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The thermodynamics of five Al₃Er compounds were investigated through first-principles density-functional theory (DFT) and experimental analysis. The Al₃Er compounds with Al₃Ho.hR20 (prototype Al₃Ho, Pearson symbol hR20), Cu₃Au.cP4, AlNd_3.hP8, Ni₃Ti.hP16 and Al₃Gd.hR12 structures exhibited formation energies of −0.412(−0.417), −0.411(−0.416), −0.400(−0.413), −0.399(−0.345) and −0.342(−0.345) meV/atom when using DFT with “standard” potential (“frozen core” potential) of Er. The results indicated that the Al₃Ho.hR20 structure was the thermodynamic stable phase and the other structures were metastable. The formation energy of Cu₃Au.cP4 structure was only 1 meV/atom less than that of Al₃Ho.hR20. Experimentally, the Al-30 wt.% Er alloys were cooled from 900 °C to 500 °C at the rate of 5 ± 2 °C/h and 60 ± 2 °C/h, respectively. The corresponding XRD analysis showed that the Al₃Ho.hR20 was formed at the cooling rate of 5 ± 2 °C/h and the Cu₃Au.cP4 was formed at the cooling rate of 60 ± 2 °C/h, which indicated that the Al₃Ho.hR20 was in a thermodynamic stable phase and the Cu₃Au.cP4 was in a metastable phase with high stability. The structural analysis indicated that the tiny energy difference between Al₃Ho.hR20 and Cu₃Au.cP4 might be attributed to a similar structure with varied stacking sequences.