An exact analytical solution of the Fick’s second law was developed and applied to the mixed-mode growth of a multicomponent ellipsoidal precipitate growing with constant eccentricities in the quasi-stationary regime. The solution is exact if the nominal composition, equilibrium concentrations and material properties are assumed constant, and can be applied to compounds having no limitations in the number of components. The solution was compared to the solution calculated by a diffusion-controlled application software and it was found that the solute concentrations at the interface can be determined knowing only the nominal composition, the full equilibrium concentrations and the coefficients of diffusion. The thermodynamic calculations owing to find alternative tie-lines are proven to be useless in the mixed-mode model. From this, it appears that the search of alternative tie-lines is computationally counterproductive, even when the interface has a very high mobility. A more efficient computational scheme is possible by considering that a moving interface is not at equilibrium.

中文翻译：

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准稳态状态下多组分沉淀物的混合模式生长

拟定了Fick第二定律的精确解析解，并将其应用于在准平稳状态下以恒定偏心率生长的多组分椭圆形沉淀物的混合模式生长。如果名义组成，平衡浓度和材料性能假定恒定，则该解决方案是准确的，并且可以应用于对组分数量没有限制的化合物。将溶液与由扩散控制的应用软件计算出的溶液进行比较，发现仅知道标称组成，完全平衡浓度和扩散系数，即可确定界面上的溶质浓度。在混合模式模型中，由于找到替代联络线而进行的热力学计算被证明是无用的。由此，似乎即使接口具有很高的移动性，对替代联系线的搜索在计算上也会适得其反。通过考虑运动界面不处于平衡状态，可以实现更有效的计算方案。