Кафедра фізико-математичних наук

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Reality conditions for the KdV equation and exact quasi-periodic solutions in finite phase spaces
(2024) Bernatska, Julia
In the present paper reality conditions for quasi-periodic solutions of the KdV equation are determined completely. As a result, solutions in the form of non-linear waves can be plotted and investigated. The full scope of obtaining finite-gap solutions of the KdV equation is presented. It is proven that the multiply periodic }1, 1-function on the Jacobian variety of a hyperelliptic curve of arbitrary genus serves as the finite-gap solution, the genus coincides with the number of gaps. The subspace of the Jacobian variety where }1, 1, as well as other }-functions, are bounded and real-valued is found in any genus. This result covers every finite phase space of the KdV hierarchy, and can be extended to other completely integrable equations. A method of effective computation of this type of solutions is suggested, and illustrated in genera 2 and 3.
Electronic Spectrum and Conductivity in Graphene with Impurities
(2023) Kruchinin, Sergei; Repetsky, Stanislav; Vyshyvana, Iryna; Polishchuk, Arkadiy
In the tight-binding one-electron model, the influence of substitutional impurity atoms on the energy spectrum and electrical conductance of graphene is studied. It is established that the ordering of substitutional impurity atoms on nodes of the crystal lattice causes the appearance of a gap in the energy spectrum of graphene 𝜂|𝛿| in width centered at the point 𝑦𝛿, where 𝜂 is the parameter of ordering, 𝛿 is the difference of the scattering potentials of impurity atoms and carbon atoms, and 𝑦 is the impurity concentration. If the Fermi level is located outside the gap, then the electrical conductance increases with the parameter of order 𝜂. It is shown that an increase in the electrical conductance with the order parameter is a result of both the growth of the density of states at the Fermi level and the time of relaxation of electron states. We have demonstrated the presence of a domain of localized states on the edges of the energy gap arising at the ordering of atoms of the admixture.
Effect of MgO/ZnO ratio on the formation process of MgxZn1-xO ceramics
(2024) Korsunska, Nadiia; Polishchuk, Yuliya; Ponomaryov, Semyon; Kozoriz, K.; Chusnutdinow, S.; Melnichuk, Olexandr; Melnichuk, Lyudmyla; Khomenkova, Larysa
The structural characteristics, chemical composition, and element spatial distribution in MgxZn1-xO ceramics were investigated using X-ray diffraction, scanning electron microscopy, Auger electron spectroscopy, energy-dispersive X-ray spectroscopy, and cathodoluminescence techniques. The study revealed that the morphology of the ceramic samples, as well as the mechanism of solid solution formation, depend on the relative contribution of both oxides in the charge. It was discovered that hexagonal and cubic phases of the solid solution were found to form simultaneously. An increase in the MgO content in the charge results in the magnesium content rise in the hexagonal grains continuously, reaching approximately 13 at.%. It was discovered an enrichment of grain boundaries with zinc and magnesium playing a significant role in doping ZnO and MgO grains. Obtained results allowed to propose two mechanisms involved in the formation of solid solution ceramics: i) diffusion of Mg and Zn along grain boundaries, followed by their incorporation into ZnO or MgO grains, respectively, and ii) interdiffusion of Mg into ZnO and Zn into MgO due to direct contact of ZnO and MgO grains. The second mechanism appears to dominate when both ZnO and MgO contribute comparably, increasing the probability of their direct contact. This study significantly advances the understanding of the process of the formation of MgxZn1-xO ceramics under thermodynamic conditions. These insights are crucial for optimizing the doping process and improving the material properties, thereby promoting innovations in the ceramics industry.
