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Magnets play a major role in our rapidly developing world of technology. Electric motors and generators, transformers, data storage devices, MRI machines, cellphones, and NMR are some of the many applications for magnets. However, almost all the magnets currently being used have rare-earth heavy metals in them. Despite their high-energy product, the presence of rare-earth metals increases the cost significantly. Also, the processes involved in the mining of rare-earth metals are hazardous to the environment, and to all life forms. In the past few decades, oxide based magnets have gained a lot of attention as potential replacements for the rare-earth magnets. Oxide based magnetic nanocrystals are attracting a lot of attention as a potential replacement for rare-earth magnets. They are stable in ambient condition and their manufacturing cost is very low when compared to the rare-earth magnets. My work deals with the synthesis of core-shell magnetic structure for high frequency applications (Chapter 1) and the synthesis of high energy product magnetic nanocrystals (Chapter 2) and the synthesis of soft magnetic nanocrystals for high frequency measurement. NiZn ferrite, a soft oxide based magnet cannot be directly implied at high frequencies as they fail at the frequency which over the MHz range. On the other hand, BaZn ferrite is a Y-type magnets, which is robust at higher frequencies. Therefore, using the latter magnet as a protective shell for core material, made of former magnet, enables us to manufacture a cheap solution to the rare-earth magnets used in our cell phones and other devices that work on high frequency signals. On the other hand, successful coating of a very soft magnetic material on a hard-magnetic core increases the total energy product of the magnetic composite, which enhances its versatility. / Mechanical Engineering

Yes / Cerium (Ce3+) substituted Ni-Co ferrites with composition Ni0.3Co0.7CexFe2−xO4 (x = 0.0–0.20, with step size 0.05) were synthesized by sol-gel method. Face-centered cubic (FCC) spinel structure was revealed by X-ray analysis. The crystalline size was calculated ranging between 17.1 and 18.8 nm, lattice constant showed a decreasing trend with increase of Ce3+ contents, furthermore, X-ray density was calculated between 5.30 and 5.69 g/cm3. The two characteristic spinel ferrites absorption bands were seen around 550 (cm−1) and 415 (cm−1) in Fourier transform infra-red (FTIR) spectroscopy. The microstructural and elemental studies were carried out by field emission transmission electron microscopy (FE-TEM) and energy dispersive X-ray (EDX) respectively, the average particle size was calculated around 21.83 nm. Magnetic studies were per- formed by vibrating sample magnetometer (VSM), which showed that saturation magnetization Ms and remanence Mr decreased with substitution up to x = 0.10 due to small magnetic moment of Ce3+ than Fe3+. The coercivity Hc increased with substitution up to 908.93 Oe at x = 0.05, then it decreased following the trend of anisotropy constant. The dielectric studies exhibited decrease in dielectric parameters with fre- quency due to decreasing polarization in material. The dielectric loss was significantly decreased in material at high frequency. The Cole-Cole interpretation exhibited conduction mechanism being caused by grain boundary density. These attributes of Ce3+ substituted Ni-Co ferrites suggest their possible use in memory storage, switching and high frequency devices like antenna and satellite systems. / The authors would like to acknowledge the Researcher's Supporting Project Number (RSP-2021/269) King Saud University, Riyadh, Saudi Arabia, for their support in this work. / The full-text of this article will be released for public view at the end of the publisher embargo on 28 Dec 2023.

