Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO
The spin Hamiltonian parameters for the two Cu²⁺ centers A1 and A2 in the calcined catalysts CuO-ZnO are theoretically investigated using the high order perturbation formulas of these parameters for a 3d⁹ ion in tetragonally elongated octahedra. In the above formulas, the tetragonal field parameters...
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| Дата: | 2011 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2011
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/120003 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO / H.M. Zhang, S.Y. Wu, Z.H. Zhang // Condensed Matter Physics. — 2011. — Т. 14, № 2. — С. 23703:1-6. — Бібліогр.: 25 назв. — англ. |
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irk-123456789-1200032017-06-11T03:02:55Z Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO Zhang, H.M. Wu, S.Y. Zhang, Z.H. The spin Hamiltonian parameters for the two Cu²⁺ centers A1 and A2 in the calcined catalysts CuO-ZnO are theoretically investigated using the high order perturbation formulas of these parameters for a 3d⁹ ion in tetragonally elongated octahedra. In the above formulas, the tetragonal field parameters Ds and Dt are determined from the superposition model, by considering the relative axial elongation of the oxygen octahedron around the Cu²⁺ due to the Jahn-Teller effect. Based on the calculations, the relative elongation ratios of about 5% and 3% are obtained for the tetragonal Cu²⁺ centers A1 and A2, respectively. The theoretical spin Hamiltonian parameters are in good agreement with the observed values for both systems. The larger axial elongation in center A1 is ascribed to the more significant low symmetrical (tetragonal) distortion of the Jahn-Teller effect. The local structures characterized by the above axial elongations are discussed. Параметри спiнового гамiльтонiану для двох центрiв Cu²⁺, A1 i A2, у кальцинованих каталiзаторах CuO–ZnO дослiджуються теоретично, використовуючи формули теорiї збурень високого порядку для цих параметрiв для iона 3d⁹ у тетрагонально видовжених октаедрах. В цих формулах параметри тетрагонального поля Dsi Dt визначаються з суперпозицiйної моделi, шляхом розгляду вiдносного аксiйного видовження октаедра кисню навколо Cu²⁺ вiдповiдно до ефекту Яна-Теллера. Базуючись на цих розрахунках, отримано коефiцiєнти вiдносного видовження приблизно 5% i 3% для тетрагональних Cu²⁺ центрiв A1 i A2, вiдповiдно. Параметри теоретичного спiнового гамiльтонiану добре узгоджуються з i спостережуваними величинами для обох систем. Бiльше аксiйне видовження в центрi A1 приписується до вагомiшої низько симетричної(тетрагональної) дисторсiї ефекту Яна-Телера. Обговорюються локальнi структури, що характеризуються вище згаданим аксiйним видовженням. 2011 Article Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO / H.M. Zhang, S.Y. Wu, Z.H. Zhang // Condensed Matter Physics. — 2011. — Т. 14, № 2. — С. 23703:1-6. — Бібліогр.: 25 назв. — англ. 1607-324X PACS: 76.30.Fc, 75.10.Dg, 71.70.Ch DOI:10.5488/CMP.14.23703 arXiv:1107.3757 http://dspace.nbuv.gov.ua/handle/123456789/120003 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The spin Hamiltonian parameters for the two Cu²⁺ centers A1 and A2 in the calcined catalysts CuO-ZnO are theoretically investigated using the high order perturbation formulas of these parameters for a 3d⁹ ion in tetragonally elongated octahedra. In the above formulas, the tetragonal field parameters Ds and Dt are determined from the superposition model, by considering the relative axial elongation of the oxygen octahedron around the Cu²⁺ due to the Jahn-Teller effect. Based on the calculations, the relative elongation ratios of about 5% and 3% are obtained for the tetragonal Cu²⁺ centers A1 and A2, respectively. The theoretical spin Hamiltonian parameters are in good agreement with the observed values for both systems. The larger axial elongation in center A1 is ascribed to the more significant low symmetrical (tetragonal) distortion of the Jahn-Teller effect. The local structures characterized by the above axial elongations are discussed. |
| format |
Article |
| author |
Zhang, H.M. Wu, S.Y. Zhang, Z.H. |
| spellingShingle |
Zhang, H.M. Wu, S.Y. Zhang, Z.H. Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO Condensed Matter Physics |
| author_facet |
Zhang, H.M. Wu, S.Y. Zhang, Z.H. |
| author_sort |
Zhang, H.M. |
| title |
Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO |
| title_short |
Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO |
| title_full |
Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO |
| title_fullStr |
Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO |
| title_full_unstemmed |
Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO |
| title_sort |
theoretical studies of the spin hamiltonian parameters for the two tetragonal cu²⁺ centers in the calcined catalysts cuo-zno |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120003 |
| citation_txt |
Theoretical studies of the spin Hamiltonian parameters for the two tetragonal Cu²⁺ centers in the calcined catalysts CuO-ZnO / H.M. Zhang, S.Y. Wu, Z.H. Zhang // Condensed Matter Physics. — 2011. — Т. 14, № 2. — С. 23703:1-6. — Бібліогр.: 25 назв. — англ. |
| series |
Condensed Matter Physics |
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