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Dans cette thèse, deux méthodes de couplage sont proposées pour la simulation multi-échelle des procédés de mise en forme. Dans la première partie, une procédure simplifiée (couplage indirect) est adoptée pour coupler les codes éléments finis (Abaqus et LAM3) au modèle polycristallin avec un schéma de transition autocohérente basée sur le comportement élastoplastique du monocristal écrit dans le formalisme des grandes déformations. Cette procédure simplifiée consiste à lier le modèle polycristallin avec l'analyse EF par l'extraction de l'histoire de l'incrément de déformation et de contrainte macroscopique, obtenue à partir d'une simulation EF préliminaire avec une loi phénoménologique, et à l'utiliser comme trajet de chargement dans le modèle polycristallin. Cette méthode est appliquée pour la simulation multi-échelle du procédé de skin-pass. Le suivi du trajet de chargement extrait dans la demi-épaisseur de la tôle a permis de prédire l'évolution des grandeurs physiques associées au modèle de plasticité en particulier la texture cristallographique, la texture morphologique et l'écrouissage. Dans la seconde partie de cette thèse, un modèle polycristallin élastoplastique du type autocohérent en petites déformations est couplé au code EF Abaqus via la routine utilisateur UMAT. Ce couplage (dit couplage direct) consiste à utiliser la théorie de la plasticité cristalline comme loi de comportement à chaque point d'intégration du maillage EF. Le polycristal est représenté par un ensemble de N monocristaux. Chaque fois que le code EF a besoin d'information sur le comportement mécanique aux points d'intégration de chaque EF, le modèle polycristallin est appelé. Pour valider ce couplage développé, nous avons effectué des cas tests de simulation de trajets rhéologiques. Les résultats issus de ce couplage ont été validés avec des modèles de référence. À la différence des modèles phénoménologiques, ce couplage permet non seulement d'avoir des informations sur le comportement macroscopique de la structure mais aussi d'obtenir des informations sur l'état de la microstructure du matériau. / In this thesis, two coupling methods are proposed for the multiscale simulation of forming processes. In the first part, a simplified procedure (indirect coupling) is adopted to couple the finite element codes (Abaqus and LAM3) with a polycrystalline selfconsistent model based on the large strain elastoplastic behavior of single crystals. This simplified procedure consists in linking the polycrystalline model with the FE analysis by extracting the history of the increment of macroscopic strain and stress, obtained from a preliminary FE simulation with a phenomenological law, and then using it as loading path prescribed to the polycrystalline model. This method is applied to multiscale simulation of skin-pass processes. By following on the loading path extracted at the halfthickness of the sheet, we can predict the evolution of some physical parameters associated with the plasticity model, in particular the crystallographic texture, the morphological texture and hardening. In the second part on this thesis, a small strain version of the elastoplastic polycristalline self-consistent model is coupled to the Abaqus FE code via the user material subroutine UMAT. This coupling (called direct coupling) consists in using crystal plasticity theory as constitutive law at each integration point of the FE mesh. The polycristal is represented by a set of N single crystals. Each time the FE code needs information on the mechanical behavior at the integration points considered, the full polycrystalline constitutive model is called. In order to validate this coupling, simulations of simple mechanical tests have been conducted. The results of this coupling have been validated through comparison with reference models. Unlike phenomenological models, this coupling provides not only information on the overall macroscopic response of the structure, but also important information related to its microstructure

