Singularities in quantum spectra - ground state and excited-state quantum phase transitions - are often connected with singularities in the classical limit of the system and have influence on other properties, such as quantum entanglement, as well. In the first part of the thesis we study quantum phase transitions within the U(2)-based Lipkin model. The relation between quasistationary points of the classical potential and the respective singularities in the spectrum is shown. In the second part, a system of two-level atoms interacting with electromagnetic field in an optical cavity is studied within two simplified models (non-integrable Dicke model and its integrable approximation known as Jaynes-Cummings model). The behaviour of quantum entanglement in these models is shown with a focus on the vicinity of the singular points.

Les phases topologiques sont des phases qui existent au delà du paradigme de Ginzburg-Landau qui dominait jusqu’à présent la compréhension des phases et transitions de phases qui apparaissent dans les systèmes de matière condensée. Des exemples paradigmatiques ont été créés pour établir un nouveau socle théorique qui rend compte de cet aspect topologique. La phase de Haldane de spin 1 est l’exemple souvent retenu pour les systèmes unidimensionnels.La présente thèse propose d’étudier cette phase et de lui trouver des généralisations en se concentrant sur l’étude d’un moyen de l’implémenter expérimentalement à l’aide d’atomes alcalino-terreux fermioniques ultra-froids qui présentent la symétrie SU(N). Le modèle qui explique cette expérience, dit de double-puits car il décrit un réseau de deux chaînes en interactions, est analysé dans son régime de couplage faible, de couplage fort et par l’outil numérique. Au demi-remplissage, et dans le régime où les répulsions entre particules au sein d’un même puits, et entre puits qui se font face, sont importantes, une phase topologiqueprotégée par la symétrie de type Haldane est systématiquement attendue pour tout N, dont la phase "chirale" Haldane. Le modèle effectif obtenu lorsque N Æ 3, l’échelle de spin 3-3bar (à deux chaînes de spins, l’une dans la représentation fondamentale de SU(3), l’autre dans sa représentation conjuguée), y est détaillée. / Topological phases exist beyond the standard Ginzburg-Landau paradigmthat dominated the understanding of phases and phase transitions in condensed matter systems. Paradigmatic examples have been derived to establish a new theoretical basis that takes into consideration these topological aspects. The spin 1 Haldane phase is one of them for the unidimensional case. The present thesis aims to study this phase as well as its suggested generalizations by focusing on a way to implement them experimentally using ultracold fermionic alkaline-earth atoms, that involve an internal SU(N) symmetry. The model describing the experiment is called the double-well model and depicts a lattice of two interacting chains. The model is analysed at weak coupling, strong coupling and using a numerical tool. At half-filling and inthe regime of srong repulsions between particles in the same well as well as two facing wells, a Haldane-like symmetry-protected topological phase is systematically expected for all N, including the "chiral" Haldane phase. The effective model obtained when N Æ 3 is the 3-3bar ladder model (describing two spin chains, one in the fondamental representation of SU(N), and the other in its conjuguate) and is particulary explored.

