Estudamos o modelo predador-presa estocástico definido em uma rede com interações entre os primeiros vizinhos, cada sítio podendo assumir três estados: vazio, ocupado por presa e ocupado por predador. Introduzimos ainda um parâmetro que controla a possibilidade de difuãao dos estados, a difusão é permitida entre quaisquer estados. O modelo exibe uma fase oscilante, uma fase não-oscilante e uma fase absorvente. As duas primeiras fases possibilitam a coexistência entre as espécies biológicas enquanto na fase absorvente a rede é totalmente preenchida por presas e o sistema fica preso nessa configuração. Determinamos a linha de transição da fase não-oscilante para a fase absorvente por meio de simulações dependentes do tempo. Também, determinamos a linha de transição da fase oscilante para a fase não-oscilante através da análise das funções de autocorrelação das séries temporais de presas e predadores. Além disso, estudamos o modelo por meio de aproximações de campo médio dinâmico. Concluímos que a inclusão da difusão no modelo predador-presa leva a uma maior região de coexistência das espécies no diagrama de fases. Nossos resultados sugerem que o componente difusivo é irrevelevante quanto ao comportamento crítico, pois ele não exclui o modelo da classe de universalidade da percolação direcionada. / We have studied the predator-prey stochastic model defined on a lattice with first neighbour interactions. Each site of the lattice may assume one of three states: vacant, occupied by prey and occupied by predator. We have introduced a parameter that controls the possibility of difusion among sites. The model shows an oscilating phase, a non-oscilating phase and an absorbing phase. In the first two phases the system exhibits coexistence of biological species while in the absorbing phase the lattice is filled with prey and the system becomes trapped. We have determined the transition line between the non-oscilating and absorbing phases using time-dependent simulations. We have also determined the transition lines between oscilating and non-oscilating phases using time-autocorrelation functions of the prey time-series. In addition, we have studied the model by means of dynamical mean-field aproximations. We conclude that the introduction of diffusion in the predator-prey model leads to a larger region of coexistence in the phase diagram. Our results suggest that difusion is irrelevant for the critical behavior since it does not change the universatility class of the model.

Nesta dissertação, mostramos as primeiras aplicações do recém criado Anstz do Produto Matricial [8] na solução exata das matrizes de transferência associadas a modelos de vértices. A integrabilidade dos modelos é obtida diagonalizando-se a matriz de transferência diagonal-para-diagonal. Foram estudados duas classes de modelos. Na primeira delas introduzimos novos modelos de vértices, que denominamos de modelos de 5 vértices interagentes. Nestes modelos os vértices além das interações usuais de vizinhos próximos, dadas pela regra do gelo, possuem também interações de natureza repulsiva ao longo da diagonal. O famoso modelo de 6 vértices é obtido num limite particular deste novo modelo. O espectro da matriz de transferência, analogamente ao que acontece no ansatz de Bethe tradicional é dado em termos de solução de equações não lineares. Um estudo analítico e numérico destas equações foi feito para o modelo de 6 vértices que está contido nesta primeira classes de modelos. Tais resultados, juntamente com as idéias de invariância conforme, nos permitiram estudar o modelo em seu regime crítico. A segunda classe de modelos que estudamos foram os modelos de 10 vértices que satisfazem às regras do gelo. Obtivemos todos os possíveis modelos exatamente integráveis desta classe, reobtendo resultados da literatura bem como novos resultados. / In this dissertation we present the first application of a recent introduces Matrix Product Ansatz [8], in the exact solution of the transfer matrices associated to vertex models. The exact integrability is obtained through the diagonalization of the diagonal-to-diagonal transfer matrix. We studied two classes of models. In the first one we introduced new vertex models, that we call as interacting 5 vertex models. On these models beyond the nearest-neighbor interactions among the vertices, imposed by the ice rule, they also have repulsive interactions along the diagonal. The famous 6-vertex model is just a special case this class of models. The eigenspectrum of this transfer matrix, analogously as in the traditional Bethe ansatz, is obtained in terms of the roots of nonlinear equation. An analytical and numerical study of these equations we done on the first class. These results together with the machinery coming from conformal invariance allow us the study the model on its critical region. The second class of models we considered were the 10 vertex models that satisfy ice rules we obtained all the possible exact integrable models on this class, rederiving earlier results on the literature as were producing new ones.

