Abstract
Abstract The phason disorder observed in a large class of quasicrystals is discussed within a stochastic model. Basic assumption is that the growth front of a sample moves in one direction and that the phason fields accumulate linearly with the size of the domain. Treating the domain size and the linear phason strain as random variables, we show that the phason fluctuation behaves very differently depending on the probability distribution of the domain size. To yield the experimentally observed diffraction peak broadening, the uniform phason strain is not sufficient but the distribution of the domain size of strained quasicrystals has to be such a singular one that an arbitrarily large domain can be found in samples. A physical mechanism realizing the singular probability distribution is discussed.
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