Effect of dopant loading and calcination conditions on structural and optical properties of ZrO2 nanopowders doped with copper and yttrium
(2024) Khomenkova, Larysa; Marchylo, Oleg; Polishchuk, Yulia; Ponomaryov, Semyon; Isaieva, Oksana; Vorona, Igor; Melnichuk, Liudmyla; Portier, Xavier; Melnichuk, Olexandr; Korsunska, Nadiia
Undoped, Cu and/or Y doped ZrO2 nanopowders were synthesized with Zr, Y, and Cu nitrates using a co-precipitation approach. Their structural and optical properties were examined regarding dopant content (0.1–8.0 mol.% of CuO and 3–15 mol.% of Y2O3) and calcination conditions (400 °C– 1000 °Cand, 1,2 or 5 h) through Raman scattering, XRD, TEM, EDS, AES, EPR,UV–vis and FTIR diffused reflectance methods. The results showed that both Cu and Y dopants promoted the appearance of additional oxygen vacancies in ZrO2 host, while the formation of tetragonal and cubic ZrO2 phases was primarily influenced by the Y content, regardless of Cu loading. The bandgap of most of the powders was observed within the 5.45–5.65 eV spectral range, while for those with high Y content it exceeded 5.8 eV. The (Cu,Y)-ZrO2 powders with 0.2 mol.% CuO and 3 mol.% Y2O3 calcined at 600 °Cfor 2 h demonstrated nanoscaled tetragonal grains (8–12 nm) and a significant surface area covered with dispersed CuxOspecies. For higher calcination temperatures, the formation of CuZr 2+ EPR centers, accompanied by tetragonal-to-monoclinic phase transformation, was found. For fitting of experimental FTIR reflection spectra, theoretical models with one, five, and seven oscillators were constructed for cubic, tetragonal, and monoclinic ZrO2 phases, respectively. Comparing experimental and theoretical spectra, the parameters of various phonons were determined. It was found that the distinct position of the high-frequency FTIR reflection minimum is a unique feature for each crystalline phase. It was centered at 700–720 cm−1, 790–800 cm−1, and 820–840 cm−1 for cubic, tetragonal, and monoclinic phases, respectively, showing minimal dependence on phonon damping coefficients. Based on the complementary nature of results obtained from structural and optical methods, an approach for monitoring powder properties and predicting catalytic activity can be proposed for ZrO2–based nanopowders.
Influence of compacting pressure on the electrical properties of ZnO and ZnO:Mn ceramics
(2024) Korsunska, N.; Markevich, Iryna; Stara, T.; Polishchuk, Yu.; Ponomaryov, S.; Kozoriz, K.; Tsybrii, Zinoviia; Melnichuk, O.; Melnichuk, L.; Venger, E.; Khomenkova, Larysa
Undoped and Mn-doped ZnO ceramics were prepared from the powders compacted at different pressures and sintered in air at high temperature. Their structural, optical, light emitting and electrical characteristics as well as the distribution of chemical elements were studied. It was found that an increase in compacting pressure stimulates an increase in direct current conductivity in both undoped and doped samples. In the case of doped samples, this effect was accompanied by a decrease in the height of potential barriers at the grain boundaries. It is found that electron concentration in ceramic grains, estimated from the modelling of infrared reflection spectra, remained relatively constant. The analysis of luminescence spectra and spatial zinc distribution revealed that the increase in compacting pressure results in the accumulation of interstitial zinc at the grain boundaries forming channels with enhanced conductivity. These findings provide an explanation for the evolution of electrical properties of ceramic samples with compacting pressure.
Вплив термічно та радіаційно стимульованих процесів дифузії на властивості матеріалів мікроелектроніки та приладів на їх основі : монографія
(Вид-во НДУ ім. М. Гоголя, 2019) Корсунська, Надія; Маркевич, Ірина; Борковська, Людмила; Хоменкова, Лариса; Савкіна, Рада; Смірнов, Олексій; Венгер, Євген; Мельничук, Людмила; Мельничук, Олександр
Наведено результати досліджень трансформації структурних, оптичних, електричних та люмінесцентних властивостей напівпровідникових та діелектричних матеріалів внаслідок термічної, ультразвукової та радіаційної обробки. Описані методи виготовлення матеріалів. Приділяється увага процесам термічної дифузії домішок та власних дефектів, їх дифузії під дією світла, а також дрейфу дефектів в електричному полі; взаємодії об’ємних дефектів; утворенню різного типу радіаційних дефектів, а також процесам фазово-структурних перетворень в різних сполуках та їх твердих розчинах. Розглянуто вплив цих процесів на стабільність роботи приладів на основі таких матеріалів та визначено чинники, що відповідають за процеси деградації приладів. Для студентів, аспірантів фізичних факультетів, а також для науковців, які працюють у галузі фізики твердого тіла.
