Mechanical properties of solids are governed by crystal imperfections. Computational materials science is largely concerned with the modelling of such defects, e.g. their formation, migration, and interaction energies. Atomistic simulations of systems containing lattice defects are inherently difficult because of the generally complicated geometrical structure of the defects, the need for large simulation cells, etc. In this thesis, the role of lattice defects in the mechanism behind homogeneous melting is demonstrated. Also, a generic calculational scheme for studying atomic vibrations close to extended defects (applied to a dislocation) has been considered. Furthermore, heat capacities in the solid and liquid phases of aluminium have been calculated, as well as various thermophysical defect properties. The work was carried out using classical atomistic simulations, mainly molecular dynamics, of aluminium and copper. The interatomic forces were modelled with effective interactions of the embedded-atom type. The main results of this thesis are the following: • The thermal fluctuation initiating melting is an aggregate typically with 6-7 interstitials and 3-4 vacancies. • In the initial stage of melting, no signs of a shear modulus melting mechanism, or the presence of line-like defects (dislocations), can be seen. • The typical time interval from when melting initiates to the time at which the liquid phase is fully developed is of the order of 1000τ, where the period τ corresponds to the maximum vibrational frequency in the solid. • The solid-liquid boundary advances at a pace comparable to that of thermal transport by vibrating atoms in the crystal at high temperatures. • The seemingly small anharmonic effect in the heat capacity of aluminium is caused by a partial cancellation of the low-order term linear in the temperature and anharmonic terms of higher order in the temperature. • The core region of an edge dislocation in face-centred cubic aluminium has compressed and expanded regions. The excess volume associated with the dislocation core is small, about 6 percent of the atomic volume, as a result of a partial cancellation between the volume changes of the compressed and expanded regions. • The compressed and expanded regions of the edge dislocation core give negative and positive contributions, respectively, to the excess vibrational entropy. The overall effect is a positive vibrational excess entropy of the dislocation core which is about 2kB per atomic repeat length along the dislocation core. • The atomic vibrations near the dislocation core are modelled by considering an atomic cluster with about 500-1000 atoms containing the core of dislocation, embedded in a large discrete, but relaxed, lattice of about 23 000 atoms. An atomic region that is four atomic layers thick and about 18 atomic diameters long in the direction parallel to the Burgers vector, accounts for most of the excess entropy. • The constant-pressure heat capacity of aluminium shows a minimum as a function of temperature in the liquid phase. / QC 20101013

<p>The present thesis is a theoretical study of several x-ray spectroscopies { x-ray absorption, xray photoelectron, radiative and non-radiative resonant Raman scattering spectroscopy. The main focus point is investigating the role of the nuclear dynamics in molecules (naphthalene, biphenyl, the water dimer, HCl) on these spectra.</p><p>The theoretical tools we use consist of the basic equations of the relevant x-ray spectroscopy. Wave packet methods are also used. The molecular parameters needed for our simulations are obtained through suitable quantum chemical calculations, mainly based on either wave function or density functional methods. Our simulations are compared with experimental data, where available.</p><p>Simulations of x-ray absorption and x-ray photoionization spectra for naphthalene and biphenyl show that the spectral shapes are heavily inuenced by the joint e ect of two factors { chemical shifts and excitations of vibrational progression. In both of the studied molecules, similar vibrational modes are excited, giving rise to a signi cant vibrational broadening of the spectra. Comparison between the two molecules and also comparison to the reference case { benzene, provides useful insight into the molecular behavior under core excitation.</p><p>In a further step, we consider the O1s x-ray photoelectron spectrum of the water dimer. A substantial broadening of the two bands originating from the donor and the acceptor oxygen is found. It is caused by excitations of soft intermolecular vibrational modes, associated with the hydrogen bond.</p><p>Another strong inuence of the nuclear dynamics is clearly seen in the resonant x-ray Raman scattering of HCl. Vibrational collapse is observed experimentally and con rmed theoretically for two cases: resonant excitation of the K line and o -resonant excitation of the elastic peak. These two collapses can be strictly realized for excitations in the hard x-ray region. Our considerations show that using this technique, one can eliminate the broadenings caused by the lifetime of the core excited state and the vibrational broadening, and hence, considerably increase the spectral resolution.</p><p>Finally, we predict an interference e ect in the resonant Auger scattering from xed-inspace molecules. By exciting a molecule to a dissociative state and measuring the angular distribution of the Auger electrons in coincidence with the molecular ion, one can observe this e ect. The interference pattern can be used after Fourier transformation for extracting structural data about the studied system.</p>

Diss. (sammanfattning) Linköping : Univ., 2002. / Härtill 5 uppsatser.

