Theoretical Studies On Sodium Clusters, Bismuth Nanotubes And Si(15,3,23) Surface With First-Principles Methods

In this dissertation, we show the importance of the first-principles calculations to the nano-science and nano-technology with applying the first-principles methods to determine the groud-state atomic-structures of sodium clusters, investigate the mechanical and electronic properties of bismuth nanotubes and study the reconstruction of Si(15,3,23) surface.In Chapter One, we introduce the experimental developments of nano-science in generating, characterizing and assembling of nano-materials and the main first-principles methods to investigate the properties of nano-materials. The developments of computing conditions in hardwares and softwares are also introduced in this chapter.In Chapter Two, the optimum metallic-bond scheme is presented to investigate the ground-state atomic-structures of sodium clusters Na_n, n≤l5. In the optimum metallic-bond scheme, the characters of metallic bonds of Na_n cluster are combined to construct the initial geometrical coordinates of Na_n+1 cluster, and then the corresponding stable stucture of Na_n+1 is obtained by first-principles structure relaxation. The ground-state structure of Na_n+1 can be determined by comparing the total energies of its various stable stuctures. The optimum metallic-bond scheme reduces the initial guesses of geometrical coordinates of clusters dramatically. Some interesting features have been revealed from the ground-state structures of sodium clusters, for instance, there are plane-like subunits in Na₁₃, Na₁₄ and Na₁₅ that are similar to the frags of (110) surface of sodium crystal. The systematic research on the ground-state structures make it possible to elucidate the mass spectra of sodium clusters quantitatively. We find that the quasi-steady processes through capturing or dissociating a sodium atom dominate the main features of the mass spectra. The quasi-steady processes through capturing or dissociating a sodium dimer are also important to understand the detailed features of mass spectra, especially for small size clusters.In Chapter Three, the mechanical and electronic properties of bismuth nanotubes Bi(n,n), 2≤n≤10 and Bi(n,0), 4≤n≤18 are investigated with first-principles methods.We find that the bismuth nanotubes have comparative strain energies to carbon nanotubes, and the strain energies of armchair bismuth nanotubes follow the classical strain theory while the small size zigzag bismuth nanotubes deviate the theory with much larger strain energies. The bismuth nanotubes have a Young's modulus in the order of 0.06TPa(0.25TPaA), which is approximately 5% that of carbon nanotubes. All the bismuth nanotubes are found to be semi-conducting materials independent of their diameters and helicities. For bismuth nanotubes with small diameters, the band structures and bandgaps vary evidently with the strong hybridization effect. When the diameters are larger than 18A, the bandgaps of bismuth nanotubes approach 0.63 eV, corresponding to that of bismuth sheet at the T point. In addition, we expect the constant-bandgap bismuth nanotubes to be a potential semiconducting nano-material in future nano-electronics.In Chapter Four, a reconstruction model is presented to explain the experimental STM images of Si(15,3,23) surface. The calculated STM images of the model with first-principles methods agree well with experiment which indicates that our model is a possible candidate of the reconstruction of Si(15,3,23). This chapter also introduces the stable high index silicon surfaces and their family territories, and the principles and theories of STM.