Ces dernières années, les besoins en électronique de puissance s’orientent vers la miniaturisation globale des cartes électroniques, parallèlement à une augmentation des puissances de travail. C’est dans ce contexte que s’inscrivent les travaux de cette thèse, principalement axée sur l’élaboration, l’amélioration des performances et l’intégration de composants passifs (inductances, transformateurs…) en électronique de puissance.Les matériaux choisis pour remplir les fonctions magnétiques de ces composants dans leurs conditions de travail sont les ferrites NixZn1-xFe2O4 (0<x<1). Du cuivre est ajouté pour diminuer la température de frittage, de plus de 1200 °C à moins de 950°C, permettant le cofrittage avec un métal conducteur, et du cobalt pour diminuer les pertes totales en puissance du ferrite formé. La formulation finale devient alors (NixZnyCuz)1-εCoεFe2-δO4 (x+y+z=1). Enfin, de l’oxyde de bismuth Bi2O3 est ajouté comme fondant pour abaisser encore la température de frittage et éviter les problèmes de diffusion.Après une étude bibliographique, les travaux se sont orientés selon différents axes. Il s’agissait tout d’abord d’optimiser la formulation du ferrite pour élaborer des échantillons aux propriétés électromagnétiques et physicochimiques ciblées. Cet axe de travail regroupe de nombreuses études sur la formulation des ferrites Ni-Zn-Cu-Co, parmi lesquelles les principales sont l’étude de l’influence de la stœchiométrie en fer, du rapport Ni/Zn dans la formulation et du procédé d’ajout de cobalt selon son taux. Ces travaux ont permis de mettre en évidence qu’un léger défaut de fer maîtrisé (~Fe1,98) pouvait améliorer les propriétés et les performances de ces ferrites. L’étude de l’influence du rapport Ni/Zn a permis la réalisation de ferrites à perméabilités très faibles, de 40 à 135, et aux bonnes performances en puissance. Les résultats de cette étude ont été publiés dans le Journal of the Japan Society of Powder and Metallurgy. Tout au long de la thèse, l’élaboration d’échantillons céramiques, base incontournable de chaque étude, a été réalisé au laboratoire, comme la plupart des tests et caractérisations. Ces derniers peuvent être microstructuraux et physicochimiques (DRX, MEB, BET, ATD/ATG…), ou électromagnétiques (mesures d’aimantation, de perméabilité, de pertes en puissances, etc…).La finalité de ces travaux étant l’intégration de puissance, cette dernière représente le second axe majeur, et regroupe également de nombreuses études, parmi lesquelles les principales sont les études des influences du bobinage sur les pertes d’un composant de type inductance et de l’entrefer (espacement amagnétique au sein du circuit magnétique), classiquement utilisé pour diminuer la perméabilité apparente, non sans conséquence sur les performances en puissance. Une campagne de mesures de pertes totales a également été réalisée dans l’objectif de dégager des lois comportementales sur la variation de ces pertes en puissance et en fréquence.Tous ces travaux et leurs résultats sur le matériau ferrite, son utilisation en électronique de puissance, et une bonne maîtrise du procédé d’élaboration (notamment multicouche), ont permis la réalisation de microcomposants passifs intégrables, aux propriétés ciblées et aux très bonnes performances (pertes diminuées d’un facteur 6 à 10 par rapport au commerce). / In recent years, power electronics needs are moving towards the global miniaturization of electronic boards, and an increase of the working powers. The works performed during this thesis, mostly oriented on the elaboration, the performances improvement and the integration of passive components (inductors, transformers…) in power electronics, are inscribed in this context.The materials chosen to perform the magnetic functions of those components in their work conditions are the NixZn1-xFe2O4 (0<x<1) ferrites. Copper is added to reduce the firing temperature, from more than 1200 °C to less than 950 °C, allowing cofiring with a conducting metal, and cobalt is added to reduce the power core losses of the sintered ferrite. The final formulation then becomes (NixZnyCuz)1-εCoεFe2-δO4 (x+y+z=1). Finally, bismuth oxide Bi2O3 is added as a sintering aid to lower even more the sintering temperature and avoid diffusion problems.After a bibliographic study, the works were oriented along different axes. Firstly, the ferrite formulation was optimized to elaborate samples with targeted electromagnetic and physicochemical properties. This working axis gathers numerous studies on the Ni-Zn-Cu-Co ferrites formulation, among which the main ones are the study of the influence of iron stoichiometry, the Ni-Zn ratio in the formulation and the cobalt adding process and level. These studies have shown that a light and controlled iron deficiency (~Fe1,98) could improve the properties and the performances of these ferrites. The study of the influence of the Ni/Zn ratio allowed the production of very low permeability ferrites, from 40 to 135, with good power performances. Its results were published in the Journal of the Japan Society of Powder and Metallurgy. Throughout this thesis, the elaboration of ceramic samples, the essential basis of every study, was undertaken at the laboratory, as most of the tests and characterizations. These can be microstructural and physicochemical (XRD, SEM, BET, TDA/TGA…), or electromagnetic (magnetization and permeability measurements, power losses…).The final purpose of this work is power integration, and it represents the second main axis. It also gathers many studies, among which the main ones are the study of the influence of the winding on the losses of an inductor-type component and the influence of the air gap, commonly used to reduce the apparent permeability, not without consequences on the power performances. A total losses measurement campaign has also been undertaken in order to bring out behavioral laws on core losses variation according to induction and frequency.All this work and the results on the ferrite material, his power electronic application, and a good control of the elaboration process (multilayer especially), allowed the production of passive micro-components for integration, with targeted properties and very high performances (core losses reduced by 6 to 10 relative to commercial materials).

