In this paper, the thermodynamic configurational force associated with a moving interface is used to derive the conditions for phase growth and nucleation in bodies with multiple diffusing species and arbitrary surface stress at the phase interface. First, the mass, momentum and energy balances are derived on the evolving phase interface. The thermodynamic conditions that result from free energy inequality at the interface are derived leading to the analytical form of the configurational force for bodies subject to mechanical loads, heat and multiple diffusing species. The derived second law condition naturally extends the Eshelby energy–momentum tensor to include species diffusion terms. The above second law restriction is then used to derive the condition for the growth of new phases in a body undergoing finite deformation subject to inhomogeneous as well as anisotropic interface stress, and multiple diffusing species. The growth conditions are derived in both current and reference configurations. The statistical temperature-dependent growth velocity is next derived using the Boltzmann distribution. The derived finite deformation form of growth requirement is simplified to obtain the small deformation diffusive void growth condition. Next, a general, finite deformation, arbitrary surface stress form of phase nucleation condition is derived by considering uncertainty in growth of a small nucleus. The probability of nucleation is shown to naturally depend on a theoretical estimate of critical volumetric energy density, which is directly related to the surface stress. The classical nucleation theory is shown to result from a simplified special case of the general criterion. As an application of the developed theory, the classical Blech electromigration experiment is simulated to estimate the critical energy density corresponding to the onset of electromigration voids at Al–TiN interface.

中文翻译：

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具有不均匀表面应力的多相固体的界面平衡定律，相生长和成核条件

在本文中，与移动界面相关的热力学构型力被用于推导在相界面处具有多种扩散种类和任意表面应力的物体中相生长和成核的条件。首先，质量，动量和能量平衡在演化相界面上导出。导出了由界面处的自由能不等式引起的热力学条件，从而导致了受机械载荷，热量和多种扩散物质作用的物体的构型力的解析形式。导出的第二定律条件自然地将Eshelby能量动量张量扩展到包括物种扩散项。然后，将上述第二定律限制条件用于推导遭受有限变形的物体中新相生长的条件，该有限变形会受到非均匀以及各向异性的界面应力以及多种扩散物质的影响。生长条件是在当前和参考配置下得出的。接下来，使用玻尔兹曼分布得出统计温度相关的生长速度。简化了导出要求的有限变形形式，从而获得了小变形扩散空隙的生长条件。接下来，通过考虑小核生长的不确定性，得出相成核条件的一般的有限变形，任意表面应力形式。晶核形成的可能性自然取决于临界体积能量密度的理论估计，这直接关系到表面应力。事实证明，经典形核理论源于一般准则的简化特殊情况。作为发达理论的应用，对经典的Blech电迁移实验进行了仿真，以估计与Al-TiN界面上电迁移空洞的出现相对应的临界能量密度。