Formation rule for Al-based ternary quasi-crystals: Example of Al–Ni–Fe decagonal phase

After examining ternary Al-based quasi-crystalline phase diagrams, we pointed 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 phase composition zone. There are two decagonal phases, D-Al72.5Fe14.5Ni13 and D′-Al705Fe12Ni17.5, that correspond respectively to Al–Fe-based and Al–Ni-based decagonal phases in the same ternary system.