Le but de cette thèse est d’étudier les structures obtenues à partir des groupes de réflexion finis. Ce travail consiste en quatre articles publiés, un article soumis et un article en préparation dont les résultats partiels constituent un chapitre de cette thèse. Dans le premier article, nous présentons une réduction des orbites des groupes de Coxeter finis vers leurs sous-groupes. Nous utilisons des matrices de projection, c’est-à-dire, des applications qui transforment les racines simples d’un groupe de réflexion en les racines simples du sous-groupe associé. Les résultats présentés dans ce papier se concentrent sur les groupes finis de réflexion non crystallographiques. De plus, nous utilisons les polytopes engendrés par le groupe non crystallographique H3 pour illustrer les lois de ramification (branching rules), c’est-à-dire une réduction des orbites des groupes finis de Coxeter. Dans le deuxième article, nous étudions les polytopes avec 60 sommets engendrés par le groupe non crystallographique H3. Nous utilisons la méthode de décoration des diagrammes de Coxeter–Dynkin pour décrire leurs structures en détails et décomposer les sommets en somme des orbits de symétries de dimension inférieure. Le troisième article compare deux notations utilisées pour décrire le polyèdre engendré par le groupe de réflexion. Il s’agit du symbole de Schläfli et de la notation des points dominants. Nous y présentons les avantages de chaque méthode, expliquons les deux approches et nous les illustrons par des exemples. Dans le quatrième article, nous nous concentrons sur le graphène, c’est-à-dire un pavement d’hexagones sur le plan, qui possède de remarquables propriétés quand les sommets sont modélisés par des atomes de carbone. Dans ce travail, nous présentons différentes méthodes pour obtenir du graphène à partir de réseaux (lattices) et des orbites de dimension 3 des groupes finis de réflexion. De plus, une technique de coloriage des hexagones au moyen d’un nombre fini de couleurs est donnée avec une méthode systématique pour raffiner le graphène. Dans le cinquième article, nous utilisons des v fonctions spéciales et les transformations de Fourier pour traiter les données échantillonnées sur un réseau de carrés du groupe de Lie SU(2)×SU(2), relié au groupe de symétrie A1×A1. / The goal of this thesis is to study structures obtained from finite reflection groups. The work is contained in four published papers, one submitted article and a research paper currently in preparation, with partial results presented as a chapter of this thesis. In the first article, we present a reduction of the orbits of finite Coxeter groups to their subgroups. We use projection matrices, that is, mappings that transform the simple roots of a reflection group to the simple roots of the appropriate subgroup. The results presented in this paper focus on non-crystallographic finite reflection groups. Moreover, we use polytopes generated by the non-crystallographic group H3 to illustrate the obtained branching rules, i.e., reductions of orbits of the finite Coxeter groups. In the second article, we study polytopes with 60 vertices, generated by the non-crystallographic group H3. We use a method of decoration of the Coxeter–Dynkin diagram to describe their structure in detail, and decompose their vertices into sums of orbits of lower-dimensional symmetries. The third article compares two notations used to describe polyhedra generated by reflection groups, namely the Schläfli symbol, and the dominant point notation. Here, we present the advantages of each method, we explain the two approaches, and we illustrate them through examples. In the fourth article, we focus on graphene, i.e., a hexagonal tiling of the plane that possesses remarkable properties when the vertices are modelled with carbon atoms. In this work, we present different methods to obtain graphene from lattices and three-dimensional orbits of finite reflection groups. Moreover, a technique to colour the hexagons by a finite number of colours is provided, along with a systematic method to refine the graphene. In the fifth article, we use special functions and Fourier transforms to process data sampled on a square lattice of the Lie group SU(2) × SU(2), related to the A1 × A1 symmetry group.

