att spricka och det visade sig att kantprov och prov från en meter sprack mest. Inga kantbrakor hade uppstått på de första gjutna slabsen under varmvalsningen av försökschargerna.

Duplex Stainless Steels (DSS) are used extensively in various industrial applications where the properties of both austenite and ferrite steels are required. Higher mechanical strength and superior corrosion resistance are the advantages of DSS. One of the main drawbacks for Duplex steels is precipitation of sigma phase and other intermetallic phases adversely affecting the mechanical strength and the corrosion behavior of the steels. The precipitation of these secondary phases and the associated brittleness can be due to improper heat treatment. The instability in the microstructure of Duplex stainless steels can be studied by understanding the phase transformations especially the ones involving sigma phase. To reduce the time and effort to be put in for experimental work, computational simulations are used to get an initial understanding on the phase transformations. The present thesis work is on the phase transformations involving sigma phase for Fe-Cr system and Fe-Cr-Ni system using theoretical approach in 1D and 2D geometries. A phase field model is implemented for the microstructural evolution in DSS in combination with thermodynamic data collected from the Thermo-Calc software. The Wheeler Boettinger McFadden (WBM) model is used for Gibbs energy interpolation of the system. FiPy- Finite volume PDE solver written in python is used to simulate the phase transformation conditions first in Fe-Cr system for ferrite-austenite and ferrite-sigma phase transformations. It is then repeated for Fe-Cr-Ni ternary system. In the present study a model was developed for deriving Gibbs energy expression for sigma phase based on the common tangent condition. This model can be used to describe composition constrained phases and stoichiometric phases using the WBM model in phase field modeling. Cogswell’s theory of using phase order variable instead of an interpolating polynomial in the expression for Gibbs energy of whole system is also tried.

A fundamental quantum mechanical modelling approach is used for calculating liquid diffusion parameters in cemented carbides. Up to now, no detailed description of diffusion for alloying elements in a liquid Co matrix is available. Neither are experimental measurements found in the literature for the self- or impurity diffusion in the liquid Co system. State of the art application is the description of gradient formation in cemented carbide systems using DICTRA. In this work it is assumed that diffusion during sintering of cemented carbides takes place mainly in the liquid Co binder phase. With this assumption one can calculate the diffusion coefficient for different alloying elements like W, Ti, N and C in a liquid Co matrix phase. The mean square displacement (MSD) of the diffusing atoms is used to obtain the diffusion coefficients which could be simulated by Ab initio Molecular Dynamics (AIMD). By fitting the computed temperature dependence with the Arrhenius relation one can determine the frequency factor and the activation energy which allows to give a quantitative description of the diffusion. Three methods will be used for validating the data from this work. Available estimated literature values based on calculations (scaling laws, a modified Sutherland equation and classical molecular dynamics) will be used to compare the results in a first instance. The general agreement for diffusion in liquid metals will be done by comparison with experimental data for the liquid Fe system. In a last step, the diffusion values obtained by this work will be used to create a kinetic database for DICTRA. The gradient simulations will be compared with experimentally measured gradients. The AIMD simulations are performed for binary diffusion systems to investigate the diffusion between the liquid Co matrix and one type of alloying element. In a second approach the diffusion for a multicomponent systems with Co, W, Ti and C has been performed. The results from the present AIMD simulations could be shown to be in good agreement with the literature. Only two DICTRA simulations could be performed within the timeframe of this work. Both are predicting a ~3 times bigger gradient zone whereas the initial choice of the labyrinth factor λ = f could be identified as a possible source of disagreement. A labyrinth factor of λ = f2 with the calculated mobility values from the AIMD calculations should give improved results. Although the results from those simulations are not available to this date. The two approaches of the diffusion simulations in the binary and multicomponent system are giving matching results. The non-metallic elements C and N are diffusing two times faster than the fastest metallic element Co. The diffusivity of Ti is slightly lower than Co and W could be identified as the element with the slowest diffusion within the liquid Co matrix. Further investigations of the liquid structure could indicate the tendency to form bonds between C and W and between C and Ti. This gives slowed down diffusion of C in the multicomponent system compared to the diffusion in the binary Co-C system.