This thesis focusses on the properties of, and relationships between, several fundamental objects arising from critical physical models. In particular, we consider Schramm--Loewner evolutions, the Gaussian free field, Liouville quantum gravity and the Brownian continuum random tree. We begin by considering branching diffusions in a bounded domain $D\subset$ $R^{d}$, in which particles are killed upon hitting the boundary $\partial D$. It is known that such a system displays a phase transition in the branching rate: if it exceeds a critical value, the population will no longer become extinct almost surely. We prove that at criticality, under mild assumptions on the branching mechanism and diffusion, the genealogical tree associated with the process will converge to the Brownian CRT. Next, we move on to study Gaussian multiplicative chaos. This is the rigorous framework that allows one to make sense of random measures built from rough Gaussian fields, and again there is a parameter associated with the model in which a phase transition occurs. We prove a uniqueness and convergence result for approximations to these measures at criticality. From this point onwards we restrict our attention to two-dimensional models. First, we give an alternative, ``non-Gaussian" construction of Liouville quantum gravity (a special case of Gaussian multiplicative chaos associated with the 2-dimensional Gaussian free field), that is motivated by the theory of multiplicative cascades. We prove that the Liouville (GMC) measures associated with the Gaussian free field can be approximated using certain sequences of ``local sets" of the field. This is a particularly natural construction as it is both local and conformally invariant. It includes the case of nested CLE$_{4}$, when it is coupled with the GFF as its set of ``level lines". Finally, we consider this level line coupling more closely, now when it is between SLE$_{4}$ and the GFF. We prove that level lines can be defined for the GFF with a wide range of boundary conditions, and are given by SLE$_{4}$-type curves. As a consequence, we extend the definition of SLE$_{4}(\rho)$ to the case of a continuum of force points.

The spinel structure (general formula AB2O4) is widely occurring in natural and synthetic materials, and has a marked technological and scientific significance due to its magnetic, electric and multiferroic behaviours. The presence of transition metal cations with multiple oxidation state and the resulting charge, orbital and spin degrees of freedom of the partially occupied d-orbitals lead to uniquely ordered ground states. The coupling of all the three degrees of freedom can result in a structurally distorted ground state where the direct metal-metal interaction forms atomic clusters, or 'orbital molecules'. The Verwey phase of magnetite (Fe3O4), occurring below TV ~ 125 K, is driven by a cooperative bond distortion that forms linear Fe3+-Fe2+-Fe3+ arrangement (trimeron). The effect of non-stoichiometry and chemical modification on this complex structure has been investigated with a variety of samples through microcrystal synchrotron XRD. A mineral sample (Al, Si, Mg and Mn impurities, TV = 119 K) confirms the Verwey phase as the most complex long-range electronic order known to occur naturally; its relevance in space sciences is discussed. Moreover, the structural analysis of two synthetic magnetites (Fe3(1-δ)O4 with 3δ = 0.012 and TV = 102 K, Fe3-xZnxO4 with x = 0.03 and TV = 90 K) univocally confirmed the persistence of the transition, and its first order, at doping level > 1 %, contrary to previous reports. Moreover, the temperature evolution of the trimerons and their persistence above TV was probed through X-ray Pair Distribution Function analysis on pure Fe3O4: the data analysis between 90 K < T < 923 K show that the Verwey phase goes from long-range ordered (T < 125 K) to short-range ordered (T > 850 K). Magnetite can thus only be considered to have a regular cubic spinel structure above the Curie temperature (TC = 858 K). The pyrochlore lattice of B cations in a spinel gives the structure the potential for frustration upon antiferromagnetic ordering. Fe2GeO4 and γ-Fe2SiO4 were synthesised through conventional solid state routes, with the use of high-pressure synthesis for the latter. Magnetometry and heat capacity measurements highlighted two transitions (Tm1 = 8.6 K and Tm2 = 7.2 K, and Tm1 = 11.2 K and Tm2 = 7.5 K respectively). Powder neutron diffraction data between 2 K < T < 25 K showed that both materials stay undistorted below TN. Magnetic Rietveld refinement led to two highly unconventional magnetic structures, with incommensurate propagation vectors and modulation of the moment magnitude. γ-Fe2SiO4 also shows a spin-ice order below Tm2. The results are unique and unusual for transition metal oxides; the models are systematised by proposing a 'frustration wave' model, in which the degree of frustration is a spatial quantity that can be distributed through the structure in order to stabilise the ground state.