The thesis entitled “In situ crystallography and charge density analysis of phase transitions in complex inorganic sulfates” consists of six chapters. Structural changes exhibited by ferroic and conducting materials are studied as a function of temperature via in situ crystallography on the same single crystal. These unique experiments bring out the changes in the crystal system resulting in subtle changes in the complex polyhedra, distortions in bond lengths and bond angles, rotation of sulfate tetrahedral around metal atoms, phase separations and charge density features. The results provide new insights into the structural changes during the phase transition in terms of coordination changes, variable bond paths and variability in electrostatic potentials while suggesting possible reaction pathways hitherto unexplored. Chapter 1 gives a brief review of the basic features of structural phase transitions in terms of types of phase transitions, their mechanisms and related properties and outlines some of the key characterization techniques employed in structural phase transition studies like single crystal diffraction, thermal analysis, conductivity, dielectric relaxation, Raman spectroscopy and charge density studies. Chapter 2 deals with the group of compounds A3H(SO4)2, where A= Rb, NH4, K, Na which undergoes ferroelastic to paraelastic phase transitions with increase in temperature. Crystal structures of these compounds have been determined to a high degree of accuracy employing the same single crystal at room temperature at 100K and at higher temperatures. The data collection at 100K allows the examination of the ordered and disordered hydrogen atom positions. Rb3H(SO4)2 show two intermediate phases before reaching the paraelastic phase with increase in temperature. However, in case of (NH4)3H(SO4)2 and K3H(SO4)2, the paraelastic phase transition involves a single step. Chapter 3 deals with variable temperature in situ single crystal X-ray diffraction studies on fast super protonic conductors AHSO4, where A= Rb, NH4, K to characterize the structural phase transitions as well as the dehydration mechanism. The structure of KHSO4 at room temperature belongs to an orthorhombic crystal system with the space group symmetry Pbca and on heating to 463K it transforms to a C centered orthorhombic lattice, space group Cmca. The high temperature structure contain two crystallographically independent units of KHSO4 of which one KHSO4 unit is disordered at oxygen and hydrogen sites an shows a remarkable increase of sulfur oxygen bond distance – 1.753(4)Å. On heating to 475K, two units of disordered KHSO4 combine and loose one molecule of water to result in a structure K2S2O7 along with an ordered KHSO4 in a monoclinic system [space group P21/c]. On further heating to 485K two units of ordered KHSO4 combine, again to lose one water molecule to give K2S2O7 in a monoclinic crystal system [space group C2/c]. In the case of RbHSO4, both the high temperature structural phase transition and a serendipitous polymorph have been characterized by single crystal X-ray diffraction. The room temperature structure is monoclinic, P21/n, and on heating the crystal insitu On the diffractometer to 460K the structure changes to an orthorhombic system [space group Pmmn]. On keeping the crystallization temperature at 80°C polymorph crystals of RbHSO4 were grown. In case of NH4HSO4 both the room temperature and high temperature structures are structurally similar to those in RbHSO4, but the transition temperature is found to be 413K. Chapter 4 deals with the crystal structure, ionic conduction, dielectric relaxation, Raman spectroscopy phase transition pf a fast ion conductor Na2Cd(SO4)2. The structure is monoclinic, space group C2/c, and is built up with inter connecting CdO6 octahedra and SO4 tetrahedra resulting in a framework structure. The mobile Na atoms are present in the framework, resulting in a high ionic conductivity. The conductivity measurement shows two phase transitions one at around 280°C, which was confirmed later from DTA, dielectric relaxation, high temperature powder diffraction and Raman spectroscopy. Chapter 5 describes the structure and in situ phase separation in two different bimetallic sulfates Na2Mn1.167(SO4)2S0.33O1.1672H2O and K4Cd3(SO4)5.3H2O. These compounds were synthesized keeping them as mimics of mineral structures. The structure of Na2Mn1.167(SO4)2S0.33O1.1672H2O is trigonal, space group R . The stiochiometry can be viewed as a combination of Na2Mn(SO4)22H2O resembling the mineral Krohnkite with an additional (Mn0.167S0.333O1.167) motif. On heating the parent compound on the diffractometer to 500K and keeping the capillary at this temperature for one hour, a remarkable structural phase separation occurs with one phase showing a single crystal-single crystal transition and the other generating a polycrystalline phase. The resulting single crystal spots can be indexed in a monoclinic C2/c space group and the structure determination unequivocally suggests the formation of Na2Mn(SO4)2, isostructural to Na2Cd(SO4)z. The mechanism follows the symmetry directed pathway from the rhombohedral → monoclinic symmetry with the removal of symmetry subsequent to the loss of the two coordinated water molecules. In case of K4Cd3(SO4)5.3H2O the structure belongs to the space group P21/n at room temperature and on heating to 500K and holding the capillary at this temperature for 60 minutes as before, the CCD images can be indexed in a cubic P213 space group after the phase separation, generating K2Cd2(SO4)3, belonging to the well known Langbeinite family, while the other phase is expected to be the sought after K2Cd(SO4)2. The possible pathways have been discussed. Chapter 6 reports the charge density studies of phase transitions in a type II langbeinite, Rb2Mn2(SO4)3. The structure displays two different phases, cubic at 200K, orthorhombic at 100K respectively. After multiple refinements it is found that there are significant differences in the actual bond path (Rij) and the conventional bond length. In the cubic phase the distortions in sulfate tetrahedral are more than in the orthorhombic phase which could be the expected driving force for the phase transition to occur. Appendix contains reprints of the work done on the structures of the following: a) Rb2Cd3(SO4)3(OH)2.2H2O: structural stability at 500 K b) Structure of (NH4)2Cd3(SO4)4.5H2O c) Structure of Rb2Cd3(SO4)4.5H2O

