REDUCED ISOTROPIC CRYSTAL MODEL WITH RESPECT TO THE FOURTH-ORDER ELASTIC MODULI
Using a reduced isotropic crystal model the relationship between the fourth-order elastic moduli of an isotropic medium and the independent components of the fourth-order elastic moduli tensor of real crystals of various crystal systems is found. To calculate the coefficients of these relations, com...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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V.N. Karazin Kharkiv National University Publishing
2018-04-01
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| Series: | East European Journal of Physics |
| Subjects: | |
| Online Access: | http://periodicals.karazin.ua/eejp/article/view/10466 |
| _version_ | 1828973108286980096 |
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| author | O. Burlayenko V. Khodusov A. Naumovets |
| author_facet | O. Burlayenko V. Khodusov A. Naumovets |
| author_sort | O. Burlayenko |
| collection | DOAJ |
| description | Using a reduced isotropic crystal model the relationship between the fourth-order elastic moduli of an isotropic medium and the independent components of the fourth-order elastic moduli tensor of real crystals of various crystal systems is found. To calculate the coefficients of these relations, computer algebra systems Redberry and Mathematica for working with high order tensors in the symbolic and explicit form were used, in light of the overly complex computation. In an isotropic medium, there are four independent fourth order elastic moduli. This is due to the presence of four invariants for an eighth-rank tensor in the three-dimensional space, that has symmetries over the pairs of indices. As an example, the moduli of elasticity of an isotropic medium corresponding to certain crystals of cubic system are given (LiF, NaCl, MgO, CaF2). From the obtained results it can be seen that the reduced isotropic crystal model can be most effectively applied to high-symmetry crystal systems. |
| first_indexed | 2024-12-14T13:40:23Z |
| format | Article |
| id | doaj.art-7a3ccbaaa2694870bfe79bbff9757291 |
| institution | Directory Open Access Journal |
| issn | 2312-4334 2312-4539 |
| language | English |
| last_indexed | 2024-12-14T13:40:23Z |
| publishDate | 2018-04-01 |
| publisher | V.N. Karazin Kharkiv National University Publishing |
| record_format | Article |
| series | East European Journal of Physics |
| spelling | doaj.art-7a3ccbaaa2694870bfe79bbff97572912022-12-21T22:59:28ZengV.N. Karazin Kharkiv National University PublishingEast European Journal of Physics2312-43342312-45392018-04-0151707310242REDUCED ISOTROPIC CRYSTAL MODEL WITH RESPECT TO THE FOURTH-ORDER ELASTIC MODULIO. Burlayenko0V. Khodusov1A. Naumovets2Kharkоv V.N. Karazin National University Sq. Svobody 4, Kharkov, 61022, UkraineKharkоv V.N. Karazin National University Sq. Svobody 4, Kharkov, 61022, UkraineKharkоv V.N. Karazin National University Sq. Svobody 4, Kharkov, 61022, UkraineUsing a reduced isotropic crystal model the relationship between the fourth-order elastic moduli of an isotropic medium and the independent components of the fourth-order elastic moduli tensor of real crystals of various crystal systems is found. To calculate the coefficients of these relations, computer algebra systems Redberry and Mathematica for working with high order tensors in the symbolic and explicit form were used, in light of the overly complex computation. In an isotropic medium, there are four independent fourth order elastic moduli. This is due to the presence of four invariants for an eighth-rank tensor in the three-dimensional space, that has symmetries over the pairs of indices. As an example, the moduli of elasticity of an isotropic medium corresponding to certain crystals of cubic system are given (LiF, NaCl, MgO, CaF2). From the obtained results it can be seen that the reduced isotropic crystal model can be most effectively applied to high-symmetry crystal systems.http://periodicals.karazin.ua/eejp/article/view/10466fourth order elastic modulicubic crystal systemisotropic crystalphonon interaction |
| spellingShingle | O. Burlayenko V. Khodusov A. Naumovets REDUCED ISOTROPIC CRYSTAL MODEL WITH RESPECT TO THE FOURTH-ORDER ELASTIC MODULI East European Journal of Physics fourth order elastic moduli cubic crystal system isotropic crystal phonon interaction |
| title | REDUCED ISOTROPIC CRYSTAL MODEL WITH RESPECT TO THE FOURTH-ORDER ELASTIC MODULI |
| title_full | REDUCED ISOTROPIC CRYSTAL MODEL WITH RESPECT TO THE FOURTH-ORDER ELASTIC MODULI |
| title_fullStr | REDUCED ISOTROPIC CRYSTAL MODEL WITH RESPECT TO THE FOURTH-ORDER ELASTIC MODULI |
| title_full_unstemmed | REDUCED ISOTROPIC CRYSTAL MODEL WITH RESPECT TO THE FOURTH-ORDER ELASTIC MODULI |
| title_short | REDUCED ISOTROPIC CRYSTAL MODEL WITH RESPECT TO THE FOURTH-ORDER ELASTIC MODULI |
| title_sort | reduced isotropic crystal model with respect to the fourth order elastic moduli |
| topic | fourth order elastic moduli cubic crystal system isotropic crystal phonon interaction |
| url | http://periodicals.karazin.ua/eejp/article/view/10466 |
| work_keys_str_mv | AT oburlayenko reducedisotropiccrystalmodelwithrespecttothefourthorderelasticmoduli AT vkhodusov reducedisotropiccrystalmodelwithrespecttothefourthorderelasticmoduli AT anaumovets reducedisotropiccrystalmodelwithrespecttothefourthorderelasticmoduli |