An implantable hearing aid device is being developed by a project group which is part of an EU initiative. This device contains a diaphragm consisting of a submicron thick freestanding titanium film, which should be free of internal stresses. Stress is the force exerted per unit cross-sectional area of the film and it can impair the functionality and performance of the device. The stress that evolves in a thin film during deposition at a substrate is compressive or/and tensile and affects the bending that occurs of the substrate due to the lateral force applied to the substrate by the stressed film. The goal of this diploma work was to contribute to the understanding of in situ stress evolution in a micron thick titanium film and thereby by tuning different physical parameters to obtain minimal residual stress in the films after growth. Titanium films were deposited on silicon sistrates using DC magnetron sputtering. The stress in the material varied, by tuning different physical parameters such as working pressure, power, distance between magnetron and the sample and substrate bias. For this thesis, firstly two different series were done; one where the changing parameter was the distance between the sample and the magnetron and one where it was the working pressure. Later a last series were done to see what effect the bias has on the stress. A multi-beam optical sensor system (MOS) was used to measure the stress in real-time during deposition. X-ray diffraction (XRD) was later used to make post-deposition stress measurements to verify the stress obtained from the MOS. However, the MOS shows the stress evolution in real time and XRD shows a ’final’ average value that can be compared with the stress obtained from MOS-data when the deposition is finished. The results showed that the stress goes from compressive to tensile as the working pressure and the distance between the magnetron and the sample increases. There are other factors, such as the temperature/heating in the main chamber, base pressure of the main chamber, cleaning of the sample and also where the argon gas is let in to the process chamber (in this project called the main chamber (MC)), that influences the results. This will in turn influence the repeatability of the data/measurements, since these effects can affect the process of nucleation and coalescence. The stress evolution can change if a bias is applied during the initial stage of the deposition process when the film has still not grown thick. This is could be due to the bias not having much of an impact on the stress evolution when the film is thicker and thereby more porous.

Hard carbon is regarded as one of the most promising anode materials for sodium-ion battery. However, the ash content of the hard carbon anode inherited from the precursor have several negative impacts on the electrochemical performance of hard carbon. The traditional method utilizes strong inorganic acid washing to reduce the ash content of hard carbon. However, this method results in heavy environment pressure and safety hazards. Therefore, it’s necessary to exploring an alternative ash content removal method which is safer and environment friendly. This project develops an environmentally friendly approach to remove ash from hard carbon by using acetic acid. This approach effectively reduces the ash content and enhances the electrochemical performance of the hard carbon anode. The ash content of hard carbon decrease from 1.57 wt% to 0.655 wt% after the 4 mol /L acetic acid treatment. The two-step treatment process also studied in this project and shows a better ash removal ability than one-step treatment process. The ash content of 4 mol /L acetic acid and 20 wt% KOH only 0.28 wt%. Furthermore, the electrochemical performance of the two- step treated hard carbon exhibits notable improvements, including enhanced initial Columbic efficiency (from 84.53% to 88.11%), reversible capacity (from 244.2 mAh g-1 to 280.8 mAh g-1). The long cycle performance of chemical treated hard carbon anode need further investigations in future studies. / Hårt kol anses vara ett av de mest lovande anodmaterialen för natriumjonbatterier. Askhalten i den hårda kolanoden som ärvts från prekursorn har dock flera negativa effekter på den elektrokemiska prestandan hos hårt kol. Den traditionella metoden använder stark oorganisk syratvättning för att minska askhalten av hårt kol. Denna metod resulterar dock i hög miljöbelastning och säkerhetsrisker. Därför är det nödvändigt att utforska en alternativ metod för borttagning av askinnehåll som är säkrare och miljövänligare. Detta projekt utvecklar ett miljövänligt tillvägagångssätt för att ta bort aska från hårt kol genom att använda ättiksyra. Detta tillvägagångssätt reducerar effektivt askinnehållet och förbättrar den elektrokemiska prestandan hos den hårda kolanoden. Askhalten i hårt kol minskar från 1,57 viktprocent till 0,655 viktprocent efter 4 mol/L ättiksyrabehandlingen. Tvåstegsbehandlingsprocessen studerades också i detta projekt och visar en bättre förmåga att avlägsna aska än enstegsbehandling. Askhalten av 4 mol/L ättiksyra och 20 viktprocent KOH är endast 0,28 viktprocent. Dessutom uppvisar den elektrokemiska prestandan hos det tvåstegsbehandlade hårda kolet anmärkningsvärda förbättringar, inklusive förbättrad initial Columbic effektivitet (från 84,53 % till 88,11 %), reversibel kapacitet (från 244,2 mAh g-1 till 280,8 mAh g-1). Den långa cykelprestandan hos kemiskt behandlad hård kolanod behöver ytterligare undersökningar i framtida

Water Stuff & Sun are developing a hydrogen battery based on a technology called SFEER’s. The SFEER’s are spherical high-pressure gas storage containers that are the size of a tennis ball. They consist of a carbon fiber-shell that is lined on the inside with a polymer called PA6. The aim of this literature review is to present suitable materials that can be utilized as a coating on the PA6 liner in the SFEER’s to minimize the hydrogen permeability. The metallic coatings that were investigated are compounds based on chromium, boron, alu- minum and titanium. The non-metallic coatings that were investigated are lamellar inorganic components (LIC) in combination with PA6 and modified graphene oxide (GO). The coating methods that were investigated are some different PVD and CVD methods (sputter deposition, plasma enhanced CVD, ALD), electrodeposition and cold spray. The lowest permeability out of all the coatings was observed for alumina, Al2O3. Titanium nitride, TiN, was also found to have very low permeability. Since these two coatings had the lowest permeabilities they were further compared considering other factors. This resulted in alumina being chosen as the final recommendation for coating the SFEER’s. A comparison was also made to find the most suitable coating method for alumina. Cold spray was found to be very promising but if it can not be used the PVD and CVD methods are other potential candidates.

