ARAÚJO, Bruno Sousa. Transições de fase induzidas por pressão e tamanho de partícula no ferroelástico Pb8O5(VO4)2. 2014. 79 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2014-10-31T19:40:08Z No. of bitstreams: 1 2014_dis_bsaraujo.pdf: 4719840 bytes, checksum: 34b47793096a5251b04f1f4121ba3485 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2014-10-31T19:41:19Z (GMT) No. of bitstreams: 1 2014_dis_bsaraujo.pdf: 4719840 bytes, checksum: 34b47793096a5251b04f1f4121ba3485 (MD5) / Made available in DSpace on 2014-10-31T19:41:19Z (GMT). No. of bitstreams: 1 2014_dis_bsaraujo.pdf: 4719840 bytes, checksum: 34b47793096a5251b04f1f4121ba3485 (MD5) Previous issue date: 2014 / Ferroelastic compounds are characterized by the possibility to present two or more states of spontaneous strain which could be permuted by application of mechanical stress. Pb8O5(VO4)2 can be classified as belonging to this group. Its crystal structure is not well defined in the literature due to certain adversities found during the data analysis. However, making use of X-ray diffraction in several crystals of this compound we will discuss their probable point groups. It is also known that there is a direct relation between the states of strain and the domains pattern at ambient conditions of temperature and pressure. Several spectroscopic techniques were employed in order to analyze how the crystal structure of these compounds varies according to the dimensions of each crystal. Therefore, we observed the existence of three phases under ambient conditions as well as the possibility of a spontaneous phase transition in crystals of order to units of square micrometers. The structural behavior of Pb8O5(VO4)2 with increasing temperature has been studied in detail by different authors. They reported the existence of two phase transitions on heating, one second-order transition at about 440 K and another first-order around 520 K. The first-order phase transition leads the Pb8O5(VO4)2 crystals of ferroelastic phase to paraelastic phase. However, since ferroelastics crystals show changes of state of spontaneous strain through the application of mechanical stress, we made use of Raman scattering measures with increasing of hydrostatic pressure on samples of Pb8O5(VO4)2 to accompany the spectral behavior of the same during these pressure variations. This way we observed a phenomenon of amorphization of the sample around 11 GPa and obtained strong evidences from three phase transitions at approximately 1, 3.5 and 6 GPa. / Compostos ferroelásticos são caracterizados pela possibilidade de apresentarem dois ou mais estados de deformação ou strain espontâneos devendo haver a possibilidade de permutação entre estes estados através da aplicação de um stress mecânico. O Pb8O5(VO4)2 pode ser classificado como pertencente a este grupo. Sua estrutura cristalina ainda não é bem definida na literatura por conta de certas adversidades encontradas durante as análises das mesmas, no entanto, fazendo uso de difração de raios-X em diversos cristais deste composto discutiremos seus prováveis grupos pontuais. Sabe-se também que há uma relação direta entre os estados de strain e as estruturas de domínios sob condições ambientes de temperatura e pressão. Diversas técnicas espectroscópicas foram empregadas afim de analisar como a estrutura cristalina destes compostos pode variar de acordo com as dimensões de cada cristal. Dessa forma, verificamos a existência de três fases sob condições ambiente, bem como a possibilidade de uma transição de fase espontânea para cristais da ordem de unidades de micrometros quadrados. O comportamento estrutural do Pb8O5(VO4)2 com o aumento de temperatura foi estudado detalhadamente por diversos autores. Eles reportaram a existência de duas transições de fase durante o aquecimento, uma transição de segunda ordem por volta de 440 K e outra de primeira ordem por volta de 520 K. A transição de primeira ordem leva os cristais de Pb8O5(VO4)2 da fase ferroelástica para a fase paraelastica. Contudo, uma vez que cristais ferroelásticos apresentam mudanças de estados de strain espontâneos através da aplicação de stress mecânico, fizemos uso de medidas de espalhamento Raman com aumento de pressão hidrostática em amostras de Pb8O5(VO4)2 para acompanhar o comportamento espectral dos mesmos durante estas variações de pressão. Assim, observamos um fenômeno de amorfização da amostra por volta de 11 GPa e obtivemos fortes indícios de três transições de fase em aproximadamente 1, 3.5 e 6 GPa.

