Phason-strain analysis of the twinned approximant to the decagonal quasicrystal $\mathrm{Al_{70} Co_{15} Ni_{15}}$ : Evidence for a one-dimensional quasicrystal

In high-resolution x-ray diffraction sometimes a pronounced splitting of the strongest Bragg reflections in decagonal Al70 Co15 Ni15 is observed. So far, this has been interpreted as evidence for a twinned (micro-)crystalline state with large lattice parameters. In the present paper we show that the metrics can be perfectly reproduced by modeling a twinned one-dimensional quasicrystal rather than a twinned three-dimensional crystalline phase. The split peak positions can easily be reproduced by application of a linear phason strain on the ideal decagonal quasicrystal and subsequent fivefold twinning. New high-resolution x-ray-diffraction data are used in this analysis. An anisotropic broadening of all investigated reflections leads us to suggest a nonlinear phason-strain component