Neste trabalho estudamos a influência do tamanho molecular médio sobre a natureza da transição de fase esmética A (SA)-colestérica (C) líquido-cristalina para os compostos termotrópicos de miristato de colesterila (C14), nonanoato de colesterila (C9) e misturas binárias de C14 e C9 e caproato de colesterila (C6) e C9. Medidas de microscopia óptica foram realizadas para determinar as temperaturas de transição de fase SA C e C-isotrópica (I). Isto possibilitou a escolha dos intervalos de temperatura próximos às transições de fases, como referências para as outras técnicas utilizadas no trabalho. A natureza das transições de fase (descontínua, também denominada de primeira ordem, ou contínua) foi inferida através das análises de medidas de densidade e entálpicas. Os resultados evidenciaram que a transição passa de primeira ordem para contínua quando o tamanho molecular médio e a temperatura reduzida, r (definida como a razão entre as temperaturas de transição de fases SA C e C I ), decrescem no sistema. A ocorrência de uma transição de fase SA C contínua foi observada para a concentração de 65% de C9 na mistura C6 C9, para o valor de r ~ 0, 92. Propriedades mesoscópicas dos compostos estudados, como a distância entre as camadas esméticas na fase SA, dSA, o tamanho molecular médio, , no domínio C, e o comportamento do tamanho de correlação, , ao longo das transições de fase, foram determinadas da análise dos picos de difração de raios X. Os dados revelaram que dSA diminui com o decréscimo do tamanho molecular médio, como era esperado. Além disso, os valores de obtidos na fase C, próximos à transição I C, concordam com os tamanhos moleculares médios calculados supondo que as moléculas estejam em conformação estendida. Mais ainda, foi observado um aumento no tamanho de correlação na fase C quando a temperatura é reduzida da fase I para a fase SA, representando um aumento no grau de ordem orientacional. Contudo, o parâmetro troca abruptamente na transição C SA. Tal descontinuidade diminui com o decréscimo do tamanho molecular médio (e assim com r). Para o sistema particular composto por 65% C9 : 35% C6, onde identificamos um transição de fase contínua SA C, observamos um comportamento de (T TSAC)0,5 no domínio da fase C, em bom acordo com a teoria de campo médio. / The influence of the mean molecular length on the nature of the smectic A (SA)- cholesteric (C) liquid crystal phase transition has been studied for cholesteryl myristate (C14), cholesteryl nonanoate (C9) and binary mixtures of C14 and C9 and cholesteryl caproate (C6) and C9. Optical microscopy was carried out to determine the temperatures of the SAC as weel as the C - isotropic (I) phase transitions. This allowed the choice of the optimum temperature interval near the phase transitions. Information concerning the nature of the transitions (descontinuous, also referred to as first order, or continuous) was evaluated through the analysis of the density and enthalpic measurements. The results have evidenced that the transition crosses over from first order to continuous when both the mean molecular length and the reduced temperature, r (ratio between SAC and CI phase transition temperatures), decrease in the system. The occurrence of a continuous SA C phase transition is observed for a concentration very near 63.1 molar percent of C9 in the C6 C9 mixture (65 wt% C9 : 35 wt% C6), at r ~ 0.92. Mesoscopic properties of the systems, as the distance between the smectic layers in the SA phase, dSA, the mean molecular length, , in the C domain, and the correlation length, , behavior along the phase transitons, were determined from the X-ray difraction peaks. The data have revealed that dSA decreases as the mean molecular length is reduced, as it was expected. Moreover, values obtained in the C phase near the I C phase transition agree with the mean molecular lengths calculated from the corresponding extended molecule lengths. In addition, an increase in the correlation length in the C phase is observed, as the temperature is reduced from I to SA phases, representing an increase in the orientational order. Nevertheless, the parameter jumps in the C SA phase transition. Such discontinuity decreases as the mean molecular length (and hence the reduced temperature) diminishes. For the particular system composed of 65 wt% C9 : 35 wt% C6, where a continuous SA C phase transition was identified, a behavior of (T TSAC)0,5 in the C domain was observed, in good agreement with the mean field theory.