Al₆Mn is an important precipitate phase in many Al-alloys that contain Mn. However, the three-dimensional (3D) shapes of the Al₆Mn precipitates are still unclear because drastically different geometries have been shown in TEM images. In order to understand the equilibrium shapes of Al₆Mn precipitates as a function of their sizes, we first derive possible lattice site correspondences (LCs) between the Al₆Mn and Al-matrix phases from experimentally observed orientation relationships between and crystal structures of the two phases, which are then further discriminated by crystallographic analysis and transformation strain calculations. We then formulate a phase-field model to simulate the growth process, equilibrium shapes, and habit planes of the precipitates in 3D as a function of size under the chosen LC. Precipitate shapes of all variants at various 2D cross-sections are presented, which could be used to make direct comparisons to TEM images to facilitate the confirmation of the derived LC and to develop a better understanding of precipitate shapes in 3D in specific alloys.

Al ₆ Mn是许多含Mn铝合金中的重要析出相。_{然而，Al 6} Mn 沉淀物的三维 (3D) 形状仍不清楚，因为在 TEM 图像中显示出截然不同的几何形状。为了理解 Al ₆ Mn 析出物的平衡形状与其尺寸的函数关系，我们首先推导出 Al _{6之间可能的晶格位置对应 (LC)}Mn 和 Al 基体相来自实验观察到的取向关系和两相的晶体结构，然后通过晶体学分析和转变应变计算进一步区分。然后，我们制定了一个相场模型来模拟 3D 中沉淀物的生长过程、平衡形状和惯性平面，作为所选 LC 下尺寸的函数。呈现了各种 2D 横截面上所有变体的析出物形状，可用于与 TEM 图像进行直接比较，以促进对衍生 LC 的确认，并更好地了解特定合金中 3D 析出物的形状。