http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Computer simulation studies of phason-phonon coupling in two-dimensional quasicrystals
The discovery of an alloy in the mid-1980's that possessed non-crystallographic symmetry opened the door for a wealth of experimental and theoretical studies of this new class of materials. It was quickly named a quasicrystal" because of its crystal-like diffraction pattern which exhibited non-crystallographic symmetry. Soon after the experimental discovery, computer simulations were begun to study the formation of quasicrystals by using simple molecular models. One of the questions to be addressed by simulations was that of the elastic properties of the model and how they might relate to real-world quasicrystals. Along with the usual thermal disordering (the "phonon" degree of freedom) of such models, an additional degree of freedom was invoked to explain the anomalous behavior of the diffraction peak intensities. This was labeled the "phason" degree of freedom. Using group theory, it could also be assigned elastic constants like the phonon degree of freedom. In this study a derivation of the elastic free energy will be given, which will include a term that couples the phason and phonon degrees of freedom. The results of this derivation will be used to construct an expression for the Fourier transform of the quasicrystalline lattice. A simple two-dimensional quasi- crystal model based on harmonic interactions will be presented, and the Monte Carlo method will be applied to this model in order to generate an adequate ensemble of statistical samples from which we can estimate the elastic constants. The ensemble-averaged diffraction pattern will be used to calculate the elastic constants. The results obtained using this technique will be compared to other methods found in the current literature. By examining the diffraction pattern, we can begin to relate the results of our computational model to quantities that can be measured in the laboratory.
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Includes bibliographical references: pages 104-108.