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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, AlNd3.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.

The orientation, hardness and Young's modulus of Al3Yb single crystal were analyzed using the electron back scatter diffraction (EBSD) and nanoindentation techniques, combined with the first principles calculations. The Al3Yb single crystal of about 1 mm size could be obtained by heating hypereutectic Al-38.5 (wt%)Yb alloy to liquid state and cooling to room temperature at 60 °C/h. The results showed that the hardnesses of the Al3Yb single crystals oriented in (318), (023), (213), (112) and (122) directions varied between 5.4 ± 0.1 and 5.7 ± 0.1 GPa, and the reduced modulus were between 131.9 ± 1.6 and 140.5 ± 3.9 GPa. First principles calculations by assuming standard Yb pseudopotential with 4f electrons showed that the elastic constants of C11, C12 and C44 were 149.4, 32.94 and 66.59 GPa, respectively, and the Poisson's ratio was 0.161. Based on these calculated elastic constants and Poisson's ratio and the reduced modulus values, the Young's modulus of the Al3Yb single crystal was determined to be between 148.4 ± 2.3 and 154.9 ± 2.3 GPa for different orientations and the anisotropy coefficient (A) was 1.17 ± 0.01.