Formation of 1/1 Yb-Cd type approximants has been verified in the Ag-In-RE (RE: rare earth metals) system for RE = Tm, Tb, Er, Dy, Gd, Pr, Ce, or Eu. The compositions of the 1/1 approximants determined by wavelength dispersive X-ray analysis (WDX), are in the range of 42-48 at. % Ag, 38-42 at. % In, and 14-15 at. % REs. By employing the empirical rule of e/a ∼ 2.0, where e/a is the valence electron concentration, a number of approximants are newly found in the Au-Sn-RE systems for RE = Sm, Pr, Ce, Dy, Tb, Gd, or Eu, where the 1/1 approximants are formed in the range of 61-64 at. % Au, 20-23 at. % Sn, and 14-15 at. % REs. The 2/1 approximants only form in Ag43In 43Eu14 and Au60Sn25M15 for M = Eu, Yb, or Ca, where the atomic size for Eu, Yb, and Ca is larger than that for the other REs and they are all divalent. Basically, the 2/1 and 1/1 approximants share the same e/a as the quasicrystals found in the In-Ag-M, Au-Sn-M, and Cd-M groups. It is likely that the phase selection among the quasicrystalline and the 1/1 and 2/1 approximant phases is dominated by the effective atomic size factor, Rr,e.
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