Abstract An analytical model is derived to predict the kinetics of a peritectic transformation involving solute diffusion in the L-, δ- and γ-phases with non-zero constant diffusivities. A similarity method is adopted to solve the diffusion equations in the bulk L-, δ-, and γ-phases coupled with the solute conservation equations at the γ/L and γ/δ interfaces. The proposed model is applied to predict the kinetics of the isothermal peritectic transformation of Fe-C alloys for two conditions, zero and non-zero supersaturation, in the δ- and L-phases. An excellent match between the analytical solutions and phase-field simulations is achieved. In the case of zero supersaturation, the time evolution of γ-phase thickness and non-linear concentration distribution in the γ-phase predicted by the present analytical model agree well with the experimental data reported in the literature. When the holding temperature decreases, the parabolic rate constant at the γ/δ interface increases non-linearly, while it remains nearly unchanged at the γ/L interface. Additionally, the non-zero supersaturation in the parent phases increases the diffusion flux jump significantly at the γ/L interface but only slightly at the γ/δ interface. As a result, the growth velocity increases noticeably at the γ/L interface, but it is nearly unchanged at the γ/δ interface.

中文翻译：

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在所有三相中具有非线性溶质分布的包晶转变：解析解、相场建模和实验比较

摘要 推导出了一个分析模型来预测包晶转变的动力学，该转变涉及 L 相、δ 相和 γ 相中的溶质扩散，具有非零常数扩散系数。采用相似方法求解体L-、δ-和γ-相中的扩散方程以及γ/L和γ/δ界面处的溶质守恒方程。所提出的模型用于预测 δ 相和 L 相中 Fe-C 合金在零和非零过饱和两种条件下的等温包晶转变动力学。实现了解析解和相场模拟之间的极好匹配。在过饱和度为零的情况下，本分析模型预测的γ相厚度的时间演变和γ相中的非线性浓度分布与文献报道的实验数据非常吻合。当保温温度降低时，γ/δ 界面处的抛物线速率常数非线性增加，而在 γ/L 界面处几乎保持不变。此外，母相中的非零过饱和度在 γ/L 界面显着增加了扩散通量跳跃，但在 γ/δ 界面仅略微增加。因此，γ/L 界面处的生长速度显着增加，但 γ/δ 界面处的生长速度几乎没有变化。而它在 γ/L 界面几乎保持不变。此外，母相中的非零过饱和度在 γ/L 界面显着增加了扩散通量跳跃，但在 γ/δ 界面仅略微增加。因此，γ/L 界面处的生长速度显着增加，但 γ/δ 界面处的生长速度几乎没有变化。而它在 γ/L 界面几乎保持不变。此外，母相中的非零过饱和度在 γ/L 界面显着增加了扩散通量跳跃，但在 γ/δ 界面仅略微增加。因此，γ/L 界面处的生长速度显着增加，但 γ/δ 界面处的生长速度几乎没有变化。