Date of Award:


Document Type:


Degree Name:

Master of Science (MS)




Dr. John Robert Dennison


A theoretical approach was developed to model the vibrational dynamics of amorphous, two-dimensional materials. The materials were modeled as continuous random networks (CRN's) comprising an assemblage of planar rings of diverse size. In-plane vibrational modes for symmetric 4-, 5-, 60, 7-, and 8-membered rings were examined. Vibrational states of isolated rings were modified by coupling the rings to a continuous network to represent rings embedded in a CRN. An effective force constant was used to couple the ring vibrations to the network's collective motions. Potentials were approximated with the use of a central force model (bond-stretching force constant) and a valence force model (bond-stretching and bond-angle-bending force constants). Valence force model calculations employed group theory. Mode frequencies were calculated using the method of small oscillations and the normal coordinate treatment.

Amorphous carbon was used as a test case for the embedded ring approach. A physically consistent set of force constants for the valence force model was determined by comparing the 6-membered ring E2g mode in graphite. Frequencies for selected ring modes were calculated, resulting in a discrete line spectrum.

Calculated frequencies were fitted with gaussian peaks and convoluted into theoretical spectra for comparison with the experimental Raman spectrum of amorphous carbon. Integrated gaussian lineshape intensities were assumed to be directly proportional to the CRN ring statistics. The peaks were convoluted with the peak widths, ring statistics, and number of modes as the adjustable parameters.

Parameters consistent with previous research on the structure and dynamics of amorphous carbon provided satisfactory fits to the data. The best fit to the Raman data includes the E2g and A1g modes of 6-membered rings (present in Raman spectra of nanocrystalline graphite), and the Raman active E2' modes of 5- and 7-membered rings. The corresponding ring statistics agree with previous results, supporting the presence of a sizable percentage of 5- and 7- membered rings, but with no 4- or 8-membered rings. This positive result provides verification for the embedded ring approach, and supports a CRN model for amorphous carbon.

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