鉴于均匀形核在快速凝固晶粒细化中的重要作用，本工作选取液态金属Al为研究对象，采用团簇类型指数法，通过对团簇结构遗传性的逆向追踪，研究了Al液滴在等温结晶过程中的形核特征。结果表明，在过冷度ΔT ≈ 0.41T_m (T_m为熔点)下，形核首先出现在液滴表层，并且其稳态形核率(I₀)与临界晶核平均尺寸({\overline{n}}_{\mathrm{c}})均比芯部大。可视化分析显示，临界晶核几何构型为非球形，液/固界面为fcc-液态/hcp多相结构。与Al液体相比，Al液滴的平均形核孕育时间({\overline{\tau }}_{\mathrm{c}})较长，而液滴表层的{\overline{\tau }}_{\mathrm{c}}又比液滴芯部长，但液滴和液体都呈现出晶胚平均有效生长时间({\overline{\tau }}_{\mathrm{g}}^{\mathrm{e}\mathrm{f}\mathrm{f}})远大于晶胚平均孕育时间({\overline{\tau }}_{\mathrm{e}})的特点。比较液滴的不同形核模式发现，直接从液态原子转化成fcc临界晶核数量(q_{\mathrm{c}})很少，大多经历晶胚孕育和有效生长。由此形成的{\overline{n}}_{\mathrm{c}}最大，且晶胚孕育时间(τ_e)对{\overline{n}}_{\mathrm{c}}影响很小，但{\overline{n}}_{\mathrm{c}}越大，晶胚所需有效生长时间({\tau }_{\mathrm{g}}^{\mathrm{e}\mathrm{f}\mathrm{f}})越长。

Owing to the important role of homogeneous nucleation in grain refinement of rapidly solidified alloys, a detailed molecular dynamics simulation is performed to investigate the incubation of embryos and their evolution into nuclei during the isothermal crystallization of liquid Al droplets. Using the cluster type index method (CTIM) based on Honeycutt-Andersen (H-A) bond-type indices, various fcc critical nuclei formed during isothermal crystallization are distinguished from numerous fcc embryos through reverse tracking of atomic trajectories, relying on the structural heredity of fcc single-crystal clusters. The results show that nuclei first appear in the shell region of Al droplets with a critical size (n_{\mathrm{c}}) ranging from 2 to 100 atoms at an undercooling of ΔT ≈ 0.41T_m (T_m is melting point). Both the steady-state nucleation rate (I₀) and the average critical nucleus size ({\overline{n}}_{\mathrm{c}}) in the shell are higher than those in the core region. Visual analysis of the geometry of critical nuclei reveals that most are non-spherical, and the liquid-solid interface is not a simple fcc-liquid dual-phase configuration, but rather a multi-phase structure involving fcc-liquid and hcp components. Compared with the nucleation in Al bulk, a longer average nucleation incubation time ({\overline{\tau }}_{\mathrm{c}}) of critical nuclei is observed in Al droplets, with {\overline{\tau }}_{\mathrm{c}} in the shell region being longer than that in the core. When {\overline{\tau }}_{\mathrm{c}} is divided into the average incubation time of embryos ({\overline{\tau }}_{\mathrm{e}}) and their average effective growth time ({\overline{\tau }}_{\mathrm{g}}^{\mathrm{e}\mathrm{f}\mathrm{f}}), it is determined that {\overline{\tau }}_{\mathrm{g}}^{\mathrm{e}\mathrm{f}\mathrm{f}} is considerably longer than {\overline{\tau }}_{\mathrm{e}} in both Al droplets and Al bulk. For the four modes of nucleation, i.e., (I) embryo incubation and subsequent effective growth, (II) only effective growth of embryos, (III) direct nucleation after embryo incubation, and (IV) direct transformation from liquid atoms, a tracking analysis of atomic trajectories reveals that few critical nuclei are formed directly from liquid atoms. In contrast, most critical nuclei undergo both embryo incubation and effective growth, and these exhibit the largest {\overline{n}}_{\mathrm{c}}. Moreover, the incubation time ({\tau }_{\mathrm{e}}) of embryos has little effect on {\overline{n}}_{\mathrm{c}} of critical nuclei, whereas a large {\overline{n}}_{\mathrm{c}} typically requires a long effective growth time ({\tau }_{\mathrm{g}}^{\mathrm{e}\mathrm{f}\mathrm{f}}) of embryos during isothermal crystallization.