Photoluminescence quantum yield of carbon dots: emission due to multiple centers versus excitonic emission
(2024) Dimitriev, Oleg; Kysil, Dmytro; Zaderko, Alexander; Isaieva, Oksana; Vasin, Andrii; Piryatinski, Yuri; Fahlman, Mats; Nazarov, Alexei
Carbon dots (CDs) are recognized as promising fluorescent nanomaterials with bright emission and large variations of photoluminescence quantum yield (PLQY). However, there is still no unique approach for explanation of mechanisms and recipes for synthetic procedures/chemical composition of CDs responsible for the enhancement of PLQY. Here, we compare photophysical behavior and PLQY of two types of CDs synthesized by different routes, leading to the different extent of oxidation and composition. The first type of CDs represents a conjugated carbon system oxidized by F, N and O heteroatoms, whereas the second type represents a non-conjugated carbon system oxidized by oxygen. Photophysical data, photoemission spectroscopy and microscopy data yield the suggestion that in the first case, a structure with a distinct carbon core and highly oxidized electron-accepting shell is formed. This leads to the excitonic type non-tunable emission with single-exponent decay and high PLQY with a strong dependence on the solvent polarity, being as high as 93% in dioxane and as low as 30% in aqueous medium, but which is vulnerable to photobleaching. In the second case, the oxidized CDs do not indicate a clear core–shell structure and show poor solvatochromism, negligible photobleaching, low PLQY varying in the range of 0.7–2.3% depending on the solvent used, and tunable emission with multi-exponent decay, which can be described by the model of multiple emission centers acting through a clustering-triggered emission mechanism. The obtained results lead to a strategy that allows one to design carbon nanomaterials with principally different PLQYs that differ by orders of magnitude.
From the personal history of teaching philosophy of physics
(Талком, 2022) Kuznetsov, Volodymyr
The experience of teaching philosophy o f physics to Ukrainian physics masters is described. The goal of the course is to promote their conscious and clear understanding of i’ physical theories as complex and necessary tools for gaining new knowledge about their domains of application. Theoretical physics is viewed as a network of developing and t interrelated theories. They are practical because, on the one hand, they are learned by ft students as future physicists. On the other hand, professional physicists are constantly t improving practical theories to produce new knowledge. Thus, it is needed to analyze r theories both as changeable systems and as complex polysystems under more detailed hscrutiny. That is why the course is based on a modified structure-nominative reconstruction a of practical physical theories as polysystems consisting of interconnected and flexible I homogeneous subsystems.
The interplay of external and internal semiotics of domain-specific scientific theories
(University of Tartu, 2022) Gabovich, Alexander; Kuznetsov, Volodymyr
We suppose that those who are reading this contribution are familiar with the traditional reconstruction of domain-specific scientific theories (DSSTs) as logically ordered and static systems of statements about their domains. The latter split into separate realities with their attributes. However, any DSST (e.g., celestial mechanics, theories of superconductivity, theories of elementary particles) is an ever-improving tool for acquiring new knowledge. It means that a more realistic reconstruction is a varied polysystem. Its interacting and changing subsystems (SS) perform specific functions in the complex process of obtaining and testing the new knowledge. According to the modified structure-nominative reconstruction, there are many SSs in DSSTs [2019; 2021].
Improved parametrization of inclusive proton spectra from 3H(α,p)6He reaction using data obtained in a correlation experiment
(2022) Povoroznyk, Orest; Gorpinich, O.
The new analysis of inclusive proton spectra from 3H(α, p)6He reaction was performed. The existence of two new excited levels of 6He with energy parameters E2ex.s.*= 2.4 MeV, Γ = 0.4 MeV; E3ex.s.*= 3.0 MeV, Γ = 0.6 MeV was confirmed as a result of new parameterization performed using energy parameters obtained from the correlation kinematic-incomplete experimental study of 3H(α, pα)nn reactions at Eα = 27.2 MeV and Eα = 67.2 MeV in contrast to the initial analysis, in which the resonance observed above the known first excited 6He level E1ex.s. = 1.8 MeV was treated as the second broad excited level E2ex.s. = 2.98 (0.17) MeV, Γ2ex.s. = 2.39 (0.27) MeV.