Additive manufacturing (AM), also known as 3D printing, is a concept and method of a manufacturing process that builds a three-dimensional object layer-by-layer. Opposite to the conventional subtractive manufacturing, it conquers various limitations on component design freedom and raises interest in various fields, including aerospace, automotive and medical applications. This thesis studies the mechanical behavior of thin-walled component manufactured by a common AM technique, laser powder bed fusion (LPBF). The studied material is Hastelloy X, which is a Ni-based superalloy, and it is in connection to a component repair application in gas turbines. The influence of microstructure on the deformation mechanisms at elevated temperatures is systematically investigated. This study aims for a fundamental and universal study that can apply to different material grades with FCC crystallographic structure. It is common to find elongated grain and subgrain structure caused by the directional laser energy input in the LPBF process, which is related to the different printing parameters and brands of equipment. This thesis will start with the study of scan rotation effect on stainless steel 316L in an EOS M290 equipment. The statistic texture analysis by using neutron diffraction reveals a clear transition when different level of scan rotation is applied. Scan rotation of 67° is a standard printing parameter with intention to lower anisotropy, yet, the elongated grain and cell structure is still found in the as-built microstructure. Therefore, the anisotropic mechanical behavior study is carried out on the sample printed with scan rotation of 67° in this thesis. Thin-walled effects in LPBF are investigated by studying a group of plate-like HX specimens, with different nominal thicknesses from 4mm down to 1mm, and a reference group of rod-like sample with a diameter of 18mm. A texture similar to Goss texture is found in rod-like sample, and it becomes <011>//BD fiber texture in the 4mm specimen, then it turns to be <001> fiber texture along the transverse direction (TD) in the 1mm specimen. Tensile tests with the strain rate of 10−3 s−1 have been applied to the plate-like specimens from room temperature up to 700 ℃. A degradation of strength is shown when the sample becomes thinner, which is assumed to be due to the overestimated load bearing cross-section since the as-built surface is rough. A cross-section calibration method is proposed by reducing the surface roughness, and a selection of proper roughness parameters is demonstrated with the consideration of the calculated Taylor’s factor and the residual stress. The large thermal gradient during the LPBF process induces high dislocation density and strengthens the material, hence, the LPBF HX exhibits better yield strength than conventionally manufactured, wrought HX, but the work hardening capacity and ductility are sacrificed at the same time. Two types of loading condition reveal the anisotropic mechanical behavior, where the vertical and horizontal tests refer to the loading direction being on the BD and TD respectively. The vertical tests exhibit lower strength but better ductility that is related to the larger lattice rotation observed from the samples with different deformation level. Meanwhile, the elongated grain structure and grain boundary embrittlement are responsible for the low horizontal ductility. A ductile to brittle transition is traced at 700 ℃, so a further study with two different slow strain rates, 10−5 s−1 and 10−6 s−1, are carried out at 700 ℃. Creep damage is shown in the slow strain rates testing. Deformation twinning is found only in the vertical tests where it forms mostly in the twin favorable <111> oriented grain along the LD. The large lattice rotation and the deformation twinning make the vertical ductility remain high level under the slow strain rates. The slow strain rate tensile testing lightens the understanding of creep behavior in LPBF Ni-based superalloys. In summary, this thesis uncovers the tensile behavior of LPBF HX with different variations, including geometry-dependence, temperature-dependence, crystallographic texture-dependence and strain rate-dependence. The generated knowledge will be beneficial to the future study of different mechanical behavior such as fatigue and creep, and it will also enable a more robust design for LPBF applications. / Additiv tillverkning, eller 3D-utskrifter, är tillverkningsmetoder där man skapar ett tredimensionellt objekt genom att tillföra material lager for lager. Till skillnad från konventionella avverkande tillverkningsmetoder elimineras många geometriska begränsningar vilket ger större designfrihet och metoderna har därför väckt stort intresse inom en rad olika områden, inklusive flyg-, fordons- och medicinska tillämpningar. I denna avhandling studeras mekaniska egenskaper hos tunnväggiga komponenter tillverkade med en vanligt förekommande laserbaserad pulverbädds-teknik, laser powder bed fusion (LPBF). Det