Les gains sur la vitesse de commutation des composants actifs actuels offrent la possibilité de faire fonctionner les convertisseurs de puissance à des fréquences de découpage supérieures à 1 MHz. Le principal verrou à la montée en fréquence des convertisseurs provient des matériaux magnétiques des composants passifs qui sont le siège de dissipations thermiques. Les matériaux magnétiques utilisés, présentant un niveau de pertes acceptable entre 1 et 5 MHz, sont des ferrites de structure spinelle de type (Ni,Zn,Cu)Fe2O4. L’objectif de cette thèse est d’apporter une contribution expérimentale à la compréhension des liens entre la microstructure et les propriétés magnétiques statiques et dynamiques.Nous avons étudié deux procédés de synthèse des ferrites spinelles Ni-Zn-Cu (Ni,Zn,Cu)Fe2O4, d’une part par voie solide classique et, d’autre part, par la méthode sol-gel Pechini. Les propriétés structurales et magnétiques des échantillons produits ont été caractérisées de manière systématique et corrélées. Nous avons réussi à maîtriser l’élaboration et la mise en ordre et à obtenir une microstructure contrôlée de grains de l’ordre du µm et de forte densité (d>92%dth). Les résultats suggèrent que les ferrites synthétisés par la méthode Pechini peuvent être une alternative à la voie classique céramique pour la réalisation de composants magnétiques à faibles pertes.L’analyse des pertes magnétiques en fréquence a permis de montrer que l’ensemble des résultats obtenus était compatible avec un mécanisme de dissipation lié à l’amortissement des spins dans les parois. Ces résultats justifient la réalisation de pièces massives denses composées de petits grains avec du cobalt pour obtenir de faibles pertes sur une large plage d’induction (jusqu’à environ 25mT). / The high commutation rate of the wide gap semiconductor (GaN) allows operating with switching frequency above 1MHz in power converters. However, current magnetic materials comprising passive components in power converters cannot sustain the rise in the operating frequency, especially above 1 MHz. The main limitation comes from the sharp increase in power losses creating thermal dissipation inside the magnetic core. The core-losses are due to dynamic magnetization process (including domain wall movement and spin rotation) and they increase with the frequency. (Ni,Zn,Cu)Fe2O4 spinel ferrite is currently the best magnetic material with limited core-losses. The objective of the Ph.D. is to experimentally contribute to the understanding of the link between the microstructure and the static and dynamic magnetic properties.Synthesis process of (Ni,Zn,Cu)Fe2O4 spinel ferrite such as sold-state reaction and Pechini method were studied. The structural and magnetic properties were systematically measured and correlated together. We managed to master the elaboration and produce high density ferrite with controlled grain size (about few µm) and high density (d>92% dth). Results suggest that ferrites synthesized by Pechini method can be considered as an interesting basis for the design of low-loss magnetic components alternatively to the conventional route.The analysis on core-loss showed that the results are compatible with a dissipation mechanism linked to spin damping inside domain walls. It justifies the production of well-densified massive pieces composed of small grains and cobalt to obtain low core-loss for large amplitude excitation (up to 25mT).

The brushed DC motor is a source of electromagnetic emission that may cause interference. The main issues with brushed DC motor are arcing, which occurs between the brushes and commutator, and inrush current. It is possible to decrease the electromagnetic emissions by addressing the source (brushed dc motor) and the installation. The source may be addressed by using filters in the form of X2Y-capacitors on the terminals or ferrites on the cables. The installation does not produce any emission, but it is possible to lower its contribution. This is done by altering the installation like changing the placement of cables and provide good coupling. An effective way of decreasing inrush currents is by using negative-thermal-coefficient (NTC) thermistors. Another measure to improve the EMC properties of the brushed DC motor is to design the motor so that it can trap EM emissions. Some of these parameters are motor house material, end-cap material, vent holes or slots on motor housing, placement of power terminals, crimping tabs and motor enclosure.