Magneto-optic Kerr effect in Gd20Co80 alloy
(2022) Kudin, V.; Rozouvan, S.; Stashchuk, Vasyl
The magneto-optical Kerr effect in Gd20Co80 alloy and cobalt thin films has been studied in a broad spectral range applying spectral ellipsometry experimental technique. The results of the experiments showed the complex nature of the complex Kerr angle dispersion curves. A quantum mechanical formalism for degenerate and non-degenerate Landau levels for quasi-free electrons in ferromagnetic material has been developed in order to analyze the experimental data. The equivalence of relations for off-diagonal dielectric tensor elements for non-degenerate Landau levels to the classical case of the motion of quasi-free electrons along circular trajectories in a magnetic field has been theoretically shown. The degenerate Landau levels in this approach are the result of motion of electrons in small confined volumes near rare-earth alloy atoms. Rotation of light polarization occurs in this case due to transitions between subbands having different magnetic quantum numbers. This theoretical approach allowed us to interpret in detail shapes and sign of the complex Kerr angle dispersion curves, which actually include the contributions of optical transitions between degenerate and non-degenerate energy levels. The complex Kerr angle sign is determined by the magnetization magnetic field direction for non-degenerate Landau levels and the Hund rule for degenerate Landau levels.
З'ясування умов збудження поверхневих поляритонiв у керамiцi Mg0,2Zn0,8O методом порушеного повного внутрiшнього вiдбивання
(2022) Мельничук, О.; Корсунська, Н.; Мельничук, Л.; Хоменкова, Лариса; Венгер, Є.
Уперше для керамiки Mg0,2Zn0,8O теоретично з’ясовано умови збудження поверхневих поляритонiв та побудовано поверхню порушеного повного внутрiшнього вiдбивання 𝐼(𝜈)/𝐼0(𝜈), яка являє собою тривимiрне подання коефiцiєнта пропускання в IЧ-дiапазонi спектра. Визначено його залежнiсть вiд частоти i кута падiння випромiнювання. Для одержання оптичних i електрофiзичних параметрiв керамiки, необхiдних для розрахункiв, вимiрянi спектри зовнiшнього IЧ-вiдбивання. З них одержано вiдповiднi параметри методом дисперсiйного аналiзу. Продемонстровано можливiсть дослiджень резонансної взаємодiї оптичних фононiв та плазмонiв. Отриманi результати добре узгоджуються з вiдомими в лiтературi даними.
Peculiarities of photoluminescence excitation in ZnO ceramics doped with group-I elements
(2022) Korsunska, N.; Markevich, I.; Stara, T.; Kozoriz, K.; Melnichuk, L.; Melnichuk, O.; Khomenkova, Larysa
Extrinsic luminescence, excitation, and absorption spectra of ZnO ceramics doped with acceptors (lithium, copper, or silver), as well as undoped ZnO ceramics sintered in various atmospheres, have been studied. It is shown that the acceptor doping leads to the appearance of luminescence bands in the visible spectral interval, and their intensity significantly exceeds the intensity of the corresponding emission from undoped specimens. A selective maximum at 390–400 nm, which is usually absent in the excitation spectra of self-activated luminescence bands in undoped ZnO specimens, is found to dominate in the excitation spectra of those bands. It is supposed to be caused by the interaction between the emitting centers and defects arising near the impurities, with the Auger process being the most probable mechanism of energy transfer from these defects to the emitting centers. By sintering ZnO ceramics in the presence of carbon, it is shown that the appearance of the selective maximum in the excitation spectra occurs due to the extraction of oxygen from ZnO ceramics. An assumption has been done concerning the nature of the centers responsible for the excitation of extrinsic luminescence.
Effects of thermal treatment on the complex structure of luminescence emission of Li-doped ZnO screen-printed films
(2023) Chukova, O.; Borkovska, L.; Khomenkova, L.; Korsunska, N.; Ponomaryov, S.; Androulidaki, M.; Stratakis, E.
