Decagonal quasicrystals in Zn-Mg-RE systems (RE = rare earth) have been studied for their composition and stability. The decagonal phase was shown to have the composition Zn Mg Dy in the Zn-Mg-Dy system. This phase 58 40 2 became a major phase after annealing and thus is apparently thermodynamically stable. Further, the decagonal phase was observed for RE = Y, Dy, Ho, Er, Tm and Lu. All these RE elements have Goldschmidt atomic diameters smaller than 3.55 A, suggesting that the atomic diameter is an intrinsic parameter in stabilizing the decagonal phase.
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Sato et al. (1998) studied this question.