First-principles thermodynamic calculations were carried out at the interface level for understanding the precipitation of coherent L1₂-phase nano-structures in dilute Al–Sc–Er alloys. All energetics, relevant to bulk substitution, interface formation, interfacial coherent strain and segregation, were calculated and used to evaluate the nucleation and relative stabilities of various possible L1₂ nano-structures. Only matrix-dissolved solute Er (or Sc) can substitute Sc (or Er) in L1₂-Al₃Sc (or Al₃Er). The inter-substitution between L1₂-Al₃Sc and Al₃Er is not energy feasible. Ternary L1₂-Al₃(Er_xSc_1−x) precipitates tend to form the Al₃Er-core and Al₃Sc-shell structure with a sharp core/shell interface. Three possible formation mechanisms were proposed and examined. The effects of Er/Sc ratio and aging temperature on the relative stabilities of L1₂-phase nano-structures in Al were also discussed.

为了了解稀Al–Sc–Er合金中相干的L1 ₂相纳米结构的析出，在界面一级进行了第一性原理热力学计算。计算了与本体取代，界面形成，界面相干应变和偏析相关的所有能量，并用于评估各种可能的L1 ₂纳米结构的成核作用和相对稳定性。在L1 ₂ -Al ₃ Sc（或Al ₃ Er）中，只有基质溶解的溶质Er（或Sc）可以代替Sc（或Er）。L1 ₂ -Al ₃ Sc和Al ₃ Er之间的取代不是能量可行的。三元L1 ₂ -Al ₃（Er _x Sc _{1- x}）析出物倾向于形成具有尖锐的核/壳界面的Al ₃ Er-核和Al ₃ Sc-壳结构。提出并研究了三种可能的形成机理。还讨论了Er / Sc比和时效温度对Al中L1 ₂相纳米结构相对稳定性的影响。