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Os molibidatos constituem uma grande classe de compostos inorgÃnicos e tÃm sido o objeto de vÃrias investigaÃÃes, devido o estudo ainda nÃo realizado no mesmo usando espectroscopia Raman em funÃÃo da pressÃo e as diversas aplicabilidades em diversos campos de estudos do Na2MoO4.2H2O nos motivamos a realiza este estudo. Geralmente os membros desta famÃlia possuem fÃrmula geral Y2XO4.nH2O, onde Y = (Na, Ca), X = (Mo, S, W, Mn) com n = (0, 1, 3, 4...). O Na2MoO4.2H2O foi estudado atravÃs de experimentos de espectroscopia Raman visando investigar os efeitos da aplicaÃÃo de pressÃo hidrostÃtica em suas propriedades estruturais e vibracionais. Na cÃlula de pressÃo (DAC, do inglÃs Diamond Anvil Cell, que permite a obtenÃÃo de pressÃo de 0-10GPa) foram utilizados como meios compressores uma mistura de Ãlcoois (metanol e etanol na proporÃÃo de 4:1) e Ãleo mineral (Nujol). O material Na2MoO4.2H2O experimenta uma transiÃÃo de fase quando o meio compressor à a mistura de Ãlcoois, sendo esta transiÃÃo estrutural. Jà quando o meio compressor à o nujol (Ãleo mineral) o Na2MoO4.2H2O experimenta duas transiÃÃes de fase. A diferenÃa para tais acontecimentos à que o Na2MoO4.2H2O interage com o meio compressor Ãlcool, uma vez que ao relaxar-se a pressÃo o espectro do material apresenta-se como se estivesse semidesidratrado nÃo voltando para a fase original (fase &#945;). Quando o meio compressor à o nujol, alÃm de uma fase adicional, o Na2MoO4.2H2O, no processo de relaxamento, recupera a fase original, sendo que a fase intermediÃria à suprimida devido ao efeito de histerese. Portanto, identificam-se trÃs fases distintas no Na2MoO4.2H2O, uma no intervalo de 0 a 3,0 GPa (fase &#945;), outra entre 3,0 e 4,0 GPa (fase &#948;) e a terceira acima de 4,0 GPa (fase &#946;). A primeira transiÃÃo da fase &#945; para a fase &#948; à uma transiÃÃo conformacional, devido a distorÃÃes nos tetraedros MoO4, saindo do grupo de simetria D2h15. A segunda transiÃÃo à uma transiÃÃo estrutural devido ao colapso de dois modos em um Ãnico modo, principalmente na regiÃo dos modos da rede, o que indica uma transiÃÃo para uma estrutura de maior simetria que a anterior (possivelmente de ortorrÃmbica para tetragonal). / The molibidatos up a large class of inorganic compounds and have been the subject of several investigations. Usually the members of this family have Y2XO4.nH2O general formula, where Y = (Na, Ca), X = (Mo, S, W, Mn) with n = (0, 1, 3, 4...). The Na2MoO4.2H2O was studied through experiments of Raman spectroscopy aimed at investigating the effects of hydrostatic pressure on their properties structural and vibrational. The material Na2MoO4.2H2O experiencing a transition phase when the compressor is half the mixture of alcohols, this transition is structural. When the compressor is the way nujol (mineral oil) Na2MoO4.2H2O try the two-phase transitions. The difference for these events is that the Na2MoO4.2H2O interacts with the environment compressor alcohol, since the pressure to relax the spectrum of the material presents itself as being semidesidratrado not going back to the original phase. When the compressor means is the nujol, as well as an additional step, the Na2MoO4.2H2O, in the process of relaxation, restores the original phase, where the interim stage is deleted due to the effect of hysteresis. Therefore, it identifies three distinct phases in Na2MoO4.2H2O, in a range of 0 to 3.0 GPa (phase &#945;), another between 3.0 and 4.0 GPa (phase &#948;) and third over 4.0 GPa (phase &#946;). The first transition from phase &#945; to phase &#948; is a conformal transition, due to distortions in tetraedros MoO4, leaving the group of symmetry D2h 15. The second transition is a structural transition due to the collapse of two modes in a single event, especially in the modes of the network, which indicates a transition to a structure for greater symmetry than the previous (possibly of the orthorhombic for tetragonal).

