The origin of stability in quasicrystal has been debated since the discovery of stable quasicrystals. Both energy-stabilized and entropy-stabilized mechanisms have been proposed. To address these issues, we directly observed the growth mechanisms involved in the formation of quasicrystals and other phases in real time for a multilayer Al-Cu-Fe thin films by in-situ XRD and in-situ TEM during heating and cooling. We show that the ternary phase is more thermodynamically stable compared to the binary phase, and quasicrystal formation occurs during the cooling process, specifically at 660°C, after the sample reached a liquid state. Evidence of random tiling was observed, suggesting that entropy contributes to thermodynamic stability during the initial stage of cooling. At a lower temperature of the cooling process, however, energy plays a key role in stabilization. We provide a better understanding of the growth mechanism, which is of particular importance for developing controllable synthesis of functional nanomaterials.