Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical Approaches
Inclined threading dislocations (TDs) piercing the oriented free surface of a crystal are currently observed after growth of oriented thin films on substrates. Up to date the unique way to treat their anisotropic elastic properties nearby the free surface region is to use the integral formalism, whi...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Condensed Matter Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/3038795 |
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| author | Salem Neily Sami Dhouibi Roland Bonnet |
| author_facet | Salem Neily Sami Dhouibi Roland Bonnet |
| author_sort | Salem Neily |
| collection | DOAJ |
| description | Inclined threading dislocations (TDs) piercing the oriented free surface of a crystal are currently observed after growth of oriented thin films on substrates. Up to date the unique way to treat their anisotropic elastic properties nearby the free surface region is to use the integral formalism, which assumes no dislocation core size and needs numerical double integrations. In a first stage of the work, a new and alternative approach to the integral formalism is developed using double Fourier series and the concept of a finite core size, which is often observed in high-resolution transmission electron microscopy. In a second stage, the integral formalism and the Fourier series approaches are applied to the important case of a TD piercing the basal free surface of a hexagonal crystal. For this particular geometry, easy-to-use expressions are derived and compared to a third approach previously known for a plate-like crystal. Finally, the numerical interest and the convergence of these approaches are tested using the basal free surface of the GaN compound, in particular for TDs with Burgers vectors c and (a + c). |
| format | Article |
| id | doaj-art-ce19b0e78fd541cdaa868aed6d89ecdb |
| institution | Kabale University |
| issn | 1687-8108 1687-8124 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Condensed Matter Physics |
| spelling | doaj-art-ce19b0e78fd541cdaa868aed6d89ecdb2025-02-03T06:07:09ZengWileyAdvances in Condensed Matter Physics1687-81081687-81242018-01-01201810.1155/2018/30387953038795Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical ApproachesSalem Neily0Sami Dhouibi1Roland Bonnet2Laboratoire de Physique de la Matière Condensée et Nanosciences LR 11 ES 40, Faculté des Sciences, Université de Monastir, rue de l’Environnement, 5019 Monastir, TunisiaLaboratoire de Physique de la Matière Condensée et Nanosciences LR 11 ES 40, Faculté des Sciences, Université de Monastir, rue de l’Environnement, 5019 Monastir, TunisiaUniversité Grenoble Alpes, CNRS, SIMaP, 38000 Grenoble, FranceInclined threading dislocations (TDs) piercing the oriented free surface of a crystal are currently observed after growth of oriented thin films on substrates. Up to date the unique way to treat their anisotropic elastic properties nearby the free surface region is to use the integral formalism, which assumes no dislocation core size and needs numerical double integrations. In a first stage of the work, a new and alternative approach to the integral formalism is developed using double Fourier series and the concept of a finite core size, which is often observed in high-resolution transmission electron microscopy. In a second stage, the integral formalism and the Fourier series approaches are applied to the important case of a TD piercing the basal free surface of a hexagonal crystal. For this particular geometry, easy-to-use expressions are derived and compared to a third approach previously known for a plate-like crystal. Finally, the numerical interest and the convergence of these approaches are tested using the basal free surface of the GaN compound, in particular for TDs with Burgers vectors c and (a + c).http://dx.doi.org/10.1155/2018/3038795 |
| spellingShingle | Salem Neily Sami Dhouibi Roland Bonnet Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical Approaches Advances in Condensed Matter Physics |
| title | Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical Approaches |
| title_full | Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical Approaches |
| title_fullStr | Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical Approaches |
| title_full_unstemmed | Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical Approaches |
| title_short | Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical Approaches |
| title_sort | threading dislocations piercing the free surface of an anisotropic hexagonal crystal review of theoretical approaches |
| url | http://dx.doi.org/10.1155/2018/3038795 |
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