On the basis of the idea that a quasicrystal is a compound in which the average number of valence electrons per atom is around 2.0 and that its formation is dominated by atom size, stable icosahedral quasicrystals have been successfully synthesized in Ag-In-Ca, Ag-In-Yb, Ag-In-Ca-Mg and Ag-In-Yb-Mg systems. The Ag-In-Ca and Ag-In-Yb icosahedral quasicrystals have stoichiometry around Ag42In42Ca16 and Ag42In42Yb16. The Ag-In-Ca-Mg and Ag-In-Yb-Mg quasicrystals form in the composition ranges Ag42-x/2In42-x/2Ca16Mgx (x = 0-7.5 at.%) and Ag42-x/2In42-x/2Yb16Mgx (x = 0-10 at.%). Electron diffraction studies confirmed that the icosahedral quasicrystals have a primitive lattice. The average number of valence electrons per atom in all these quasicrystals is 2.0.
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