In strained monoatomic chains with Lennard-Jones interactions, we revealed a stable static nonhomogeneous structure appearing as a result of a certain phase transition. Positions of individual particles in this structure form an exact arithmetic progression whose difference depends on the value of the strain. For N-particle chain, this structure is characterized by one long and N-1 short interatomic distances (bonds). In the vicinity of the static structure, we found discrete breathers of new type which essentially differ from the traditional breathers in the form of Sievers-Takeno and Page modes. It is well known that these modes possess some staggered structures and demonstrate exponential decay of the particle amplitudes from the core to their tails. In contrast to such properties, our breathers are characterised by smooth decay and amplitudes of the particles form approximately a decreasing arithmetic progression. Core of these breathers is located on two particles with long bond in static structure. Our breathers demonstrate soft type of nonlinearity (the frequency decreases with increasing of amplitudes) and they are stable dynamical objects for amplitudes up to 20%-30% of interparticle distance of the strained equidistant chain. For infinitely small amplitudes these breathers tend to the above described static nonhomogeneous structure. We studied dependence of their properties on amplitude, strain and the number of particles in the chain. There exist a reason to suppose that the above static and dynamical structures can exist in real monoatomic chains consisting of carbon, boron, and other atoms.В растянутых одноатомных цепочках с взаимодействиями Леннарда-Джонса мы обнаружили устойчивую неоднородную статическую структуру, возникающую в результате некоторого фазового перехода. Положения отдельных частиц в этой структуре образуют точную арифметическую прогрессию, разность которой зависит от величины растяжения. Для Nчастичной цепочки эта структура характеризуется одним длинным и N-1 короткими межатомными расстояниями (связями). Вблизи найденной статической структуры мы обнаружили дискретные бризеры нового типа, которые существенно отличаются от традиционных бризеров в форме мод Сиверса-Такено и Пейджа. Хорошо известно, что эти моды обладают некоторыми ступенчатыми структурами и демонстрируют экспоненциальное убывание амплитуд частиц от их ядра к хвостам. В отличие от этих свойств, наши бризеры характеризуются плавным профилем, а амплитуды частиц приближенно образуют убывающую арифметическую прогрессию. Ядро этих бризеров расположено на двух частицах с длинной связью в статической структуре. Наши бризеры демонстрируют мягкий тип нелинейности (частота уменьшается с увеличением амплитуды) и являются стабильными динамическими объектами для амплитуд вплоть до 20% -30% от межчастичного расстояния растянутой эквидистантной цепочки. Для бесконечно малых амплитуд эти бризеры стремятся к описанной выше статической неоднородной структуре. Нами была изучена зависимость их свойств от амплитуды, деформации и количества ч...
We proved earlier that in the strained monoatomic chains with Lennard-Jones potential there can exist an equilibrium static bi-structure, which corresponds to N -1 equal short interatomic bonds and one long bond with inversion in its center (N is the number of atoms of the chain). In the present work, we investigate with the aid of the density functional theory (DFT modeling) similar structures that can exist in the strained carbon chains. In contrast to the Lennard-Jones model, the bi-structures in this case are inhomogeneous (they have short bonds of different lengths) and appear abruptly when the strain exceeds a certain critical value ηc as a result of a hard bifurcation of the equilibrium state (an analogue of the first-order phase transition). Such a bifurcation is associated with two different parts of potential, in which the Lennard-Jones forces can be quite small (this is the vicinity of the potential minimum and the potential tail) and, therefore, the forces acting on the particle between the long and short bonds can be equal. Since practically all interatomic potentials possess such features, the above bifurcation is universal, i.e. it must occur for any monoatomic chain. We have studied in detail the properties of the above structures, in particular, the behavior of their parameters with increasing N. With the help of DFT-modeling, the electron density of the above structures near the bifurcation point is investigated.
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