Stable icosahedral quasicrystals in the Ag-In-Ca, Ag-In-Yb, Ag-In-Ca-Mg and Ag-In-Yb-Mg systems

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 Ag_42-x/2In_42-x/2Ca₁₆Mg_x (x = 0-7.5 at.%) and Ag_42-x/2In_42-x/2Yb₁₆Mg_x (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.