ARAÚJO, Bruno Sousa. Transições de fase induzidas por pressão e tamanho de partícula no ferroelástico Pb8O5(VO4)2. 2014. 79 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-04-09T19:07:17Z No. of bitstreams: 1 2014_dis_bsaraujo.pdf: 4719840 bytes, checksum: 34b47793096a5251b04f1f4121ba3485 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-04-10T20:49:59Z (GMT) No. of bitstreams: 1 2014_dis_bsaraujo.pdf: 4719840 bytes, checksum: 34b47793096a5251b04f1f4121ba3485 (MD5) / Made available in DSpace on 2015-04-10T20:49:59Z (GMT). No. of bitstreams: 1 2014_dis_bsaraujo.pdf: 4719840 bytes, checksum: 34b47793096a5251b04f1f4121ba3485 (MD5) Previous issue date: 2014 / Ferroelastic compounds are characterized by the possibility to present two or more states of spontaneous strain which could be permuted by application of mechanical stress. Pb8O5(VO4)2 can be classified as belonging to this group. Its crystal structure is not well defined in the literature due to certain adversities found during the data analysis. However, making use of X-ray diffraction in several crystals of this compound we will discuss their probable point groups. It is also known that there is a direct relation between the states of strain and the domains pattern at ambient conditions of temperature and pressure. Several spectroscopic techniques were employed in order to analyze how the crystal structure of these compounds varies according to the dimensions of each crystal. Therefore, we observed the existence of three phases under ambient conditions as well as the possibility of a spontaneous phase transition in crystals of order to units of square micrometers. The structural behavior of Pb8O5(VO4)2 with increasing temperature has been studied in detail by different authors. They reported the existence of two phase transitions on heating, one second-order transition at about 440 K and another first-order around 520 K. The first-order phase transition leads the Pb8O5(VO4)2 crystals of ferroelastic phase to paraelastic phase. However, since ferroelastics crystals show changes of state of spontaneous strain through the application of mechanical stress, we made use of Raman scattering measures with increasing of hydrostatic pressure on samples of Pb8O5(VO4)2 to accompany the spectral behavior of the same during these pressure variations. This way we observed a phenomenon of amorphization of the sample around 11 GPa and obtained strong evidences from three phase transitions at approximately 1, 3.5 and 6 GPa. / Compostos ferroelásticos são caracterizados pela possibilidade de apresentarem dois ou mais estados de deformação ou strain espontâneos devendo haver a possibilidade de permutação entre estes estados através da aplicação de um stress mecânico. O Pb8O5(VO4)2 pode ser classificado como pertencente a este grupo. Sua estrutura cristalina ainda não é bem definida na literatura por conta de certas adversidades encontradas durante as análises das mesmas, no entanto, fazendo uso de difração de raios-X em diversos cristais deste composto discutiremos seus prováveis grupos pontuais. Sabe-se também que há uma relação direta entre os estados de strain e as estruturas de domínios sob condições ambientes de temperatura e pressão. Diversas técnicas espectroscópicas foram empregadas afim de analisar como a estrutura cristalina destes compostos pode variar de acordo com as dimensões de cada cristal. Dessa forma, verificamos a existência de três fases sob condições ambiente, bem como a possibilidade de uma transição de fase espontânea para cristais da ordem de unidades de micrometros quadrados. O comportamento estrutural do Pb8O5(VO4)2 com o aumento de temperatura foi estudado detalhadamente por diversos autores. Eles reportaram a existência de duas transições de fase durante o aquecimento, uma transição de segunda ordem por volta de 440 K e outra de primeira ordem por volta de 520 K. A transição de primeira ordem leva os cristais de Pb8O5(VO4)2 da fase ferroelástica para a fase paraelastica. Contudo, uma vez que cristais ferroelásticos apresentam mudanças de estados de strain espontâneos através da aplicação de stress mecânico, fizemos uso de medidas de espalhamento Raman com aumento de pressão hidrostática em amostras de Pb8O5(VO4)2 para acompanhar o comportamento espectral dos mesmos durante estas variações de pressão. Assim, observamos um fenômeno de amorfização da amostra por volta de 11 GPa e obtivemos fortes indícios de três transições de fase em aproximadamente 1, 3.5 e 6 GPa.