The ZnO–Li films were synthesized and investigated in an attempt to explore and develop RE-free phosphor materials capable of emitting intense visible light in a wide spectral range. The effects of both heterovalent doping with lithium and high-temperature annealing on the optical properties of ZnO films were studied. The films were deposited on the Al2O3 substrate using the screen-printing method and annealed at 800–1,000°C in air for 0.5–3 h. Both doping and annealing result in the transformation of the shape of reflectance spectra in the range of 300–400 nm and the shift of absorption edge to the long-wavelength region. At the same time, the bandgap value estimated taking into account the exciton peak position and its binding energy is independent of Li-doping. The feature at 300–400 nm and the shift of absorption edge are ascribed to the appearance of the absorption band that excited the yellow photoluminescence band. The photoluminescence spectra of undoped and Li-doped films show the emission bands in the ultraviolet and visible spectral ranges. The ultraviolet emission is due to ZnO exciton recombination. The visible emission band comprises several components peaked at 430, 482, 540, 575, and 640 nm. Their relative intensities depend on Li-doping, annealing temperature, and annealing duration. The 430- and 482-nm luminescence bands were observed in Lidoped films only. Their excitation spectra show the peak located at 330–340 nm, indicating that the energy significantly exceeds the ZnO bandgap energy. Consequently, the 430- and 482-nm luminescence bands are attributed to an additional crystal phase formed under annealing. Other components of visible emission bands are ascribed to the defect-related emission of ZnO. The possible nature of these bands is further discussed. Li-doping and annealing at intermediate temperatures result in blue emission and an enhancement of other visible bands, which makes ZnO–Li films a perspective material in photonic applications.
До епістемологічного аналізу наукових теорій
(2023) Кузнєцов, Володимир
У статті розглянуто взаємозв’язки науки та філософії науки крізь призму моделювання наукових теорій, які є значно складнішими системами, ніж зазвичай їх описують у фаховій літературі. Багато фахівців, пов’язаних з наукою, її викладанням і адмініструванням, мають спрощені уявлення про компонентний склад теорій, які є основними інструментами наукового мислення. Тому необхідно розробити об’єднуючий, але детальний погляд на теорії. Ґрунтувати його доцільно на аналізі теорій, що використовуються в науковій практиці. Автор пропонує помістити полісистемне бачення теорій у центр філософії науки та інших метанаук про науку (наукознавство, історія науки, соціологія науки, психологія науки, управління наукою тощо). Такий підхід може бути корисним для філософів і науковців, викладачів наукових дисциплін і студентів, а також для тих, хто керує наукою як соціальним інститутом з продукування нового знання, і тих, хто оцінює її результати.
Conformational flexibility of spermidine3+ interacting with DNA double helix
(2023) Perepelytsya, Sergiy; Vasiliu, Tudor; Laaksonen, Aatto; Engelbrecht, Leon De Villiers; Brancato, Giuseppe; Mocci, Francesca
Natural polyamines play a key role in many biological processes, particularly in the stabilization of DNA double helix structure in the cell nucleus. Among others, the conformational flexibility of polyamines, such as spermidine, is an essential property for the formation of complexes with DNA. Yet, the characterization of the conformational space of polyamines has not been fully elucidated. Using atomistic molecular dynamics (MD) simulations, we present a detailed study of the conformational space of spermidine3+ both in solution and in interaction with DNA. We have identified more than 2000 distinct conformations, which can be grouped into seven modes. Notably, the relative population of these modes is highly affected by the interaction of spermidine3+ with DNA, thus representing a fingerprint of complex formation. In particular, three of the seven dihedral angles of spermidine3+ are predominantly in trans conformation (with or without DNA), while the other four dihedral angles are observed to switch between trans, gauche+ and gauche-. The preference between the latter conformational states was analyzed in terms of the distinct energy contributions composing the potential energy. Overall, our results shed light on the conformational equilibrium and dynamics of spermidine3+, which in turn is important for understanding the nature of its interaction with DNA.
