We present a new semi-empirical criterion responsible for the formation and stability of the quasicrystalline state of conventionally solidified ternary Al80-xCu20Mx (M = Ru, Ph, Re, Ir) alloys with x = 7.5, 15, 20 at.%. Generally we found that decagonal (D-phase) and icosahedral (I-phase) quasicrystals exist in neighboring: composition ranges, when one of the reported criteria examined in terms of average valence electron concentration (e/a) and effective atomic radius ratio (a(eff)) is fulfilled. By conventional cooling (dT/dt approximate to 10(3) to 10(2) Ksec(-1)) decagonal and icosahedral quasicrystals were formed in all the systems, with the exception of the Al-Cu-Re system, where only crystalline phases were found. In the ternary Al-Cu-Ir system we found large (1-1.3 mm) and stable D- and I-phases. Further on, magnetic susceptibility and magnetization curves of the alloys were investigated in the temperature range from 5 to 300 K and for magnetic fields between -50 kOe less than or equal to H less than or equal to 50 kOe. From the resulting magnetization curves the I-Al60Cu20Ru20 alloy shows only paramagnetic behavior in the field range -50 kOe less than or equal to H less than or equal to 50 kOe. The other samples show a paramagnetic or a diamagnetic behavior depending on the field intensity. For the samples I-Al72.5Cu20Ru7.5, I-Al65Cu20Ru15, D-Al65Cu20Rh15 and D-Al60Cu20Rh20 a paramagnetic behavior was observed in the field range of -1 kOe less than or equal to H less than or equal to 1 kOe. Outside this field region a transition to diamagnetism takes place. On the basis of the resulting magnetic susceptibility curves we found that in the range of 20-300 K the magnetic susceptibility is temperature independent for all samples. On the contrary, in the range of 5-20 K the magnetic susceptibility is temperature dependent (the Curie-Weiss law is valid), with the exception of the samples I-Al65Cu20Ru15, D-Al65Cu20Rh15, D-Al65Cu20Rh15 and D-Al60Cu20Rh20. The measured magnetic susceptibility values of conventionally solidified ternary AI-Cu-M (M = Ru, Rh, Re, Ir) alloys lie between the pointed values of icosahedral Al55Cu9.2Li35.8 and Al65Cu20Cr15 alloys.