studerade materialet är Hastelloy X, en Ni-baserad superlegering som är vanligt förekommande for både nytillverkning och reparation av komponenter för gasturbiner. Inverkan av mikrostruktur på deformationsmekanismerna vid förhöjda temperaturer undersöks systematiskt. Detta arbete syftar till att ge grundläggande och generisk kunskap som kan tillämpas på olika materialtyper med en kubiskt tätpackad (FCC) kristallstruktur. Det är vanligt att man hittar en utdragen kornstruktur orsakad av den riktade tillförseln av laserenergi i LPBF-processen, vilket kan relateras till olika processparametrar och kan variera mellan utrustningar frän olika leverantörer. Denna avhandling inleds med studien av effekten av scanningsstrategi vid tillverkning av rostfritt stål 316L i en EOS M290-utrustning. En statistisk texturanalys med hjälp av neutrondiffraktion påvisar en tydlig övergång mellan olika mikrostrukturer när olika scanningsstrategier tillämpas. En scanningsrotation på 67 mellan varje lager är en typisk standardinställning med avsikt att sanka anisotropin i materialet, dock finns den utdragna kornstrukturen oftast kvar. I denna avhandling studeras därför de anisotropa egenskaperna hos material tillverkade med 67 scanningsrotation. Effekten av tunnväggiga strukturer i LPBF undersöks genom att studera en uppsättning platta HX-prover, med olika nominella tjocklekar från 4 mm ner till 1 mm, samt en referensgrupp med cylindriska prov med en diameter på 18 mm. Kristallografisk textur som liknar den av Goss-typ återfinns i de cylindriska proverna vilket gradvis övergår från en fibertextur med <011> i byggriktningen for 4mm-proven till en fibertextur med <001> i tvärriktningen for 1mm-proven. Dragprovning med en töjningshastighet på 10−3 s−1 har utförts på de platta provstavarna från rumstemperatur upp till 700 ℃. En sänkning av styrkan uppvisas när proven blir tunnare, vilket kan antas bero på att det lastbarande tvärsnittet överskattas på grund av den grova ytan. En metod för tvärsnittskalibrering föreslås genom att kompensera for ytråheten, och valet av lämplig ytfinhetsparameter motiveras med hänsyn till den beräknade Taylor-faktorn och förekomsten av restspänningar. Den stora termiska gradienten som uppstår for LPBF-processen inducerar en hög dislokationstäthet vilket höjer materialets styrka och följaktligen uppvisar LPBF HX högre sträckgräns an konventionellt tillverkad, smidda HX, men förmågan till deformationshårdnande samt duktiliteten i materialet sänks samtidigt. Tester utförda i två olika belastningsriktningar, vertikalt respektive horisontellt mot byggriktningen, demonstrerar det anisotropiska mekaniska beteendet. De vertikala testerna uppvisar lägre hållfasthet men bättre duktilitet vilket kan relateras till en större benägenhet for kristallstukturen att rotera när deformationsgraden ökar. Samtidigt är den utdragna kronstukturen ansvarig for den lägre duktiliteten for de horisontella proverna. En övergång från ett duktilt till ett mer sprött beteende noterades vid 700 ℃, och därför initierades ytterligare en studie där tester med två lägre töjningshastigheter, 10−5 s−1 och 10−6 s−1, utfördes vid 700 ℃. Det kan noteras att krypskador återfinns i tester med en långsam deformationshastighet och deformationstvillingar uppstår endast i de vertikala provstavarna där det främst bildas tvillingar i korn orienterade med <111> riktningen längs belastningsriktningen. Den stora förmågan till rotation i kristallstrukturen och deformationstvillingarna bidrar till att den vertikala duktiliteten förblir hög även i testerna med en låg deformationshastighet. Testerna med en långsam draghastighet bidrar därför till en bättre förståelse av krypbeteendet i LPBF Nibaserade superlegeringar. Sammanfattningsvis så bidrar denna avhandling till bättre förståelse av de mekaniska egenskaperna hos LPBF HX i olika utföranden och förhållanden, inklusive geometriberoende, temperaturberoende, deformationshastighetsberoende samt inverkan av kristallografisk textur. Den genererade kunskapen kommer att vara till stor nytta vid fortsatta studier av olika mekaniska egenskaper som utmattning och kryp, samt bidrar till att möjliggöra en mer robust design for LPBF-tillämpningar.

The thesis deals with the study and analysis of crystallographic defects on the surface of silicon wafers produced by Czochralski method. It focuses primarily on growth defects and oxygen precipitates, which play an important role in the development of appropriate nucleation centers for growth of stacking faults. The growth of stacking faults near the surface of silicon wafers is supported by their oxidation and selective etching. Such a highlighted stacking faults are known as the OISF (Oxidation Induced Stacking Fault). Spatial distribution of OISF on the wafer gives feedback to the process of pulling silicon single crystal and wafers surface quality. Moreover the work describes the device for automatic detection and analysis of OISF, which was developed for ON Semiconductor company in Rožnov Radhoštěm.