The present thesis is a theoretical study of several x-ray spectroscopies { x-ray absorption, xray photoelectron, radiative and non-radiative resonant Raman scattering spectroscopy. The main focus point is investigating the role of the nuclear dynamics in molecules (naphthalene, biphenyl, the water dimer, HCl) on these spectra. The theoretical tools we use consist of the basic equations of the relevant x-ray spectroscopy. Wave packet methods are also used. The molecular parameters needed for our simulations are obtained through suitable quantum chemical calculations, mainly based on either wave function or density functional methods. Our simulations are compared with experimental data, where available. Simulations of x-ray absorption and x-ray photoionization spectra for naphthalene and biphenyl show that the spectral shapes are heavily inuenced by the joint e ect of two factors { chemical shifts and excitations of vibrational progression. In both of the studied molecules, similar vibrational modes are excited, giving rise to a signi cant vibrational broadening of the spectra. Comparison between the two molecules and also comparison to the reference case { benzene, provides useful insight into the molecular behavior under core excitation. In a further step, we consider the O1s x-ray photoelectron spectrum of the water dimer. A substantial broadening of the two bands originating from the donor and the acceptor oxygen is found. It is caused by excitations of soft intermolecular vibrational modes, associated with the hydrogen bond. Another strong inuence of the nuclear dynamics is clearly seen in the resonant x-ray Raman scattering of HCl. Vibrational collapse is observed experimentally and con rmed theoretically for two cases: resonant excitation of the K line and o -resonant excitation of the elastic peak. These two collapses can be strictly realized for excitations in the hard x-ray region. Our considerations show that using this technique, one can eliminate the broadenings caused by the lifetime of the core excited state and the vibrational broadening, and hence, considerably increase the spectral resolution. Finally, we predict an interference e ect in the resonant Auger scattering from xed-inspace molecules. By exciting a molecule to a dissociative state and measuring the angular distribution of the Auger electrons in coincidence with the molecular ion, one can observe this e ect. The interference pattern can be used after Fourier transformation for extracting structural data about the studied system. / QC 20101215

<p>Chapter 1 to 4 give a short introduction to superconductivity, microscopic theory, phase transitions, and Monte-Carlo simulations. Chapter 2 is about Cooper pairing in different settings, but I also give a short introduction to the Hofstadter problem of lattice fermions on a square lattice in a perpendicular magnetic field. The purpose is to clarify some points in Paper-I. Chapter 3 is about phase transitions, and introduces the important concepts of spontaneous symmetry breaking, scaling, and renormalization. In the last section I stress some of the main differences between first order and second order phase transitions. Chapter 4 starts with a short elementary introduction to Monte-Carlo simulations and proceeds with the important, but somewhat more advanced topic of reweighting.</p><p>Chapter 5 to 7 are more closely related to the specific projects I have worked on, and are meant to illuminate and clarify some aspects in Paper-II and Paper-III. Chapter 5 introduce the Ginzburg-Landau model in various parametrizations, present some perturbative (mean-field) results, and introduce the concept of topological defects (vortices) and duality.</p><p>Chapter 6 is closely related to Paper-II and introduce the concept of fractal dimension and the relation between the vortex excitations of the original theory and the dual field theory. Chapter 7 is closely related to Paper-III where we studied the order of the metal to superconductor phase transition. To do this we had to do infinite volume and continuum limit extrapolations. We also had to consider ultraviolet renormalization since the Ginzburg-Landau theory is a continuum field theory with no inherent short scale cut-off. To reduce auto-correlation times we added several improvements to the standard Metropolis algorithm in the Monte-Carlo simulations, the most important being an overrelaxation algorithm for the scalar field and a global update of the scalar amplitude.</p>

<p>A parameter free approach for the calculation of the crystal field splitting of the lowest Russel-Saunders <i>J</i>-multiplet in <i>f</i>-electron systems has been developed and applied to selected compounds. The developed theory is applicable to general symmetries and is based on symmetry constrained density functional theory calculations in the local density or in the generalised gradient approximation.</p><p>The magnetocrystalline anisotropy of Gd has been analysed. It has been shown that the peculiar orientation of the easy axis of magnetisation is consistent with an <i>S</i>-ground state. Further, the temperature dependence of the easy axis of magnetisation has been investigated and it has been shown that the temperature driven reduction of the effective magnetisation is the principal mechanism responsible for it.</p><p>A new method has been developed that allows for theoretical studies of the electronic structure and total energy of elements and compounds in an intermediate valence regime. The method combines model and first-principles band structure calculations, therefore being accurate and computationally efficient. It has been applied to Yb metal under pressure obtaining a remarkable agreement with experimental observations for the equation of state and the x-ray absorption spectroscopy.</p>

