Density-functional theory of elastic moduli: Icosahedral quasicrystals

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Abstract
A recently developed density-functional method for calculating elastic moduli of crystals is generalized to include phason elasticity in incommensurate crystals. The theory is applied to hypothetical icoshedral quasicrystals based on interactions embodied in the pair correlation functions of a dense-random-packing model. It is found that the usual (phonon) elastic moduli are not dramatically different in quasicrystals and crystals. However, we show that a sufficiently strong phonon-phason coupling, which is very sensitive on the pair correlations at long wavelengths, may cause an elastic distortion with nonzero phason as well as phonon components.