Abstract
We report on the six-dimensional (6D) structural refinement of three members of the i-$R$-Cd quasicrystals ($R$ = Gd, Dy, Tm) via synchrotron x-ray diffraction from single-grain samples, and show that this series is isostructural to the i-${\mathrm{YbCd}}_{5.7}$ quasicrystal. However, our refinements suggest that the $R$ occupancy on the Yb icosahedron sites within the Tsai-type atomic cluster is approximately 80%, with the balance taken up by Cd. Similarities between the i-$R$-Cd series and i-${\mathrm{ScZn}}_{7.33}$, and their differences with i-${\mathrm{YbCd}}_{5.7}$ and i-${\mathrm{Ca}}_{15}{\mathrm{Cd}}_{85}$, indicate that there are at least two subclasses of Tsai-type icosahedral quasicrystals. We further show from x-ray resonant magnetic scattering (XRMS) measurements on a set of closely related ${\mathrm{Tb}}_{1\ensuremath{-}x}{\mathrm{Y}}_{x}{\mathrm{Cd}}_{6}$ 1/1 approximants that the dilution of the magnetic $R$ ions on the icosahedron within the Tsai-type cluster by nonmagnetic Y disrupts the commensurate magnetic ordering in the approximant phase.
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