<p>The present thesis is concerned to the application of first-principles self-consistent total-energy calculations within the density functional theory on different topics in materials science.</p><p>Crystallographic phase-transitions under high-pressure has been study for TiO2, FeI2, Fe3O4, Ti, the heavy alkali metals Cs and Rb, and C3N4. A new high-pressure polymorph of TiO2 has been discovered, this new polymorph has an orthorhombic OI (Pbca) crystal structure, which is predicted theoretically for the pressure range 50 to 100 GPa. Also, the crystal structures of Cs and Rb metals have been studied under high compressions. Our results confirm the recent high-pressure experimental observations of new complex crystal structures for the Cs-III and Rb-III phases. Thus, it is now certain that the famous isostructural phase transition in Cs is rather a new crystallographic phase transition.</p><p>The elastic properties of the new superconductor MgB2 and Al-doped MgB2 have been investigated. Values of all independent elastic constants (c11, c12, c13, c33, and c55) as well as bulk moduli in the a and c directions (Ba and Bc respectively) are predicted. Our analysis suggests that the high anisotropy of the calculated elastic moduli is a strong indication that MgB2 should be rather brittle. Al doping decreases the elastic anisotropy of MgB2 in the a and c directions, but, it will not change the brittle behaviour of the material considerably.</p><p>The three most relevant battery properties, namely average voltage, energy density and specific energy, as well as the electronic structure of the Li/LixMPO4 systems, where M is either Fe, Mn, or Co have been calculated. The mixing between Fe and Mn in these materials is also examined. Our calculated values for these properties are in good agreement with recent experimental values. Further insight is gained from the electronic density of states of these materials, through which conclusions about the physical properties of the various phases are made.</p><p>The electronic and magnetic properties of the dilute magnetic semiconductor Mn-doped ZnO has been calculated. We have found that for an Mn concentration of 5.6%, the ferromagnetic configuration is energetically stable in comparison to the antiferromgnetic one. A half-metallic electronic structure is calculated by the GGA approximation, where Mn ions are in a divalent state leading to a total magnetic moment of 5 μB per Mn atom.</p>

<p>In many materials, changes in chemical composition, pressure or temperature can induce metal to insulator transitions. It is recently observed in yttrium hydride, for example, changes from a shiny mirror (YH₂) to a transparent window (YH₃), which has important technological application in optical devices. We have tuned the above transition by choosing <i>pressure</i> instead of composition. Our predicted finding is confirmed by recent experiments and opens a new way to design optical switches.</p><p>The unique role that gold plays in society is to a large extent related to the fact that it is the most <i>noble</i> of all metals.We have studied the noble nature of gold by choosing <i>pressure</i> as tool. Our prediction shows that gold transforms from a face centered cubic to an hexagonal closed packed phase above 200 GPa whereas platinum, another noble metal, does not show any phase transition up to 500 GPa. This prediction has also been confirmed by experiments suggesting that platinum is more noble than gold.</p><p>The growing concern about climate change and fossil fuel availability, the direct conversion of solar irradiation into electricity appears to be an ideal alternative to conventional energy sources. Power generation by solar cells is a direct method of solar energy conversion. We report a new cubic phase of TiO₂ which can be stabilized at ambient conditions. This phase has an absorption three or four orders of magnitude larger than the conventional state-of-the-art solar cell based on anatase TiO₂. Therefore, we are introducing a well established material with a new structure for future generation solar cells. The same effect is also observed in cubic SnO₂.</p><p>Electronic and optical properties of other materials such as Be_xZn_1-xTe, RuO₂ and IrO₂ are also studied in present thesis. In particular, for Be_xZn_1-xTe, we have used composition as a tool to tune the optical properties.</p>

