| In resent years, quasi one-dimensional (1-D) materials, including nanowires (nanorods), nanotubes, nanobelts, heterojunction and superlattice nanowires, have attracted great attentions in the scientists of condense matter physics and chemistry, and become an important research subject in the nanomaterial science. Especially, metallic atomic chains and metallic nanowires with special nano-scales are ideal systems for investigating the dependence of electronic, transport, optical, magnetic and mechanical properties on size and dimensionality. In addition, they are expected to play an important role as interconnects and functional components of new electronic and optoelectronic devices. Now the research of the metallic nanowires has already become one of the central subjects in the nanomaterial science.The physical properties of the nanomaterials are the foundation for their applications. So the study on the structure stability and electronic properties of the nanowires will provide valuable theoretical guidance for the preparing and controlled synthesis of 1-D nanomaterials. Recently, the stable gold atomic chains suspended between two gold electrodes were realized in laboratories by two research groups. These experiments have been considered as one of the milestones in the low dimensional physics and nanoscience. Subsequently, atomic chains formed by various metals have been intensively studied both in theory and experiment. Ti and Ni are the pre-transition and latter-transition metals. The electron configurations of Ti and Ni are and , respectively. They are complements of each other. In this dissertation, by using the first-principles calculations based on the density functional theory, we have systematically studied the structural stability, electronic and magnetic properties of Ti, Ni and alloy TiNi chains. We also studied some typical structures of titanium nanowires whose cross sections are planar polygons, and 3d 2 4s23 d8 4s2...
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