GONÇALVES, Ricardo Oliveira. Espalhamento Raman polarizado em cristais de L-arginina.HCl:H2O e estudo da L-arginina.2H2O sob altas pressões e sob altas temperaturas. 2012. 127 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2012. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-06-08T19:50:33Z No. of bitstreams: 1 2012_tese_rogoncalves.pdf: 5273230 bytes, checksum: e2ecec57843458258d1b0a7a56cfc839 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-06-08T19:51:32Z (GMT) No. of bitstreams: 1 2012_tese_rogoncalves.pdf: 5273230 bytes, checksum: e2ecec57843458258d1b0a7a56cfc839 (MD5) / Made available in DSpace on 2015-06-08T19:51:32Z (GMT). No. of bitstreams: 1 2012_tese_rogoncalves.pdf: 5273230 bytes, checksum: e2ecec57843458258d1b0a7a56cfc839 (MD5) Previous issue date: 2012 / The objective of this Thesis is the study through Raman spectroscopy of two crystals containing amino acid L-arginine: L-arginine monohydrated hydrochloride (LARHCL) and L-arginine dihidrated (LARDH). In the first part of the work it was presented structural and vibrational aspects of LARHCL and LARDH, particularly the distribution of normal modes in terms of the irreducible representations of factor groups C2 and D2, respectively. The room temperature normal modes of LARHCL observed through polarized Raman spectroscopy using nine different scattering geometries was presented. Using ab initio calculations it was possible to tentatively assign the Raman-active normal modes of LARHCL. In another part of the work it is presented the analysis of Raman spectra of LARDH under several temperature and pressure conditions. It was studied the normal modes of LARDH crystal through Raman spectroscopy in the range between 30 oC and 200 oC. From this study it was observed the occurrence of anomalies in the Raman spectra, such as change in the curves dw/dT related to modes of low frequency (at about 45 oC), as well as the fact that, starting from 50 oC, in a heating process, some bands decrease intensity. Such a picture suggested that LARDH crystal undergoes a phase transition between 45o and 50oC. Also, it was possible to note that the spectra recorded between 45o and 60oC were different from those recorded for T < 45oC and for T > 60oC suggesting the coexistence of phases in this temperature interval. Another hypothesis was that the crystal undergoes a phase transition at 45oC, remaining in this phase up to the temperature of 60oC. Additionally, it was possible to perform thermal analysis measurements, differential thermal analysis (DTA) and thermogravimetric analysis (TG). From the DTA it was observed that between 45o and 50oC begins an endothermic event that is observed up to 84oC. A second endothermic event begins and remains up to 109oC. By using TG data it was possible to understand that these two events are related to water that left the crystal, although a small quantity remains in the crystal, as pointed out by Raman spectroscopy. In the final part of the work LARDH crystal under high pressure conditions was studied up to 8 GPa. From this study, in particular the analysis of external modes, it was revealed that the crystal undergoes a phase transition at ~ 2,5 GPa. However, for pressures between 2,5 and 8,0 GPa no additional phase transition was observed, pointing to a great stability of the crystal when compared with other amino acid hydrated crystals. Additionally, there is no great change in the internal mode region of the Raman spectrum, suggesting that the phase transition undergone by LARDH under high pressure conditions can be classified as a conformational one. / Esta Tese teve como objetivo o estudo por meio de espectroscopia Rama de dois cristais contendo o aminoácido L-arginina em sua constituição: a L-arginina monohidratada clorohidrato (LARHCL) e a L-arginina dihidratada (LARDH). Na primeira parte do trabalho foram discutidos aspectos estruturais gerais da LARHCL e da LARDH, em particular a distribuição dos modos normais do material em termos das representações irredutíveis do grupos fatores C2 e D2, respectivamente. Foi realizado um estudo detalhado dos modos normais de vibração da LARHCL à temperatura ambiente através de espesctroscopia Raman polarizada observando-se os modos normais de vibração do material em nove diferentes geometrias de espalhamento. Com o auxílio de cálculo ”ab initio” foi feita a classificação tentativa dos modos normais de vibração da LARHCL ativos no Raman. Numa outra etapa do trabalho analisou-se os espectros Raman da LARDH sob diversas condições de temperatura e de pressão. Realizou-se um estudo dos modos normais do cristal de LARDH através da espectroscopia Raman no intervalo entre 300 e 2000C. Deste estudo observou-se a existência de algumas anomalias nos espectros Raman, como mudança de inclinação de curvas dw/dT para modos de baixa frequência em torno de 45oC, além do fato de que a partir de 50oC algumas bandas vão perdendo intensidade. Estes fatos foram interpretados como uma transição de fase sofrida pelo cristal entre 45o e 50oC. Observou-se que os espectros Raman entre 450 e 60oC eram diferentes dos espectros Raman para T < 45oC e para T > 60oC sugerindo a coexistência de fases neste intervalo de temperatura. Uma outra hipótese foi que o cristal sofreria uma transição de fase em 45oC, ficando nesta fase até a temperatura de 60oC. Foram realizadas medidas térmicas do tipo análise térmica diferencial (DTA) e análise termogravimétrica (TG). Da análise de DTA observou-se que entre 45o e 50oC começa um evento endotérmico que se prolonga até cerca de 84oC. A seguir, um segundo evento endotérmico se inicia, prolongando-se até 109oC. Com o auxílio das medidas de TG compreendeu-se que estes dois eventos endotérmicos estão associados à expulsão das moléculas de água, embora uma pequena quantidade permaneça no cristal como demonstrado pela espectroscopia Raman. Como parte final do trabalho estudou-se cristais de LARDH sob condições de altas pressões até cerca de 8 GPa. Deste estudo inferiu-se pela análise da região dos modos externos, que o cristal sofre uma transição de fase em torno de 2,5 GPa. Entretanto, para pressões no intervalo entre 2,5 e 8,0 GPa nenhuma outra transição de fase foi percebida, o que aponta para uma grande estabilidade do cristal quando comparado a outros cristais hidratados de aminoácidos. Além disso, nas regiões dos modos internos não foram observadas grandes mudanças nos espectros Raman, sugerindo que a transição de fase com a pressão seja do tipo conformacional.

