Date of Award

Spring 5-2023

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Natural Sciences

Committee Chair

Dr. Parthapratim Biswas

Committee Chair School

Mathematics and Natural Sciences

Committee Member 2

Dr. Khin Maung Maung

Committee Member 2 School

Mathematics and Natural Sciences

Committee Member 3

Dr. Katja Biswas

Committee Member 3 School

Mathematics and Natural Sciences

Committee Member 4

Dr. Sungwook Lee

Committee Member 4 School

Mathematics and Natural Sciences

Committee Member 5

Dr. Andrew Sung

Committee Member 5 School

Computing Sciences and Computer Engineering


Several explanations have been reported in the literature about the origin of extended-range oscillations (EROs) in the atomic pair-correlation function of amorphous materials. Although the radial ordering beyond the short-range order of about 5 Å has been extensively studied in amorphous materials, the exact nature of the radial ordering beyond a nanometer is still not resolved. This dissertation address this problem and explains the nature of the EROs by using high-quality models of amorphous silicon (a-Si) obtained from Monte Carlo and Molecular Dynamics simulations. The extended-range ordering in a-Si is examined through radial oscillations on the length scale of 20-40 Å by comparing the distribution of atoms in different coordination shells in a-Si with that in partially ordered networks of Si atoms and disordered configurations of crystalline silicon. In addition, the origin and structure of the First Sharp Diffraction Peak (FSDP) of a-Si near 2 Å−1 and that of amorphous silica (a-SiO2) near 1.5 Å−1 wavevector region is studied with particular emphasis on the position, intensity, and width of the FSDP. Likewise, the effects of temperature, structural disorder, and anharmonicity on the vibrational mean-square displacement (MSD) of Si atoms of a-Si are studied using harmonic approximation and ab initio molecular dynamics simulations.

This study shows that weak radial ordering exists in the atomic correlations of a-Si extended up to 20-40 Å. The analysis of the radial shell-by-shell contribution to the FSDP of a-Si reveals that the second and fourth radial shells significantly contribute to the FSDP of a-Si. A similar analysis of the FSDP of a-SiO2 indicates the higher contribution to the FSDP of a-SiO2 is from the third and fourth radial shells. Also, an approximate functional relation has been obtained between the position of the FSDP and the average radial distance of Si atoms in the second radial shell of a-Si. On the other hand, the analysis of the effect of anharmonicity on the MSD of Si atoms suggests the vibrational motion in a-Si is practically unaffected by anharmonic effects at temperatures below 400 K.