Interplay of surface and bulk elasticity in morphological stability of ultra-thin film coatings

IF 1.9 4区工程技术 Q3 MECHANICS

Continuum Mechanics and Thermodynamics Pub Date : 2024-02-06 DOI:10.1007/s00161-024-01279-3

Gleb Shuvalov, Sergey Kostyrko, Holm Altenbach

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Abstract

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.

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超薄薄膜涂层形态稳定性中表面弹性和主体弹性的相互作用

本文探讨了纳米薄膜涂层在表面扩散机制驱动的错配应力松弛作用下，表面弹性和主体弹性对表面浮雕演化的相互作用。所提出的理论方法将 Gurtin 和 Murdoch 开发的表面弹性理论的构成方程纳入了 Asaro-Tiller-Grinfeld 形态不稳定性模型，该模型考虑到了化学势局部梯度对应力的敏感性，从而推动了沿扰动表面的质量迁移。线性稳定性分析基于线性化演化方程的求解，代表了表面扰动随时间的振幅变化，预测了导致表面拓扑缺陷早期增长的条件。这些条件取决于多种因素，如表面起伏的初始形状和波长、错位应力、表面和界面的张力，以及控制表面、界面、薄膜和基底变形的弹性特性。

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.