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

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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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Acknowledgements

G. Shuvalov and S. Kostyrko acknowledge the support of the Russian Science Foundation under grant number 22-11-00087, https://rscf.ru/en/project/22-11-00087/.

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  1. St. Petersburg State University, 7/9, Universitetskaya Nab., St. Petersburg, Russia, 199034

    Gleb Shuvalov & Sergey Kostyrko

  2. Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Holm Altenbach

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Shuvalov, G., Kostyrko, S. & Altenbach, H. Interplay of surface and bulk elasticity in morphological stability of ultra-thin film coatings. Continuum Mech. Thermodyn. (2024). https://doi.org/10.1007/s00161-024-01279-3

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