La mise au point d'une méthodologie : les mesures électrochimiques sur céramiques a été réalisée dans le but d'étudier, de façon qualitative ou quantitative, le comportement électrocatalytique des perovskites non-stoechiométriques de type La_1-xSrFe_1-zCO_zO_3-y, vis à vis de la réaction de dégagement de l'oxygène. Un mécanisme réactionnel à cinq étapes élémentaires a été proposé, et les étapes limitantes ont été discutées sur la base de calculs cinétiques et thermodynamiques. On en a déduit des critères d'amélioration des performances électrocatalytiques de ce type de matériaux.

Made available in DSpace on 2014-12-17T15:41:43Z (GMT). No. of bitstreams: 1 JoseEMS.pdf: 2230919 bytes, checksum: f0f4e57c89f3eae4282c6daae0fe0aba (MD5) Previous issue date: 2008-04-18 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / It was synthesized different Ni1-xMgxFe2O4 (0,2 &#8804; x &#8804; 0,7) compositions by use of citrate precursor method. Initially, the precursory citrates of iron, nickel and magnesium were mixed and homogenized. The stoichiometric compositions were calcined from 350?C to 1200?C at ambient atmosphere or in argon atmosphere. The calcined powders were characterized by XRD, TGA/DTG, FTIR, magnetic measures and reflectivity using the wave guide method. I was observed pure magnetic phase formation between 350?C and 500?C, with formation of ferrite and hematite after 600?C at ambient atmosphere. The calcined powder at argon atmosphere formed pure ferromagnetic phase at 1100?C and 1200?C. The Rietveld analyses calculated the cations level occupation and the crystallite size. The analyses obtained nanometric crystals (11-66 nm), that at 900?C/3h presents micrometric sizes (0,45 - 0,70 Om). The better magnetization results were 54 Am2/Kg for x= 0,2 composition, calcined at 350?C/3h and 30 min, and 55,6 Am2/Kg for x= 0,2 1200?C, calcined in argon. The hysteresis shows characteristics of soft magnetic material. Two magnetization processes were considered, superparamagnetism at low temperature and the magnetic domains formation at high temperatures. The materials presented absorption less or equal the 50 % in ranges specific frequency. As for the 2,0 and 3,0 thickness (in 11,0 - 11,8 GHz), the reflectivity of the x= 0,3, 0,5 and 0,4 compositions, all calcined at 900?C/3h showed agreement with MS and O. Various factors contribute for the final radiation absortion effect, such as, the particle size, the magnetization and the polymer characteristics in the MARE composition. The samples that presented better magnetization does not obtaining high radiation absorption. It is not clear the interrelaction between the magnetization and the radiation absorption in the strip of frequencies studied (8,2 - 12,4 GHz) / Foram sintetizadas diferentes composi??es da ferrita Ni1-xMgxFe2O4 com (0,2 &#8804; x &#8804; 0,7) pelo uso do m?todo dos citratos precursores. Para se obter a fase estequiom?trica Ni1-xMgxFe2O4, inicialmente foram misturados e homogeneizados os citratos precursores de ferro, n?quel e magn?sio. As composi??es estequiom?tricas foram calcinadas entre as temperaturas de 350?C e 1200?C, em atmosfera ambiente ou de arg?nio. Os p?s calcinados foram caracterizados por DRX, TGA/DTG, FTIR, medidas magn?ticas e refletividade pelo m?todo de guia de ondas. Foi observada a forma??o de fase pura ferrimagn?tica entre 350?C e 500?C, formando ferrita e hematita ap?s 600?C, em atmosfera ambiente. O p? calcinado em atmosfera de arg?nio formou fase ferrimagn?tica pura em 1100?C e 1200?C. A an?lise pelo m?todo de Rietveld calculou o n?vel de ocupa??o dos c?tions e o tamanho de cristalito. A an?lise obteve tamanhos de cristais nanom?tricos, (11 - 66 nm), que a 900?C/3h apresentam tamanhos microm?tricos (0,45 0,70 Om). Os melhores resultados de magnetiza??o foram 54 Am2/Kg para a composi??o x= 