Temperature Dependence of a Period of the Modulated Structurein Atom-Vacancy Solid Solution Based on F.C.C. Nickel
The effective vacancy–vacancy interaction is considered. Based on the continuum approximation for the Fourier components of strain-induced vacancy–vacancy-interaction energies, approximating expressions for their expansion coefficients are obtained, depending on the elasticity moduli, longitudinal a...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sumy State University
2012-03-01
|
| Series: | Журнал нано- та електронної фізики |
| Subjects: | |
| Online Access: | http://jnep.sumdu.edu.ua/download/numbers/2012/1/articles/jnep_2012_V4_01023.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850179097914769408 |
|---|---|
| author | V.A. Tatarenko O.V. Oliinyk |
| author_facet | V.A. Tatarenko O.V. Oliinyk |
| author_sort | V.A. Tatarenko |
| collection | DOAJ |
| description | The effective vacancy–vacancy interaction is considered. Based on the continuum approximation for the Fourier components of strain-induced vacancy–vacancy-interaction energies, approximating expressions for their expansion coefficients are obtained, depending on the elasticity moduli, longitudinal and transverse phonon frequencies, and vacancy-concentration-dependent lattice parameter. A non-analytical behaviour of the k-dependent Fourier components of the strain-induced vacancy–vacancy-interaction energies near the Brillouin zone centre, Avv(n) + Bvv(n)|k|2, is analysed. As shown, Avv(n) 0 and Bvv(n) 0 along all the high-symmetry [100], [110], [111] directions in reciprocal space for f.c.c. crystals with negative anisotropy factor. The criterion of modulated-structure formation for interacting vacancies in f.c.c. crystals is considered. Dependence of the f.c.c.-Ni–vacancies modulated-structure period on temperature is plotted. <br> The effective vacancy–vacancy interaction is considered. Based on the continuum approximation for the Fourier components of strain-induced vacancy–vacancy-interaction energies, approximating expressions for their expansion coefficients are obtained, depending on the elasticity moduli, longitudinal and transverse phonon frequencies, and vacancy-concentration-dependent lattice parameter. A non-analytical behaviour of the k-dependent Fourier components of the strain-induced vacancy–vacancy-interaction energies near the Brillouin zone centre, Avv(n) + Bvv(n)|k|2, is analysed. As shown, Avv(n) 0 and Bvv(n) 0 along all the high-symmetry [100], [110], [111] directions in reciprocal space for f.c.c. crystals with negative anisotropy factor. The criterion of modulated-structure formation for interacting vacancies in f.c.c. crystals is considered. Dependence of the f.c.c.-Ni–vacancies modulated-structure period on temperature is plotted. <br> The effective vacancy–vacancy interaction is considered. Based on the continuum approximation for the Fourier components of strain-induced vacancy–vacancy-interaction energies, approximating expressions for their expansion coefficients are obtained, depending on the elasticity moduli, longitudinal and transverse phonon frequencies, and vacancy-concentration-dependent lattice parameter. A non-analytical behaviour of the k-dependent Fourier components of the strain-induced vacancy–vacancy-interaction energies near the Brillouin zone centre, Avv(n) + Bvv(n)|k|2, is analysed. As shown, Avv(n) 0 and Bvv(n) 0 along all the high-symmetry [100], [110], [111] directions in reciprocal space for f.c.c. crystals with negative anisotropy factor. The criterion of modulated-structure formation for interacting vacancies in f.c.c. crystals is considered. Dependence of the f.c.c.-Ni–vacancies modulated-structure period on temperature is plotted. |
| format | Article |
| id | doaj-art-be3542a2498342aeb126fbe93d08690a |
| institution | OA Journals |
| issn | 2077-6772 |
| language | English |
| publishDate | 2012-03-01 |
| publisher | Sumy State University |
| record_format | Article |
| series | Журнал нано- та електронної фізики |
