After examining ternary Al-based quasi-crystalline phase diagrams, we point
ed out that the presence of e/a-constant and e/a-variant lines is a common
phenomenon. Ternary quasi-crystal compositions are located at the crossing
point of these lines in ternary phase diagrams. Such an empirical rule can
be used to predict the ternary quasi-crystal compositions from binary ones.
We applied this rule to the Al-Fe-Ni system and clarified the decagonal ph
ase composition zone. There are two decagonal phases, D-Al72.5Fe14.5Ni13 an
d D'-Al705Fe12Ni17.5, that correspond respectively to Al-Fe-based and Al-Ni
-based decagonal phases in the same ternary system.