The efficiency of multicrystalline (mc) silicon solar cells depends strongly on the fraction of recombination active crystal defects. This work focuses on a systematic analysis of how the area fraction of recombination active crystal defects and thus the solar cell efficiency is af-fected by the grain structure of mc-silicon wafers, i.e. grain size, grain orientation and type of the grain boundaries between adjacent grains. For that purpose a new characterization method was developed which allows the measurement of the grain orientation and grain boundary type of full 156x156 mm² mc-silicon wafers. The results of the grain structure analysis were correlated with the etch pit density, the recombination active area fraction measured by photo-luminescence imaging, and the solar cell efficiency in order to quantify the most important features of the grain structure, which were relevant to obtain high quality mc-silicon wafer material. For the determination of the grain orientation and grain boundary type two metrology sys-tems were combined. The so-called grain detector determines the geometrical data of each grain (size and form) by a reflectivity measurement. Afterwards the wafer with the geomet-rical information of all grains is transferred into the so-called Laue Scanner. This system irra-diates each grain larger 3 mm² with white x-rays and creates a backscatter diffraction pattern (Laue pattern) for each grain. From this Laue pattern the grain orientation and the grain boundary type of neighboured grains is calculated and statistically analysed in combination with the geometrical data of the grain detector. In this work the grain structure of twelve industrially grown mc-silicon bricks, which were produced by different manufacturers, and two laboratory grown bricks were investigated. Seven of these bricks show a fine grain structure. This material named class F is considered to be typical for so-called High Performance Multi (HPM) silicon. The other bricks show a coarse-grained structure. This grain structure was called class G and corresponds to the con-ventional mc-silicon material. The results show that the grain structures of the start of the crystallization process differ sig-nificantly between class F and class G. The class F mc-silicon wafers have a uniform initial grain size (characterized by coefficient of variation CV¬KG < 2.5) and grain orientation (charac-terized by coefficient of variation CVKO < 1.5) distribution with a small mean grain size (< 4 mm²) and a high length fraction of random grain boundaries (> 60 %) in comparison to the class G wafers. Despite the totally different initial grain structure for the class F and class G bricks, the grain structure of the wafers which represent the end of the crystallization process is more or less comparable. It can be concluded that the development of the grain structure along the crystal height of the class F bricks is driven by an energy minimization due to the surface energy and the grain boundary energy, that means that the share of (111) oriented grains having the lowest surface energy and the share of ∑3 grain boundaries having the lowest interface energy increase from the start of crystallization to the end. This phenomenon could not be observed for the class G bricks, which show a decreasing ∑3 length fraction and a decreasing area fraction of {111} oriented grains. This energetically unfavourable grain structure development is not clear so far but it means another kind of energy minimization effect must exist within class G. This could be for instance the formation of dislocations. The grain structure investigations show clearly that especially the initially fine-grained struc-ture of the class F bricks, i.e. at the start of crystallization, influences beneficially the area fraction of recombination active defects and the solar cell efficiency subsequently. This ob-servation can be explained as follows. Reduced dislocation cluster formation: • The small grain sizes in combination with the low length fraction of ∑3 grain bounda-ries capture the dislocations within a grain. Dislocations are not able to move across the grain boundaries which have not the ∑3-type within moderate stress and tempera-ture fields. This prohibits the formation and expansion