| This dissertation consists of two parts. The first part employs existing computational techniques to study the electronic, and structural properties of novel group-IV and related materials, namely, carbon nanotubes, boron nitride nanotubes, and crystalline group-IV alloys. In the second part, we develop a new electronic structure calculation technique based on finite element methods with multigrid acceleration. The computation time of our new technique scales quadratically with the number of atoms in the system i.e., O( N2), as opposed to the unfavorable cubic scaling ( O(N3)) for most existing ab initio methods.; Chapter 1 gives an overview of theoretical methods involved in this dissertation. Chapter 2 focuses on the structural properties of carbon and boron nitride nanotubes. First, a new nucleation model for carbon nanotubes is proposed. Second, plastic deformation of carbon nanotube under high tensile stress is studied using a tight-binding total energy model. The elastic limits of carbon nanotubes are found to be higher than any other known materials and very sensitive to the so-called wrapping angle of nanotubes.; Chapter 3 is devoted to the electronic and structural properties of novel group-IV alloys formed from CVD precursor. Group-IV alloys have attracted considerable research interest recently. Using the newly developed UltraHigh Vacuum Chemical Vapor Deposition (UHV CVD) technique, group-IV alloys such as Si4C and Ge4C, which contain 20 atomic % carbon, have been realized.; The computational time of traditional ab initio techniques such as pseudopotential planewave methods scales at least as O( N3), where N is the number of atoms in the system. This unfavorable scaling limits the number of atoms one can study using these methods to several hundreds, even with the most powerful supercomputers available today. In chapter 4, we develop an O( N2) ab initio electronic structure calculation technique based on the finite element methods with multigrid acceleration. O(N2) scaling is achieved by avoiding explicit re-orthogonalization between eigenvectors, which is made possible by a multigrid algorithm. With these new techniques, we can perform ab initio calculations for systems containing more than 32 atoms on a single workstation (Compaq alpha DS10). (Abstract shortened by UMI.)... |
