Self-Consistent Phonon Theory of Aperiodic Solids and Density Functional Theories of Freezing and Vitrification
Stoessel, James Peter
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https://hdl.handle.net/2142/77314
Description
Title
Self-Consistent Phonon Theory of Aperiodic Solids and Density Functional Theories of Freezing and Vitrification
Author(s)
Stoessel, James Peter
Issue Date
1985
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Chemistry, Physical
Language
eng
Abstract
We extend Fixman's self-consistent phonon theory of the thermodynamic properties and fluctuations of the hard sphere crystal to an amorphous lattice. In doing so, we develop a theory of lattice vibrations in amorphous materials via a perturbation theory around the Einstein oscillator approximation. This development is analogous to the mean spherical model description of electronic excitations in liquids. The theory exhibits a mechanical instability rather close to computer simulated glass transitions, suggesting the possibility that the simulations probe only linear stability because of the short simulation times.
In addition, a density functional theory of freezing into an aperiodic lattice is presented. With use of free energy functionals for inhomogeneous hard-sphere fluids, the stability of a density wave with the structure of Bernal random packing is evaluated. Although the properties of the transition are sensitive to the form of the direct correlation function, the present calculations indicate a limit of metastability at a density (rho) = 1.03. The frozen lattice becomes more stable than the liquid at a density (rho) = 1.14.
Finally, with analogy to the "highly accurate" summation of cluster diagrams for hard sphere fluids a la Carnahan-Starling, we present for arbitrary potential systems, based on the generalization of the second virial coefficient to inhomogeneous systems, which, when applied to hard-sphere, soft-sphere, and Lennard-Jones freezing, yield melting characteristics in remarkable agreement with experiment. Implications for the liquid-glass transition in all three potential systems are also presented.
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