of large dislocation cluster. • The previously described energetically driven grain selection and the continuously in-creasing grain size from bottom to top leads to an overgrowth of grains. This means that also dislocated grains will disappear which also prohibits the formation of large dislocation cluster. Reduced possibility of dislocation formation: • Compared to the class G bricks the area fraction of {111} oriented grains is reduced. Therefore, the possibility of the formation of dislocations is reduced, because they would be activated first in {111} oriented grains taking the Schmidt factor in account which is lowest for {111} oriented grains. After the dislocation generation within a {111} oriented grain, the dislocation can move forward on 3 of 4 possible {111} slip planes which have an angle of 19.5° with regard to the growth direction. No other ori-entation has more slip planes for the dislocation movement which have an angle smaller 20° with regard to the growth direction. These arguments in combination with the high reproducibility of the characteristic initial class F structure can explain the observed low recombination active area fraction from start to end of crystallization which was smaller 5 % and especially the low variation of 2 % of the electrical active wafer area in between the class F bricks. One can also easily explain the higher recombination active area fraction up to 14 % and the large variation of 10 % between the class G bricks due to the obtained grain structure data. These differences in the recombination active area fractions are reflected in the solar cell efficiency which is 0.4 % higher for the class F bricks compared to the class G bricks. In consideration of the above mentioned reasons it is not beneficial for the industrial ingot production technology to increase the ingot height further, due to the fact that the advanta-geous initial grain structure properties of class F bricks disappear with increasing crystal height.:Abstract 1. Einleitung 1.1 Photovoltaik 1.2 Stand der Technik 1.2.1 Blockerstarrung von multikristallinem Silizium 1.2.2 Kornorientierungsbestimmung 1.3 Zielsetzung und Gliederung der Arbeit 2. Grundlagen 2.1 Silizium 2.1.1 Elektrische Eigenschaften 2.1.2 Oberflächenenergien des Siliziums 2.2 Kristalldefekte in multikristallinem Silizium 2.2.1 Versetzungen 2.2.2 Korngrenzen 2.2.3 Wechselwirkung zwischen Versetzungen und Korngrenzen 3. Mess- und Auswertemethodik 3.1 Detektion der Körner 3.1.1 Aufbau und Funktionsweise 3.1.2 Definition der Kenngrößen 3.1.3 Fehlerbetrachtung 3.2 Detektion der Kornorientierungen und Korngrenztypen 3.2.1 Theoretische Betrachtung 3.2.2 Aufbau und Funktionsweise 3.2.3 Definition der Kenngrößen 3.2.4 Fehlerbetrachtung 3.3 Detektion der Ätzgrubendichte 3.3.1 Aufbau und Funktionsweise 3.3.2 Definition der Kenngrößen 3.3.3 Fehlerbetrachtung 3.4 Detektion des rekombinationsaktiven Flächenanteils 3.4.1 Aufbau und Funktionsweise 3.4.2 Definition der Kenngrößen 3.4.3 Fehlerbetrachtung 3.5 Korrelation der rekombinationsaktiven Kristalldefekte mit der Kornorientierung 4. Probeninformation 5. Ergebnisteil 5.1 Korngrößenverteilung 5.1.1 Säulenklassifizierung 5.1.2 Klasse F Säulen 5.1.3 Klasse G Säulen 5.2 Kornorientierungsverteilung 5.2.1 Klasse F Säulen 5.2.2 Klasse G Säulen 5.3 Korngrenztypverteilung 5.3.1 Klasse F Säulen 5.3.2 Klasse G Säulen 5.4 Ätzgrubendichte 5.4.1 Klasse F Säulen 5.4.2 Klasse G Säulen 5.5 Rekombinationsaktiver Flächenanteil 5.5.1 Klasse F Säulen 5.5.2 Klasse G Säulen 5.6 Korrelation der Ergebnisse 5.6.1 Mittlere Korngröße und Variationskoeffizient vs. rekombinationsaktiver Flächenanteil 5.6.2 Korngrenztyplängenanteil vs. rekombinationsaktiver Flächenanteil 5.6.3 Kornorientierung vs. rekombinationsaktiver Flächenanteil 5.6.4 Ätzgrubendichte vs. rekombinationsaktiver Flächenanteil 6. Diskussion der Ergebnisse 6.1 Einfluss des Kristallzüchtungsprozesses auf die Korngrößen-, die Kornorientierungs- und Korngrenztypverteilung 6.2 Einfluss der Kornstruktur auf den elektrisch aktiven Defektanteil 6.3 Einfluss der Kornorientierung auf den elektrisch aktiven Defektanteil 6.4 Einfluss der Kornstruktur auf die elektrische Aktivierung von Versetzungsclustern 6.5 Einfluss der Verunreinigungen auf die Solarzelleneffizienz 7. Zusammenfassung und Ausblick Verwendete Abkürzungen und Symbole Literaturverzeichnis Veröffentlichungen Betreute studentische Arbeiten Danksagung

