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+1AX_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 Nb₂GeC and Mn₂GaC, 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 M₂AlC phases are studied, and the results show that oxygen prefer different sites depending on M-element, through the number of available non-bonding M d-electrons. The theory also predicts that oxygen substituting for carbon in Ti₂AlC stabilizes the material, which explains the  experimentally observed 12.5 at% oxygen (x = 0.5) in Ti₂Al(C_1-xO_x).

Magnetism 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 electron correlations approximations for theoretical evaluation of the magnetic ground state of Cr₂AC (A = Al, Ga, Ge). Furthermore, alloying Cr₂AlC with Mn to obtain the first magnetic MAX phase have been theoretically predicted and experimentally verified. Using Mn₂GaC as model system, Heisenberg Monte Carlo simulations have been used to explore also noncollinear magnetism, suggesting a large set of possible spin configurations (spin waves and spin spirals) to be further investigated in future theoretical and experimental work.