0,2, calcinada a 350?C/3h e 30 min, e 55,6 Am2/Kg para x= 0,2 a 1200?C, calcinada em arg?nio. As histereses mostraram um perfil de materiais magn?ticos moles. Dois processos de magnetiza??o foram considerados, o superparamagnetismo a baixa temperatura e a forma??o de dom?nios magn?ticos em altas temperaturas. Os materiais apresentaram absor??o igual ou inferior a 50 % em faixas de freq??ncias espec?ficas. Para as espessuras 3,0 e 2,0 mm (em 11-11,8 GHz), as refletividades das composi??es x= 0,3, x= 0,5 e x= 0,4, todas a 900?C/3h demonstraram concord?ncia com MS e O. V?rios fatores contribuem para o efeito final de absor??o de radia??o, tais como, o tamanho de part?culas, a magnetiza??o, e as caracter?sticas do pol?mero na composi??o do MARE. As amostras que apresentaram maiores magnetiza??es n?o atingiram alta absor??o de radia??o. N?o ficou esclarecido a interrela??o entre a magnetiza??o e a absor??o de radia??o na faixa de freq??ncia estudada (8,2 12,4 GHz)

Made available in DSpace on 2014-12-17T15:41:56Z (GMT). No. of bitstreams: 1 ManuellaKCR_DISSERT.pdf: 3952261 bytes, checksum: 56cf586893164ffedc3ec29beb8e775a (MD5) Previous issue date: 2010-08-31 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Were synthesized ferrites of NiZn on systems Ni0,5Zn0,5Fe2O4, the precursors citrate method. The decomposition of the precursors was studied by thermogravimetric analysis and spectroscopy in the infrared region, the temperature of 350?C/3h. The evolution of the phases formed after calcinations at 350?C/3h, 600, 1000 and 1100?C/2h was accompanied by X-ray diffraction using the Rietveld refinement method for better identification os structures formed. Was observed for samples calcined at different temperatures increased crystallinity with increasing calcination temperature, being observed for the samples calcined at 900 and 1100 ? C/2h was the precipitation of a secondary phase, the phase hematite. The ferrocarbonila of industrial origin was analyzed by X-ray diffraction and Rietveld for the identification of its structure. The carbonyl iron was added NiZn ferrite calcined at 350?C/3h, 600, 900, 1000 and 1100?C/2h to the formation of hybrid mixtures. They were then analyzed by Xray diffraction and Rietveld. The NiZn ferrite and ferrocarbonila as well as the hybrid mixtures were subjected to analysis of scanning electron microscopy, magnetic measurements and reflectivity. The magnetic measurements indicated that the ferrite, the ferrocarbonila, as well as hybrid mixtures showed characteristics of soft magnetic material. The addition of ferrocarbonila in all compositions showed an increase in the results of magnetic measurements and reflectivity. Best result was observed in the increase of the magnetization for the hybrid mixture of Ferrocarbonila / ferrite of NiZn calcined at 600?C/2h. The mixture Ferrocarbonila / ferrite calcined 1000?C/2h presented better absorption of electromagnetic radiation in the microwave / Foram sintetizadas ferritas de NiZn no sistema Ni0,5Zn0,5Fe2O4, pelo m?todo dos citratos precursores. A decomposi??o dos precursores foi estudada por an?lise termogravim?trica e espectroscopia na regi?o do infravermelho na temperatura de 350?C/3h. A evolu??o das fases formadas ap?s calcina??es a 350?C/3h, 600, 1000 e 1100?C/2h foi acompanhada por difra??o de raios X utilizando o refinamento de Rietveld para melhor identifica??o das estruturas formadas. Foi observado para as amostras calcinadas em diferentes temperaturas o aumento da cristalinidade com o aumento da temperatura de calcina??o, sendo verificado que para as amostras calcinadas a 900 e 1100?C/2h ocorreu a precipita??o de uma fase secund?ria, a fase hematita. A ferrocarbonila de proced?ncia industrial foi analisada por Difra??o de raios X e por Rietveld para a identifica??o de sua estrutura. A ferrocarbonila foi