In this thesis I have studied some problems of condensed matter at high pressures and temperatures by means of numerical simulations based on Density Functional Theory (DFT). The stability of MgCO3 and CaCO3 carbonates at the Earth's mantle conditions may play an important role in the global carbon cycle through the subduction of the oceanic crust. By performing ab initio electronic structure calculations, we observed a new high-pressure phase transition within the Pmcn structure of CaCO3. This transformation is characterized by the change of the sp-hybridization state of carbon atom and indicates a change to a new crystal-chemical regime. By performing ab initio Molecular Dynamics simulations we show the new phase to be stable at 250 GPa and 1000K. Thus, the formation of sp3 hybridized bonds in carbonates can explain the stability of MaCO3 and CaCO3 at pressures corresponding to the Earth's lower mantle conditions. We have also calculated phase transition sequence in CaCO3, SrCO3 and BaCO3, and have found that, despite the fact that these carbonates are isostructural and undergo the same type of aragonite to post-aragonite transition, their phase transformation sequences are different at high pressures. The continuous improvement of the high-pressure technique led to the discovery of new composite structures at high pressures and complex phases of many elements in the periodic table have been determined as composite host-guest incommensurate structures. We propose a procedure to accurately describe the structural parameters of an incommensurate phase using ab initio methods by approximating it with a set of analogous commensurate supercells and exploiting the fact that the total energy of the system is a function of structural parameters. By applying this method to the Sc-II phase, we have determined the incommensurate ratio, lattice parameters and Wyckoff positions of Sc-II in excellent agreement with the available experimental data. Moreover, we predict the occurrence of an incommensurate high-pressure phase in Ca from first-principle calculations within this approach. The implementation of DFT in modern electronic structure calculation methods proved to be very successful in predicting the physical properties of a solid at low temperature. One can rigorously describe the thermodynamics of a crystal via the collective excitation of the ionic lattice, and the ab initio calculations give an accurate phonon spectra in the quasi-harmonic approximation. Recently an elegant method to calculate phonon spectra at finite temperature in a self-consistent way by using first principles methods has been developed. Within the framework of self-consistent ab initio lattice dynamics approach (SCAILD) it is possible to reproduce the observed stable phonon spectra of high-temperature bcc phase of Ti, Zr and Hf with a good accuracy. We show that this method gives also a good description of the thermodynamics of hcp and bcc phases of Ti, Zr and Hf at high temperatures, and we provide a procedure for the correct estimation of the hcp to bcc phase transition temperature.

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No description available.

This work is focused on the parent compounds of the Fe-chalcogenide superconductors. For this purpose poly- and single-crystalline forms of tetragonal β-FexSe, Fe1+yTe, Fe1+yTe1-xSex and Fe(1+y)-xMxTe (M = Ni, Co) have been prepared. Second focal points of this study are the low-temperature structural phase transitions and physical property changes in tetragonal Fe1+yTe which are induced by composition, external pressure, and cationic substitution.

The response of materials under extreme temperature and pressure conditions is a topic of great significance because of its relevance in astrophysics, geophysics, and inertial confinement fusion. In recent years, environments exceeding several hundred gigapascals in pressure have been produced in the laboratory via laser-based dynamic loading techniques. Shock-loading is of particular interest as the shock provides a fiducial for measuring time-dependent processes in the lattice such as phase transitions. Time-resolved x-ray diffraction is the only technique that offers an insight into these shock-induced processes at the relevant spatial (atomic) and temporal scales. In this study, nanosecond resolution x-ray diffraction techniques were developed and implemented towards the study of shock-induced phase transitions in polycrystalline materials. More specifically, the capability of a focusing x-ray diffraction geometry in high-resolution in situ lattice measurements was demonstrated by probing shock-compressed Cu and amorphous metallic glass samples. In addition, simultaneous lattice and free surface velocity measurements of shock-compressed Mg in the ambient hexagonal close packed (hcp) and shock-induced body centered cubic (bcc) phases between 12 and 45 GPa were performed. These measurements revealed x-ray diffraction signals consistent with a compressed bcc lattice above a shock pressure of 26.2±1.3 GPa, thus capturing for the first time direct lattice evidence of a shock-induced hcp to bcc phase transition in Mg. Our measurement of the hcp-bcc phase boundary in Mg was found to be consistent with the calculated boundary from generalized pseudopotential theory in the pressure and temperature region intersected by the principal shock Hugoniot. Furthermore, the subnanosecond timescale of the phase transition implied by the shock-loading conditions was in agreement with the kinetics of a martensitic transformation. In conclusion, we report on the progress and future work towards time-resolved x-ray diffraction measurements probing solid-liquid phase transitions in high Z polycrystalline materials, specifically Bi. / text