<p>This thesis is divided into two parts. In the first part we focus mainly on certain aspects of the AdS/CFT correspondence. The AdS/CFT correspondence is a proposed duality between Type IIB superstring theory on AdS₅ xS⁵ and N = 4 supersymmetric Yang-Mills theory. In the BMN limit string states located in the center of AdS₅ rotate quickly around the equator of the S⁵ and correspond, in the dual theory, to operators constructed as long chains of sub-operators. This structure of the operators can be formulated as a spin chain and by using the Bethe ansatz their properties can be obtained by solving a set of Bethe equations. Having infinitely many sub-operators, there are methods for solving the Bethe equations in certain sectors. In paper III finite size corrections to the anomalous dimensions in the SU(2) sector are calculated to leading order.</p><p>Inspired by the chain structure of the corresponding operators, the theory of string bits treats the strings as a discrete sets of points. This theory suffers from the problem of fermion doubling, a general pathology of fermions on a lattice. In paper II we show how to adjust the theory in order to avoid this problem and, in fact, use the fermion doubling to our advantage. The second part of the thesis studies the low energy behaviour of SU(2) Yang-Mills theory in 4 space-time dimensions. In paper I we perform numerical calculations on an effective action for this theory. We propose the existence of a knotted trajectory within the dynamics of this effective action.</p>

An important, but also difficult, research field in condensed matter physics is that of strongly correlated systems. This thesis considers two topics in this field. The first topic is disorder and frustration in spin models. The introduction of disorder into quantum spin chains creates a complex problem. The ground state of the random-bond spin-1 Heisenberg chain is studied by means of stochastic series expansion quantum Monte Carlo simulation, applying the concept of directed loops. It is found that this system undergoes a phase transition to the random-singlet phase if the bond disorder is strong enough. Further a frustrated spin system is investigated. The frustration is introduced by having spins positioned on a triangular lattice. Performing a quantum Monte Carlo simulation for such a frustrated lattice leads to the occurrence of the infamous sign problem. This problem is investigated and it is shown that it is possible to use a meron cluster approach to reduce its effect for some specific models. The second topic concerns atomic condensates in optical lattices. A system of trapped bosonic atoms in such a lattice is described by a Bose-Hubbard model with an external confining potential. Using quantum Monte Carlo simulations it is demonstrated that the local density approximation that relates the observables of the unconfined and the confined models yields quantitatively correct results in most of the interesting parameter range of the model. Further, the same model with the addition that the atoms carry spin-1 is analyzed using density matrix renormalization group calculations. The anticipated phase diagram, with Mott insulating regions of dimerized spin-1 chains for odd particle density, and on-site singlets for even density is confirmed. Also an ultracold gas of bosonic atoms in an anisotropic two dimensional optical lattice is studied. It is found that if the system is finite in one direction it exhibits a quantum phase transition. The Monte Carlo simulations performed show that the transition is of Kosterlitz-Thouless type. / QC 20100628

Chapter 1 to 4 give a short introduction to superconductivity, microscopic theory, phase transitions, and Monte-Carlo simulations. Chapter 2 is about Cooper pairing in different settings, but I also give a short introduction to the Hofstadter problem of lattice fermions on a square lattice in a perpendicular magnetic field. The purpose is to clarify some points in Paper-I. Chapter 3 is about phase transitions, and introduces the important concepts of spontaneous symmetry breaking, scaling, and renormalization. In the last section I stress some of the main differences between first order and second order phase transitions. Chapter 4 starts with a short elementary introduction to Monte-Carlo simulations and proceeds with the important, but somewhat more advanced topic of reweighting. Chapter 5 to 7 are more closely related to the specific projects I have worked on, and are meant to illuminate and clarify some aspects in Paper-II and Paper-III. Chapter 5 introduce the Ginzburg-Landau model in various parametrizations, present some perturbative (mean-field) results, and introduce the concept of topological defects (vortices) and duality. Chapter 6 is closely related to Paper-II and introduce the concept of fractal dimension and the relation between the vortex excitations of the original theory and the dual field theory. Chapter 7 is closely related to Paper-III where we studied the order of the metal to superconductor phase transition. To do this we had to do infinite volume and continuum limit extrapolations. We also had to consider ultraviolet renormalization since the Ginzburg-Landau theory is a continuum field theory with no inherent short scale cut-off. To reduce auto-correlation times we added several improvements to the standard Metropolis algorithm in the Monte-Carlo simulations, the most important being an overrelaxation algorithm for the scalar field and a global update of the scalar amplitude.

A parameter free approach for the calculation of the crystal field splitting of the lowest Russel-Saunders J-multiplet in f-electron systems has been developed and applied to selected compounds. The developed theory is applicable to general symmetries and is based on symmetry constrained density functional theory calculations in the local density or in the generalised gradient approximation. The magnetocrystalline anisotropy of Gd has been analysed. It has been shown that the peculiar orientation of the easy axis of magnetisation is consistent with an S-ground state. Further, the temperature dependence of the easy axis of magnetisation has been investigated and it has been shown that the temperature driven reduction of the effective magnetisation is the principal mechanism responsible for it. A new method has been developed that allows for theoretical studies of the electronic structure and total energy of elements and compounds in an intermediate valence regime. The method combines model and first-principles band structure calculations, therefore being accurate and computationally efficient. It has been applied to Yb metal under pressure obtaining a remarkable agreement with experimental observations for the equation of state and the x-ray absorption spectroscopy.