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III-valent dopants have shown to be most effective in stabilizing the ferroelectric, crystalline phase in atomic layer deposited, polycrystalline HfO₂ thin films. On the other hand, such dopants are commonly used for tetragonal and cubic phase stabilization in ceramic HfO₂. This difference in the impact has not been elucidated so far. The prospect is a suitable doping to produce ferroelectric HfO₂ ceramics with a technological impact. In this paper, we investigate the impact of Al, Y, and La doping, which have experimentally proven to stabilize the ferroelectric Pca21 phase in HfO₂, in a comprehensive first-principles study. Density functional theory calculations reveal the structure, formation energy, and total energy of various defects in HfO₂. Most relevant are substitutional electronically compensated defects without oxygen vacancy, substitutional mixed compensated defects paired with a vacancy, and ionically compensated defect complexes containing two substitutional dopants paired with a vacancy. The ferroelectric phase is strongly favored with La and Y in the substitutional defect. The mixed compensated defect favors the ferroelectric phase as well, but the strongly favored cubic phase limits the concentration range for ferroelectricity. We conclude that a reduction of oxygen vacancies should significantly enhance this range in Y doped HfO₂ thin films. With Al, the substitutional defect hardly favors the ferroelectric phase before the tetragonal phase becomes strongly favored with the increasing concentration. This could explain the observed field induced ferroelectricity in Al-doped HfO₂. Further Al defects are investigated, but do not favor the f-phase such that the current explanation remains incomplete for Al doping. According to the simulation, doping alone shows clear trends, but is insufficient to replace the monoclinic phase as the ground state. To explain this fact, some other mechanism is needed.

Les structures magnétiques de deux familles de composés sont déterminées et discutées : (i) celles des hydrures RTXH (R = terre rare, T = métal de transition et X = Si, Ge) cristallisant dans la structure de type ZrCuSiAs et obtenus par insertion d’hydrogène dans les intermétalliques quadratiques de type CeFeSi. L’hydrogénation induit des transitions magnétiques variées engendrées par la compétition entre la dilatation anisotrope de la maille cristalline causée par l’absorption d’hydrogène et l’apparition de la liaison chimique R-H; (ii) celles des siliciures ternaires R6T1.67Si3 (R = Ce, Nd, Gd, Tb et T = Co, Ni) présentant des propriétés magnétocaloriques significatives autour de leur température de Curie, en particulier ceux à base de gadolinium Gd6T1.67Si3. Les composés à base de Ce, Nd et Tb présentent des comportements magnétiques originaux qui sont expliqués par la détermination de leurs structures magnétiques. La nature complexe de ces propriétés résulte en partie de la présence de deux sites magnétiques pour R et d’un désordre atomique de l’élément T dans la structure cristallographique. / Magnetic structures of two families of compounds are determined and discussed : (i) those of the hydrides RTXH (R = Rare earth, T = transition metal and X = Si, Ge) crystallizing in the ZrCuSiAs-type structure and obtained by hydrogen insertion in the intermetallics adopting the tetragonal CeFeSi-type structure. Hydrogenation induces various magnetic transitions governed by the competition between the anisotropic unit cell expansion linked to hydrogen absorption and the occurrence of the R-H chemical bonding ; (ii) those of the ternary silicides R6T1.67Si3 (R = Ce, Nd, Gd, Tb and T = Co, Ni) which show significant magnetocaloric properties around their Curie temperature, especially those based on gadolinium Gd6T1.67Si3. The compounds based on Ce, Nd and Tb present original magnetic behaviors which are explained by their magnetic structures determination. The origin of these complex properties results especially from the presence of two magnetic sites for R and from an atomic disorder of the T element in the crystallographic structure.