Approximants in the Ag–In–M and Au–Sn–M (M = Ca or Rare Earth Metals) Systems

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 Ag 43 In 43 Eu 14 and Au 60 Sn 25 M 15 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 , R r,e .