We present an analytical framework to study the impact of electromechanical properties on the growth of a ferroelectric nucleus. Ferroelectric domain evolution is typically simulated by phase-field models, which have shown that nuclei evolve from needle-like structures into complex domain patterns. However, there has been limited in-depth analysis of the interplay between electrostatics, mechanics and piezoelectricity and their effect on nucleus growth because of the complexity involved in the phase-field description. In this study, we describe the ferroelectric domain wall as a sharp interface and solve for the fields inside an elliptic ferroelectric nucleus via Eshelby’s inclusion problem. We analytically determine the driving traction profile around the nucleus to gain insight into the movement of the domain wall with and without applied electromechanical loading. We analyze how the growth is affected by the permittivity, elasticity, and piezoelectricity as well as the nucleus’ eccentricity. We further demonstrate that applied loads do not significantly affect nucleus growth, which is primarily determined by the self-equilibrated mechanical and electric field, and that the anisotropy in material properties is essential in determining the growth of a ferroelectric nucleus.

中文翻译：

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铁电畴核的生长：锐界面模型的见解


我们提出了一个分析框架来研究机电特性对铁电核生长的影响。铁电域演化通常通过相场模型来模拟，该模型表明原子核从针状结构演化为复杂的域模式。然而，由于相场描述的复杂性，对静电、力学和压电之间的相互作用及其对核生长的影响的深入分析有限。在这项研究中，我们将铁电畴壁描述为尖锐的界面，并通过埃谢尔比夹杂问题求解椭圆形铁电核内部的场。我们通过分析确定核周围的驱动牵引力曲线，以深入了解在施加和不施加机电负载的情况下磁畴壁的运动。我们分析了介电常数、弹性、压电性以及原子核偏心率对生长的影响。我们进一步证明，施加的载荷不会显着影响核生长，这主要由自平衡机械和电场决定，并且材料特性的各向异性对于确定铁电核的生长至关重要。