The series of compounds [M(H2O)2(15-crown-5)](NO3)2, M = Mg, Mn, Co, Cu and Zn, has been extended to include two new phases for M = Fe and two new phases for M = Ni. The system [M(H2O)2(15-crown-5)](NO3)2 is remarkable for having many high-Z’ phases (Z’ > 1) with similar packing and for having solid-solid phase transitions through which there is no significant loss of crystallinity. The synthesis of the analogous Ni complex was carried out. Single-crystal X-ray diffraction showed that the coordination of the Ni2+ ion is different from that of the other six M2+ ions in the system [M(H2O)2(15-crown- 5)](NO3)2. High temperature phases with high Z’ (8) were isolated for M = Mg, Fe and Zn. The refinements of such phases are challenging because of the lack of information in the diffraction patterns. Full details of the refinements for these three phases are discussed. Six other Ni(II) complexes consisting of Ni2+, NO3-, 15-crown-5 and different solvents were found when efforts were made to synthesize the compound [Ni(H2O)2(15-crown- 5)](NO3)2. In these chemically different environments, the Ni2+ ions are not coordinated by the 15-crown-5 molecules; rather, one-dimensional H-bonded chains are formed from uncomplexed 15-crown-5 molecules and the Ni(II) complexes. Among these six Ni(II) complexes, the compounds [Ni(H2O)6](NO3)2·(15-crown-5)·H2O, [Ni(H2O)6](NO3)2·(15-crown-5)·2H2O and [Ni(H2O)2(MeCN)(NO3)2]·(15-crown- 5)·MeCN were found to have reversible solid-solid phase transitions between structurally related phases. In all of these transitions, no significant crystal damage was detectable. The two latter systems are unusual because their phase sequences include three transitions and four phases between 90 and 295 K and because of the existence of high-Z’ phases. These high-Z’ phases are best depicted as being intermediate to low- and hightemperature phases. A method based on thermal analyses and X-ray diffraction has been developed for studying such sets of phase transitions.

<p>In this thesis, material properties have been examined under extreme conditions in computer-based calculations.</p><p>The research on iron (Fe), nickel (Ni), and ferropericlase (Mg_1-xFe_xO) are not only important for our understanding of the Earth, but also for an improved knowledge of these materials <i>per se</i>.</p><p>An embedded-atom model for Fe demonstrated to reproduce properties such as structure factors, densities and diffusion constants, and was employed to evaluate temperature gradients at Earth core conditions. A similar interaction together with a two-temperature method was applied for the analysis of shock-induced melting of Ni. For Mg_1-xFe_xO, the magnetic transition pressure was shown to increase with iron content. Furthermore, the C₄₄ softening with pressure and iron composition supports the experimentally observed phase transition for Mg_0.8Fe_0.2O at 35 GPa.</p><p>The properties of high density helium (He) is of great interest as the gas is one of the most abundant elements in the solar system. Furthermore, He and neon (Ne) are often used as pressure media in diamond anvil cells. The melting of He showed a possible fcc-bcc-liquid transition starting at T=340 K, P=22 GPa with a Buckingham potential, whereas the bcc phase was not seen with the Aziz form. For Ne, Monte Carlo calculations at ambient pressure showed very accurate results when extrapolating the melting temperatures to an infinite cluster limit. At high pressure, a one-phase <i>ab initio</i> melting curve showed a match with one-phase L-J potential results, which could imply a correspondence between <i>ab initio</i>/classical one-phase/two-phase calculations.</p><p>In the search for hard materials, <i>ab initio</i> calculations for four TiO₂ phases were compared. Just as imposed by experiment, the cotunnite phase was found to be very hard. The anomalous elastic behavior of the superconducting group-<i>V</i> metals V, Nb, Ta was found to be related to shrinking nesting vectors and the electronic topological transition (ETT).</p>