This paper explores the interplay of surface and bulk elasticity on the evolution of surface relief within nanosized thin-film coatings, driven by the relaxation of misfit stresses through surface diffusion mechanism. The proposed theoretical approach incorporates the constitutive equations of surface elasticity theory developed by Gurtin and Murdoch into the Asaro–Tiller–Grinfeld model of morphological instability, which takes into account the stress sensitivity of the local gradient in chemical potential driving mass transport along the perturbed surface. Linear stability analysis, based on the solution of the linearized evolution equation representing the amplitude change of surface perturbation with time, predicts the conditions leading to the early growth of surface topological defects. These conditions depend on factors, such as the initial shape and wavelength of the surface undulations, misfit stresses, tension at the surface and interface, and the elastic properties governing the deformation of the surface, interface, film, and substrate.

本文探讨了表面弹性和体弹性对纳米薄膜涂层内表面起伏演变的相互作用，这是由表面扩散机制松弛失配应力所驱动的。所提出的理论方法将 Gurtin 和 Murdoch 开发的表面弹性理论本构方程纳入形态不稳定性的 Asaro-Tiller-Grinfeld 模型中，该模型考虑了沿扰动表面驱动质量传递的化学势局部梯度的应力敏感性。线性稳定性分析基于代表表面扰动随时间变化幅度的线性演化方程的解，预测导致表面拓扑缺陷早期生长的条件。这些条件取决于多种因素，例如表面起伏的初始形状和波长、失配应力、表面和界面处的张力以及控制表面、界面、薄膜和基底变形的弹性特性。