As transformações de fase em cristais de cianeto de potássio (KCN) a 168&#176K e 83&#176K e suas ligas com KC1, foram estudadas através da absorção ótica no infravermelho do íon de impureza OCN&#8254 e dos íons CN&#8254 da rede. Por aplicação de tensão uniaxial foram obtidos pela primeira vez cristais únicos, da KCN-KCl, nas duas fases de mais baixa temperatura. A absorção ótica dicróica devida à vibração interna do íon CN&#8254 nesses monocristais, permitiu a determinação de seu arranjo estrutural direcional, de forma inequívoca, como também correções a modelo recentemente proposto para esse arranjamento, baseado em experiências com cristais de muitos domínios. O estudo do modo de flexão da impureza OCN&#8254 permitiu o seguimento das transformações de fase anteriormente observadas por meio de medidas de calor específico em cristais puros de KCN. A evolução dessas transformações em função da concentração do íon esférico de Cl&#8254 em substituição do íon elipsoidal CN&#8254 foi estudada numa larga faixa de concentrações. Um modelo para a fase de mais baixa temperatura e proposto com arranjo antiferroelétrico dos dipolos CN&#8254 e com distinção na sub-rede dos íons positivos. Em vista do modelo proposto, duas alternativas para as duas transições de fase poderiam ocorrer. Na transição de mais alta temperatura (168&#176K), ocorreria o alinhamento ferroelástico e antiferroelétrico, dos dipolos CN&#8254, e a transição de mais baixa temperatura (83&#176K) corresponderia somente à distorção na sub-rede dos íons positivos (e possivelmente dos negativos). Na outra possibilidade, a 168&#176K ocorreria somente um arranjo ferroelástico e a 83&#176K o arranjo antiferroelétrico e a distorção na rede. / The phase transformations in potassium cyanide crystals (KCN) at 168&#176K and 83&#176K and KCN-KCl mixed crystals, were studied through the I-r optical absorption of the CN&#8254 stretching mode and the OCN&#8254 impurity bending mode and Fermi resonance application of uniaxial stress in KCN-KCl mixed crystals gives, by the first time, oriented single crystals in the lower temperature phases. The dichroic optical absorption of the CN&#8254 stretching mode in these oriented single crystals allowed the explicit determination of the structural arrangement of the C\'N POT.-\' dipole. The results of our measurements are not in agreement recently proposed by Julian and Luty based on electrical experiments with polidomain crystals. The bending mode and Fermi resonances of the substitutional OC\'N POT.\'impurity give further information in agreement with previous specif heat measurements. The evolution of the phase transformation was studied as a function of the spheroidal Cl&#8254 íon concentration replacing the CN&#8254 ellipsoidal íon. A model for the lower temperature phase is proposed with antiferroelectric ordering of the CN&#8254 dipoles and additional distortion on positive and negative sub lattices. As a consequence of the proposed model the phase transitions, may occur in two different ways that can not be distinguished with the used techniques. In the first possibility during the higher temperature phase transition (168&#176K) would occur the ferroelastic and antiferroelectric alignement of the CN&#8254 dipoles and the lower phase transition (83&#176K) would be due to a lattice distortion as necessary to explain our results. In the other possibility the 168&#176K phase transition would occur only the ferroelastic transition;and at 83&#176K the antiferroelectric ordering of the CN&#8254 ions and the lattice distortion would occur

A multivariate generalization of mutual information, multi-information, is defined in the thermodynamic limit. The definition takes phase coexistence into account by taking the infimum over the translation-invariant Gibbs measures of an interaction potential. It is shown that this infimum is attained in a pure state. An explicit formula can be found for the Ising square lattice, where the quantity is proved to be maximized at the phase-transition point. By this, phase coexis-tence is linked to high model complexity in a rigorous way.

No description available.

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.