| spelling | doaj-art-be3542a2498342aeb126fbe93d08690a2025-08-20T02:18:35ZengSumy State UniversityЖурнал нано- та електронної фізики2077-67722012-03-0141010231Temperature Dependence of a Period of the Modulated Structurein Atom-Vacancy Solid Solution Based on F.C.C. NickelV.A. TatarenkoO.V. OliinykThe effective vacancy–vacancy interaction is considered. Based on the continuum approximation for the Fourier components of strain-induced vacancy–vacancy-interaction energies, approximating expressions for their expansion coefficients are obtained, depending on the elasticity moduli, longitudinal and transverse phonon frequencies, and vacancy-concentration-dependent lattice parameter. A non-analytical behaviour of the k-dependent Fourier components of the strain-induced vacancy–vacancy-interaction energies near the Brillouin zone centre, Avv(n) + Bvv(n)|k|2, is analysed. As shown, Avv(n) 0 and Bvv(n) 0 along all the high-symmetry [100], [110], [111] directions in reciprocal space for f.c.c. crystals with negative anisotropy factor. The criterion of modulated-structure formation for interacting vacancies in f.c.c. crystals is considered. Dependence of the f.c.c.-Ni–vacancies modulated-structure period on temperature is plotted. <br> The effective vacancy–vacancy interaction is considered. Based on the continuum approximation for the Fourier components of strain-induced vacancy–vacancy-interaction energies, approximating expressions for their expansion coefficients are obtained, depending on the elasticity moduli, longitudinal and transverse phonon frequencies, and vacancy-concentration-dependent lattice parameter. A non-analytical behaviour of the k-dependent Fourier components of the strain-induced vacancy–vacancy-interaction energies near the Brillouin zone centre, Avv(n) + Bvv(n)|k|2, is analysed. As shown, Avv(n) 0 and Bvv(n) 0 along all the high-symmetry [100], [110], [111] directions in reciprocal space for f.c.c. crystals with negative anisotropy factor. The criterion of modulated-structure formation for interacting vacancies in f.c.c. crystals is considered. Dependence of the f.c.c.-Ni–vacancies modulated-structure period on temperature is plotted. <br> The effective vacancy–vacancy interaction is considered. Based on the continuum approximation for the Fourier components of strain-induced vacancy–vacancy-interaction energies, approximating expressions for their expansion coefficients are obtained, depending on the elasticity moduli, longitudinal and transverse phonon frequencies, and vacancy-concentration-dependent lattice parameter. A non-analytical behaviour of the k-dependent Fourier components of the strain-induced vacancy–vacancy-interaction energies near the Brillouin zone centre, Avv(n) + Bvv(n)|k|2, is analysed. As shown, Avv(n) 0 and Bvv(n) 0 along all the high-symmetry [100], [110], [111] directions in reciprocal space for f.c.c. crystals with negative anisotropy factor. The criterion of modulated-structure formation for interacting vacancies in f.c.c. crystals is considered. Dependence of the f.c.c.-Ni–vacancies modulated-structure period on temperature is plotted.http://jnep.sumdu.edu.ua/download/numbers/2012/1/articles/jnep_2012_V4_01023.pdfVacanciesStrain-induced interactionElectrochemical interactionModulated structuresCohesive energVacanciesStrain-induced interactionElectrochemical interactionModulated structuresCohesive energVacanciesStrain-induced interactionElectrochemical interactionModulated structuresCohesive energ |
| spellingShingle | V.A. Tatarenko O.V. Oliinyk Temperature Dependence of a Period of the Modulated Structurein Atom-Vacancy Solid Solution Based on F.C.C. Nickel Журнал нано- та електронної фізики Vacancies Strain-induced interaction Electrochemical interaction Modulated structures Cohesive energ Vacancies Strain-induced interaction Electrochemical interaction Modulated structures Cohesive energ Vacancies Strain-induced interaction Electrochemical interaction Modulated structures Cohesive energ |
| title | Temperature Dependence of a Period of the Modulated Structurein Atom-Vacancy Solid Solution Based on F.C.C. Nickel |
| title_full | Temperature Dependence of a Period of the Modulated Structurein Atom-Vacancy Solid Solution Based on F.C.C. Nickel |
| title_fullStr | Temperature Dependence of a Period of the Modulated Structurein Atom-Vacancy Solid Solution Based on F.C.C. Nickel |
| title_full_unstemmed | Temperature Dependence of a Period of the Modulated Structurein Atom-Vacancy Solid Solution Based on F.C.C. Nickel |
| title_short | Temperature Dependence of a Period of the Modulated Structurein Atom-Vacancy Solid Solution Based on F.C.C. Nickel |
| title_sort | temperature dependence of a period of the modulated structurein atom vacancy solid solution based on f c c nickel |
| topic | Vacancies Strain-induced interaction Electrochemical interaction Modulated structures Cohesive energ Vacancies Strain-induced interaction Electrochemical interaction Modulated structures Cohesive energ Vacancies Strain-induced interaction Electrochemical interaction Modulated structures Cohesive energ |
| url | http://jnep.sumdu.edu.ua/download/numbers/2012/1/articles/jnep_2012_V4_01023.pdf |
| work_keys_str_mv | AT vatatarenko temperaturedependenceofaperiodofthemodulatedstructureinatomvacancysolidsolutionbasedonfccnickel AT ovoliinyk temperaturedependenceofaperiodofthemodulatedstructureinatomvacancysolidsolutionbasedonfccnickel |