Wetting and phase transitions play a very important role our daily life. Molecularly thin films of long-chain alkanes at solid/vapour interfaces (e.g. C30H62 on silicon wafers) are very good model systems for studying the relation between wetting behaviour and (bulk) phase transitions. Immediately above the bulk melting temperature the alkanes wet partially the surface (drops). In this temperature range the substrate surface is covered with a molecularly thin ordered, solid-like alkane film ("surface freezing"). Thus, the alkane melt wets its own solid only partially which is a quite rare phenomenon in nature. The thesis treats about how the alkane melt wets its own solid surface above and below the bulk melting temperature and about the corresponding melting and solidification processes.<br> Liquid alkane drops can be undercooled to few degrees below the bulk melting temperature without immediate solidification. This undercooling behaviour is quite frequent and theoretical quite well understood. In some cases, slightly undercooled drops start to build two-dimensional solid terraces without bulk solidification. The terraces grow radially from the liquid drops on the substrate surface. They consist of few molecular layers with the thickness multiple of all-trans length of the molecule. By analyzing the terrace growth process one can find that, both below and above the melting point, the entire substrate surface is covered with a thin film of mobile alkane molecules. The presence of this film explains how the solid terrace growth is feeded: the alkane molecules flow through it from the undercooled drops to the periphery of the terrace.<br> The study shows for the first time the coexistence of a molecularly thin film ("precursor") with partially wetting bulk phase. The formation and growth of the terraces is observed only in a small temperature interval in which the 2D nucleation of terraces is more likely than the bulk solidification. The nucleation mechanisms for 2D solidification are also analyzed in this work. More surprising is the terrace behaviour above bulk the melting temperature. The terraces can be slightly overheated before they melt. The melting does not occur all over the surface as a single event; instead small drops form at the terrace edge. Subsequently these drops move on the surface "eating" the solid terraces on their way. By this they grow in size leaving behind paths from were the material was collected. Both overheating and droplet movement can be explained by the fact that the alkane melt wets only partially its own solid. For the first time, these results explicitly confirm the supposed connection between the absence of overheating in solid and "surface melting": the solids usually start to melt without an energetic barrier from the surface at temperatures below the bulk melting point. Accordingly, the surface freezing of alkanes give rise of an energetic barrier which leads to overheating. / Sowohl Benetzung als auch Phasenübergänge spielen eine sehr wichtige Rolle im täglichen Leben. Molekular dünne Filme langkettiger Alkane an Festkörper/Gas-Grenzflächen (z. B. C30H62 an Silizium-Waferoberflächen) sind sehr gute Modellsysteme um die Wechselbeziehung zwischen Benetzungsverhalten und (Volumen-)Phasenübergängen zu untersuchen. In einem Temperaturbereich knapp oberhalb der Volumenschmelztemperatur benetzt die Alkanschmelze die Substratoberfläche nur partiell (Alkantropfen). In diesem Temperaturbereich ist die Substratoberfläche mit einer molekular dünnen, festkörperartig geordneten Alkanschicht bedeckt ("Oberflächengefrieren" ). Die Alkanschmelze benetzt also die eigene Festkörperoberfläche nur partiell, ein in der Natur ziemlich seltenes Phänomen. Die Dissertation beschäftigt sich damit wie die Alkanschmelze ihre eigene Festkörperoberfläche über und unter dem Volumenschmelzpunkt benetzt und mit den entsprechenden Vorgängen beim Schmelzen bzw. Erstarren. Flüssige Alkantropfen lassen sich einige Grad unter ihren Schmelzpunkt unterkühlen ohne sich sofort zu verfestigen. Dieses "Unterkühlungsverhalten" ist üblich und es ist theoretisch qualitativ gut verstanden. Allerdings beobachtet man bei den Alkanen bei leichter Unterkühlung statt einer eventuellen Volumenverfestigung oft die Ausbildung von zweidimensionalen Terrassen aus erstarrtem Alkanen. Die Terrassen wachsen auf der Substratoberfläche radial aus den flüssigen Tropfen. Sie bestehen aus wenigen Alkanlagen