Formation of Al-Cu binary phase. To dynamically monitor the crystallization of the Al-Cu-Fe multilayer structure, both in-situ XRD and in-situ TEM methods were used to collect data at different temperatures. For the in-situ XRD experiment, the sample sequence layer was SiO₂ /Fe/Cu/Al/SiO₂/Si. For the in-situ TEM experiment, the sample sequence layer was Pt/SiO₂/Fe/Cu/Al/Al₂O₃/SiO₂/Si, with added protection layers for technical purposes only. Full details of sample preparation can be found in the Methods section below. The temperature was first ramped up to 350°C from RT (Figure 1.a), and data were collected at these initial temperatures. The in-situ XRD data indicate that interactions between any of the layers did not begin until the temperature reached 200°C (Figure 1.b). However, a changing peak position for Al, Cu and Fe in this graph between RT and 300°C can be seen, which represents the change in the lattice constant for Al, Cu and Fe. The lattice parameter for Al, Cu and Fe were calculated by using the Bragg's law, and the results shows that the lattice parameter of Al, Cu and Fe at RT change from 4.0496 Å, 3.6146Å and 2.8767Å to 4.07074 Å, 3.6314Å and 2.8883Å at 300°C, respectively.

The TEM data confirmed that Al and Cu did not interact until the temperature reached 200°C. The in-situ TEM image shows that at 200°C, Cu diffused into the Al layer. At this point, there is evidence of a solid solution of Al and Cu, indicated by “A” in Figure 1.c. The sample was kept at 200°C, which allowed Cu to mix to a greater extent with Al. The vacancy migration energies for a single interstitial Cu is calculated to be 0.9 eV, which is higher than the vacancy migration energy for an Al interstitial (0.66 eV) in pure Al \cite{Wynblatt_1968}. This indicates that Cu should be more mobile than Al. Also, Cu prefers to segregate to interstitial sites because of a smaller atomic radius (1.28 Å) compared to that of Al (1.43 Å). The voids at the Al-Cu interface were observed in the in-situ TEM images. The Cu diffused to the Al layer, and the two started to form the Al₂Cu (θ-phase) and AlCu (η-phase) after the sample was kept for 5 minutes at 200°C (Figure 1.d). The diffraction pattern of AlCu (η-phase) was seen at 200°C with [020] orientation. Samples were kept at 200°C for 5 more minutes (total 10 minutes), which allowed Cu to mix more with Al. The formation of θ and η phases can be observed in the in-situ XRD graph which was confirmed by diffraction pattern in the in-situ TEM image.

At this low temperature, Fe could not react with Cu because there is a positive deviation for the Fe-Cu system leading to complete immiscibility in a solid state \cite{TOMILIN_2006}. However Al and Cu did interact when the temperature was gradually increased to 350°C. Initially, the temperature was raised to 300°C for 10 minutes, but no differences were observed in the XRD data in this 10-minute window. To understand the in-situ XRD data, the sample for in-situ TEM was also heated to 300°C. After ten minutes at this temperature, more Cu started to diffuse into the bottom layer (i.e. the Al-Cu area) and the void areas continued to increase, which is indicated by “B” in Figure 1.e. When the temperature was increased to 350°C, the XRD data shows that the Al and Cu peaks completely disappeared, indicating that the two layers had completely mixed. The in-situ TEM sample was kept at 350°C for 22 minutes, at which point it was observed that more Cu had diffused into the Al-Cu layer and the void area significantly increased between Al-Cu and Cu-Fe (Figure 1.f, g and h). The diffraction pattern of θ-phase with [200] orientation was captured at 350°C (Figure 1.g). The in-situ TEM image shows that in the Al-Cu binary system, the θ-phase was the dominant phase when the sample reached 350°C.

The interaction between Al and Cu and crystallization was not observed at this lower temperature, because a certain amount of Cu needed to diffuse to Al in order to form the binary phases (83% Al, 17% Cu) \cite{Ben__1982}. Using the composition of the lowest eutectic of the binary system as a measure of the relative effective concentrations of the reactants, rules can be formulated to predict first phase formation and phase formation sequence \cite{Pretorius_1991}. During the solid state interaction entropy changes are usually insignificant. The heat of formation is therefore a better measure of the free energy change in the system. The heat of formation (\(\triangle H\)^o) and effective heat of formation (\(\triangle H\)′) for Cu-Al binary systems were calculated in different compositions from Cu rich to Cu poor. The ∆H′ for Cu:62.5% Al:37.5%, Cu:50% Al:50% and Cu:33.3% Al:66.7% were -4.08, -5.1 and -6.13 kJ (mole of atoms)^-1, respectively, when the \(\triangle H\)^o for these three compositions was -15 kJ (mole of atoms)^-1\cite{Niessen_1988}. However, different sequences of phase formation in Al-Cu thin film system have been reported \cite{Niessen_1988,Pelzer_2012,Hang_2008,Xu_2009} . Reports on Al-Cu formation in the comparable temperature range observed three or fewer phases, including Al₄Cu₉, AlCu, Al₂Cu \cite{Pelzer_2012,Hang_2008,Xu_2009} . In an Al-rich composition, it has been reported that the AlCu-phase growth occurs at a temperature above 175°C , and when the temperature increases, the AlCu phase changes to Al₂Cu \cite{Koerner_2014}. This was seen here, as the AlCu phase and Al₂Cu formed at 200°C and Al₂Cu grew continuously at a temperature of up to 350°C . Takeda et al. point out that to form the Al₄Cu₉ phase, longer annealing time is necessary \cite{Takeda_1993}.