ДИНАМІКА НЕСПІВМІРНОЇ НАДСТРУКТУРИ В КРИСТАЛАХ ІЗ СИМЕТРІЄЮ ТЕРМОДИНАМІЧНОГО ПОТЕНЦІАЛУ n=4
In the Python software environment, Fourier spectra, Lyapunov exponents, maps of dynamic modes, wave vector of an incommensurate superstructure for a system of differential equations of the second order, where the appearance of an incommensurable superstructure is due to the Lifshitz invariant, unde...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Ivan Franko National University of Lviv
2024-09-01
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| Series: | Електроніка та інформаційні технології |
| Subjects: | |
| Online Access: | http://publications.lnu.edu.ua/collections/index.php/electronics/article/view/4475 |
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| Summary: | In the Python software environment, Fourier spectra, Lyapunov exponents, maps of dynamic modes, wave vector of an incommensurate superstructure for a system of differential equations of the second order, where the appearance of an incommensurable superstructure is due to the Lifshitz invariant, under the condition n = 4 was performed.
The influence of surface energy on an incommensurate superstructure in crystals of the A2BX4 family with n = 4 causes a change in the magnitude of the anisotropic interaction. In the incommensurable phase, the magnitude of the anisotropic interaction increases at a distance from the temperature of the phase transition, causing a decrease in the magnitude of the long-range interaction. This leads to the transition of the incommensurate superstructure from the sinusoidal to the soliton, and then from the soliton to the stochastic state.
As the maps of dynamic regimes show, the stochastic regime of an incommensurable superstructure has the coexistence of commensurate long-period phases with incommensurate phases that alternate with each other. These commensurate long-period phases have different periodicity. The existence of this mode on the maps of dynamic modes can be traced during the transition from a chaotic state to a commensurate state. The intervals of existence of commensurate long-period phases are insignificant in comparison with the intervals inherent in them in commensurate phases.
According to the Fourier diagram of spectra from the magnitude of the anisotropic interaction in the interval K=1.7÷2.5, a redistribution of the frequency spectrum of the amplitude function of an incommensurate superstructure can be traced. According to the maps of dynamic modes, under the condition T = 1, it can be assumed that in a given system described by the parameter n = 4 in the incommensurable phase there is a transition from one incommensurable state to another, which may be separated by the region of localization of the wave vector of incommensurability at a commensurate value of a higher order. However, the authors do not know the results of the study of the wave vector of incommensurability in crystals with q=(1/4+δ)/c, and for the crystal (NH4)2ZnCl4. Therefore, we are inclined to assume that in the interval K=1.7÷2.5 there is most likely a change in the regime of the incommensurate superstructure from sinusoidal to soliton mode. |
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| ISSN: | 2224-087X 2224-0888 |