Abstract The nucleation properties and stability of the ordered precipitates in Al-Sc-Er alloy were extensively studied by first-principles calculation. The calculated substitutional formation energy revealed that the dissolved Sc or Er in the Al matrix is very favorable to substitute the X sublattice site in L12-Al3X (X = Sc/Er). The calculated solubility curve demonstrate the significant contribution of vibrational entropy to nucleation. The interface energies for Al/Al3Sc, Al/Al3Er and Al3Sc/Al3Er are calculated in the three directions of [100], [110] and [111], and find that the interface structure in (100) plane is the most desirable, and the interface energy of Al/Al3Er is the largest. Regardless of temperature and Sc/Er ratio, the L12-Al3ScxEr1-x precipitation phase mainly formed as the core-shell structure with Al3Er as the core and Al3Sc as the shell due to lower nucleation energy. The core-shell structure behaved higher stability once the particle radius is greater than 1 nm. Furthermore, the thermodynamic driving force for the segregating of Si or Zr in Al-Sc-Er alloy should accelerate the precipitation kinetics, where Si partitions occurred preferentially to the Al3Er and Zr partitions preferentially to the Al matrix. Overall, these theoretical results can offer solid explanations to the available experimental results.

中文翻译：

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Al-Sc-Er-(Si/Zr)合金中有序析出物的第一性原理研究

摘要 通过第一性原理计算，广泛研究了Al-Sc-Er合金有序析出物的形核特性和稳定性。计算的置换形成能表明，Al 基体中溶解的 Sc 或 Er 非常有利于替代 L12-Al3X 中的 X 亚晶格位点（X = Sc/Er）。计算出的溶解度曲线表明振动熵对成核的显着贡献。在[100]、[110]和[111]三个方向计算Al/Al3Sc、Al/Al3Er和Al3Sc/Al3Er的界面能，发现(100)面的界面结构最理想， Al/Al3Er 的界面能最大。无论温度和 Sc/Er 比如何，由于较低的成核能，L12-Al3ScxEr1-x析出相主要以Al3Er为核、Al3Sc为壳的核壳结构形成。当粒子半径大于 1 nm 时，核壳结构表现出更高的稳定性。此外，Al-Sc-Er 合金中 Si 或 Zr 偏析的热力学驱动力应加速析出动力学，其中 Si 分配优先发生于 Al3Er，Zr 分配优先发生于 Al 基体。总的来说，这些理论结果可以为可用的实验结果提供可靠的解释。Al-Sc-Er 合金中 Si 或 Zr 偏析的热力学驱动力应加速析出动力学，其中 Si 分配优先发生于 Al3Er，Zr 分配优先发生于 Al 基体。总的来说，这些理论结果可以为可用的实验结果提供可靠的解释。Al-Sc-Er 合金中 Si 或 Zr 偏析的热力学驱动力应加速析出动力学，其中 Si 分配优先发生于 Al3Er，Zr 分配优先发生于 Al 基体。总的来说，这些理论结果可以为可用的实验结果提供可靠的解释。