Thermocouples are one of the most commonly used instruments for thermometry at elevated  temperatures. As of today, there are only a few types of thermocouples that are built to withstand a temperature beyond 1600 °C,however they usually have a temperature measurement uncertainty of around 1% at these high temperatures. Beyond the 1600 °C temperature span, most high temperature thermocouples tend to drift in the measurements, causing it to output a faulty and inaccurate read of the actual temperature. This thesis explores the usage of carbon fibers as a material to be used in thermocouples, by the combination of two dissimilar carbon fibers. Polyacrylonitrile (PAN) and rayon based fibers were used up to a temperature of 200 °C, where the output voltage of the thermocouple was logged. The study shows a promising and stable linear output of the electromotive force for this type of thermocouple using commercially available carbon fibers at lower temperatures. A comparison is made between the commonly used thermocouples type K and S, results shows that the carbon thermocouple have around 21% of the thermoelectrical efficiency of that of a type K or S thermocouple at 25 °C. For the case of its functionality at higher temperatures, similar graphite material has been studied through literature and found a potential increase in the thermoelectrical stability at higher temperatures beyond 2000 °C, which show that carbon-based thermocouples are well suited for high temperature measurements. / Termoelement är ett av de mest använda instrumenten för temperaturavläsning vid upphöjda temperaturer. Idag finns det bara några få typer av termoelement som är byggda för temperaturer över 1600 ℃, däremot innehar dom vanligtvis en temperaturmätnings osäkerhet på cirka 1% vid dessa höga temperaturer. Över 1600 ℃ temperaturintervallet har de flesta högtemperatur termoelement en tendens att skifta i mätningarna vilket orsakar en felaktig och inexakt mätning av den faktiska temperaturen. Denna avhandling undersöker användningen av kolfiber som ett material för användning i termoelement, genom kombinationen av två olika grafitfibrer. Polyacrylonitrile- (PAN) och Rayon-baserade fibrer användes i en sammansatt kombination upp till en temperatur av 200 ℃, där spänningen mättes mot temperaturen. Studien visar en lovande och stabil linjär effekt av dess elektromotoriska spänning för denna typ av termoelement med kommersiellt tillgängliga kolfibrer vid lägre temperaturer. En jämförelse görs mellan de vanliga termoelementen av typ K och S vid rumstemperaturer, resultaten visar att grafittermoelementen har cirka 21% av den termoelektriska effektiviteten hos den för en typ K eller S termoelement vid 25 ℃. När det gäller dess funktionalitet vid högre temperaturer har liknande grafitmaterial studerats och funnit en potentiell ökning av den termoelektriska stabiliteten vid högre temperaturer över 2000 ℃, vilket visar att grafitbaserade termoelement gör sig väl lämpade för högtemperaturmätningar.

This paper discusses the search of an FeNi25-based alloy with a face-centered cubic crystal structure exhibiting a Curie point around room temperature, for magnetocaloric applications. Fe was substituted in various amounts with FCC-stabilising elements Mn and Co as these elements respectively decrease and increase the Curie Temperature, thus enabling to tune the Curie point. Three characterization methods were carried out on the samples: Magneto- thermo-gravimetry (MTG), X-ray diffraction (XRD) and finally, vibrating sample magnetometer (VSM) measurements were performed. All samples displayed several Curie points, each corresponding to various FCC phases. Also, the last sample, FeNi25Mn6Co2, had an FCC phase fraction of almost 99% and presented two Curie points in the continuity of one another one at -35°C and another at 91°C. Hence, at room temperature, the sample underwent a magnetic phase transition passing from its ferromagnetic state to a paramagnetic one. / Detta arbete består i att utröna möjligheterna att med utgångspunkt från den binära sammansättningen FeNi25 erhålla en ytcentrerad kubisk fas (fcc) med en Curie punkt vid rumstemperatur. Syftet är att använda dessa legeringar i magnetokaloriska tillämpningar. Strategin är att både Mn och Co är fcc stabliliserande grundämnen, och att Mn sänker och Co ökar Curie temperaturen. Tre olika karakteriseringsmetoder användes; röntgendiffraktometri (struktur), Magneto-Termo-Gravimetri (magnetisering vs temperatur) och konventionell magnetometri vid rumstemperatur (magnetisering vs magnetiskt fält, Vibrating Sample Magnetometry VSM). Resultaten visar att även om kristallstrukturen i det närmaste är fullständigt fcc, så ger de magnetiska mätningarna vid handen att flera olika faser är vid handen med avesvärt olika Curie temperaturer. Som en illustration av detta förhållande kan nämnas att sammansättningen FeNi25Mn6Co2 uppvisar en fcc-fraktion på i det närmaste 99%, men har vid en M(T) mätning ett förlopp som enklast förklaras med en Curie punkt vid ca -35C och en ytterligare vid ca 90°C. Denna observation signalerar att de magnetiska egenskaperna torde vara mer beroende av exakt distribution av de ingående atomslagen i fcc strukturen än vad de röntgendiffraktometriska undersökningarna kan detektera.