mit jeweils der Dicke einer Moleküllänge. Die Analyse der Terrassen-Wachstumsprozesse zeigt, dass die gesamte Substratoberfläche einschliesslich der Terrassen sowohl oberhalb als auch unterhalb der Volumenschmelztemperatur mit einer dünnen Schicht mobiler Alkanmoleküle bedeckt ist. Durch diese Schicht fliessen bei Unterkühlung die Alkane vom unterkühlten Tropfen zur Terrassenkante und liefern den Nachschub für deren Wachstum. Die Untersuchungen zeigen damit erstmalig die Koexistenz eines molekular dünnen Films ("Precursor") mit einer partiell benetzenden Volumenphase. Die Entstehung und das Wachstum der Terrassen wird nur in einem engen Temperaturfenster beobachtet in dem die Keimbildung zweidimensionaler Terrassen wahrscheinlicher ist als die dreidimensionale Volumenverfestigung. Auch dieses Keimbildungsverhalten wird in der Dissertation genauer analysiert. Noch erstaunlicher als das Terrassenwachstum, d. h. das Verfestigungsverhalten ist das Schmelzverhalten der Terrassen. Sie lassen sich bis zu einer gewissen Temperatur überhitzen bevor sie schmelzen! Weiterhin findet bei genügender Überhitzung das Schmelzen nicht gleichzeitig überall statt sondern es entstehen zuerst kleine Alkantropfen an den Terrassenrändern. Diese bewegen sich dann über die Substratoberfläche und "fressen" sich durch die festen Terrassen. Dabei wachsen sie weil sie das geschmolzene Material aufnehmen und hinterlassen eine alkanfreie Spur. Sowohl die Überhitzung als auch die Tropfenbewegung lassen sich damit erklären dass die flüssige Alkanschmelze ihren eigenen Festkörper nur partiell benetzt. Die Ergebnisse bestätigen erstmals explizit den seit vielen Jahrzehnten vermuteten Zusammenhang zwischen der üblicherweise nicht beobachtbaren Überhitzung von Festkörpern und Oberflächenschmelzen: Festkörper beginnen normalerweise ohne Energiebarriere von der Oberfläche an zu schmelzen. Entsprechend bildet das Oberflächengefrieren der Alkane eine Energiebarriere und erlaubt damit deren Überhitzen.

The present thesis is concerned to the application of first-principles self-consistent total-energy calculations within the density functional theory on different topics in materials science. Crystallographic phase-transitions under high-pressure has been study for TiO2, FeI2, Fe3O4, Ti, the heavy alkali metals Cs and Rb, and C3N4. A new high-pressure polymorph of TiO2 has been discovered, this new polymorph has an orthorhombic OI (Pbca) crystal structure, which is predicted theoretically for the pressure range 50 to 100 GPa. Also, the crystal structures of Cs and Rb metals have been studied under high compressions. Our results confirm the recent high-pressure experimental observations of new complex crystal structures for the Cs-III and Rb-III phases. Thus, it is now certain that the famous isostructural phase transition in Cs is rather a new crystallographic phase transition. The elastic properties of the new superconductor MgB2 and Al-doped MgB2 have been investigated. Values of all independent elastic constants (c11, c12, c13, c33, and c55) as well as bulk moduli in the a and c directions (Ba and Bc respectively) are predicted. Our analysis suggests that the high anisotropy of the calculated elastic moduli is a strong indication that MgB2 should be rather brittle. Al doping decreases the elastic anisotropy of MgB2 in the a and c directions, but, it will not change the brittle behaviour of the material considerably. The three most relevant battery properties, namely average voltage, energy density and specific energy, as well as the electronic structure of the Li/LixMPO4 systems, where M is either Fe, Mn, or Co have been calculated. The mixing between Fe and Mn in these materials is also examined. Our calculated values for these properties are in good agreement with recent experimental values. Further insight is gained from the electronic density of states of these materials, through which conclusions about the physical properties of the various phases are made. The electronic and magnetic properties of the dilute magnetic semiconductor Mn-doped ZnO has been calculated. We have found that for an Mn concentration of 5.6%, the ferromagnetic configuration is energetically stable in comparison to the antiferromgnetic one. A half-metallic electronic structure is calculated by the GGA approximation, where Mn ions are in a divalent state leading to a total magnetic moment of 5 μB per Mn atom.