| n the first part of this thesis, a general discussion on powder X-ray diffraction of low-dimensional materials is presented. Two approaches have been used to obtain the diffraction patterns of a low-dimensional system: (1) direct numerical computation using the Debye formula, and (2) an analytical method. In general, a Bragg line of the diffraction pattern for a low-dimensional powder has a strongly asymmetric shape, and consists of a spike, which is size dependent, and a long tail to the high angle side, which is size independent. Using a linear approximation for the interference function, an analytic solution is obtained for a simple two-dimensional lattice. By comparing the analytic solution to direct computer computation, it is found that the results are more accurate than the previous work of Warren.;For a "two-dimensional" structure consisting of more than one monolayer of atoms, the line shape of a Bragg peak is modulated by the structure factor and may differ dramatically from that for a simple two-dimensional lattice. This structure factor effect provides valuable information about the structure of the layer. A detailed study of X-ray diffraction patterns for transition metal dichacogenide single molecular layers has been carried out, and a structure identification using the Bragg line profile is demonstrated.;In the second part of this thesis, a study on the structural, optical, electrical and vibrational properties of single molecular layer... |
