This thesis deals with various functional materials from first-principles methods and is divided into two major parts according to the underlying atomic structure of the system under study. The first part of the thesis deals with the temperature-induced structural phase transitions in metallic  β'-AuZn and perovskite oxide LiOsO3. The former one, i.e. binary AuZn, belongs to a class of shape-memory alloys that regain their initial shape due to a reversible martensitic phase transformation. Here, by means of density functional and density functional perturbation theories, we show that the martensitic transition is due to coupling between the Fermi surface nesting and anomalies in the phonon dispersion relations. The other metallic system, perovskite LiOsO3, exhibits a ferroelectric-like transition and is currently the first and sole realization of the Anderson and Blount idea. By means of ab initio molecular dynamics simulations, we investigate the mechanism behind this structural phase transformation. Another part of the thesis is dedicated to modelling and characterization of topologically disordered materials on atomic level. The structural and electronic properties of amorphous W-S-N are addressed regarding its outstanding tribological properties, i.e. almost vanishing friction coefficient. Molecular dynamics “melt-and-quench” technique has been employed in order to construct a model structure of amorphous W-S-N. Further analysis of the atomic structure revealed a formation of quasi-free N2 molecules trapped in S cages, which, together with the complex atomic structure of W-S-N, is the key to ultra-low-friction in this functional material. In the last chapter of the thesis a magnetic class of amorphous materials is addressed. Magnetic order in amorphous Gd-Fe ferrimagnet has been shown to undergo magnezation switching driven by a femtosecond laser pulse. Here, we combine first-principles density functional theory and atomistic spin dynamics simulations to explore this phenomena. A possible mechanism behind magnetization reversal in Gd-Fe based on a combination of the Dzyaloshinskii-Moriya interaction and exchange frustration is proposed.

A first-principles linear scaling real-space method for investigating non-collinear magnetic behaviour of nanostructured materials has been developed. With this method, the magnetic structures of small supported transition metal clusters have been examined. The geometric constraints imposed on the clusters by the underlying surface is found to cause non-collinear behaviour for V, Cr, and Mn clusters on Cu(111). Fe clusters supported on Cu and Ni have been studied and both spin and orbital moments are found to be enhanced for the Fe atoms, which is attributed to the recuced symmetry present at the surface. Atoms in Co clusters have been found to order antiferromagnetically, and some times in a non-collinear fasion, when deposited on a W surface. Small clusters of fcc Fe embedded in Cu have been examined and a new type of ordering, not present in larger fcc Fe systems was found. Several theoretical studies of Fe and Co based nanostructures consisting of multilayers or embedded clusters have been conducted, with the aim of predicting high moment materials for use in data storage applications. In agreement with previous experiments an enhancement of the magnetic moment is found compared to the magnetic moment of bcc Fe. The enhancement has been shown to be caused by increased spin moments for Fe atoms in close proximity with Co atoms, and this enhancement depends on the number of Co neighbours. As a result of these studies, a possible method of increasing the magnetic moment of cluster based materials has been proposed. Fermi surface analysis have been performed both on bulk materials, in order to investigate mechanisms for stabilizing non-collinear magnetic states, and in layered structures where the effect of the Fermi surface on the interlayer exchange coupling has been investigated. In addition to the development of a real-space electronic structure method for non-collinear magnetism, a density matrix purification method has been implemented in the framework of linear muffin-tin orbitals.

<p>The elastic constants of Mg_(1-x)Al_xB₂ have been calculated in the regime 0<x<0.25. The calculations show that the ratio, B/G, between the bulk- and the shear-modulus stays well below the empirical ductility limit, 1.75, for all concentrations, indicating that the introduction of Al will not change the brittle behaviour of the material considerably. Furthermore, the tetragonal elastic constant C’ has been calculated for the transition metal alloys Fe-Co, Mo-Tc and W-Re, showing that if a suitable tuning of the alloying is made, these materials have a vanishingly low C'. Thermal expansion calculations of the 4d transition metals have also been performed, showing good agreement with experiment with the exception of Nb and Mo. The calculated phonon dispersions of the 4d metals all give reasonable agreement with experiment. First principles calculations of the thermal expansion of hcp Ti have been performed, showing that this element has a negative thermal expansion along the c-axis which is linked to the closeness of the Fermi level to an electronic topological transition. Calculations of the EOS of fcc Au give support to the suggestion that the ruby pressure scale might underestimate pressures with ~10 GPa at pressures ~150 GPa. The high temperature bcc phase of the group IV metals has been calculated with the novel self-consistent ab-initio dynamical (SCAILD) method. The results show good agreement with experiment, and the free energy resolution of < 1 meV suggests that this method might be suitable for calculating free energy differences between different crystallographic phases as a function of temperature.</p>

The elastic constants of Mg(1-x)AlxB2 have been calculated in the regime 0&lt;x&lt;0.25. The calculations show that the ratio, B/G, between the bulk- and the shear-modulus stays well below the empirical ductility limit, 1.75, for all concentrations, indicating that the introduction of Al will not change the brittle behaviour of the material considerably. Furthermore, the tetragonal elastic constant C’ has been calculated for the transition metal alloys Fe-Co, Mo-Tc and W-Re, showing that if a suitable tuning of the alloying is made, these materials have a vanishingly low C'. Thermal expansion calculations of the 4d transition metals have also been performed, showing good agreement with experiment with the exception of Nb and Mo. The calculated phonon dispersions of the 4d metals all give reasonable agreement with experiment. First principles calculations of the thermal expansion of hcp Ti have been performed, showing that this element has a negative thermal expansion along the c-axis which is linked to the closeness of the Fermi level to an electronic topological transition. Calculations of the EOS of fcc Au give support to the suggestion that the ruby pressure scale might underestimate pressures with ~10 GPa at pressures ~150 GPa. The high temperature bcc phase of the group IV metals has been calculated with the novel self-consistent ab-initio dynamical (SCAILD) method. The results show good agreement with experiment, and the free energy resolution of &lt; 1 meV suggests that this method might be suitable for calculating free energy differences between different crystallographic phases as a function of temperature.