Abstract
The origin of glass formation and the systematics of quasicrystal formation in Zr-Ti-Ni-(Cu-Be)-based metallic glasses is unraveled. Both are found to rely on frustration of the stable ${\text{Zr}}_{41.5}{\text{Ti}}_{41.5}{\text{Ni}}_{17}$ quasicrystal. A systematic change in composition of the stable Zr-Ti-Ni quasicrystal prevents icosahedral order from direct growth in the deeply undercooled liquid and induces the glass transition. Quasicrystals form in the amorphous phase to reduce frustration, i.e., to recover the ideal symmetry and composition of the stable Zr-Ti-Ni quasicrystal. This relation is established especially by the discovery of a new type of sequential phase transformations of icosahedral quasicrystalline phases involving chemical redistribution.
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