adicionada ? ferrita de NiZn calcinada a 350?C/3h, 600, 1000 e 1100?C/2h para a forma??o das misturas h?bridas. Em seguida foram analisadas por difra??o de raios X e por Rietveld. A ferrita de NiZn, a ferrocarbonila, assim como as misturas h?bridas foram submetidas ? an?lises de Microscopia Eletr?nica de Varredura, medidas magn?ticas e refletividade. As medidas magn?ticas indicaram que a ferrita, a ferrocarbonila, como tamb?m as misturas h?bridas apresentaram caracter?sticas de material magn?tico macios. A adi??o de ferrocarbonila em todas as composi??es indicou um aumento nos resultados de medidas magn?ticas e de refletividade. Foi verificado melhor resultado no aumento da magnetiza??o para a mistura h?brida de Ferrocarbonila/ferrita de NiZn calcinada 600?C/2h. A mistura Ferrocarbonila/ferrita calcinada 1000?C/2h apresentou melhor resultado absor??o da radia??o eletromagn?tica na faixa de microondas em rela??o ?s outras misturas

Made available in DSpace on 2014-12-17T15:42:27Z (GMT). No. of bitstreams: 1 MariaJOSB.pdf: 5434037 bytes, checksum: 1a000204d534c8f41a3acbfce7dfaef5 (MD5) Previous issue date: 2007-09-17 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / It was synthesized MnZn ferrite with general formulae Mn1-xZnxFe2O4 (mol%), 0,3 &#8804; x &#8804; 0,7 by using the citrate precursor method. The precursors decomposition was studied by thermogravimetric analysis (TGA), differential thermogravimetric analysis (DTG), differential thermal analysis (DTA) and Fourier transform infrared (FTIR) of powder calcined at 350?C/3,5h. X-ray diffraction pattern (XRD) of samples was done from 350 to 1200?C/2h using various atmospheres. The power calcined at 350?C/3,5h formed spinel phase. It is necessary atmosphere control to avoid secondary phase such as hematite. From 900 to 1200?C was obtained 90,66 and 100% of MnZn spinel ferrite phase, respectively. Analysis by dispersive energy scanning (EDS) at 350?C shows high Mn and Zn dispersion, indicating that the diffusion process was homogeneous. Semi-quantitative analysis by EDS verified that despite the atmosphere control during calcinations at high temperatures (< 800?C) occurred ZnO evaporation causing stoichiometric deviation. Vibrating sample magnetometer (VSM) measures show soft ferrite material characteristics with Hc from 6,5 x 10-3 to 11,1 x 10-2 T. Saturation magnetization (Ms) and initial permeability (?i) of MnZn spinel phase obtained, respectively, from 14,3 to 83,8 Am2/kg and 14,1 to 62,7 (Am2/kg)T / Foi sintetizada ferrita de MnZn com f?rmula geral Mn1-xZnxFe2O4 (mol%) para 0,3 &#8804; x &#8804; 0,6 com uso do m?todo dos citratos precursores. A decomposi??o dos precursores foi estudada por an?lise termogravim?trica (TGA), termogravim?trica diferencial (DTG), an?lise t?rmica derivada (DTA) e espectroscopia na regi?o do infravermelho (FTIR) dos p?s calcinados em 350?C/3,5h. Foram feitas difra??es de raios X (DRX) entre 350 e 1200?C/2h usando v?rias atmosferas. O p? calcinado a 350?C/3,5h formou fase espin?lio. ? necess?rio o controle da atmosfera para evitar fases secund?rias como a hematita. Em 900 e 1200?C foram obtidos respectivamente, 90,7 e 100% de fase ferrita espin?lio. An?lises por espectroscopia de energia dispersiva (EDS) em 350?C mostrou alta dispers?o de Mn e Zn, indicando que o processo de difus?o foi homog?neo. A an?lise semi-quantitativa por EDS verificou que apesar do controle da atmosfera durante a calcina??o em altas temperaturas (> 800?C), ocorreu vaporiza??o de ZnO causando desvio estequiom?trico. Medidas por magnet?metro de amostra vibrante (MAV) mostraram caracter?sticas de materiais magneticamente macios com Hc de 6,5 x 10-3 at? 11,1 x 10-2 T. A magnetiza??o de satura??o e a permeabilidade inicial da fase espin?lio de MnZn foi obtida entre 14,3 a 83,8 Am2/kg e 14,1 a 62,7 (Am2/kg)T, respectivamente