The search for effective methods to fabricate bulk single-phase quasicrystalline Al-Cu-Fe alloys is currently an important task. Crucial to solving this problem is to understand mechanisms of phase formation in this system. Here we study crystallization sequence during solidification as well as the conditions of solid phase formation in slowly solidified Al-Cu-Fe alloys in a wide range of compositions. Concentration dependencies of undercoolability were also constructed by differential thermal analysis method. These experimental results are compared with data on chemical short-range order in the liquid state determined from textit{ab initio} molecular dynamic simulations. We observe that main features of interatomic interaction in the Al-Cu-Fe alloys are similar for both liquid and solid states and they change in the vicinity of i-phase composition. In the concentration region, where the i-phase forms from the melt, both the undercoolability and the crystallization character depend on the temperature of the melts before cooling.
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