Doctoral Dissertations

Date of Award

12-2001

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Physics

Major Professor

Chia C. Shih

Committee Members

Geoffrey S. Canright, John J. Quinn, Charles R. Collins

Abstract

Perhaps the most fundamental questions we can ask about a solid are "What is it made of?" and "How are the constituent parts assembled?" This is so elementary, and yet so basic to any detailed understanding of the thermal, electrical, magnetic, optical, and elastic properties of materials. At the beginning of the twenty-first century, concern over the placement of the atoms in a solid seems quaint and anachronistic, more suited to the dawn of the twentieth century. X-ray diffraction, electron diffraction, optical microscopy, x-ray diffraction tomography, to name a few, are powerful techniques to uncover structure in solids. With this arsenal of tools, and the efforts of many researchers, surely we can have nothing novel to say about the discovery and description of structure in solids, save perhaps the refinement of well-worn techniques or the analysis of particularly obstinate cases. But careful examination of present technology reveals that while we are quite good at finding and describing periodic order in nature, cases that lack such order are much more difficult. Certainly in the complete absence of structural order, as in a gas, statistical methods exist that permit a satisfying understanding of the properties of the system without knowing ( or even wanting to know) the details of the microscopic placement of the constituents. But it is the in-between cases, where order and disorder coexist, that has proven so elusive to both analyze and describe. In this thesis, we will tackle these in-between cases for a special type of layered material, called polytypes. They exhibit disorder in one dimension only, making the analysis more tractable. We will give a method for determining the structure of these solids from experimental data and demonstrate how this structure, both the random and the non-random part, can be compactly expressed. From our solution, we will be able to calculate the effective range of the inter-layer interactions, as well as the configurational energies of the disordered stacking sequences.

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