Version 1
: Received: 31 March 2024 / Approved: 1 April 2024 / Online: 1 April 2024 (16:25:00 CEST)
How to cite:
Hamieh, T.; Ibrahim, A.; Khatir, Z. New Solution of the Grain Boundary Grooving Problem in Polycrystalline Thin Films when Evaporation and Diffusion meet in Power Electronic Devices. Preprints2024, 2024040118. https://doi.org/10.20944/preprints202404.0118.v1
Hamieh, T.; Ibrahim, A.; Khatir, Z. New Solution of the Grain Boundary Grooving Problem in Polycrystalline Thin Films when Evaporation and Diffusion meet in Power Electronic Devices. Preprints 2024, 2024040118. https://doi.org/10.20944/preprints202404.0118.v1
Hamieh, T.; Ibrahim, A.; Khatir, Z. New Solution of the Grain Boundary Grooving Problem in Polycrystalline Thin Films when Evaporation and Diffusion meet in Power Electronic Devices. Preprints2024, 2024040118. https://doi.org/10.20944/preprints202404.0118.v1
APA Style
Hamieh, T., Ibrahim, A., & Khatir, Z. (2024). New Solution of the Grain Boundary Grooving Problem in Polycrystalline Thin Films when Evaporation and Diffusion meet in Power Electronic Devices. Preprints. https://doi.org/10.20944/preprints202404.0118.v1
Chicago/Turabian Style
Hamieh, T., Ali Ibrahim and Zoubir Khatir. 2024 "New Solution of the Grain Boundary Grooving Problem in Polycrystalline Thin Films when Evaporation and Diffusion meet in Power Electronic Devices" Preprints. https://doi.org/10.20944/preprints202404.0118.v1
Abstract
This paper constituted an extension of two previous studies concerning the mathematical development of the grain boundary grooving in polycrystalline thins films in the cases of the evaporation/condensation and diffusion taken separately. The thermal grooving processes are deeply controlled by the various mass transfer mechanisms of evaporation–condensation, surface diffusion, lattice diffusion, and grain boundary diffusion. This study proposed a new original analytical solution to the mathematical problem governing the grain groove profile in the case of simultaneous effects of evaporation-condensation and diffusion in polycrystalline thin films submitted to thermal and mechanical stress, and fatigue effects; by resolving the corresponding fourth-order partial differential equation ∂y∂t=C∂2y∂x2-B∂4y∂x4 obtained from the approximation y'2≪1. The comparison of the new solution to that of diffusion alone proved an important effect of the coupling of evaporation and diffusion on the geometric characteristics of the groove profile. A second analytical solution based on the series development was also proposed. It was proved that change of the boundary conditions of the grain grooving profile largely affected the different geometric characteristics of the groove profile.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
