The front cover image is a close up of M (red and blue spheres) and X (grey sphere) in M 2 AX. In the background its nanolaminated structure consisting of ordered, clustered, and disordered atoms or magnetic moments is illustrated.The spine image shows charge redistribution for an interstitial oxygen atom in Cr 2 AlC where blue indicate gain of electrons and red loss of electrons.The back cover image shows charge redistribution when oxygen substitutes for carbon in Ti 2 AlC where blue indicate gain of electrons and red loss of electrons. My daughter described it as "a planet, with water, and trees, and blue leaves". © Martin Dahlqvist, unless otherwise stated. Printed by LiU-Tryck, Linköping, Sweden, 2014 To my JETs ♥ v ABSTRACT In this thesis, first-principles calculations within density functional theory are presented, with a principal goal to investigate the phase stability of so called M n+1 AX n (MAX) phases. MAX phases are a group of nanolaminated materials comprised of a transition metal (M), a group 12-16 element (A), and carbon or nitrogen (X). They combine ceramic and metallic characteristics, and phase stability studies are motivated by a search for new phases with novel properties, such as magnetism, and for the results to be used as guidance in attempted materials synthesis in the lab.To investigate phase stability of a hypothetical material, a theoretical approach has been developed, where the essential part is to identify the set of most competing phases relative to the material of interest. This approach advance beyond more traditional evaluation of stability, where the energy of formation of the material is generally calculated relative to its single elements, or to a set of ad hoc chosen competing phases. For phase stability predictions to be reliable, validation of previous experimental work is a requirement prior to investigations of new, still hypothetical, materials. It is found that the predictions from the developed theoretical approach are consistent with experimental observations for a large set of MAX phases. The predictive power is thereafter demonstrated for the new phases Nb 2 GeC and Mn 2 GaC, which subsequently have been synthesized as thin films. It should be noted that Mn is used for the first time as sole M-element in a MAX phase. Hence, the theory is successfully used to find new candidates, and to guide experimentalists in their work on novel promising materials. Phase stability is also evaluated for MAX phase alloys. Incorporation of oxygen in different M 2 AlC phases are studied, and the results show that oxygen prefer different sites depending on M-element, through the number of available non-bonding M delectrons. The theory also predicts that oxygen substituting for carbon in Ti 2 AlC stabilizes the material, which explains the experimentally observed 12.5 at% oxygen (x = 0.5) inMagnetism is a recently attained property of MAX phase materials, and a direct result of this Thesis work. We have demonstrated the importance of choice of magnetic spin configuration and elec...