| Autor: |
Tayssir Hamieh, Ali Ibrahim, Zoubir Khatir |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
Micromachines, Vol 14, Iss 9, p 1781 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2072-666X |
| DOI: |
10.3390/mi14091781 |
| Popis: |
In a previous paper, we solved the partial differential equation of Mullins’ problem in the case of the evaporation–condensation in electronic devices and gave an exact solution relative to the geometric profile of the grain boundary grooving when materials are submitted to thermal and mechanical solicitation and fatigue effect. In this new research, new modelling of the grain groove profile was proposed and new analytical expressions of the groove profile, the derivative and the groove depth were obtained in the case of diffusion in thin polycrystalline films by the resolution of the fourth differential equation formulated by Mullins that supposed y′2≪1. The obtained analytical solution gave more accurate information on the geometric characteristics of the groove that were necessary to study the depth and the width of the groove. These new findings will open a new way to study with more accuracy the problem of the evaporation–condensation combined to the diffusion phenomenon on the material surfaces with the help of the analytical solutions. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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