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Al-Cu-Fe based quasicrystal thin films exhibit unique surface and mechanical properties. To better understand the formation of the quasicrystal thin films, we observe direct growth of quasicrystals, prepared in a multilayer Al-Cu-Fe thin films with subsequent heat treatment, by in-situ synchrotron x-ray diffraction and in-situ transmission electron microscopy during heating and cooling. Using these two methods, we show that the ternary phase is more thermodynamically stable compared to the binary phases at temperature higher than 470 °C during the heating process, and quasicrystal formation occurs during the cooling process, specifically at 660 °C, after the sample has reached a liquid state. To distinguish quasicrystal from approximant crystals in the obtained thin film samples, we use high resolution x-ray diffraction to analyze the sample at room temperature. We reveal that the peak broadening increases monotonically along the twofold, threefold, and fivefold high-symmetry directions with the physical scattering vector but does not have systematic dependence on the phason momentum, which suggests that the thin film sample is indeed a quasicrystal instead of approximant crystals and it is almost free of phason strain. Our study provides a complete understanding of the growth mechanism for thin film Al-Cu-Fe quasicrystals, which is of particular importance for developing versatile applications of quasicrystal thin films. Image 1 [ABSTRACT FROM AUTHOR]