Optical properties of Zn0.75Mg0.25O:Mn ceramics
(2023) Markevich, I.; Korsunska, N.; Stara, T.; Polishchuk, Yu.; Vorona, I.; Kozoriz, K.; Ponomaryov, S.; Melnichuk, O.; Melnichuk, L.; Cremades, A.; Khomenkova, Larysa
Mn-doped ZnO, MgO and Zn0.75Mg0.25O samples ([Mn] = 0.1 at.%) were produced by conventional solid-state technique and investigated by means of XRD, EPR, absorption, photocurrent, photo- and cathodoluminescence methods. It was shown that Zn0.75Mg0.25O solid solution with hexagonal structure has the bandgap of Eg ~3.65 eV. The quenching of host defect-related luminescence in ZnO:Mn and in hexagonal Zn0.75Mg0.25O:Mn was observed, while the Mn-related emission being absent. The energy level of Mn2Z+n center in hexagonal Zn0.75Mg0.25O:Mn was found to be at 2.16 eV below conduction band (c-band) bottom and all excited states of Mn2Z+n ions, including the lowest one, reside in c-band, as it takes place in ZnO:Mn. It is concluded that the necessary condition to obtain Mn-related light emission in Mn-doped alloys is to make deeper the lowest excited level of Mn2Z+n ions. One of the solutions is to produce Zn1-xMgxO:Mn solid solution with the bandgap energy larger than 4.0 eV using nonequilibrium fabrication approaches.
Representations of solutions of Lamé system with real coefficients via monogenic functions in the biharmonic algebra
(2023) Gryshchuk, Serhii
New representations of solutions of Lamé system with real coefficients via monogenic functions in the biharmonic algebra are found.
A mathematical model of transport kinetics of 99mTc radiotracers
(2021) Shevtsova, Oksana
The proposed four-compartment mathematical model describes transport kinetics of 99m-technetium radiotracers at intravenous administration process with taking into account radiopharmaceutical accumulation, elimination and radioactive decay. The analytical solution of the model in a form of the well-known sum-of exponential solution was obtained. The dependencies of the tracer concentration versus the time are analyzed. The model can be easily verified by the radioactive tracer concentration data in the circulatory/lymphatic system measured at some time points, and the obtained data can be used to determine the transport coefficients. Time-activity dependencies were obtained and analyzed for each compartment. The model can be used for individual transport parameter calculation at administration of diagnostic/therapeutic dose loads.
Two excitation pathways of Pr3+ ion emission in HfO2:Si:Pr films depending on crystalline phase transformations in annealing
(2023) Garcia Andrade, Maria Alejandra; Torchynska, T.; Casas Espinola, Jose Luis; Vel´azquez Lozada, E.; Polupan, G.; Khomenkova, Larysa; Gourbilleau, F.
The impact of annealing on the emission and transformation of the crystalline phases in Si rich HfO2:Pr films was investigated by analyzing the morphology, chemical composition, structure, and photoluminescence (PL) characteristics. Films were prepared by RF magnetron sputtering and monitored as-prepared and after annealing at 1000 ◦C for 5–60 min. Emission through host HfO2 defects has only been detected in spectra of as-prepared Si rich HfO2:Pr films. Heat treatment for 30 min stimulates a phase transformation together with the appearance of a tetragonal HfO2 phase and Si quantum dot (QDs). This last process is accompanied by appearance of bright emission of rare earth (RE) ions Pr3+ related to the transitions in the 4f energy levels. Additional annealing for 60 min stimulates the complete oxidation of the Si QDs with the formation of the SiO2 phase along with partial destruction of a tetragonal HfO2 phase. This last process is accompanied by the significant increase of the intensity of Pr3+ ion emission. Two forms of luminescence excitation in 4f energy levels of Pr3+ ions are discussed, related to energy transfer to Pr3+ ions, first from Si QDs and then from host defects in HfO2. These changes in the excitation pathways of Pr3+ ion emissions are stimulated by the transformations of the crystalline phases in the thermal treatment together with the generation of host HfO2 defects. Hafnia-based materials doped with RE elements are interesting for telecommunication technology and applications in waveguides and optoelectronic devices.

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